· Collider Phenomenology — From basic knowledge to new physics searches Tao Han University of Wisconsin – Madison Asian School of Particles, Strings and Cosmology Nasu, Japan,

Collider Phenomenology

— From basic knowledge

to new physics searches

Tao Han

University of Wisconsin – Madison

Asian School of Particles, Strings and Cosmology

Nasu, Japan, Sept. 25 – 26, 2006

Collider Phenomenology

— From basic knowledge

to new physics searches

Tao Han

University of Wisconsin – Madison

Asian School of Particles, Strings and Cosmology

Nasu, Japan, Sept. 25 – 26, 2006

I. Colliders and DetectorsII. Basics Techniques and Tools for Collider PhysicsIII. An e+e− Linear ColliderIV. Hadron Colliders PhysicsV. From Kinematics to DynamicsVI. Physics Beyond the Standard ModelVII. Search for New Physics at Hadron Colliders

I. Colliders and Detectors

(A). High-energy Colliders:

The energy:

Ecm ≡√s ≈

2E1 ≈ 2E2 in the c.m. frame ~p1 + ~p2 = 0,√

2E1m2 in the fixed target frame ~p2 = 0.

s ≡ (p1 + p2)2 =

(E1 + E2)

2 in the c.m. frame ~p1 + ~p2 = 0,

m21 +m2

2 + 2(E1E2 − ~p1 · ~p2).

I. Colliders and Detectors

(A). High-energy Colliders:

The energy:

Ecm ≡√s ≈

2E1 ≈ 2E2 in the c.m. frame ~p1 + ~p2 = 0,√

2E1m2 in the fixed target frame ~p2 = 0.

s ≡ (p1 + p2)2 =

(E1 + E2)

2 in the c.m. frame ~p1 + ~p2 = 0,

m21 +m2

2 + 2(E1E2 − ~p1 · ~p2).

The luminosity:

. . . . . . . .

Colliding beamn1 n2

t = 1/f

L ∝ fn1n2/a,

in units of #particles/cm2/s

⇒ 1033 cm−2s −1 = 1 nb−1 s−1 ≈ 10 fb−1/year.

Current and future high-energy colliders:

Hadron√s L δE/E f #/bunch L

Colliders (TeV) (cm−2s−1) (MHz) (1010) (km)

Tevatron 1.96 2.1 × 1032 9 × 10−5 2.5 p: 27, p: 7.5 6.28

LHC 14 1034 0.01% 40 10.5 26.66




Tevatron 1.96 2.1 × 1032 9 × 10−5 2.5 p: 27, p: 7.5 6.28

LHC 14 1034 0.01% 40 10.5 26.66

e+e−√s L δE/E f polar. L

Colliders (TeV) (cm−2s−1) (MHz) (km)

ILC 0.5−1 2.5 × 1034 0.1% 3 80,60% 14 − 33CLIC 3−5 ∼ 1035 0.35% 1500 80,60% 33 − 53




Tevatron 1.96 2.1 × 1032 9 × 10−5 2.5 p: 27, p: 7.5 6.28

LHC 14 1034 0.01% 40 10.5 26.66

e+e−√s L δE/E f polar. L

Colliders (TeV) (cm−2s−1) (MHz) (km)

ILC 0.5−1 2.5 × 1034 0.1% 3 80,60% 14 − 33CLIC 3−5 ∼ 1035 0.35% 1500 80,60% 33 − 53

(B). An e+e− Linear Collider

The collisions between e− and e+ have major advantages:

• The system of an electron and a positron has zero charge,

zero lepton number etc.,

=⇒ it is suitable to create new particles after e+e− annihilation.

• With symmetric beams between the electrons and positrons,

the laboratory frame is the same as the c.m. frame,

=⇒ the total c.m. energy is fully exploited to reach the highest

possible physics threshold.

• With well-understood beam properties,

=⇒ the scattering kinematics is well-constrained.

• Backgrounds low and well-undercontrol.

• It is possible to achieve high degrees of beam polarizations,

=⇒ chiral couplings and other asymmetries can be effectively explored.

• With well-understood beam properties,

=⇒ the scattering kinematics is well-constrained.

• Backgrounds low and well-undercontrol.

• It is possible to achieve high degrees of beam polarizations,

=⇒ chiral couplings and other asymmetries can be effectively explored.

Disadvantages

• Large synchrotron radiation due to acceleration,

∆E ∼ 1

R

(E

me

)4

.

Thus, a multi-hundred GeV e+e− collider will have to be made

a linear accelerator.

• This becomes a major challenge for achieving a high luminosity

when a storage ring is not utilized;

beamsstrahlung severe.

(C). Hadron CollidersLHC: the next high-energy frontier

“Hard” Scattering

proton

underlying event underlying event

outgoing parton

outgoing parton

initial-stateradiation

final-stateradiation

proton

(C). Hadron CollidersLHC: the next high-energy frontier

“Hard” Scattering

proton

underlying event underlying event

outgoing parton

outgoing parton

initial-stateradiation

final-stateradiation

proton

Advantages

• Higher c.m. energy, thus higher energy threshold:√S = 14 TeV: M2

new ∼ s = x1x2S ⇒ Mnew ∼ 0.2√S ∼ 3 TeV.

• Higher luminosity: 1034/cm2/s ⇒ 100 fb−1/yr.

Annual yield: 1B W±; 100M tt; 10M W+W−; 1M H0...



• Multiple (strong, electroweak) channels:

qq′, gg, qg, bb→ colored; Q = 0,±1; J = 0,1,2 states;

WW, WZ, ZZ, γγ → IW = 0,1,2; Q = 0,±1,±2; J = 0,1,2 states.






Disadvantages

• Initial state unknown:

colliding partons unknown on event-by-event basis;

parton c.m. energy unknown: E2cm ≡ s = x1x2S;

parton c.m. frame unknown.

⇒ largely reply on final state reconstruction.






Disadvantages






• The large rate turns to a hostile environment:

⇒ Severe backgrounds!






Disadvantages








Our primary job !

(D). Particle Detection:

The detector complex:

hadronic calorimeter

E-CAL

tracking

vertex detector

muon chambers

beam

pipe

( in B field )

What we “see” as particles in the detector: (a few meters)

For a relativistic particle, the travel distance:

d = (βcτ)γ ≈ (300 µm)(τ

10−12 s) γ



d = (βcτ)γ ≈ (300 µm)(τ

10−12 s) γ

• stable particles directly “seen”:

p, p, e±, γ• quasi-stable particles of a life-time τ ≥ 10−10 s also directly “seen”:

n,Λ,K0L, ..., µ

±, π±,K±...



d = (βcτ)γ ≈ (300 µm)(τ

10−12 s) γ



n,Λ,K0L, ..., µ

±, π±,K±...

• a life-time τ ∼ 10−12 s may display a secondary decay vertex,

“vertex-tagged particles”:

B0,±, D0,±, τ±...



d = (βcτ)γ ≈ (300 µm)(τ

10−12 s) γ



n,Λ,K0L, ..., µ

±, π±,K±...

• a life-time τ ∼ 10−12 s may display a secondary decay vertex,

“vertex-tagged particles”:

B0,±, D0,±, τ±...

• short-lived not “directly seen”, but “reconstructable”:

π0, ρ0,±... , Z,W±, t,H...• missing particles are weakly-interacting and neutral:

ν, χ0, GKK...

† For stable and quasi-stable particles of a life-time

τ ≥ 10−10 − 10−12 s, they show up as

A closer look:

A closer look:

Theorists should know:

For charged tracks : ∆p/p ∝ p,

typical resolution : ∼ p/(104 GeV ).

For calorimetry : ∆E/E ∝ 1√E,

typical resolution : ∼ (5 − 80%)/√E.

† For vertex-tagged particles τ ≈ 10−12 s,

heavy flavor tagging: the secondary vertex:

† For vertex-tagged particles τ ≈ 10−12 s,

heavy flavor tagging: the secondary vertex:

Typical resolution: d0 ∼ 30 − 50 µm or so

⇒ need at least two charged tracks, that are not colinear.

For theorists: just multiply a “tagging efficiency” ǫb ∼ 40 − 60% or so.

† For short-lived particles: τ < 10−12 s or so,

make use of kinematics to reconstruct the resonance.



† For missing particles:

make use of energy-momentum conservation to deduce their existence.

(or transverse direction only for hadron colliders.)

pi1 + pi2 =obs.∑

f

pf+pmiss.



† For missing particles:

make use of energy-momentum conservation to deduce their existence.

(or transverse direction only for hadron colliders.)

pi1 + pi2 =obs.∑

f

pf+pmiss.

But in hadron collisions, the longitudinal momenta unkown:

0 =obs.∑

f

~pf T+~pmiss T .

What we “see” for the SM particles

Leptons Vetexing Tracking ECAL HCAL Muon Cham.e± × ~p E × ×µ± × ~p

√ √~p

τ±√× √

e± h±; 3h± µ±

νe, νµ, ντ × × × × ×Quarksu, d, s × √ √ √ ×c→ D

√ √e± h’s µ±

b→ B√ √

e± h’s µ±

t→ bW± b√

e± b+ 2 jets µ±

Gauge bosonsγ × × E × ×g × √ √ √ ×

W± → ℓ±ν × ~p e± × µ±

→ qq′ × √ √2 jets ×

Z0 → ℓ+ℓ− × ~p e± × µ±

→ qq (bb)√ √

2 jets ×

How to search for new particles?

Leptons(e, µ)

Photons

Taus

JetsMissing ET

y98014_416dPauss rd

H → WW→lνjjH → ZZ→lljjZZH

H→WW→lνlν

H→WW→lνlν

→ → νν

H →

Z Z

→

4 le

pton

s*(

(H γγ→

H ZZ→0

n lept.+ x

∼g → n jets + E

MT

→ n leptons + Xq similar∼

H+→τν

0H, A , h0 0→ττ(H ) γγ→h0 0

g∼ → h + x0

χ χ∼ ∼0 +→

*( (

W'→lν

V,ρ →WZTC→ lνll

Z' → ll

unpredicted discovery

4l→

g, q →b jets + X∼ ∼

b- Jet-tag

WH→

lνbb

ttH→lν

bb+X

––

H ll→ ττZZ→

Homework:

Exercise 1.1: For a π0, µ−, or a τ− respectively, calculate its decay

length for E = 10 GeV.

Exercise 1.2: An event was identified to have µ+, µ− along with some

missing energy. What can you say about the kinematics of the system of

the missing particles? Consider for both an e+e− and a hadron collider.

Exercise 1.3: A 120 GeV Higgs boson will have a production cross section

of 20 pb at the LHC. How many events per year do you expect to produce

for the Higgs boson with a designed LHC luminosity 1033/cm2/s?

Do you expect it to be easy to observe and why?

II. Basic Techniques

and Tools for Collider Physics

(A). Scattering cross section

For a 2 → n scattering process:

σ(ab→ 1 + 2 + ...n) =1

2s

∑|M|2 dPSn,

dPSn ≡ (2π)4 δ4

P −n∑

i=1

pi

Πni=11

(2π)3d3~pi2Ei

,

s = (pa + pb)2 ≡ P2 =

n∑

i=1

pi

2

,

where∑|M|2 dynamics; dPSn kinematics (Lorentz invariant).

II. Basic Techniques

and Tools for Collider Physics

(A). Scattering cross section

For a 2 → n scattering process:

σ(ab→ 1 + 2 + ...n) =1

2s

∑|M|2 dPSn,

dPSn ≡ (2π)4 δ4

P −

n∑

i=1

pi

Πni=1

1

(2π)3d3~pi2Ei

,

s = (pa + pb)2 ≡ P2 =

n∑

i=1

pi

2

,

where∑|M|2 dynamics; dPSn kinematics (Lorentz invariant).

For a 1 → n decay process, the total width:

Γ(a→ 1 + 2 + ...n) =1

2Ma

∑|M|2 dPSn.

τ = Γ−1tot .

(B). Phase space and kinematics ∗

One-particle Final State a+ b→ 1:

dPS1 ≡ (2π)d3~p12E1

δ4(P − p1)

.= π|~p1|dΩ1δ

3(~P − ~p1).= 2π δ(s−m2

1).

where the last equal sign made use of the identity

d3~p

2E=∫d4p δ(p2 −m2).

∗E.Byckling, K. Kajantie: Particle Kinemaitcs (1973).



dPS1 ≡ (2π)d3~p12E1

δ4(P − p1)

.= π|~p1|dΩ1δ

3(~P − ~p1).= 2π δ(s−m2

1).


d3~p

2E=∫d4p δ(p2 −m2).

Kinematical relations:

~P ≡ ~pa + ~pb = ~p1, Ecm1 =√s in the c.m. frame,

s = (pa + pb)2 = m2

1.




dPS1 ≡ (2π)d3~p12E1

δ4(P − p1)

.= π|~p1|dΩ1δ

3(~P − ~p1).= 2π δ(s−m2

1).


d3~p

2E=∫d4p δ(p2 −m2).

Kinematical relations:

~P ≡ ~pa + ~pb = ~p1, Ecm1 =√s in the c.m. frame,

s = (pa + pb)2 = m2

1.

The “dimensinless phase-space volume” is s(dPS1) = 2π.


Two-particle Final State a+ b→ 1 + 2:

dPS2 ≡ 1

(2π)2δ4 (P − p1 − p2)

d3~p12E1

d3~p22E2

.=

1

(4π)2|~pcm1 |√s

dΩ1 =1

(4π)2|~pcm1 |√s

d cos θ1dφ1

=1

4π

1

2λ1/2

(1,m2

1

s,m2

2

s

)dx1dx2.


dPS2 ≡ 1

(2π)2δ4 (P − p1 − p2)

d3~p12E1

d3~p22E2

.=

1

(4π)2|~pcm1 |√s

dΩ1 =1

(4π)2|~pcm1 |√s

d cos θ1dφ1

=1

4π

1

2λ1/2

(1,m2

1

s,m2

2

s

)dx1dx2.

The magnitudes of the energy-momentum of the two particles are

fully determined by the four-momentum conservation:

|~pcm1 | = |~pcm2 | = λ1/2(s,m21,m

22)

2√s

, Ecm1 =s+m2

1 −m22

2√s

, Ecm2 =s+m2

2 −m21

2√s

,

λ(x, y, z) = (x− y − z)2 − 4yz = x2 + y2 + z2 − 2xy − 2xz − 2yz.


dPS2 ≡ 1

(2π)2δ4 (P − p1 − p2)

d3~p12E1

d3~p22E2

.=

1

(4π)2|~pcm1 |√s

dΩ1 =1

(4π)2|~pcm1 |√s

d cos θ1dφ1

=1

4π

1

2λ1/2

(1,m2

1

s,m2

2

s

)dx1dx2.

The magnitudes of the energy-momentum of the two particles are

fully determined by the four-momentum conservation:

|~pcm1 | = |~pcm2 | = λ1/2(s,m21,m

22)

2√s

, Ecm1 =s+m2

1 −m22

2√s

, Ecm2 =s+m2

2 −m21

2√s

,

λ(x, y, z) = (x− y − z)2 − 4yz = x2 + y2 + z2 − 2xy − 2xz − 2yz.

The phase-space volume of the two-body is scaled down

with respect to that of the one-particle by a factor

dPS2

s dPS1≈ 1

(4π)2.

just like a “loop factor”.

Consider a 2 → 2 scattering process pa + pb → p1 + p2,

the Mandelstam variables are defined as

s = (pa + pb)2 = (p1 + p2)

2 = E2cm,

t = (pa − p1)2 = (pb − p2)

2 = m2a +m2

1 − 2(EaE1 − pap1 cos θa1),

u = (pa − p2)2 = (pb − p1)

2 = m2a +m2


s+ t+ u = m2a +m2

b +m21 +m2

2.

