Physics Expectations at the LHC

Sreerup Raychaudhuri

IPM String School 2008, Isfahan, Iran

Tata Institute of Fundamental ResearchMumbai, India

April 10,2008

II

Plan of the Lectures

1. About the LHC

(the six-billion dollar experiment…)

2. Standard Model of Particle Physics

(what we already know…)

3. Physics beyond the Standard Model

(what we would like to know…)

4. Physics Prospects at the LHC

(what we could find in the next few years…)

Part 3

Physics beyond the Standard Model

(what we would like to know…)

Achievements of the Standard Model

• Common framework to describe weak, electromagnetic and strong interactions

• Mechanism to have short-range interactions for weak force

• Common mechanism for generation of mass

•Incorporates global and discrete symmetries like quark flavor, lepton number, C, P and T, etc.

• ‘Explains’ the origin of flavour violation

• Arranges for maximal P violation in weak sector

• Accommodates CP violation in CC interactions

The Standard Model has (till date) resisted all attempts to overturn it…

What’s wrong with the Standard Model?

We haven’t found the Higgs boson…

We didn’t look hard enough…

We haven’t found any other elementary scalars

Elementary scalars are the simplest reps of the Lorentz group

Why have only one scalar doublet when there are three fermion doublets?

Let’s find one first… SM can accommodate more scalar doublets easily

Can a model with 18 (20) undetermined parameters be a fundamental theory?

That’s more of an aesthetic issue … the SM works, doesn’t it?

2, ,sinS W ,W HM M

, , , , , ,, ,e u c t d s bm m m 12 23 13, , ,

QCD CP,

There’s a desert of 17 orders of magnitude between 102 GeV and 1019 GeV with no new physics

1.Maybe that’s the way Nature is…

2.The SM may well be a low-energy effective theory

Folklore: Every time we probed a new energy

scale, we discovered new sub-structures and new interactions…

Symmetries observed at lower energy scales indicate different arrangement of these substructures…

…periodic table… eightfold way…

We now have three generations of fermions with repeated properties…

Historical development is not a valid scientific reason…

Fermion replication may well be (a) accidental, or (b) a sign of some (broken) global

symmetry, e.g. SU(3), S3

The strong interactions are not unified with the electroweak one…

All the generators of SU(3)C commute with all the generators of SU(2)LU(1)Y

1.Unification would require a higher gauge symmetry at higher energies — GUTs

2.There is no compelling empirical reason to unify strong with electroweak interactions….

1

11~ 10tm m

eV meV eV keV MeV GeV TeV

1,2,3, ,e

, ,d s b

, ,u c t

Neutrino masses are unnaturally small

The Naturalness Argument

• If there are very large/small parameters in a quantum theory, there must be a

good reason why they are so small….

• In general, there will be large quantum corrections to such parameters in higher orders of perturbation theory, in terms of other parameters which

are not so small.

• These quantum corrections can cancel out only if there is some underlying symmetry causing them to

cancel... The parameter is said to be ‘protected’ by the symmetry.

• This applies specially to masses and couplings, which are known to run.

Neutrinos have always been a slight embarrassment in the Standard Model

• Earlier they were thought to be massless accommodated in the Standard Model by assuming there is no right-handed neutrino

• All that is special about a right-handed neutrino is that it is a gauge singlet

• There is as much reason to suppose that gauge singlet fermions exist as there is to suppose that they do not exist

• Hence the huge number of models for neutrino mass(es) constructed in the 1980s

13 2

Q T Y

The SuperKamiokande Experiment

SuperK has changed the scene since neutrinos undergo flavor oscillations they must have nonzero masses

But the masses are very very small…. Why?

Are we really bound to answer this question?

The mass of the neutrino is not just a mass, it is also the strength of the Yukawa interaction of the neutrino with Higgs bosons…similarly for top quarks…

Yukawa . .v L R L R

mH m H c

L

Variation in interaction strength over 11 orders of magnitude is like the difference between weak and electromagnetic interactions does this mean a new type of force between neutrinos and Higgs bosons?