Consider a 2 → 2 scattering process pa + pb → p1 + p2,

the Mandelstam variables are defined as

s = (pa + pb)2 = (p1 + p2)

2 = E2cm,

t = (pa − p1)2 = (pb − p2)

2 = m2a +m2


u = (pa − p2)2 = (pb − p1)

2 = m2a +m2


s+ t+ u = m2a +m2

b +m21 +m2

2.

The two-body phase space can be thus written as

dPS2 =1

(4π)2dt dφ1

s λ1/2(1,m2

a/s,m2b /s

).

Exercise 2.1: Assume that ma = m1 and mb = m2. Show that

t = −2p2cm(1 − cos θ∗a1),

u = −2p2cm(1 + cos θ∗a1) +(m2

1 −m22)

2

s,

where pcm = λ1/2(s,m21,m

22)/2

√s is the momentum magnitude in the

c.m. frame. This leads to t→ 0 in the collinear limit.

Exercise 2.2: A particle of mass M decays to two particles

isotropically in its rest frame. What does the momentum distribution

look like in a frame in which the particle is moving with a speed βz?

Compare the result with your expectation for the shape change

for a basket ball.

Three-particle Final State a+ b→ 1 + 2 + 3:

dPS3 ≡ 1

(2π)5δ4 (P − p1 − p2 − p3)

d3~p12E1

d3~p22E2

d3~p32E3

.=

|~p1|2 d|~p1| dΩ1

(2π)3 2E1

1

(4π)2|~p(23)

2 |m23

dΩ2

=1

(4π)3λ1/2

(1,

m22

m223

,m2

3

m223

)2|~p1| dE1 dx2dx3dx4dx5.

d cos θ1,2 = 2dx2,4, dφ1,2 = 2πdx3,5, 0 ≤ x2,3,4,5 ≤ 1,

|~pcm1 |2 = |~pcm2 + ~pcm3 |2 = (Ecm1 )2 −m21,

m223 = s− 2

√sEcm1 +m2

1, |~p232 | = |~p23

3 | = λ1/2(m223,m

22,m

23)

2m23,

Three-particle Final State a+ b→ 1 + 2 + 3:

dPS3 ≡ 1

(2π)5δ4 (P − p1 − p2 − p3)

d3~p12E1

d3~p22E2

d3~p32E3

.=

|~p1|2 d|~p1| dΩ1

(2π)3 2E1

1

(4π)2|~p(23)

2 |m23

dΩ2

=1

(4π)3λ1/2

(1,

m22

m223

,m2

3

m223

)2|~p1| dE1 dx2dx3dx4dx5.

d cos θ1,2 = 2dx2,4, dφ1,2 = 2πdx3,5, 0 ≤ x2,3,4,5 ≤ 1,

|~pcm1 |2 = |~pcm2 + ~pcm3 |2 = (Ecm1 )2 −m21,

m223 = s− 2

√sEcm1 +m2

1, |~p232 | = |~p23

3 | = λ1/2(m223,m

22,m

23)

2m23,

The particle energy spectrum is not monochromatic.

The maximum value (the end-point) for particle 1 in c.m. frame is

Emax1 =s+m2

1 − (m2 +m3)2

2√s

, m1 ≤ E1 ≤ Emax1 ,

|~pmax1 | =λ1/2(s,m2

1, (m2 +m3)2)

2√s

, 0 ≤ p1 ≤ pmax1 .

More intuitive to work out the end-point for the kinetic energy,

– recall the direct neutrino mass bound in β-decay:

Kmax1 = Emax1 −m1 =

(√s−m1 −m2 −m3)(

√s−m1 +m2 +m3)

2√s

.

In general, the 3-body phase space boundaries are non-trivial.

That leads to the “Dalitz Plots”.

One practically useful formula leave to you as:

Exercise 2.3: A particle of mass M decays to 3 particles M → abc.

Show that the phase space element can be expressed as

dPS3 =1

27π3M2dxadxb.

xi =2EiM

, (i = a, b, c,∑

i

xi = 2).

where the integration limits for ma = mb = mc = 0 are

0 ≤ xa ≤ 1, 1 − xa ≤ xb ≤ 1.

Recursion relation P → 1 + 2 + 3...+ n:

p pnpn−1, n

p1 p2 . . .pn−1

Recursion relation P → 1 + 2 + 3...+ n:

p pnpn−1, n

p1 p2 . . .pn−1

dPSn(P ; p1, ..., pn) = dPSn−1(P ; p1, ..., pn−1,n)

dPS2(pn−1,n; pn−1, pn)dm2

n−1,n

2π.

For instance,

dPS3 = dPS2(i)dm2

prop

2πdPS2(f).

Breit-Wigner Resonance andthe Narrow Width Approximation

An unstable particle of mass M and total width ΓV , the propagator is

R(s) =1

(s−M2V )2 + Γ2

VM2V

.

Consider an intermediate state V ∗

a→ bV ∗ → b p1p2.

By the reduction formula, the resonant integral reads

∫ (mmax∗ )2=(ma−mb)2

(mmin∗ )2=(m1+m2)2dm2

∗ .

Variable change

tan θ =m2∗ −M2

V

ΓVMV,

resulting in a flat integrand over θ

∫ (mmax∗ )2

(mmin∗ )2

dm2∗(m2∗ −M2

V )2 + Γ2VM

2V

=∫ θmax

θmin

dθ

ΓVMV.

In the limit

(m1 +m2) + ΓV ≪MV ≪ ma − ΓV ,

θmin = tan−1 (m1 +m2)2 −M2

V

ΓVMV→ −π,

θmax = tan−1 (ma −mb)2 −M2

V

ΓVMV→ 0,

then the Narrow Width Approximation

1

(m2∗ −M2V )2 + Γ2

VM2V

≈ π

ΓVMVδ(m2

∗ −M2V ).

In the limit

(m1 +m2) + ΓV ≪MV ≪ ma − ΓV ,

θmin = tan−1 (m1 +m2)2 −M2

V

ΓVMV→ −π,

θmax = tan−1 (ma −mb)2 −M2

V

ΓVMV→ 0,

then the Narrow Width Approximation

1

(m2∗ −M2V )2 + Γ2

VM2V

≈ π

ΓVMVδ(m2

∗ −M2V ).

Exercise 2.4: Consider a three-body decay of a top quark,

t→ bW ∗ → b eν. Making use of the phase space recursion relation

and the narrow width approximation for the intermediate W boson,

show that the partial decay width of the top quark can be expressed as

Γ(t → bW ∗ → b eν) ≈ Γ(t→ bW ) ·BR(W → eν).

(C). Matrix element: The dynamics

Traditional “Trace” Techniques:

∗ You should be good at this — QFT course!

With algebraic symbolic manipulations:

∗ REDUCE

∗ FORM

∗ MATHEMATICA, MAPLE ...





∗ REDUCE

∗ FORM


Helicity Techniques:

More suitable for direct numerical evaluations.

∗ Hagiwara-Zeppenfeld: best for massless particles... (NPB)

∗ CalCul Method (by T.T. Wu et al., Parke-Mangano: Phys. Report);

∗ New techniques in loop calculations

∗ (by Z.Bern, L.Dixon, W. Giele, N. Glover, K.Melnikov...)





∗ REDUCE

∗ FORM


Helicity Techniques:

More suitable for direct numerical evaluations.

∗ Hagiwara-Zeppenfeld: best for massless particles... (NPB)

∗ CalCul Method (by T.T. Wu et al., Parke-Mangano: Phys. Report);

∗ New techniques in loop calculations

∗ (by Z.Bern, L.Dixon, W. Giele, N. Glover, K.Melnikov...)

Exercise 2.5: Calculate the squared matrix element for∑|M(ff → ZZ)|2,

in terms if s, t, u, in whatever technique you like.

Some properties of the scattering amplitudes:

Partial wave expansion for a+ b→ 1 + 2:

M(s, t) = 16π∞∑

J=M

(2J + 1)aJ(s)dJµµ′(cos θ)

aJ(s) =1

32π

∫ 1

−1M(s, t) dJµµ′(cos θ)d cos θ.

where µ = sa − sb, µ′ = s1 − s2, J = max(|µ|, |µ′|).



M(s, t) = 16π∞∑

J=M


aJ(s) =1

32π

∫ 1



The partial wave amplitude have the properties:

(a). partial wave unitarity: Im(aJ) ≥ |aJ |2, or |Re(aJ)| ≤ 1/2,

(b). kinematical thresholds: aJ(s) ∝ βlii β

lff (J = L+ S).



M(s, t) = 16π∞∑

J=M


aJ(s) =1

32π

∫ 1






lff (J = L+ S).

⇒ well-known behavior: σ ∝ β2lf+1

f .



M(s, t) = 16π∞∑

J=M


aJ(s) =1

32π

∫ 1






lff (J = L+ S).

⇒ well-known behavior: σ ∝ β2lf+1

f .

Exercise 2.6: Appreciate the properties (a) and (b) by explicitly

calculating the helicity amplitudes for

e−Le+R → γ∗ → H−H+, e−Le

+L,R → γ∗ → µ−Lµ

+R , H−H+ → G∗ → H−H+.

Calculational Tools

• Monte Carlo packages for phase space integration:

(1) VEGAS by P. LePage: adaptive important-sampling MC

http://en.wikipedia.org/wiki/Monte-Carlo integration

(2) SAMPLE, RAINBOW, MISER ...

• Automated software for matrix elements:

(1) REDUCE — an interactive program designed for general algebraic

computations, including to evaluate Dirac algebra, an old-time program,

http://www.uni-koeln.de/REDUCE;

http://reduce-algebra.com.

(2) FORM by Jos Vermaseren: A program for large scale symbolic

manipulation, evaluate fermion traces automatically,

and perform loop calculations,s commercially available at

http://www.nikhef.nl/ form

(3) FeynCalc and FeynArts: Mathematica packages for algebraic

calculations in elementary particle physics.

http://www.feyncalc.org;

http://www.feynarts.de

(4) MadGraph: Helicity amplitude method for tree-level matrix elements

available upon request or

http://madgraph.hep.uiuc.edu

Example:Standard Model particles include:Quarks: d u s c b t d u s c b tLeptons: e- mu- ta- e+ mu+ ta+ ve vm vt ve vm vtBosons: g a z w+ w- h

Enter process you would like calculated in the form e+ e- → a.(return to exit MadGraph.)

a a → w+ w-

Generating diagrams for 4 external legsThere are 3 graphs.Writing Feynman graphs in file aa wpwm.psWriting function AA WPWM in file aa wpwm.f.

• Automated evaluation of cross sections:

(1)MadGraph/MadEvent and MadSUSY:

Generate Fortran codes on-line!

http://madgraph.hep.uiuc.edu

(2) CompHEP: computer program for calculation of elementary particle

processes in Standard Model and beyond. CompHEP has a built-in numeric

interpreter. So this version permits to make numeric calculation without

additional Fortran/C compiler. It is convenient for more or less simple

calculations.

— It allows your own construction of a Lagrangian model!

http://theory.npi.msu.su/kryukov

(3) GRACE and GRACE SUSY:

http://minami-home.kek.jp

(4) Pandora by M. Peskin:

C++ based package for e+e−, including beam effects.

http://www-sldnt.slac.stanford.edu/nld/new/Docs/

Generators/PANDORA.htm

The program pandora is a general-purpose parton-level event generator

which includes beamstrahlung, initial state radiation, and full treatment

of polarization effects. (An interface to PYTHIA that produces fully

hadronized events is possible.)

This version includes the SM physics processes:

e+e− → ℓ+ℓ−, qq, γγ, tt, Zγ, ZZ, W+W−

→ Zh, ννh, e+e−h, ννγγγ → ℓ+ℓ−, qq, tt, e+e−, W+W−, heγ → eγ, eZ, νW

e−e− → e−e−.

and some illustrative Beyond the SM processes:

e+e− → Z ′ → ℓ+ℓ−, qq→ KK − gravitons→ ℓ+ℓ−, qq, γγ, ZZ, W+W−

→ γ gravitonM → ρTCW

+W−.

• Numerical simulation packages:

(1) PYTHIA:

PYTHIA and JETSET are programs for the generation of high-energy

physics events, i.e. for the description of collisions at high energies

between elementary particles such as e+, e-, p and pbar in various

combinations. Together they contain theory and models for a number

of physics aspects, including hard and soft interactions, parton

distributions, initial and final state parton showers, multiple interactions,

fragmentation and decay.

http://www.thep.lu.se/ torbjorn/Pythia.html


(1) PYTHIA:









(2) ISAJET

ISAJET is a Monte Carlo program which simulates p-p, pbar-p, and e-e

interactions at high energies. It is based on perturbative QCD plus

phenomenological models for parton and beam jet fragmentation.

http://www.phy.bnl.gov/ isajet


(1) PYTHIA:









(2) ISAJET

ISAJET is a Monte Carlo program which simulates p-p, pbar-p, and e-e

interactions at high energies. It is based on perturbative QCD plus

phenomenological models for parton and beam jet fragmentation.

http://www.phy.bnl.gov/ isajet

(3) HERWIG

HERWIG is a Monte Carlo program which simulates p-p, pbar-p

interactions at high energies. It has the most sophisticated perturbative

treatments, and possible NLO QCD matrix elements in parton showing.

http://hepwww.rl.ac.uk/theory/seymour/herwig/

III. An e+e− Linear Collider (ILC)

(A.) Simple Formalism

Event rate of a reaction:

R(s) = σ(s)L, for constant L= L

∫dτdL

dτσ(s), τ =

s

s.

III. An e+e− Linear Collider (ILC)

(A.) Simple Formalism

Event rate of a reaction:

R(s) = σ(s)L, for constant L= L

∫dτdL

dτσ(s), τ =

s

s.

As for the differential production cross section of two-particle a, b,

dσ(e+e− → ab)

d cos θ=

β

32πs

∑|M|2

where

• β = λ1/2(1,m2a/s,m

2b /s), is the speed factor for the out-going particles

in the c.m. frame, and pcm = β√s/2,

• ∑|M|2 the squared matrix element, summed and averaged over quantum

numbers (like color and spins etc.)

• unpolarized beams so that the azimuthal angle trivially integrated out,

Total cross sections and event rates for SM processes:

(B). Resonant production: Breit-Wigner formula

1

(s−M2V )2 + Γ2

VM2V

If the energy spread δ√s≪ ΓV , the line-shape mapped out:

σ(e+e− → V → X) =4π(2j + 1)Γ(V → e+e−)Γ(V → X)

(s−M2V )

2 + Γ2VM

2V

s

M2V

,


1

(s−M2V )2 + Γ2

VM2V


σ(e+e− → V → X) =4π(2j + 1)Γ(V → e+e−)Γ(V → X)

(s−M2V )

2 + Γ2VM

2V

s

M2V

,

If δ√s≫ ΓV , the narrow-width approximation:

1

(s−M2V )2 + Γ2

VM2V

→ π

MVΓVδ(s = M2

V ),

σ(e+e− → V → X) =4π2(2j + 1)Γ(V → e+e−)BF (V → X)

M3V

dL(s = M2V )

dτ


1

(s−M2V )2 + Γ2

VM2V


σ(e+e− → V → X) =4π(2j + 1)Γ(V → e+e−)Γ(V → X)

(s−M2V )

2 + Γ2VM

2V

s

M2V

,


1

(s−M2V )2 + Γ2

VM2V

→ π

MVΓVδ(s = M2

V ),


M3V

dL(s = M2V )

dτ

Exercise 3.1: sketch the derivation of these two formulas,

assuming a Gaussian distribution for dL/dτ .


1

(s−M2V )2 + Γ2

VM2V


σ(e+e− → V → X) =4π(2j + 1)Γ(V → e+e−)Γ(V → X)

(s−M2V )

2 + Γ2VM

2V

s

M2V

,


1

(s−M2V )2 + Γ2

VM2V

→ π

MVΓVδ(s = M2

V ),


M3V

dL(s = M2V )

dτ

Exercise 3.1: sketch the derivation of these two formulas,

assuming a Gaussian distribution for dL/dτ .

Away from resonance

For finite-angle scattering:

σ ∼ 1

sor σ ∼ 1

M2V

ln2 s

M2V

.

(C). Fermion production:

Common processes: e−e+ → ff .For most of the situations, the scattering matrix element can be castedinto a V ±A chiral structure of the form (sometimes with the help of Fierztransformations)

M =e2

sQαβ [ve+(p2)γ

µPαue−(p1)] [ψf(q1)γµPβψ′f(q2)],

where P∓ = (1 ∓ γ5)/2 are the L,R chirality projection operators, andQαβ are the bilinear couplings governed by the underlying physics of theinteractions with the intermediate propagating fields.With this structure, the scattering matrix element squared:

∑|M|2 =

e4

s2

[(|QLL|2 + |QRR|2) uiuj + (|QLL|2 + |QRL|2) titj

+ 2Re(Q∗LLQLR +Q∗

RRQRL)mfmfs],

where ti = t−m2i = (p1 − q1)

2 −m2i and ui = u−m2

i = (p1 − q2)2 −m2

i .

Exercise 3.2: Verify this formula.

(D). Typical size of the cross sections:

• The simplest reaction

σ(e+e− → γ∗ → µ+µ−) ≡ σpt =4πα2

3s.

In fact, σpt ≈ 100 fb/(√s/TeV)2 has become standard units to measure

the size of cross sections.



σ(e+e− → γ∗ → µ+µ−) ≡ σpt =4πα2

3s.



• The Z resonance prominent (or other MV ),



σ(e+e− → γ∗ → µ+µ−) ≡ σpt =4πα2

3s.




• At the ILC√s = 500 GeV,

σ(e+e− → e+e−) ∼ 100σpt ∼ 40 pb.

(anglular cut dependent.)



σ(e+e− → γ∗ → µ+µ−) ≡ σpt =4πα2

3s.





σ(e+e− → e+e−) ∼ 100σpt ∼ 40 pb.


σpt ∼ σ(ZZ) ∼ σ(tt) ∼ 400 fb;

σ(u, d, s) ∼ 9σpt ∼ 3.6 pb;

σ(WW ) ∼ 20σpt ∼ 8 pb.



σ(e+e− → γ∗ → µ+µ−) ≡ σpt =4πα2

3s.





σ(e+e− → e+e−) ∼ 100σpt ∼ 40 pb.


σpt ∼ σ(ZZ) ∼ σ(tt) ∼ 400 fb;

σ(u, d, s) ∼ 9σpt ∼ 3.6 pb;

σ(WW ) ∼ 20σpt ∼ 8 pb.

and

σ(ZH) ∼ σ(WW → H) ∼ σpt/4 ∼ 100 fb;

σ(WWZ) ∼ 0.1σpt ∼ 40 fb.

(E). Gauge boson radiation:

A qualitatively different process is initiated from gauge boson radiation,

typically off fermions:

ff

apγ / f

X

’

The simplest case is the photon radiation off an electron, like:

e+e− → e+, γ∗e− → e+e−.

The dominant features are due to the result of a t-channel singularity,

induced by the collinear photon splitting:

σ(e−a→ e−X) ≈∫dx Pγ/e(x) σ(γa → X).

The so called the effective photon approximation.

For an electron of energy E, the probability of finding a collinear photon

of energy xE is given by

Pγ/e(x) =α

2π

1 + (1 − x)2

xlnE2

m2e,

known as the Weizsacker-Williams spectrum.

Exercise 3.3: Try to derive this splitting function.

We see that:

• me enters the log to regularize the collinear singularity;

• 1/x leads to the infrared behavior of the photon;

• This picture of the photon probability distribution is also valid for other

photon spectrum:

Based on the back-scattering laser technique, it has been proposed to

produce much harder photon spectrum, to construct a “photon collider”...

(massive) Gauge boson radiation:

A similar picture may be envisioned for the electroweak massive gauge

bosons, V = W±, Z.

Consider a fermion f of energy E, the probability of finding a (nearly)

collinear gauge boson V of energy xE and transverse momentum pT (with

respect to ~pf) is approximated by

PTV/f(x, p2T ) =

g2V + g2A8π2

1 + (1 − x)2

x

p2T(p2T + (1 − x)M2

V )2,

PLV/f(x, p2T ) =

g2V + g2A4π2

1 − x

x

(1 − x)M2V

(p2T + (1 − x)M2V )2

.

Although the collinear scattering would not be a good approximation un-

til reaching very high energies√s ≫ MV , it is instructive to consider the

qualitative features.

(F). Beam polarization:

One of the merits for an e+e− linear collider is the possible high polarization

for both beams.

Consider first the longitudinal polarization along the beam line direction.

Denote the average e± beam polarization by PL±, with PL± = −1 purely

left-handed and +1 purely right-handed.

The polarized squared matrix element, based on the helicity amplitudes

Mσe−σe+:

∑|M|2 =

1

4[(1 − PL−)(1 − PL+)|M−−|2 + (1 − PL−)(1 + PL+)|M−+|2

+(1 + PL−(1 − PL+)|M+−|2 + (1 + PL−)(1 + PL+)|M++|2].

Since the electroweak interactions of the SM and beyond are chiral:

Certain helicity amplitudes can be suppressed or enhanced by properly

choosing the beam polarizations: e.g., W± exchange ...

Furthermore, it is possible to produce transversely polarized beams with

the help of a spin-rotator.

If the beams present average polarizations with respect to a specific direc-

tion perpendicular to the beam line direction, −1 < PT± < 1, then there will

be one additional term in the limit me → 0,

1

42 PT−P

T+ Re(M−+M∗

+−).

The transverse polarization is particularly important when

the interactions produce an asymmetry in azimuthal angle, such as the

effect of CP violation.

IV. Hadron Collider Physics

(A). New HEP frontier: the LHCMajor discoveries and excitement ahead ...

Feb.16, 2006: ATLAS (90m underground) CMS

(pilot run at the end of 2007.)

LHC Event rates for various SM processes:

LHC Event rates for various SM processes:

1034/cm2/s ⇒ 100 fb−1/yr.


Great potential to open a new chapter of HEP!

Experimental challenges:


≈ 1 billion event/sec: impossible read-off !

≈ 1 interesting event per 1,000,000: selection (triggering).

Experimental challenges:


≈ 1 billion event/sec: impossible read-off !

≈ 1 interesting event per 1,000,000: selection (triggering).

≈ 25 overlapping events/bunch crossing:

. . . . . . . .

Colliding beamn1 n2

t = 1/f


Triggering thresholds:

ATLAS

Objects η pT (GeV)

µ inclusive 2.4 6 (20)

e/photon inclusive 2.5 17 (26)Two e’s or two photons 2.5 12 (15)

1-jet inclusive 3.2 180 (290)3 jets 3.2 75 (130)4 jets 3.2 55 (90)

τ/hadrons 2.5 43 (65)

/ET 4.9 100Jets+/ET 3.2, 4.9 50,50 (100,100)

(η = 2.5 ⇒ 10; η = 5 ⇒ 0.8.)

Triggering thresholds:

ATLAS

Objects η pT (GeV)

µ inclusive 2.4 6 (20)

e/photon inclusive 2.5 17 (26)Two e’s or two photons 2.5 12 (15)

1-jet inclusive 3.2 180 (290)3 jets 3.2 75 (130)4 jets 3.2 55 (90)

τ/hadrons 2.5 43 (65)

/ET 4.9 100Jets+/ET 3.2, 4.9 50,50 (100,100)

(η = 2.5 ⇒ 10; η = 5 ⇒ 0.8.)

With optimal triggering and kinematical selections:

pT ≥ 30 − 100 GeV, |η| ≤ 3 − 5; /ET ≥ 100 GeV.

(B). Before further details ...

Appreciate the beautiful results from the Tevatron!At the Tevatron Run II:

Peak luminosity record high ≈ 2 × 1032 cm−2 s−1;

Integrated luminosity over 1 fb−1, leading the HEP frontier.

(B). Before further details ...

Appreciate the beautiful results from the Tevatron!At the Tevatron Run II:

Peak luminosity record high ≈ 2 × 1032 cm−2 s−1;

Integrated luminosity over 1 fb−1, leading the HEP frontier.

D0 Z → e+e− CDF W → µν

0

50

100

150

200

250

300

60 70 80 90 100 110 120m(ee) (GeV)

num

ber

of e

vent

s

) (GeV)νµ(Tm60 80 100

even

ts /

0.5

GeV

0

500

1000

1500 CDF RUN IIPRELIMINARY

/dof = 64 / 582χ

CDF 1-jet inclusive D0 1-jet in rapidity ranges

(GeV)TInclusive Jet E0 100 200 300 400 500 600

(nb

/GeV

)η

dT

/ dE

σ2d

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1

10

102

CDF Run II Preliminary

Integrated L = 177 pb -1

0.1 < |ηDet| < 0.7

JetClu Cone R = 0.7

Run II Data

+/- Systematic Uncertainty

NLO pQCD (CTEQ 6.1)

CDF W+jets sample and top-quark events

Number of jets in W+jets1 2 3 4

Num

ber

of ta

gged

eve

nts

1

10

102

Background

Background errorstBackground+t

errorstBackground+t)

-1 11 pb±Data (194

=6.7 pbtt

σ scaled to tt

≥

3 jets≥>200 GeV for TRequire H

CDF Mee and E/T

)2

Dielectron Mass (GeV/c

100 200 300 400 500

)2E

vent

s / 5

(G

eV/c

10-1

1

10

102

103

104

Data

Drell - Yan

QCD Background, WW, WZ, ttττ

)2


100 200 300 400 500

)2E

vent

s / 5

(G

eV/c

10-1

1

10

102

103

104

)-1

CDF Run II Preliminary (200 pb CDF preliminary

1

10

10 2

50 75 100 125 150 175 200 225 250 275 300

Z+jets

W+jets

tt+WW+WZ+ZZ

data (L=87 pb-1)

E/ T (GeV)dN

/dE/

T

CDF Mee and E/T

)2


100 200 300 400 500

)2E

vent

s / 5

(G

eV/c

10-1

1

10

102

103

104

Data

Drell - Yan


)2


100 200 300 400 500

)2E

vent

s / 5

(G

eV/c

10-1

1

10

102

103

104

)-1


1

10

10 2

50 75 100 125 150 175 200 225 250 275 300

Z+jets

W+jets

tt+WW+WZ+ZZ

data (L=87 pb-1)

E/ T (GeV)dN

/dE/

T

LHC – first (crucial) steps:Re-discover the Standard Model.

CDF Mee and E/T

)2


100 200 300 400 500

)2E

vent

s / 5

(G

eV/c

10-1

1

10

102

103

104

Data

Drell - Yan


)2


100 200 300 400 500

)2E

vent

s / 5

(G

eV/c

10-1

1

10

102

103

104

)-1


1

10

10 2

50 75 100 125 150 175 200 225 250 275 300

Z+jets

W+jets

tt+WW+WZ+ZZ

data (L=87 pb-1)

E/ T (GeV)dN

/dE/

T

LHC – first (crucial) steps:Re-discover the Standard Model.

• Z/γ∗, W± Drell-Yan rate and spectrum;

• jet inclusive to pjT ∼ 300 − 500 GeV;

• near thresholds of WW, WZ, ZZ, Wγ, γ+jets.

(C). Special kinematics for hadron colliders

Hadron momenta: PA = (EA,0,0, pA), PB = (EA,0,0,−pA),

The parton momenta: p1 = x1PA, p2 = x2PB.

Then the parton c.m. frame moves randomly, even by event:

βcm =x1 − x2x1 + x2

, or :

ycm =1

2ln

1 + βcm

1 − βcm=

1

2lnx1x2, (−∞ < ycm <∞).

(C). Special kinematics for hadron colliders

Hadron momenta: PA = (EA,0,0, pA), PB = (EA,0,0,−pA),

The parton momenta: p1 = x1PA, p2 = x2PB.

Then the parton c.m. frame moves randomly, even by event:

βcm =x1 − x2x1 + x2

, or :

ycm =1

2ln

1 + βcm

1 − βcm=

1

2lnx1x2, (−∞ < ycm <∞).

The four-momentum vector transforms as(E′p′z

)=

(γ −γ βcm−γ βcm γ

)(Epz

)

=

(cosh ycm − sinh ycm− sinh ycm cosh ycm

)(Epz

).

This is often called the “boost”.

One wishes to design final-state kinematics invariant under the boost:

For a four-momentum p ≡ pµ = (E, ~p),

ET =√p2T +m2, y =

1

2lnE + pz

E − pz,

pµ = (ET cosh y, pT sinφ, pT cosφ, ET sinh y),

d3~p

E= pTdpTdφ dy = ETdETdφ dy.



ET =√p2T +m2, y =

1

2lnE + pz

E − pz,


d3~p


Due to random boost between Lab-frame/c.m. frame event-by-event,

y′ =1

2lnE′ + p′zE′ − p′z

=1

2ln

(1 − βcm)(E + pz)

(1 + βcm)(E − pz)= y − ycm.



ET =√p2T +m2, y =

1

2lnE + pz

E − pz,


d3~p


Due to random boost between Lab-frame/c.m. frame event-by-event,

y′ =1

2lnE′ + p′zE′ − p′z

=1

2ln

(1 − βcm)(E + pz)

(1 + βcm)(E − pz)= y − ycm.

In the massless limit, rapidity → pseudo-rapidity:

y → η =1

2ln

1 + cos θ

1 − cos θ= lncot

θ

2.

Exercise 4.1: Verify all the above equations.

The “Lego” plot:

A CDF di-jet event on a lego plot in the η − φ plane.

The “Lego” plot:

A CDF di-jet event on a lego plot in the η − φ plane.

φ,∆y = y2 − y1 is boost-invariant.

Thus the “separation” between two particles in an event

∆R =√

∆φ2 + ∆y2 is boost-invariant,

and lead to the “cone definition” of a jet.

(D). Parton Distribution Functions (PDF)

Another very important aspect:

Observable cross sections at hadron level:

σpp(S) =∫dx1dx2P1(x1, Q

2)P2(x2, Q2) σparton(s).

CTEQ 5 parton distribution functions

where

• P(x,Q2) is the “Parton Distribution Functions” (PDF), the probability

of finding a parton P with a momentum fraction x inside a proton.

P(x,Q2) cannot be calculated from first principles, only extracted

by fitting data, assuming a boundary condition at Q20 ∼(2 GeV)2.

The PDF’s should match the parton-level cross section σparton(s)

at a given order in αs.

• Q2 is the “factorization scale”, below which it is collinear physics.

It is NOT uniquely determined, leading to intrinsic uncertainty

in QCD perturbation predictions. But its uncertainty is reduced

with higher order calculations.

• σparton(s) is theoretically calculated by perturbation theory in the SM

and models beyond the SM.

More accurate results and better understanding of the SM cross section,

in particular in QCD are crucial for observing new physics

as deviations from the SM.

An improved treatment for calculations in hadronic collisions:

Note that

s ≡ τS, τ = x1x2 =s

S. ycm =

1

2lnx1x2.

The parton energy fractions are thus given by

x1,2 =√τ e±ycm.


Note that

s ≡ τS, τ = x1x2 =s

S. ycm =

1

2lnx1x2.


x1,2 =√τ e±ycm.

The integration over the energy fractions:

∫ 1

τ0dx1

∫ 1

τ0/x1dx2 =

∫ 1

τ0dτ∫ −1

2 ln τ

12 ln τ

dycm.

• τ0 = m2res/S and mres the threshold for the parton final state.

• τ characterizes the (invariant) mass of the partonic reaction,

particularly suitable for a resonant production.

• τ − ycm variables are better for numerical evaluations.


Note that

s ≡ τS, τ = x1x2 =s

S. ycm =

1

2lnx1x2.


x1,2 =√τ e±ycm.