There is an elegant explanation…

The Seesaw mechanism:

mass

0 . .ew R

L Lew R

V nn N H c

V M N

L

Diagonalise:

2

( ) ( ) ( )ew

ew

Vx n x N x

M

Vm

M

M ~ 100 TeV

Majorana mass: ; c c

R L R Ln n N N

Many variations of the simplest seesaw mechanism exist

many of them proposed to explain the large mixing angle found by SuperK

many of them require the right-handed neutrino to have some special properties… Majorana mass….

All require a heavy mass scale M

new physics at scales of TeV or higher… SM is inadequate…

1.The seesaw argument is pretty but not empirically compelling…

2. In the SM fermion masses are put in by hand anyway…we do not even try to understand them…

3.Hierarchy of Yukawa couplings may just be the way Nature is…

4.Fermion masses get at best logarithmic corrections from high scale physics because of chiral symmetry… naturalness is not such a serious problem…

The Higgs boson mass is not UV stable

Umm… er….

The Higgs Boson and the Hierarchy Problem

A light Higgs boson?• The mass of the Higgs boson is an

undetermined parameter in the Standard Model

• The scalar self-coupling grows with

and becomes non-perturbative around

• Electroweak precision data predict a light Higgs with

• LEP saw a few candidates around 114 GeV

800 GeVHM

237 (480) GeVHM

HM

2 2 212 vHM

HM

Higgs candidate: e+e-  bbbb, with 3 secondary vertices (20.09.2000)

237 GeVHM at 68% C.L.

LEPEWWG 2001

480 GeVHM at 95% C.L.

Large uncertainties because of the weak dependence on Higgs mass : log MH

6945114 GeVHM

• At the LHC we are almost sure to find a light Higgs boson…

– What if we don’t find it?•We will have to find an equally good

mechanism to generate masses for all elementary particles

•We must explain the radiative corrections to the W-boson self-energy which are precisely measured

•We must explain how WW scattering does not violate perturbative unitarity

W WW

H2

22

~ log HW

W

MM

M

W

W

W

W

ZW

W

W

W

H

Sum preserves perturbative unitarity : without H cross-section grows too fast with energy

• If we do find it?

We must understand why it is so light…

This is not just a piece of theoretical fussiness….

The Standard Model is a quantum (field) theory

• Even tree-level results are just the lowest order in perturbation theory

• One-loop predictions are also tested to great accuracy at LEP etc.

• It is meaningless to consider only tree-level results, unless we can prove that higher orders give small contributions

• Higher order corrections to Higgs boson mass are very large…

The scalar sector of the Standard Model is basically a theory coupled to a (nonAbelian) gauge theory and some fermion multiplets

Higgs boson has quartic self couplings

there are self-energy corrections with

quadratic divergences

4H H

H H

H H

H

2 2HM soft finite

is the cutoff for the SM

This effect cannot be wished away…

The Hierarchy Problem was pointed out by ‘Hooft more than thirty years ago. Over these three decades it has become clear that it cannot be

• ignored (SM is a quantum theory)

• removed by renormalisation-type tricks (reappears at next order)

• resolved without some new physics (at the electroweak or TeV scale ?)

Beyond the Standard Model

Q. How can we protect the Higgs boson mass from these large quantum corrections?

Only two ways:

• bring down the cutoff to the TeV scale

• composite models

• brane-worlds

• introduce some new symmetry into the theory

• supersymmetry

• little Higgs models

new physics at a TeV

symmetry must be broken around TeV…

Further Hints of New Physics:

• CP-Violation: baryon asymmetry

• Cold dark matter: what could it be?

• Cosmological constant: > 0

Modelling is heavily dependent on individual prejudices

Do not indicate the TeV scale per se

Grand Unification

Unification of forces has been a cherished goal of scientists from the days of Demokritos

They say some things are sweet

They say some things are sour

But in reality there are only atoms and the void…

Early (fanciful) model of unification…Modern Theories of unification:

Maxwell (gauge theoretic approach)

Einstein (geometric approach)

Glashow-Salam-Weinberg

Electroweak unification shows up very nicely in experimental results

Deep inelastic scattering data from the HERA collider at DESY, Hamburg

Programme of unification:

• Electric + magnetic = electromagnetic

• Electromagnetic + weak = electroweak

• Electroweak + strong = grand unification

• GUT + gravity = super-unification

Running coupling constants

22

2 2

2

( )( )

( )1 ( ) log

3

QQ

f n

SUSY SU(5)-based one-step grand unification

U.