The integration over the energy fractions:

∫ 1

τ0dx1

∫ 1

τ0/x1dx2 =

∫ 1

τ0dτ∫ −1

2 ln τ

12 ln τ

dycm.

• τ0 = m2res/S and mres the threshold for the parton final state.

• τ characterizes the (invariant) mass of the partonic reaction,

particularly suitable for a resonant production.

• τ − ycm variables are better for numerical evaluations.

Exercise 4.2: Make a program to calculate the total cross section for

e+e− → ZZ as a function of√s. How would you change the program

to calculate pp → ZZ?

V. From Kinematics to Dynamics

(A). Characteristic observables:Crucial for uncovering new dynamics.



Selective experimental events

=⇒ Characteristic kinematical observables

(spatial, time, momentaum phase space)

=⇒ Dynamical parameters

(masses, couplings)



Selective experimental events

=⇒ Characteristic kinematical observables

(spatial, time, momentaum phase space)

=⇒ Dynamical parameters

(masses, couplings)

Energy momentum observables =⇒ mass parameters

Angular observables =⇒ nature of couplings;

Production rates, decay branchings/lifetimes =⇒ interaction strengths.

(B). Kinematical features:(a). s-channel singularity: bump search we do best.

• invariant mass of two-body R → ab : m2ab = (pa + pb)

2 = M2R.

combined with the two-body Jacobian peak in transverse momentum:

dσ

dm2ee dp

2eT

∝ ΓZMZ

(m2ee −M2

Z)2 + Γ2ZM

2Z

1

m2ee

√1 − 4p2eT/m

2ee

(B). Kinematical features:(a). s-channel singularity: bump search we do best.

• invariant mass of two-body R → ab : m2ab = (pa + pb)

2 = M2R.

combined with the two-body Jacobian peak in transverse momentum:

dσ

dm2ee dp

2eT

∝ ΓZMZ

(m2ee −M2

Z)2 + Γ2ZM

2Z

1

m2ee

√1 − 4p2eT/m

2ee

0

50

100

150

200

250

300

60 70 80 90 100 110 120m(ee) (GeV)

num

ber

of e

vent

s

(GeV)elecTE

20 30 40 50 60 70 80

Eve

nts

0

1000

2000

3000

4000

5000

6000

- W CandidateTElectron EDataPMCS+QCDQCD bkg

D0 Run II Preliminary

- W CandidateTElectron E

Z → e+e− W → eν

• “transverse” mass of two-body W− → e−νe :

m2eν T = (EeT +EνT )2 − (~peT + ~pνT )2

= 2EeTEmissT (1 − cosφ) ≤M2

W .

Transverse mass(GeV)40 50 60 70 80 90 100 110 120

Eve

nts

0

1000

2000

3000

4000

5000

6000

7000

Transverse Mass - W CandidateDataPMCS+QCDQCD bkg


Transverse Mass - W Candidate

MET(GeV)20 30 40 50 60 70 80

Eve

nts

0

1000

2000

3000

4000

5000

6000

7000

- W CandidateTMissing EDataPMCS+QCDQCD bkg


- W CandidateTMissing E

If pWT = 0, then meν T = 2EeT = 2EmissT .

Exercise 5.1: For a two-body final state kinematics, show that

dσ

dpeT=

4peT

s√

1 − 4p2eT/s

dσ

d cos θ∗.

where peT = pe sin θ∗ is the transverse momentum and θ∗ is the polar angle

in the c.m. frame. Comment on the apparent singularity at p2eT = s/4.

Exercise 5.2: Show that for an on-shell decay W− → e−νe :

m2eν T ≡ (EeT + EνT)

2 − (~peT + ~pνT )2 ≤ M2W .

Exercise 5.3: Show that if W/Z has some transverse motion, δPV , then:

p′eT ∼ peT [1 + δPV /EV ],

m′2eν T ∼ m2

eν T [1 + (δPV /EV )2],

m′2ee = m2

ee.

• H0 →W+W− → j1j2 e−νe :

cluster transverse mass (I):

m2WW T = (EW1T + EW2T)

2 − (~pjjT + ~peT + ~p missT )2

= (

√p2jjT +M2

W +√p2eνT +M2

W )2 − (~pjjT + ~peT + ~p missT )2 ≤ M2

H.

where ~p missT ≡ ~p/T = −∑

obs ~p obsT .

• H0 →W+W− → j1j2 e−νe :




= (

√p2jjT +M2

W +√p2eνT +M2


H.


obs ~p obsT .

HW

W

`11`22 • H0 →W+W− → e+νe e−νe :

“effecive” transverse mass:

m2eff T = (Ee1T + Ee2T + E miss

T )2 − (~pe1T + ~pe2T + ~p missT )2

meff T ≈ Ee1T +Ee2T +E missT

• H0 →W+W− → j1j2 e−νe :




= (

√p2jjT +M2

W +√p2eνT +M2


H.


obs ~p obsT .

HW

W

`11`22 • H0 →W+W− → e+νe e−νe :

“effecive” transverse mass:

m2eff T = (Ee1T + Ee2T + E miss

T )2 − (~pe1T + ~pe2T + ~p missT )2

meff T ≈ Ee1T +Ee2T +E missT

cluster transverse mass (II):

m2WW C =

(√p2T,ℓℓ +M2

ℓℓ + p/T

)2

− (~pT,ℓℓ +~p/T )2

mWW C ≈√p2T,ℓℓ +M2

ℓℓ + p/T

MWW invariant mass (WW fully reconstructable): - - - - - - - -

MWW, T transverse mass (one missing particle ν): —————

Meff, T effetive trans. mass (two missing particles): - - - - - - -

MWW, C cluster trans. mass (two missing particles): ————–

MWW invariant mass (WW fully reconstructable): - - - - - - - -

MWW, T transverse mass (one missing particle ν): —————

Meff, T effetive trans. mass (two missing particles): - - - - - - -

MWW, C cluster trans. mass (two missing particles): ————–

YOU design an optimal variable/observable for the search.

• cluster transverse mass (III):

H0 → τ+τ− → µ+ ντ νµ, ρ− ντ

A lot more complicated with (many) more ν′s? H

p+




p+

Not really!

τ+τ− ultra-relativistic, the final states from a τ decay highly collimated:

θ ≈ γ−1τ = mτ/Eτ = 2mτ/mH ≈ 1.5 (mH = 120 GeV).

We can thus take

~pτ+ = ~pµ+ + ~p ν′s+ , ~p ν′s

+ ≈ c+~pµ+.

~pτ− = ~pρ− + ~p ν′s− , ~p ν′s

− ≈ c−~pρ−.

where c± are proportionality constants, to be determined.




p+

Not really!

τ+τ− ultra-relativistic, the final states from a τ decay highly collimated:

θ ≈ γ−1τ = mτ/Eτ = 2mτ/mH ≈ 1.5 (mH = 120 GeV).

We can thus take

~pτ+ = ~pµ+ + ~p ν′s+ , ~p ν′s

+ ≈ c+~pµ+.

~pτ− = ~pρ− + ~p ν′s− , ~p ν′s

− ≈ c−~pρ−.

where c± are proportionality constants, to be determined.

This is applicable to any decays of fast-moving particles, like

T →Wb→ ℓν, b.

Experimental measurements: pρ−, pµ+, p/T :

c+(pµ+)x + c−(pρ−)x = (p/T )x,

c+(pµ+)y + c−(pρ−)y = (p/T )y.

Unique solutions for c± exist if

(pµ+)x/(pµ+)y 6= (pρ−)x/(pρ−)y.

Physically, the τ+ and τ− should form a finite angle,

or the Higgs should have a non-zero transverse momentum.

Experimental measurements: pρ−, pµ+, p/T :

c+(pµ+)x + c−(pρ−)x = (p/T )x,

c+(pµ+)y + c−(pρ−)y = (p/T )y.

Unique solutions for c± exist if

(pµ+)x/(pµ+)y 6= (pρ−)x/(pρ−)y.

Physically, the τ+ and τ− should form a finite angle,

or the Higgs should have a non-zero transverse momentum.

mττ [ GeV ]

1/σ

dσ/d

m

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

20 40 60 80 100 120 140 160 180 200

mττ [ GeV ]

0

0.01

0.02

0.03

0.04

0.05

20 40 60 80 100 120 140 160 180 200

In a recent analysis, however, CDF collaboration used a “visible mass”∗:

m2(vis) = (∑

vis

Evis + /ET)2 − (

∑

vis

pL,vis)2 − (

∑

vis

~pT,vis + ~p/T)2.

∗Phys.Rev.Lett.96:011802 (2006), or hep-ex/0508051.

(b). Two-body versus three-body kinematics

• Energy end-point and mass edges:

utilizing the “two-body kinematics”

Consider a simple case:

e+e− → µ+R µ−R

with two − body decays : µ+R → µ+χ0, µ−R → µ−χ0.

In the µ+R -rest frame: E0

µ =M2µR

−m2χ

2MµR.

In the Lab-frame:

(1 − β)γE0µ ≤ Elabµ ≤ (1 + β)γE0

µ

with β =(1 − 4M2

µR/s)1/2

, γ = (1 − β)−1/2.

Energy end-point: Elabµ ⇒M2µR

−m2χ.

Mass edge: mmaxµ+µ− =

√s− 2mχ.

(b). Two-body versus three-body kinematics

• Energy end-point and mass edges:

utilizing the “two-body kinematics”

Consider a simple case:

e+e− → µ+R µ−R

with two − body decays : µ+R → µ+χ0, µ−R → µ−χ0.

In the µ+R -rest frame: E0

µ =M2µR

−m2χ

2MµR.

In the Lab-frame:

(1 − β)γE0µ ≤ Elabµ ≤ (1 + β)γE0

µ

with β =(1 − 4M2

µR/s)1/2

, γ = (1 − β)−1/2.

Energy end-point: Elabµ ⇒M2µR

−m2χ.

Mass edge: mmaxµ+µ− =

√s− 2mχ.

Same idea can be applied to hadron colliders ...

Consider a squark cascade decay:

~q ~01l+q ~02 Z l1st edge : Mmax(ℓℓ) ≈Mχ0

2−Mχ0

1;

2nd edge : Mmax(ℓℓj) ≈Mq −Mχ01.

0

50

100

150

200

0 50 100 150

m ll (GeV)

dσ/

dmll

(Eve

nts/

100f

b-1

/0.3

75G

eV)

(a)

0

100

200

300

400

0 200 400 600 800 1000

m llq (GeV)

dσ/

dmllq

(E

vent

s/10

0fb

-1/5

GeV

)

(b)

0

100

200

300

400

0 200 400 600 800 1000

High m lq (GeV)

dσ/

dmlq

(E

vent

s/10

0fb

-1/5

GeV

)

(c1)

0

200

400

600

0 200 400 600 800 1000

Low m lq (GeV)

dσ/

dmlq

(E

vent

s/10

0fb

-1/5

GeV

)

(c2)

0

50

100

150

0 200 400 600 800 1000

m (GeV)

dσ/

dmllq

(E

vent

s/10

0fb

-1/5

GeV

)

(d)

0

20

40

60

80

100

0 200 400 600 800 1000

m (GeV)

dσ/

dmhq

(E

vent

s/10

0fb

-1/5

GeV

)

(e)

(c). t-channel singularity: splitting.

• Gauge boson radiation off a fermion:

The familiar Weizsacker-Williams approximation

ff

apγ / f

X

’

σ(fa → f ′X) ≈∫dx dp2T Pγ/f(x, p

2T ) σ(γa → X),

Pγ/e(x) =α

2π

1 + (1 − x)2

xlnE2

m2e,

(c). t-channel singularity: splitting.

• Gauge boson radiation off a fermion:

The familiar Weizsacker-Williams approximation

ff

apγ / f

X

’

σ(fa → f ′X) ≈∫dx dp2T Pγ/f(x, p

2T ) σ(γa → X),

Pγ/e(x) =α

2π

1 + (1 − x)2

xlnE2

m2e,

† The kernel is the same as q → qg∗ ⇒ generic for parton splitting;

† The high energy enhancement ln(E/me) reflects the collinear behavior.

• Generalize to massive gauge bosons:

PTV/f(x, p2T ) =

g2V + g2A8π2

1 + (1 − x)2

x

p2T(p2T + (1 − x)M2

V )2,

PLV/f(x, p2T ) =

g2V + g2A4π2

1 − x

x

(1 − x)M2V

(p2T + (1 − x)M2V )2

.

• Generalize to massive gauge bosons:

PTV/f(x, p2T ) =

g2V + g2A8π2

1 + (1 − x)2

x

p2T(p2T + (1 − x)M2

V )2,

PLV/f(x, p2T ) =

g2V + g2A4π2

1 − x

x

(1 − x)M2V

(p2T + (1 − x)M2V )2

.

Special kinematics for massive gauge boson fusion processes:

For the accompanying jets,

At low-pjT ,

p2jT ≈ (1 − x)M2V

Ej ∼ (1 − x)Eq

forward jet tagging

At high-pjT ,

dσ(VT )

dp2jT∝ 1/p2jT

dσ(VL)dp2jT

∝ 1/p4jT

central jet vetoing

has become important tools for Higgs searches, single-top signal etc.

(C). Charge forward-backward asymmetry AFB:

The coupling vertex of a vector boson Vµ to an arbitrary fermion pair f

iL,R∑

τgfτ γ

µ Pτ → crucial to probe chiral structures.

The parton-level forward-backward asymmetry is defined as

Ai,fFB ≡ NF −NB

NF +NB=

3

4AiAf ,

Af =(gfL)

2 − (gfR)2

(gfL)

2 + (gfR)2

.

where NF (NB) is the number of events in the forward (backward) direction

defined in the parton c.m. frame relative to the initial-state fermion ~pi.

At hadronic level:

ALHCFB =

∫dx1

∑qA

q,fFB

(Pq(x1)Pq(x2) − Pq(x1)Pq(x2)

)sign(x1 − x2)

∫dx1

∑q

(Pq(x1)Pq(x2) + Pq(x1)Pq(x2)

) .

At hadronic level:

ALHCFB =

∫dx1

∑qA

q,fFB


)sign(x1 − x2)

∫dx1

∑q


) .

Perfectly fine for Z/Z ′-type:

In pp collisions, ~pproton is the direction of ~pquark.

In pp collisions, however, what is the direction of ~pquark?

At hadronic level:

ALHCFB =

∫dx1

∑qA

q,fFB


)sign(x1 − x2)

∫dx1

∑q


) .




It is the boost-direction of ℓ+ℓ−.

At hadronic level:

ALHCFB =

∫dx1

∑qA

q,fFB


)sign(x1 − x2)

∫dx1

∑q


) .





How about W±/W ′±-type?

In pp collisions, ~pproton is the direction of ~pquark, AND:

u(⇐) d(⇐) →W+ → ℓ+(⇐) ν(⇐).

So (known): ℓ+ (ℓ−) goes along the direction with q (q)

⇒ OK at the Tevatron.

At hadronic level:

ALHCFB =

∫dx1

∑qA

q,fFB


)sign(x1 − x2)

∫dx1

∑q


) .





How about W±/W ′±-type?

In pp collisions, ~pproton is the direction of ~pquark, AND:

u(⇐) d(⇐) →W+ → ℓ+(⇐) ν(⇐).

So (known): ℓ+ (ℓ−) goes along the direction with q (q)

⇒ OK at the Tevatron.

But don’t have a good idea for pp collisions yet ...

(D). CP asymmetries ACP :

To non-ambiguously identify CP -violation effects,

one must rely on CP-odd variables.




Definition: ACP vanishes if CP-violation interactions do not exist

(for the relevant particles involved).

This is meant to be in contrast to an observable:

that’d be modified by the presence of CP-violation,

but is not zero when CP-violation is absent.

e.g. M(χ± χ0), σ(H0, A0), ...




Definition: ACP vanishes if CP-violation interactions do not exist

(for the relevant particles involved).

This is meant to be in contrast to an observable:

that’d be modified by the presence of CP-violation,

but is not zero when CP-violation is absent.

e.g. M(χ± χ0), σ(H0, A0), ...

Two ways:

a). Compare the rates between a process and its CP-conjugate process:

R(i → f) −R(i→ f)

R(i → f) +R(i→ f), e.g.

Γ(t →W+q) − Γ(t →W−q)Γ(t →W+q) + Γ(t →W−q)

.

b). Construct a CP-odd kinematical variable for an initially CP-eigenstate:

M ∼ M1 +M2 sin θ,

ACP = σF − σB =

∫ 1

0

dσ

d cos θd cos θ −

∫ 0

−1

dσ

d cos θd cos θ

b). Construct a CP-odd kinematical variable for an initially CP-eigenstate:

M ∼ M1 +M2 sin θ,

ACP = σF − σB =

∫ 1

0

dσ

d cos θd cos θ −

∫ 0

−1

dσ

d cos θd cos θ

E.g. 1: H → Z(p1)Z∗(p2) → e+(q1)e

−(q2), µ+µ−

Z µ( p1)

Z ν( p2)

h

Γµν( p1, p2)

Γµν(p1, p2) = i2

vh[a M2

Zgµν+b (p

µ1pν2 − p1 · p2gµν)+b ǫµνρσp1ρp2σ]

a = 1, b = b = 0 for SM.

In general, a, b, b complex form factors,

describing new physics at a higher scale.

For H → Z(p1)Z∗(p2) → e+(q1)e

−(q2), µ+µ−, define:

OCP ∼ (~p1 − ~p2) · (~q1 × ~q2),

or cos θ =(~p1 − ~p2) · (~q1 × ~q2)

|~p1 − ~p2||~q1 × ~q2)|.

For H → Z(p1)Z∗(p2) → e+(q1)e


OCP ∼ (~p1 − ~p2) · (~q1 × ~q2),

or cos θ =(~p1 − ~p2) · (~q1 × ~q2)

|~p1 − ~p2||~q1 × ~q2)|.

E.g. 2: H → t(pt)t(pt) → e+(q1)ν1b1, e−(q2)ν2b2.

−mt

vt(a+ bγ5)t H

OCP ∼ (~pt − ~pt) · (~pe+ × ~pe−).

thus define an asymmetry angle.

Still need optimal thinking about the asymmetry definition.

For H → Z(p1)Z∗(p2) → e+(q1)e


OCP ∼ (~p1 − ~p2) · (~q1 × ~q2),

or cos θ =(~p1 − ~p2) · (~q1 × ~q2)

|~p1 − ~p2||~q1 × ~q2)|.

E.g. 2: H → t(pt)t(pt) → e+(q1)ν1b1, e−(q2)ν2b2.

−mt

vt(a+ bγ5)t H

OCP ∼ (~pt − ~pt) · (~pe+ × ~pe−).

thus define an asymmetry angle.

Still need optimal thinking about the asymmetry definition.

E.g. 3: g1g2 → qQ1, qQ1 → χ±χ∓ + jets → e±(q1)e∓(q2) + jets.

probing CP phases θ3, θ2, θµ etc., by

OCP ∼ ~pj · (~pe+ × ~pe−).

We must “purify” the sample for the initial state.

VI. Physics Beyond the Standard Model

(A). The SM as a Low-Energy Effective Theory

• Simple structure and particle contents:

Leptons:(νee

)

L

,

(νµµ

)

L

,

(νττ

)

L

, eR, µR, τR, (ν′R s ?)

Quarks:(ud

)

L

,

(cs

)

L

,

(tb

)

L

, uR, dR, cR, sR, tR, bR

Gauge interactions: SU(3)C ⊗ SU(2)L ⊗ U(1)Y =⇒gauge bosons: 8 (masless) gluons, a (massless) photon, (massive) W±, Z0.

• The Higgs mechanism for mass generation:

An effective background potential:

V = −µ2Φ2 + λΦ4,

Φ =

(φ+

φ0

)=

iw+

H0+iz0√2

, 〈Φ〉 =

0

v√2

=

√µ2

2λ

.



V = −µ2Φ2 + λΦ4,

Φ =

(φ+

φ0

)=

iw+

H0+iz0√2

, 〈Φ〉 =

0

v√2

=

√µ2

2λ

.

All masses in place:

MW,Z =1

2gV v, mf =

gf√2v, v−2 =

√2 GF .



V = −µ2Φ2 + λΦ4,

Φ =

(φ+

φ0

)=

iw+

H0+iz0√2

, 〈Φ〉 =

0

v√2

=

√µ2

2λ

.


MW,Z =1

2gV v, mf =

gf√2v, v−2 =

√2 GF .

“Spontaneous symmetry breaking”

(known in Nature: QCD, condensed matter ...)



V = −µ2Φ2 + λΦ4,

Φ =

(φ+

φ0

)=

iw+

H0+iz0√2

, 〈Φ〉 =

0

v√2

=

√µ2

2λ

.


MW,Z =1

2gV v, mf =

gf√2v, v−2 =

√2 GF .

“Spontaneous symmetry breaking”

(known in Nature: QCD, condensed matter ...)

Crucial prediction of SM: The Higgs boson H, mH =√

2λ v.

• SUc(3) QCD as the theory of strong interactions:

Confirmation of asymptotic freedom (2004 Nobel Prize);

as well as significant progress in lattice gauge calculatioins.

• SUL(2) ⊗ UY (1) EW theory and precision measurements:

Measurement Fit |Omeas−Ofit|/σmeas

0 1 2 3

0 1 2 3

∆αhad(mZ)∆α(5) 0.02761 ± 0.00036 0.02770

mZ [GeV]mZ [GeV] 91.1875 ± 0.0021 91.1874

ΓZ [GeV]ΓZ [GeV] 2.4952 ± 0.0023 2.4965

σhad [nb]σ0 41.540 ± 0.037 41.481

RlRl 20.767 ± 0.025 20.739

AfbA0,l 0.01714 ± 0.00095 0.01642

Al(Pτ)Al(Pτ) 0.1465 ± 0.0032 0.1480

RbRb 0.21630 ± 0.00066 0.21562

RcRc 0.1723 ± 0.0031 0.1723

AfbA0,b 0.0992 ± 0.0016 0.1037

AfbA0,c 0.0707 ± 0.0035 0.0742

AbAb 0.923 ± 0.020 0.935

AcAc 0.670 ± 0.027 0.668

Al(SLD)Al(SLD) 0.1513 ± 0.0021 0.1480

sin2θeffsin2θlept(Qfb) 0.2324 ± 0.0012 0.2314

mW [GeV]mW [GeV] 80.425 ± 0.034 80.390

ΓW [GeV]ΓW [GeV] 2.133 ± 0.069 2.093

mt [GeV]mt [GeV] 178.0 ± 4.3 178.4

150 160 170 180 190 200m t [GeV]

80.2

80.3

80.4

80.5

80.6

MW

[GeV

]

direct (1 σ)

indirect (1 σ)

all (90% CL)

MH [GeV]10

020

040

080

0

• SUL(2) ⊗ UY (1) EW theory and precision measurements:Measurement Fit |Omeas−Ofit|/σmeas

0 1 2 3

0 1 2 3

∆αhad(mZ)∆α(5) 0.02761 ± 0.00036 0.02770

mZ [GeV]mZ [GeV] 91.1875 ± 0.0021 91.1874

ΓZ [GeV]ΓZ [GeV] 2.4952 ± 0.0023 2.4965

σhad [nb]σ0 41.540 ± 0.037 41.481

RlRl 20.767 ± 0.025 20.739

AfbA0,l 0.01714 ± 0.00095 0.01642

Al(Pτ)Al(Pτ) 0.1465 ± 0.0032 0.1480

RbRb 0.21630 ± 0.00066 0.21562

RcRc 0.1723 ± 0.0031 0.1723

AfbA0,b 0.0992 ± 0.0016 0.1037

AfbA0,c 0.0707 ± 0.0035 0.0742

AbAb 0.923 ± 0.020 0.935

AcAc 0.670 ± 0.027 0.668

Al(SLD)Al(SLD) 0.1513 ± 0.0021 0.1480

sin2θeffsin2θlept(Qfb) 0.2324 ± 0.0012 0.2314

mW [GeV]mW [GeV] 80.425 ± 0.034 80.390

ΓW [GeV]ΓW [GeV] 2.133 ± 0.069 2.093

mt [GeV]mt [GeV] 178.0 ± 4.3 178.4

150 160 170 180 190 200m t [GeV]

80.2

80.3

80.4

80.5

80.6

MW

[GeV

]

direct (1 σ)

indirect (1 σ)

all (90% CL)

MH [GeV]10

020

040

080

0The Standard Model: experimentally tested to a level 0.1% !

Triumph for the HEP theory and experiments! (1999 Nobel)

• A viable low-energy theory:

MH

[GeV

/c2]

600

400

500

100

200

300

03 5 7 9 11 13 15 17 19

log10 Λ [GeV]

Triviality

EW vacuum is absolute minimum

EWPrecision

• A viable low-energy theory:

MH

[GeV

/c2]

600

400

500

100

200

300

03 5 7 9 11 13 15 17 19

log10 Λ [GeV]

Triviality

EW vacuum is absolute minimum

EWPrecision

SM with a light H could be an effective theory to Λ ∼Mpl.

a stable vacuum;

non-trivial interactions;

renormalizability ...

Q: Would you need physics beyond the Standard Model?

A: ... ...

(The Garden of Aden)

(B). The Need For Going Beyond the SM

Vastly Separated Scales for Fundamental Interactions:

• QCD condensate: fπ

At the scale ΛQCD, the interaction becomes non-perturbative:

fπ ∝ 〈qLqR〉1/30 ∼ 100 MeV.

Perfectly natural! We understand the dynamics.





fπ ∝ 〈qLqR〉1/30 ∼ 100 MeV.


• EW condensate: v

Empirically (Fermi’s weak interaction) and theoretically (EWSB):

v =1

(√

2 GF )1/2=

2MW

g≈ 250 GeV.

We do NOT know the underlining dynamics!





fπ ∝ 〈qLqR〉1/30 ∼ 100 MeV.


• EW condensate: v

Empirically (Fermi’s weak interaction) and theoretically (EWSB):

v =1

(√

2 GF )1/2=

2MW

g≈ 250 GeV.

We do NOT know the underlining dynamics!

• Quantum Gravity?

MPl =hc√GN

≈ 1019 GeV.

We have NO clue about it ...

Light Higgs Boson Is Sick: a Large Hierarchy

Quantum corrections drag m2h to ultra-violet modes ∼ Λ2.

(a) (c)(b)

t

W,B

h

hh h h

h h

tc



(a) (c)(b)

t

W,B

h

hh h h

h h

tc

m2H = m2

H0 − 3

8π2y2t Λ

2 +1

16π2g2Λ2 +

1

16π2λ2Λ2



(a) (c)(b)

t

W,B

h

hh h h

h h

tc

m2H = m2

H0 − 3

8π2y2t Λ

2 +1

16π2g2Λ2 +

1

16π2λ2Λ2

(200 GeV)2 = m2H0 +

[−(2 TeV)2 + (700 GeV)2 + (500 GeV)2

] ( Λ

10 TeV

)2

.



(a) (c)(b)

t

W,B

h

hh h h

h h

tc

m2H = m2

H0 − 3

8π2y2t Λ

2 +1

16π2g2Λ2 +

1

16π2λ2Λ2

(200 GeV)2 = m2H0 +

[−(2 TeV)2 + (700 GeV)2 + (500 GeV)2

] ( Λ

10 TeV

)2

.

• If Λ ∼ Mpl, then 1030-digits cancellation (Anthropic principle)!

• Naturalness: less than 90% cancellation on m2h ⇒ Λ <∼ 3 TeV.



(a) (c)(b)

t

W,B

h

hh h h

h h

tc

m2H = m2

H0 − 3

8π2y2t Λ

2 +1

16π2g2Λ2 +

1

16π2λ2Λ2

(200 GeV)2 = m2H0 +

[−(2 TeV)2 + (700 GeV)2 + (500 GeV)2

] ( Λ

10 TeV

)2

.

• If Λ ∼ Mpl, then 1030-digits cancellation (Anthropic principle)!

• Naturalness: less than 90% cancellation on m2h ⇒ Λ <∼ 3 TeV.

Other New Physics must show up at TeV scale!

Yet Another Large Hierarchy: all way down to mν

• Now that we know:

1.9 × 10−3 eV2 < ∆m2atm < 3.0 × 10−3 eV2

7 × 10−5 eV2 < ∆m2sol < 9 × 10−5 eV2.



1.9 × 10−3 eV2 < ∆m2atm < 3.0 × 10−3 eV2

7 × 10−5 eV2 < ∆m2sol < 9 × 10−5 eV2.

• The simplest (Majorana) neutrino mass termyνΛHLHL ∼ yν

v2

Λ (νL)c νL.

Taking mν <∼ 1 eV,

=⇒ Λ ∼ yν2v2

mν>∼ yν (1014 GeV).

It implies a large scale, even we take yν ∼ ye ≈ 10−6.



1.9 × 10−3 eV2 < ∆m2atm < 3.0 × 10−3 eV2

7 × 10−5 eV2 < ∆m2sol < 9 × 10−5 eV2.

• The simplest (Majorana) neutrino mass termyνΛHLHL ∼ yν

v2

Λ (νL)c νL.

Taking mν <∼ 1 eV,

=⇒ Λ ∼ yν2v2

mν>∼ yν (1014 GeV).

It implies a large scale, even we take yν ∼ ye ≈ 10−6.

The smaller the fermion masses are, the larger the new physics scale is!

New Physics way beyond the SM!

Mass Spectrum in a Wide Range:

Mass Spectrum in a Wide Range:

EW scale: v ≈ O(1 TeV); mν : 10−15 down ? Mpl : 1015 up ?.

The “Little Hierarchy”: 4πv − Λnew

On the one hand, the “naturalness” argument prefers

Λew <∼ 4πv, just like in QCD: ΛQCD <∼ 4πfπ.

On the other hand,

• EW precision data indicate “decoupling” behavior ∗

Λew >∼ 2 − 10 TeV.

(based on generic dim-6 operators.)

• FCNC (K0 − K0 mixing etc.) constraints set

Λflavor >∼ 70 − 100 TeV.

(based on generic strong dynamics,† or generic MSSM‡ )

∗Barbieri, Strumia, hep-ph/9905281.†Chivukula, Evans, Simmons.‡Bagger, Feng, Polonsky, Zhang.

The “Little Hierarchy”: 4πv − Λnew

On the one hand, the “naturalness” argument prefers

Λew <∼ 4πv, just like in QCD: ΛQCD <∼ 4πfπ.

On the other hand,

• EW precision data indicate “decoupling” behavior ∗

Λew >∼ 2 − 10 TeV.

(based on generic dim-6 operators.)

• FCNC (K0 − K0 mixing etc.) constraints set

Λflavor >∼ 70 − 100 TeV.

(based on generic strong dynamics,† or generic MSSM‡ )

=⇒ imply special structure or symmetry.

New Physics just beyond the SM!

∗Barbieri, Strumia, hep-ph/9905281.†Chivukula, Evans, Simmons.‡Bagger, Feng, Polonsky, Zhang.

Observational Cosmology/Astrophysics


• Baryogenesis:

The fact that we exist is beyond the SM.

Particle physics issues:

Baryon number violation; large CP violation.


• Baryogenesis:




• Dark matter:

The fact that more things are invisible is beyond the SM.

Particle physics origin: WIPMs?


• Baryogenesis:




• Dark matter:



• Dark energy:

The fact that we are insignificant is beyond the SM.

Particle physics origin: Quentansense?


• Baryogenesis:




• Dark matter:



• Dark energy:

The fact that we are insignificant is beyond the SM.

Particle physics origin: Quentansense?

• Ultra-High Energy Cosmic Rays:

May help shed light on physics beyond the SM.