Am

ald

i et

al

1996

16GUT ~ 10 GeV

Positive thinking:

• Unification of forces is not just a theoretician’s dream but it is the culmination towards

which all fundamental science tends

•Supersymmetric SU(5) theories did provide a simple and elegant model for one-step grand unification with SUSY particles at a few TeV…

predicts a rather small p

• Problems with proton lifetime can be easily resolved by considering SUSY SO(10) GUTs…

• Hierarchy problem remains anyway GUT » TeV

• Maybe unification of forces occurs in various steps at different energies, the lowest of which may be far beyond a TeV

• Maybe unification of couplings occurs only in a (string) theory at the Planck

scale

• Maybe gauge theories are only effective theories at low energies and when we go higher something completely different happens

• Maybe there is no single force in the Universe and Grand Unification is just a dream

• In any case, speculating about 16 orders of magnitude is useless without more information

DEVIL’S ADVOCATE

Grand Unification is still very much a conjecture…

Technicolour

• Inspired by superconductivity, quark model and QCD…

• Just as mesons are composites of quarks and pion masses are related to QCD scale in a SU(3)

gauge theory…

...so Higgs bosons are composites of techni-fermions and electroweak scale is related to a technicolour scale in a SU(N) gauge theory

Idea is simple and elegant ─ implementation is not

SU(N)

• How are quark & lepton masses obtained?

Need to relate composite Higgs to fermions…

Extended technicolour (ETC)

( ) (3)ETC TC CG SU N SU

Symmetry-breaking scale is around 10-100 TeV

Generates quark and lepton masses through self-energy corrections with composite Higgs; also predicts heavy technipions around 100 GeV – few TeV

ETC models fail to explain:

• small value of mixing

• precision data on the S parameter

• the large t quark mass

Invention of walking technicolour

TC (Q2) evolves very slowly

• small contribution to mixing

• small contribution to S parameter

00 KK

00 KK

Large top quark mass is still a problem in ETC models

Invention of topcolour

new (gauge) interaction: leads to formation of

condensate Higgs-like particle tt

State of the art: topcolour-assisted ETC

TeV

,(3) (1) (3) (1) (3) (1)tb C Yud cs

SU U SU U SU U

Quite a bit of fine-tuning has to be done: still predicts mt ≈ 250 GeV

Invention of top-seesaw models Getting messy…

Compositeness is still a very attractive idea

• Too complicated to be credible: epicycles?

• Too slavish in following QCD? Naïve?

• TeV scale interactions may be non-gauge interactions after all

Copernican theory ● Sommerfeld atom ● Sakata model

Supersymmetry and the MSSM

bosonsfermions aa QQ ,

1N

In a supersymmetric theory the bosons and fermions have the same mass and couplings

H H

H

g2

g2

H~

H

H

g

g

g

finitesoftgM H 222

finitesoftgM H 222

Quadratic divergences cancel

no hierarchy problem

If SUSY partners have the same masses as the Standard Model particles they should have been discovered by now…

ergo, they must be heavy

SUSY must be badly broken

Spontaneous breaking is ruled out

• There are no goldstinos

• All the superpartners are heavy (sum rule)

Must have explicit SUSY-breaking terms

Constructing the MSSM

Use the superfield formalism…

Scalar superfield :

Vector superfield:

ˆ , ,F

V̂ v , ,D

Every SM particle is embedded in the appropriate superfield…

Notation: use the symbol for the SM particle with carat and tilde…e.g.

Chiral spinor

Majorana spinor

ˆ ( , , )LL L L ee e e F

L. electron s.f.

L. selectron

A Supersymmetry Primer : S.P. Martin hep-ph/9709356

^

^^

^

^

^

^

General form of a SUSY gauge + Yukawa + 4 theoryˆ† V

superpotential

ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ H.c.gi i i i ij i j ijk i j ki ie a b c

L

'ˆ ˆ2 2 ˆ

ˆ ˆˆ

aa

a

gg W B

LL L

L

e ee

σ

Interactions: , , , L L L L Le W Z e e Z e e

, , , L L L L Le W Z e e Z e e , , , L L L L Le W Z e e Z e e , , , L L L L Le W Z e e Z e e

Gauge-fermionYukawa

Scalar e.d.