Theoretical issues to address:

• Vastly different mass scales:

EW gauge symmetry breaking;

charged fermion masses;

neutrino masses.

• Nontrivial fermion structure:

three fermion generations;

quark small mixing; neutrino (nearly) maximal mixing;

CP violation.

• Unified description:

gauge interactions;

Yukawa couplings;

mass relations.





neutrino masses.




CP violation.


gauge interactions;

Yukawa couplings;

mass relations.

• Gravitation and cosmology:

quantum gravity and Planck scale physics;

particle cosmology: inflation ...





neutrino masses.




CP violation.


gauge interactions;

Yukawa couplings;

mass relations.

• Gravitation and cosmology:

quantum gravity and Planck scale physics;

particle cosmology: inflation ...

=⇒ All indicate the need for physics beyond the SM.

(C). Our “Theory Bank”

Weak-scale Supersymmetry:Extended symmetry between opposite spin & statistics

particles symbol spin mass param.gluino g 1/2 M3

charginos χ±1 , χ±

2 1/2 M2

neutralinos χ01, χ

02, χ

03, χ

04 1/2 M1, µ, B

m2Hu, m2

Hd

sleptons eL, νeL, eR 0 m2ℓL

µL, νµL, µR 0τ1,τ2, ντL 0 m2

ℓR

squarks uL, dL, uR,dR 0 m2qL

cL,sL, cR,sR 0t1, t2, b1,b2 0 m2

qR

Higgs h0, H0, A0, H± 0 m2A, tan β





2 1/2 M2


02, χ

03, χ

04 1/2 M1, µ, B

m2Hu, m2

Hd



ℓR



qR


A natural cancellation mechanism:

t versus t; W versus W ; H versus H; Hd versus Hu,

∆m2H ∼ (M2

SUSY −M2SM)

λ2f

16π2ln

(Λ

MSUSY

).





2 1/2 M2


02, χ

03, χ

04 1/2 M1, µ, B

m2Hu, m2

Hd



ℓR



qR


A natural cancellation mechanism:

t versus t; W versus W ; H versus H; Hd versus Hu,

∆m2H ∼ (M2

SUSY −M2SM)

λ2f

16π2ln

(Λ

MSUSY

).

Weak scale SUSY stabilizes the hierarchy MW −Mpl

only if the “soft-SUSY breaking”: MSUSY ∼ O(MSM).

√predict TeV scale new physics:

light Higgs bosons H0, A0, H±; SUSY partners W±..., g, q, l±...



√radiative EWSB by the large top Yukawa coupling:

M2Z/2 =

m2Hd

−m2Hu

tan2 β

tan2 β−1− µ2.




M2Z/2 =

m2Hd

−m2Hu

tan2 β

tan2 β−1− µ2.

√imply a (possible) grand desert

in MSUSY −MGUT , and gauge

coupling unification.

0

10

20

30

40

50

60

10 10 10 10 10 10 10 10 2 4 6 8 10 12 14 16

1/α i

µ(GeV)

1

1/α

2

1/α

3

1/α




M2Z/2 =

m2Hd

−m2Hu

tan2 β

tan2 β−1− µ2.

√imply a (possible) grand desert

in MSUSY −MGUT , and gauge

coupling unification.

0

10

20

30

40

50

60

10 10 10 10 10 10 10 10 2 4 6 8 10 12 14 16

1/α i

µ(GeV)

1

1/α

2

1/α

3

1/α

√The “LSP” is a good dark matter candidate χ0 ∼ B.

What about MSUSY (in a hidden sector)?

× Supersymmetry breaking mechanism is unknown.

Fermionic masses:

M1, M2, M3, µ →Mχ±1,2

, Mχ01,2,3,4

;

Scalar masses:

MqL,R, MlL,R

;

Mixings:

tanβ, sinα ... ...

CP Phases:

φ1,2,3µ ... ...

What about MSUSY (in a hidden sector)?

× Supersymmetry breaking mechanism is unknown.

Fermionic masses:

M1, M2, M3, µ →Mχ±1,2

, Mχ01,2,3,4

;

Scalar masses:

MqL,R, MlL,R

;

Mixings:

tanβ, sinα ... ...

CP Phases:

φ1,2,3µ ... ...

Parameter count in the SM and MSSM

masses and CP-viol.model mixing ang. phases TOTALSM 17 2 19

MSSM 79 45 124(MSSM)BV 97 62 159(MSSM)LV 157 122 279(MSSM)BLV 175 140 315

Guidance and Assumptions:

Based on observation:

* Proton stability:

⇒ R-parity conservation; or B,L not broken

simultaneously (in 1st,2nd generations).

* No excessively large CP-violation/FCNC:

⇒ no (or small) phases; sfermion mass degenerate (or heavy).

* Direct mass bounds from collider searches:

>∼ O(100 − 400 GeV).

Most part of the parameter-space ruled out!

Guidance and Assumptions:

Based on observation:

* Proton stability:

⇒ R-parity conservation; or B,L not broken

simultaneously (in 1st,2nd generations).

* No excessively large CP-violation/FCNC:

⇒ no (or small) phases; sfermion mass degenerate (or heavy).

* Direct mass bounds from collider searches:

>∼ O(100 − 400 GeV).

Most part of the parameter-space ruled out!

Pure theoretical considerations:

* Naturalness:

<∼ O(1 TeV).

* Gauge-coupling/Yukawa Unification:

⇒ universal masses at the GUT scale

* Radiative E.W.S.B.;

* LSP cold dark matter; ...

SUSY breaking/mediation scenarios:

(*) “Minimal Super-gravity” (mSUGRA) scenario:

m0, m1/2, A, tanβ, and sign(µ)

0

100

200

300

400

500

600

700

800

mas

s (G

eV)

Evolution of sparticle masses

Q (GeV)

10 2 10 4

10 6 10 10 10 17

M 3

m b R ,Q ~ L

m t R

m 1

m τ L

M 2

m τ R ~

~

~

~

M 1

m 2

m

m

m +

0

1/2

0 2 2 µ / \

___




0

100

200

300

400

500

600

700

800

mas

s (G

eV)


Q (GeV)

10 2 10 4

10 6 10 10 10 17

M 3

m b R ,Q ~ L

m t R

m 1

m τ L

M 2

m τ R ~

~

~

~

M 1

m 2

m

m

m +

0

1/2

0 2 2 µ / \

___

(*) “Gauge mediation” scenario: M, F, tanβ, nm.

(*) “Anomaly mediation” scenario: ......




0

100

200

300

400

500

600

700

800

mas

s (G

eV)


Q (GeV)

10 2 10 4

10 6 10 10 10 17

M 3

m b R ,Q ~ L

m t R

m 1

m τ L

M 2

m τ R ~

~

~

~

M 1

m 2

m

m

m +

0

1/2

0 2 2 µ / \

___

(*) “Gauge mediation” scenario: M, F, tanβ, nm.

(*) “Anomaly mediation” scenario: ......

Only experiments can tell: A real challenge!

Dynamical approach for mass generation:

• Technicolor: A lesson from QCD

SU(NTC) gauge theory, TC fermions Q = U,D, ...

EWSB by TC-fermion condendation at ΛTC:

v ∼ 〈QLQR〉1/3 ∼ 246 GeV.





v ∼ 〈QLQR〉1/3 ∼ 246 GeV.

√no elementary scalar, like Higgs.√theory natural: ΛTC dynamical.√predicts new strong dynamics at the TeV scale: πT , ηT , ρT , ωT ...





v ∼ 〈QLQR〉1/3 ∼ 246 GeV.

√no elementary scalar, like Higgs.√theory natural: ΛTC dynamical.√predicts new strong dynamics at the TeV scale: πT , ηT , ρT , ωT ...

× leads to too large radiative corrections:

S ≈ 0.25NTC, while Sexp ∼ −0.07 ± 0.11.

× no fermion masses.

• Extended Technicolor:∗ Fermion mass generation

GETC gauge theory, ETC fermions: U,D, ..., u, d...

After intrgrating out ETC gauge bosons at the scale ΛETC,

with TC-fermion condensate,SM fermion mass generated:

mf ∼ 〈QLQR〉/Λ2ETC ∼ Λ3

TC/Λ2ETC.

∗Eichten and Lane;For a review, Hill and Simmons






TC/Λ2ETC.

√theory natural: ΛETC dynamical.√predicts new fermion flavor physics at the TeV scale...







TC/Λ2ETC.


× a devastating problem:

On the one hand: small FCNC: 1ΛETC

< 1103 TeV

.

On the other hand, heavy quark mc ∼ 1 GeV ⇒ ΛETC < 30 × ΛTC1 TeV







TC/Λ2ETC.


× a devastating problem:

On the one hand: small FCNC: 1ΛETC

< 1103 TeV

.

On the other hand, heavy quark mc ∼ 1 GeV ⇒ ΛETC < 30 × ΛTC1 TeV

=⇒ Non-QCD like: Walking TC

TC gauge coupling running very slowly.

〈QLQR〉 almost constant over ΛTC − ΛETC.

〈QLQR〉ETC enhanced by 100−1000.


• “Topcolor/Top-seesaw”: Top quark special?

mt ≈ v/√

2 = 174 GeV.


mt ≈ v/√

2 = 174 GeV.

Introducing an additional fermion pair χL, χR:

(1) topcolor∗ generates the condensation H ∼ (χRtL, χRbL)

⇒ EWSB and a heavy Higgs mH ∼ 1 TeV.

(2) topseesaw§ leads to a SM t, and a heavy state χ, with Mχ ≈ 4 TeV.

∗C. Hill.§B. Dobrescu and C. Hill.


mt ≈ v/√

2 = 174 GeV.

Introducing an additional fermion pair χL, χR:

(1) topcolor∗ generates the condensation H ∼ (χRtL, χRbL)

⇒ EWSB and a heavy Higgs mH ∼ 1 TeV.

(2) topseesaw§ leads to a SM t, and a heavy state χ, with Mχ ≈ 4 TeV.

0.0

0.0

−0.3 0.3

−0.2

0.2

S

T

Higgs

M χ

4.0 TeV

m =1000 GeV

100

300

8.0 TeV

fit EW precision data well!‡

∗C. Hill.§B. Dobrescu and C. Hill.‡H.-J. He, C. Hill, T. Tait.

• Little Higgs Models: A less ambitious approach

Accept the existence of a light Higgs;

keep the Higgs boson “naturally” light (at 1-loop level).




† Higgs is a pseudo-Goldstone boson from global symmetry breaking (at scale 4πf)‡

† Higgs acquires a mass radiatively at the EW scale v, by collective explicit breaking

† Consequently, quadratic divergences absent at one-loop level∗

W,Z,B ↔WH , ZH , BH; t ↔ T ; H ↔ Φ.

(cancellation among same spin states!)

‡Dimopoulos, Preskill, 1982; H.Georgi, D.B.Kaplan, 1984; T. Banks, 1984.∗Arkani-Hamed, Cohen, Georgi, hep-ph/0105239.




† Higgs is a pseudo-Goldstone boson from global symmetry breaking (at scale 4πf)‡

† Higgs acquires a mass radiatively at the EW scale v, by collective explicit breaking

† Consequently, quadratic divergences absent at one-loop level∗

W,Z,B ↔WH , ZH , BH; t ↔ T ; H ↔ Φ.

(cancellation among same spin states!)

LR

f2_ λ t__

x

λ t λ th

top

x

χ χχL χR

f

h h

λ t

W

_

λλ _

h φ

2g 2 g

W

An alternative way to keep H light (naturally)

‡Dimopoulos, Preskill, 1982; H.Georgi, D.B.Kaplan, 1984; T. Banks, 1984.∗Arkani-Hamed, Cohen, Georgi, hep-ph/0105239.

New heavy states in the littlest Higgs:

Heavy particles Mass

T√λ21 + λ2

2 f

ZH m2w

f2

s2c2v2

WH m2w

f2

s2c2v2

φ0, ±, ±± 2m2Hf

2

v21

1−(4v′f/v2)2

AH m2zs

2w

f2

5s′2c′2v2

(mh ≈ 115 GeV)

New heavy states in the littlest Higgs:


T√λ21 + λ2

2 f

ZH m2w

f2

s2c2v2

WH m2w

f2

s2c2v2

φ0, ±, ±± 2m2Hf

2

v21

1−(4v′f/v2)2

AH m2zs

2w

f2

5s′2c′2v2

(mh ≈ 115 GeV)

√If T -parity imposed, AH can be a good dark matter candidate.

Extra-dimensions:A new approach to the hierarchy problem

• Large Extra-dimension Scenario: ADD∗

In a world with D = 4 + n dimensions, the 4-dim Planck scale

is related to the D-dim one MD as

M2PL ∼Mn+2

D Vn.

tyi

x

∗N. Arkani-Hamed, Dimopoulos, Dvali

Extra-dimensions:A new approach to the hierarchy problem

• Large Extra-dimension Scenario: ADD∗

In a world with D = 4 + n dimensions, the 4-dim Planck scale

is related to the D-dim one MD as

M2PL ∼Mn+2

D Vn.

tyi

x

Thus the fundamental scale:

MD ∼ (M2pl/Vn)

n+2 −→ O(1 TeV).

or the radius:

R ∼M

2/npl

M2/n+1D

≈

O(0.1 mm) for n = 2O(1.0 fm) for n = 7

∗N. Arkani-Hamed, Dimopoulos, Dvali

The Kaluza-Klein excitations:

If an extra dimension y becomes compact (a circle of radius R),

then all fields (gravitational, electromagnetic etc.)

in y-dimension are periodic functions :

F (x, y) =

∞∑

n=−∞F n(x) ein·y/R.

Equation of motion:

(∂µ∂µ − ∂y∂y)F(x, y) ⇒ (∂µ∂µ +n2

R2)Fn(x)

⇒ mn ∼ n

R(a set of tower!)





F (x, y) =

∞∑


Equation of motion:

(∂µ∂µ − ∂y∂y)F(x, y) ⇒ (∂µ∂µ +n2

R2)Fn(x)

⇒ mn ∼ n

R(a set of tower!)

n = 0: Zero modes as graviton and photon;

n 6= 0: Massive Kaluza-Klein (KK) excitations

Very interesting mass generation !





F (x, y) =

∞∑


Equation of motion:

(∂µ∂µ − ∂y∂y)F(x, y) ⇒ (∂µ∂µ +n2

R2)Fn(x)

⇒ mn ∼ n

R(a set of tower!)




So, search for the massive KK states:

equivalent to searching for compact extra dimensions

∆MKK = 1/R.





F (x, y) =

∞∑


Equation of motion:

(∂µ∂µ − ∂y∂y)F(x, y) ⇒ (∂µ∂µ +n2

R2)Fn(x)

⇒ mn ∼ n

R(a set of tower!)




So, search for the massive KK states:

equivalent to searching for compact extra dimensions

∆MKK = 1/R.

No γKK, e−KK, ... found ⇒ R−1 large; or γ, e− ... don’t go there.

• “Warped” Extra-dimension Scenario: The Randall-Sundrum model

In a 5-dim space, Randall and Sundrum found a static solution of the form:∗

ds2 ∼ e−2ky ηµν dxµdxν − dy2,

where k is the curvature scale in the 5th-dim.

∗L. Randall, R. Sundrum.

• “Warped” Extra-dimension Scenario: The Randall-Sundrum model

In a 5-dim space, Randall and Sundrum found a static solution of the form:∗

ds2 ∼ e−2ky ηµν dxµdxν − dy2,

where k is the curvature scale in the 5th-dim.

The extra dimension y is “warped”.

SM

planck brane

gravity

Randall-Sundrum

Mply0

m ey0MplM = e−kyMpl.

∗L. Randall, R. Sundrum.

• New ideas with extra-dimensions:

Symmetry breaking by boundary conditions/terms



† SUSY GUTs with extra-dimensions: ∗

5d SUSY GUTs model, with SUSY/GUT symmetry breaking by

orbifolding on the boundary.

† Higgsless model in extra-dimensions: †

5d non-SUSY model, with gauge symmetry breaking by

orbifolding/boundary condition.

Bulk KK states serve as pseudo-Glodstone bosons, no Higgs left.

∗Hall, Nomura; Nomura, Smith.†C. Csaki et al.; Y. Nomura,



† SUSY GUTs with extra-dimensions: ∗

5d SUSY GUTs model, with SUSY/GUT symmetry breaking by

orbifolding on the boundary.

† Higgsless model in extra-dimensions: †

5d non-SUSY model, with gauge symmetry breaking by

orbifolding/boundary condition.

Bulk KK states serve as pseudo-Glodstone bosons, no Higgs left.

Particularly interesting: AdS/CFT correspondence

5d AdS theory ⇐⇒ 4d strongly interacting walking TC!

∗Hall, Nomura; Nomura, Smith.†C. Csaki et al.; Y. Nomura,

• Observable signatures for extra-dim models:

⊲ At “low” energies

† “very low”: E ≪ 1/R, MD:

4d effective theory: as the Standard Model; weak effects from gravity.





† march into the extra-dimensions: 1/R < E ≪MD,

(4 + n)−dim physics directly probed, and gravity effects observable:∗

mainly via light KK gravitons of mass

mKK ∼ nk/R,

or whatever propagate there ⇒ an effective theory (SM+KK).

∗Arkani-Hamed, Dimopoulos, Dvali (1998); Giudice, Rattazzi, Wells (1999); Han, Lykken,Zhang. (1999); Mirabelli, Peskin, Perelstein (1999); Hewett (1999); Rizzo (1999).





† march into the extra-dimensions: 1/R < E ≪MD,

(4 + n)−dim physics directly probed, and gravity effects observable:∗

mainly via light KK gravitons of mass

mKK ∼ nk/R,

or whatever propagate there ⇒ an effective theory (SM+KK).

⊲ Intermediate energy regime E ∼MD: stringy/winding states significant:†

s-channel poles as resonances:‡

M(s, t) ∼ t

s−M2n, Mn =

√nsMS, nwRM

2S .

∗Arkani-Hamed, Dimopoulos, Dvali (1998); Giudice, Rattazzi, Wells (1999); Han, Lykken,Zhang. (1999); Mirabelli, Peskin, Perelstein (1999); Hewett (1999); Rizzo (1999).

†G. Shui and H. Tye (1998); K. Benakli (1999).

⊲ At “trans Planckian” energies E > MD,MS:

(4 + n)−dim physics directly probed;

gravity dominant: black hole production‡√s = MBH > MD for b < rbh.

‡T. Banks and W. Fischler (1999); E. Emparan et al. (2000); S. Giddings and S. Thomas(2002); S. Dimopoulos and G. Landsberg (2001).

⊲ At “trans Planckian” energies E > MD,MS:

(4 + n)−dim physics directly probed;

gravity dominant: black hole production‡√s = MBH > MD for b < rbh.

rbh =1√πMD

MBH

MD

8Γ

(n+32

)

n+ 2

1n+1

→MBH/M2pl in 4d

σ = πr2bh.

r (s)i

j

3-brane

h

‡T. Banks and W. Fischler (1999); E. Emparan et al. (2000); S. Giddings and S. Thomas(2002); S. Dimopoulos and G. Landsberg (2001).

We are entering a “data-rich” era:


Electroweak precision constraints;



muon g − 2; µ→ eγ...; neutron/electron EDMs;




Neutrino masses and mixing;





K/B rare decays and CP violation: B → Xsγ; J/ψKS, φKS, η′KS;






Nucleon stability;






Nucleon stability;

Direct/Indirect dark matter searches;






Nucleon stability;


Cosmology constraints on mν, and dark energy (?).






Nucleon stability;


Cosmology constraints on mν, and dark energy (?).

Yet more to come:

Tevatron: EW, top sector, Higgs (?), new particle searches...

LHC: Higgs studies, comprehensive new particle searches...

LC: more on top sector, precision Higgs and new light particles...

High energy cosmic rays: AUGER, ICECUBE ... ...

VII. Search for New Physics

at Hadron Colliders

Tevatron is reaching a record-high luminosity:

2 × 1032/cm2/s ⇒ 2 fb−1/yr/detector.


at Hadron Colliders



LHC will take a “pilot run” by the end of the next year,

and will start useful data collection in 2008:

Initially about 30 pb−1/detector.


at Hadron Colliders



LHC will take a “pilot run” by the end of the next year,

and will start useful data collection in 2008:

Initially about 30 pb−1/detector.

In (almost) ANY TeV scale new physics scenario,

the LHC will significantly contribute!

(A). Higgs Searches at the Tevatron and the LHC:

The crucial features: Couplings proportional to masses.

(A). Higgs Searches at the Tevatron and the LHC:

The crucial features: Couplings proportional to masses.

SM Higgs boson decay branching fractions:

BR(H)

bb_

τ+τ−

cc_

gg

WW

ZZ

tt-

γγ Zγ

MH [GeV]50 100 200 500 1000

10-3

10-2

10-1

1

preferably to heavier particles.

SM Higgs boson production rates:

σ(pp_→hSM+X) [pb]

√s = 2 TeV

Mt = 175 GeV

CTEQ4Mgg→hSM

qq→hSMqqqq

_’→hSMW

qq_→hSMZ

gg,qq_→hSMtt

_

gg,qq_→hSMbb

_

bb_→hSM

Mh [GeV]SM

10-4

10-3

10-2

10-1

1

10

10 2

80 100 120 140 160 180 200

σ(pp→H+X) [pb]√s = 14 TeV

Mt = 175 GeV

CTEQ4Mgg→H

qq→Hqqqq

_’→HW

qq_→HZ

gg,qq_→Htt

_

gg,qq_→Hbb

_

MH [GeV]0 200 400 600 800 1000

10-4

10-3

10-2

10-1

1

10

10 2

SM Higgs boson production rates:

σ(pp_→hSM+X) [pb]

√s = 2 TeV

Mt = 175 GeV

CTEQ4Mgg→hSM

qq→hSMqqqq

_’→hSMW

qq_→hSMZ

gg,qq_→hSMtt

_

gg,qq_→hSMbb

_

bb_→hSM

Mh [GeV]SM

10-4

10-3

10-2

10-1

1

10

10 2

80 100 120 140 160 180 200

σ(pp→H+X) [pb]√s = 14 TeV

Mt = 175 GeV

CTEQ4Mgg→H

qq→Hqqqq

_’→HW

qq_→HZ

gg,qq_→Htt

_

gg,qq_→Hbb

_

MH [GeV]0 200 400 600 800 1000

10-4

10-3

10-2

10-1

1

10

10 2

• At the Tevatron: hundreds of Higgs bosons may have been produced,

for mh <∼ 200 GeV with 1 fb−1.

• At the LHC: hundreds of thousand may be produced,

for mh <∼ 700 GeV with 100 fb−1.

• Higgs first shot at the Tevatron:

qq′ →Wh, Zh, h→ bb

gg → h, h→WW ∗, ZZ∗, τ+τ−

1

10

10 2

10 3

110 120 130 140 150 160 170 180 190mH (GeV)

95%

CL

Lim

it/S

M

D0 combined261-385 pb-1

March 20, 2006

D0 combinedwith updated H→WW: 950 pb-1

Tevatron Run II Preliminary

H→WW(*)→lνlνD0: 300-325 pb-1

H→WW(*)→lνlνCDF: 360 pb-1

WH→WWWCDF: 194 pb-1

WH→WWWD0: 363-384 pb-1

WH→lνbb–

CDF: 319 pb-1

WH→lνbb–

D0: 378 pb-1

ZH→νν–bb

–

D0: 261 pb-1

ZH→νν–bb

–

CDF 289 pb-1

• SM Higgs fully covered at the LHC:

1

10

10 2

102

103

mH (GeV)

Sig

nal s

igni

fica

nce

H → γ γ + WH, ttH (H → γ γ ) ttH (H → bb) H → ZZ(*) → 4 l

H → ZZ → llνν H → WW → lνjj

H → WW(*) → lνlν

Total significance

5 σ

∫ L dt = 100 fb-1

(no K-factors)

ATLAS

ATLAS report: combining multiple channels,

10σ observation achievable.

• SUSY Higgs fully covered at the LHC:

In MSSM, 5 Higgs bosons: h0, H0, A0, H±,

two independent parameters: tanβ −MA.

200

50

40

30

20

10

400 600 800 1000

mA (GeV)

tanβ

mtop = 175 GeV, mSUSY = 1 TeV, no stop mixing ;

two-loop / RGE-improved radiative corrections

5 σ significance contours

explorable through various SUSY Higgs channelsRegions of the MSSM parameter space (mA, tgβ)

Significance contours for SUSY Higgses

→

CMS, 3.104

pb-1

A, H ττ h++ h- + X

→ →

D_D

_202

1.c

A, H, h ττ± + τ jet + XA, H, h ττ

→→

→→

→

e + µ +X

h γγ

H± τν104 pb-1

LEP II s = 200 GeV

(B). Weak Scale SupersymmetryHadron colliders can be a S-particle factory:

QCD production: qq, gq, gg → q¯q, qg, gg.

E.W. production: qq → χ+1 χ

−1 , χ

±1 χ

01, χ

±1 χ

02.

10-3

10-2

10-1

1

10

100 150 200 250 300 350 400 450 500

⇑⇑

⇑

⇑⇑

⇑

χ2oχ1

+

t1t−1

qq−

gg

νν− χ2

og

NLOLO

√S = 2 TeV

m [GeV]

σtot[pb]: pp− → gg, qq

−, t1t

−1, χ2

oχ1+, νν

−, χ2

og

10-2

10-1

1

10

10 2

10 3

100 150 200 250 300 350 400 450 500

⇑

⇑ ⇑ ⇑

⇑

⇑χ2oχ1

+

t1t−1

qq−

gg

νν−

χ2og NLO

LO

√S = 14 TeV

m [GeV]

σtot[pb]: pp → gg, qq−, t1t

−1, χ2

oχ1+, νν

−, χ2

og

Typically,

σ(Tevatron) ≈ O(0.1 − 1 pb); σ(LHC) ≈ O(10 − 100 pb).

New ball-game for signal searches:

The lightest SUSY particle (LSP χ01) is stable (R-parity),

and nearly non-interacting (in detectors),

⇒ large missing energy is the characteristics;

difficult to reconstruct a mass peak for the sparticle.

New ball-game for signal searches:

The lightest SUSY particle (LSP χ01) is stable (R-parity),

and nearly non-interacting (in detectors),

⇒ large missing energy is the characteristics;

difficult to reconstruct a mass peak for the sparticle.

Details depend on the model...

• mSUGRA scenario: SUSY breaking near MGUT .

Supergravity as messenger to transmit SUSY breaking effects.


Sparticle decays:

χ+1 → χ0

1ℓ+ν, χ0

1qq′

χ02 → χ0

1ℓ+ℓ−, χ0

1qq

g → χ02qq, g → χ+

1 qq, g → qq,

t1 → χ01t, t1 → χ0

2t, t1 → χ+1 b.

• mSUGRA scenario: SUSY breaking near MGUT .

Supergravity as messenger to transmit SUSY breaking effects.


Sparticle decays:

χ+1 → χ0

1ℓ+ν, χ0

1qq′

χ02 → χ0

1ℓ+ℓ−, χ0

1qq

g → χ02qq, g → χ+

1 qq, g → qq,

t1 → χ01t, t1 → χ0

2t, t1 → χ+1 b.

Generically, χ01 leads to missing energy signal:

“missing E/T plus jets”: E/T+jets

“dilepton plus missing E/T” ℓℓ+ E/T (±± or + −)

“trilepton plus missing E/T” ℓℓℓ+ E/T

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

LHC, ET miss

-2

-5

-10

-30

5

4

5

mSUGRA: tanβ=45, A0=0, µ<0

m0(TeV)

m1/

2(T

eV)

LEP2no REWSB

Z~

1 no

t LS

P

mh LEP2 limit aµSUSY×1010 Br(b→sγ)×104

Br(Bs→µ+µ-)×108 0.094<Ωh2<0.129 stage 3

fσ(Z~

1p)×1011 pb 100 10 1

LHC: m0 > 4000 GeV, m1/2 > 1400 GeV, tanβ >∼ 45.

• Gauge mediation scenario: SUSY breaking at Λ ∼ 10 − 100 TeV,

Gauge interactions as messengers to mediate SUSY breaking effects.

Λ, M, tanβ, and NM

0

100

200

300

400

500

600

700

800

900

1000

m [GeV]

lR

lL νl

τ1

τ2

χ0

1

χ0

2

χ0

3

χ0

4

χ±

1

χ±

2

qR

qL

g

t1

t2

b1

b2

h0

H0, A0 H±

Squarks and gluinos are typically heavier; Gravitino G LSP.

The NLSP dominates phenomenology: x

x

G1/F

Squarks and gluinos are typically heavier; Gravitino G LSP.

The NLSP dominates phenomenology: x

x

G1/F

NLSP Decay to the G

Bino-like Neutralino χ01 → γ G

Higgsino-like Neutralino χ01 → (h, Z, γ) G

Stau τ → τ G

Slepton Co-NLSP ℓ→ ℓ G

Squark q → (q, q′W ) G

Gluino g → g G

cτ(x→ xG) ≈ 100 µm

(100 GeV

mx

)5( √F

100 TeV

)4

.

could lead to a displaced vertex in decay, or quasi-stable charged track.

LHC reach:

50 100 150 200 250 300 350

123 246 371 496 622 748 874

10-1

1

10

10 2

10 3

10 4

Λ (TeV)

σ(fb

)

τ∼

1 Mass(GeV)

g∼g∼ + g

∼q∼ + q

∼q∼

W∼

iW∼

j + W∼

iZ∼

j + Z∼

iZ∼

j

l∼l∼ + l

∼ν∼ + ν

∼ν∼

50 100 150

123 246 371

10-1

1

10

10 2

10 3

Λ (TeV)

Max

(σS/

√σB)

τ∼

1 Mass(GeV)

(C). New gauge bosons and heavy fermions

(C). New gauge bosons and heavy fermions

Little Higgs models as an exampleIn the Littlest Higgs model:∗


AH m2zs

2w

f2

5s′2c′2v2

ZH m2w

f2

s2c2v2

WH m2w

f2

s2c2v2

φ0, ±, ±± 2m2Hf

2

v21

1−(4v′f/v2)2

T√λ21 + λ2

2 f (where mw = gv/2.)

∗Arkani-Hamed, Cohen, Katz, Nelson, hep-ph/0206021.

tan θ = sc = g2

g1New SU(2) gauge coupling

(or equivalently mixing angle θ)

tan θ′ = s′c′ =

g′2g′1

New U(1) gauge coupling

(or equivalently mixing angle θ′)

f Symmetry breaking scale O (TeV)

v′ Triplet φ vacuum expectation value,v′/v <∼ v/4f

mH Regular SM Higgs mass

MT Heavy vector top mass, we trade λ2 for MT

• New gauge bosons in DY process:

Recall CDF searches for a Z ′ → µ+µ−: [PRL 79, (1997)]

• New gauge bosons in DY process:

Recall CDF searches for a Z ′ → µ+µ−: [PRL 79, (1997)]

including:

pp→ Z, γ → µ+µ−X,pp→W+W− → µ+νµµ

−νµX,

pp→ bb→ µ+µ− + hadrons+X,

pp→ tt→W+b W−b→ µ+νµµ−νµbb X.

• New gauge bosons in DY process:Recall CDF searches for a Z ′ → µ+µ−: [PRL 79, (1997)]

including:

pp→ Z, γ → µ+µ−X,pp→W+W− → µ+νµµ

−νµX,

pp→ bb→ µ+µ− + hadrons+X,

pp→ tt→W+b W−b→ µ+νµµ−νµbb X.

σ < 40 fb ⇒ MZ′ > 600 GeV.

• AH should be the lightest new state;

• large DY production AH → ℓ+ℓ− (ℓ = e, µ)

• AH should be the lightest new state;

• large DY production AH → ℓ+ℓ− (ℓ = e, µ)

Tevatron: MAH > 0.5 TeV or f > 3 TeV;

LHC: MAH ∼ 3 TeV or f ∼ 18 TeV.

• ZH/WH rebust new state

• DY production rate large

• ZH/WH rebust new state

• DY production rate large

Tevatron: not quite accessible (except for AH);

LHC: MZH∼ 5 TeV or f ∼ 8 TeV.

ATLAS simulations for Z → ℓ+ℓ−:

10-1

1

10

10 2

1600 1800 2000 2200 2400mee (GeV)

Eve

nts/

10 G

eV/1

00 fb

-1

ZH cotθ=1.0

ZH cotθ=0.2

Drell-Yan

ATLAS

0

0.5

1

1.5

2

2000 4000 6000m(ZH) (GeV)

cotθ

ZH→ee 5 σ reach for 300 fb-1

ATLAS

Reach MZH ∼ several TeV for cot θ > 0.1:

ATLAS simulations for Z → ℓ+ℓ−:

10-1

1

10

10 2

1600 1800 2000 2200 2400mee (GeV)

Eve

nts/

10 G

eV/1

00 fb

-1

ZH cotθ=1.0

ZH cotθ=0.2

Drell-Yan

ATLAS

0

0.5

1

1.5

2

2000 4000 6000m(ZH) (GeV)

cotθ

ZH→ee 5 σ reach for 300 fb-1

ATLAS

Reach MZH ∼ several TeV for cot θ > 0.1:

Cross-sectiions measure cot θ : N(ℓ+ℓ−) versus N(Zh).

Mass peak MZH determines f .

Significant differences for FB asymmetry among Z ′s:

Ai,fFB = 34AiAf , Ai =

g2L−g2

R

g2L+g2

R

.

AhadFB =

∫dx1

∑q=u,dA

qeFB (Fq(x1)Fq(x2) − Fq(x1)Fq(x2)) sign(x1 − x2)∫

dx1

∑q=u,d,s,c (Fq(x1)Fq(x2) + Fq(x1)Fq(x2))

,

-0.1

0

0.1

0.2

0.3

0.4

0.5

1000 2000 3000 4000 5000

AF

Bha

d

Z’ mass (GeV)

LHC pp 14 TeV, CTEQ5L

Littlest Higgs

Simple group, univ

Simple group, anom-free

E6 Z’ψE6 Z’χ

LR sym

• Heavy quark signals:

Recall the top-quark searches at hadron colliders

The leading production channels:

qq → tt, Tevatron 90%; LHC 10%

gg → tt, Tevatron 10%; LHC 90%

with tt→W+b W−b→ ...

Top-quark discovered (1993): mt ≈ 178 GeV.








Interesting sub-leading (electroweak) production channels: the single-top

qq′ →W ∗ → tb, a lot smaller

gb→ tW, smaller too

qb→ q′W ∗b→ q′ t 1/3 of QCD.








Interesting sub-leading (electroweak) production channels: the single-top

qq′ →W ∗ → tb, a lot smaller

gb→ tW, smaller too

qb→ q′W ∗b→ q′ t 1/3 of QCD.

measure Vtb and test tbWL coupling ⇐ surely new at the Tevatron.

The heavy T signal at the LHC

gg → T T phase-space suppression;

qb → q′T via t-channel WLb→ T .

ATLAS simulations for T → tZ, bW :

Invariant Mass (GeV)

0 500 1000 1500 2000

-1E

vent

s/40

GeV

/300

fb

0.5

1

1.5

2

2.5

3

3.5

4

ATLAS


0 500 1000 1500 2000

-1E

vent

s/40

GeV

/300

fb

50

100

150

200

250

300

350

400

ATLAS

Reach MT ∼ 1 (2) TeV for xλ = 1 (2).

ATLAS simulations for T → tZ, bW :


0 500 1000 1500 2000

-1E

vent

s/40

GeV

/300

fb

0.5

1

1.5

2

2.5

3

3.5

4

ATLAS


0 500 1000 1500 2000

-1E

vent

s/40

GeV

/300

fb

50

100

150

200

250

300

350

400

ATLAS

Reach MT ∼ 1 (2) TeV for xλ = 1 (2).

Cross-sectiions measure coupling xλ.

Mass peak MT determines f : v/f = mt/MT (xλ + x−1λ )

=⇒ check consistency with f from MZH.

If there is either a U-type or D-type heavy quark, must observe

W+d→ U or W−u→ D:

Note that σD ≈ 1.2 σU .

If there is either a U-type or D-type heavy quark, must observe

W+d→ U or W−u→ D:

Note that σD ≈ 1.2 σU .

Interesting to note:

• σU ≈ 10σU ; σD ≈ 10σD;

• U → dℓ+ν ⇒ sequential fermion embedding;

D → uℓ−ν ⇒ anomaly-free fermion embedding.

Kinematical features: W+d→ U → ℓ+νj:

forward jet

high pT jet

q qQ

W

l ν+−

+−

Kinematical features: W+d→ U → ℓ+νj:

forward jet

high pT jet

q qQ

W

l ν+−

+−

(D). Deep into extra-dimensions at the LHC:

• Collider Searches for Extra Dimensions:

A. Collider Signals I (ADD)

Real KK Emission: Missing Energy Signature

a. e+e− → γ +KK (γ+missing energy)

k2

k1q1

q2

n − dim : at LEP2n = 4 MS > 730 (GeV)n = 6 MS > 520 (GeV)

(D). Deep into extra-dimensions at the LHC:

• Collider Searches for Extra Dimensions:

A. Collider Signals I (ADD)

Real KK Emission: Missing Energy Signature

a. e+e− → γ +KK (γ+missing energy)

k2

k1q1

q2

n − dim : at LEP2n = 4 MS > 730 (GeV)n = 6 MS > 520 (GeV)

b. pp → jet+KK (mono-jet+missing energy)

n − dim : at Tevatron at LHCn = 4 MS > 900 (GeV) 3400n = 6 MS > 810 (GeV) 3300

B. Collider Signals II (ADD)

Virtual KK Graviton Effects

On four-particle contact interactions:

f−1

f1

KK graviton f−2

f2

f−1

f1

KK grav. V2

V1

Sum over virtual KK exchanges:

iM ∼ fOif fOjf∫ ∞

0

dm2~n κ

2ρ(m~n)

s−m2~n + iǫ

∼ s2

M4S

fOif fOjf.

Again, effective coupling κ2 ∼ 1M2pl

→ 1M2S

!

Qualitative differences for signal/background distributions,

due to the spin-2 exchange:

LR asymmetry for e+e− → bb at√s = 500 GeV.

Solid: SM; “data” points for λ = ±1 with = 75 fb−1.

C. KK Resonant States at Colliders: (RS)

If the SM fields (photons, electrons, Z,W,H0...) also propagate

in extra dimensions, then they have KK excitations.

Direct search bounds:

M∗γ,Z,W ∼ 1

R> 4 TeV.

C. KK Resonant States at Colliders: (RS)

If the SM fields (photons, electrons, Z,W,H0...) also propagate

in extra dimensions, then they have KK excitations.

Direct search bounds:

M∗γ,Z,W ∼ 1

R> 4 TeV.

Resonant production at the LHC:

D. Stringy States at Colliders

Future colliders may reach the TeV string threshold

thus directly produce the “stringy” resonant states.

Amplitude factor near the resonance

M(s, t) ∼ t

s− nM2S

, its mass Mn =√nMS.

D. Stringy States at Colliders

Future colliders may reach the TeV string threshold

thus directly produce the “stringy” resonant states.

Amplitude factor near the resonance

M(s, t) ∼ t

s− nM2S

, its mass Mn =√nMS.

where T is an unkown gauge factor (Chan-Simon factor), typically 1 − 4.

Very rich structure of angular distributions:

LHC 95% C.L. sensitivity from ℓ+ℓ− mode:

LHC 95% C.L. sensitivity from ℓ+ℓ− mode:

With 300 fb−1, if no signal seen, we expect to reach bounds for

MS > 8 (10) TeV for T = 1 − 4.

E. Black Hole Production at Colliders

For a black hole of mass MBH, its size is

rbh ≈ 1

MD

(MBH

MD

) 1n+1

→ MBH

M2pl

in 4d.



rbh ≈ 1

MD

(MBH

MD

) 1n+1

→ MBH

M2pl

in 4d.

At higher energies and shorter distances (impact parameter)

Ecm > MBH > MD, bimpact < rbh,

black holes formation is the dominant quantum gravity phenomena.



rbh ≈ 1

MD

(MBH

MD

) 1n+1

→ MBH

M2pl

in 4d.

At higher energies and shorter distances (impact parameter)

Ecm > MBH > MD, bimpact < rbh,

black holes formation is the dominant quantum gravity phenomena.

Black holes copiously produced at the LHC energies:

MBH n = 4 n = 6

5 TeV 1.6 × 105 fb 2.4 × 105 fb7 TeV 6.1 × 103 fb 8.9 × 103 fb10 TeV 6.9 fb 10 fb

Black holes “decay” via Hawking radiation:

γ, ν, e±, hadrons, ... W±, Z..., gravitons

3-brane

Black hole

1

10

10 210 310 410 510 610 710 8

0 2000 4000 6000 8000 10000MBH, GeV

dN/d

MB

H ×

500

GeV

MP = 1 TeV

MP = 3 TeV

MP = 5 TeV

MP = 7 TeV

Spectacular events:

• very luminous in the detector!

• lepton-number/baryon-number violation (?)

• spherical/angular momentum orientation (?) ... ...

(E). A general phenomenological Method: (mine!)

– From a theory to experimental predictions

When I have or encounter a favorite theory, how do I carry out

the phenomenology (to the end)?





• Grasp the key points of the theory:

(motivation, and its key consequences)

EWSB ⇒ Higgs or WLWL scattering.

SUSY ⇒ s-particles.

Little Higgs ⇒ heavy T plus WH, ZH.





• Grasp the key points of the theory:

(motivation, and its key consequences)

EWSB ⇒ Higgs or WLWL scattering.

SUSY ⇒ s-particles.

Little Higgs ⇒ heavy T plus WH, ZH.

• Display the key structure of the theory:

(new particle spectrum, interactions, basic parameters L)

EWSB ⇒ mH and WLWL interactions.

full interaction Lagrangian

• Identify the most characteristic state for signal observation:

EWSB ⇒ Higgs or WLWL interactions.

SUSY ⇒ LSP, g, t, χ...

Little Higgs ⇒ heavy T , and WH, ZH.





• Identify the best signal channels and calculate the S/B:

(in tersm of the production rate, signal identification versu background...)

EWSB ⇒ gg → H,WW → H...,H → bb,WW...


Little Higgs ⇒ gg → T T , Wb→ T , DY WH , ZH.





• Identify the best signal channels and calculate the S/B:

(in tersm of the production rate, signal identification versu background...)

EWSB ⇒ gg → H,WW → H...,H → bb,WW...


Little Higgs ⇒ gg → T T , Wb→ T , DY WH , ZH.

• Either start a topic or finish a topic !

(F). Final remarks:

(a.) Kinematics can help a lot!

Basic techniques/considerations seeking for new particles and interactions.

are applicable to many new physics searches.

(F). Final remarks:




Prominent examples include:

• Drell-Yan type of new particle production in s-channel:

Z ′ → ℓ+ℓ−, W+W−; W ′ → ℓν, W±Z;

ZH → ZH; WH →W±H;

V 0,± → tt, W+W−; tb, W±Z;

heavy KK/stringy states → ℓ+ℓ−, γγ, ...;single q, ℓ via R parity violation.

• t-channel gauge boson fusion processes:

W+W−, ZZ, W±Z → H, V 0,±, light SUSY partners;

W+W+ → H++;

W+b→ T.

(F). Final remarks:




Prominent examples include:

• Drell-Yan type of new particle production in s-channel:

Z ′ → ℓ+ℓ−, W+W−; W ′ → ℓν, W±Z;

ZH → ZH; WH →W±H;

V 0,± → tt, W+W−; tb, W±Z;

heavy KK/stringy states → ℓ+ℓ−, γγ, ...;single q, ℓ via R parity violation.

• t-channel gauge boson fusion processes:

W+W−, ZZ, W±Z → H, V 0,±, light SUSY partners;

W+W+ → H++;

W+b→ T.

However, at hadron collider environments, certain class of experimental

signals may be way more complex than the simple examples above.

The following scenarios make the new physics identification difficult:

• A new heavy particle may undergo a complicated cascade decay,

so that it is impossible to reconstruct its mass, charge etc.

For example, a typical gluino decay in SUSY theories

g → q q → q q′χ+ → q q′ χ0W+ → q q′ χ0 e+ν.

• New particles involving electroweak interactions often yield weakly cou-

pled particles in the final state, resulting in missing transverse momentum

or energy, making it difficult for reconstructing the kinematics:

ν′s, χ01, γ1, A

0, ...

• Many new particles may be produced only in pair due to a conserved

quantum number, such as the R-parity in SUSY, KK-parity in UED, and

T-parity in LH, leading to a smaller production rate due to phase space

suppression and more involved kinematics, lack of characteristics.

On the other hand, one may consider to take the advantage:

• Substantial missing transverse energy is an important hint

for new physics beyond the SM.

• High multiplicity of isolated high pT particles,

such as multiple charged leptons and jets,

may indicate the production and decay of new heavy particles.

• Heavy flavor enrichment is another important feature for new physics:

H →, bb, τ+τ−; H+ → tb, τ+ν; H → χH; t→ χ+b, χ0t; V8, ηt → tt etc.

On the other hand, one may consider to take the advantage:

• Substantial missing transverse energy is an important hint

for new physics beyond the SM.

• High multiplicity of isolated high pT particles,

such as multiple charged leptons and jets,

may indicate the production and decay of new heavy particles.

• Heavy flavor enrichment is another important feature for new physics:

H →, bb, τ+τ−; H+ → tb, τ+ν; H → χH; t→ χ+b, χ0t; V8, ηt → tt etc.

Major discoveries highly anticipated at the LHC,

but very challenging!

(b). LHC–Cosmology complementarity:

Folk theorem:Precision EW data need a symmetry (R, T,KK,Z2 ...)

for new physics to “decouple”.

That leads to a cold dark matter (CDM) candidate.

⇒ LHC discovery for missing particles (WIMP)

would be a strong/sweet support.

(b). LHC–Cosmology complementarity:

Folk theorem:Precision EW data need a symmetry (R, T,KK,Z2 ...)

for new physics to “decouple”.

That leads to a cold dark matter (CDM) candidate.

⇒ LHC discovery for missing particles (WIMP)

would be a strong/sweet support.

However,

Indirect/Direct cosmological CMD searches

more conclusive than collider discovery!

(A WIMP needs only to live for about 1 µs to be “DM” ...)

Final Recap:

Final Recap:

• The SM is incomplete:

Naturalness/hierarchy problem with mh

Many free parameters, over incomprehensible ranges

Final Recap:




• Many ideas to go beyond:

new strong dynamics

weak-scale SUSY

extra-dimensions, low scale gravity/strings

... ...

Final Recap:





new strong dynamics

weak-scale SUSY


... ...

• Only experiments can tell.

uncover new signatures

differentiate underlying dynamics

Final Recap:





new strong dynamics

weak-scale SUSY


... ...

• Only experiments can tell.

uncover new signatures

differentiate underlying dynamics

Realize the Tevatron potential, go for the LHC!

Major breakthrough ahead of us!

Documents

· Collider Phenomenology — From basic knowledge to new physics searches Tao Han University of Wisconsin – Madison Asian School of Particles, Strings and Cosmology Nasu, Japan,