Can use this prescription to construct MSSM with unbroken SUSY

Require to add explicit SUSY-breaking termsmust be soft (i.e. positive dimension coupling

constants) to avoid new quadratic divergences

Origin of all these terms requires an explanation outside of the MSSM

Gaugino mass terms

Sfermion mass termsTrilinear terms

Higgsino mass terms

In a SUGRA model, SUSY can be broken spontaneously in a ‘hidden sector’, where the goldstinos are absorbed into the gravitino by a super-Higgs mechanism… the SUSY breaking is then communicated to the visible sector by gravity, creating soft SUSY-breaking effective operators … note that the physical and ‘hidden’ sectors can be in the same spacetime… it’s just that they do not interact (other than gravity, of course)…

MSSM Superpotential^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

Doublets are combined as SU(2) products: ' 'ab a b Colour and flavour indices are suppressed : 3 3 matrices

L L L

0ˆ ˆˆ ˆe d L d Ry H e H e

Interactions: 0, d L L de H e e H

0, d L L de H e e H 0, d L L de H e e H

0 0 0, , etc.d d L L d de H H e e H H

Yukawa

Seagull terms

Electroweak symmetry-breaking causes many of the gauge-SUSY eigenstates to mix…

Higgs bosons0u

u

u

HH

H

0d

d

d

HH

H

0 0 0, , ,H H h A

*cos sin

sin cosu

d

G H

H H

00

00

cos sin Im

sin cos Imu

d

H

HA

G

00

00

cos sin Re

sin cos Reu

d

Hh

HH

Physical Higgs bosons:

Charged Higgs

Neutral pseudoscalar

Light neutral scalar

Heavy neutral scalar

vn

v ta u

d

cos 2 91 GeVh Zm M 140 GeV+ Radiative Corrections

A light Higgs boson is the most robust phenomenological prediction of the MSSM

G. Weiglein, Nature (2004)

Winos, Binos and Higgsinos…

30

0

0102

0303

u

d

B

W

H

H

N

N

N

N

Z

Four physical NEUTRALINO states (all Majorana fermions)

'v 'v

1 2 2

v v

2 2 2

'v v

2 2

'v v

2 2

0

0

0

0

†g gd u

g gd u

g gd d

g gu u

M

MZ Z

is diagonal

2 2 2v v vu d

Winos, Binos and Higgsinos…

Two physical CHARGINO states (both Dirac fermions) from mixing:

1

2

C W

C H

Roughly …

Two physical SQUARK states (both scalars) from mixing of left- and right-squarks through electroweak vev…

With CKM effects, we get 66 squark mass/mixing matrices

Sparticle Spectrum (neglecting small fermion masses)

•The MSSM has 124 unknown parameters!

• Constrain it in various ways. e.g. embed in a SUSY-GUT

• Different mechanisms for SUSY-breaking lead to different predictions for SUSY mass spectrum

─ Gravity mediation (mSugra)

─ Gauge mediation (GMSB)

─ Anomaly mediation (AMSB)

─ Gaugino mediation

Phenomenological consequences depend very strongly on the mass spectrum and couplings

S.P. Martin hep-ph/9709356

Sample Sparticle spectra:

Ma

ss

es →

mSUGRA GMSB

Phenomenological predictions are somewhat different in the two cases…

S.P. Martin hep-ph/9709356

Supersymmetry is probably the best solution to the hierarchy problem

Also has aesthetic appeal and close link with Planck-scale physics

• Proliferation of fields and parameters

• SUSY-breaking schemes are ad hoc

• Phenomenology is very model-dependent

SUSY predicts a light Higgs boson which we must find at the LHC to keep MSSM alive…

Brane worlds

• The Universe has more than 1+3 dimensions, but the Standard Model fields (us!) are confined to a 1+3 dimensional hyper-surface (brane)

• The extra dimensions are compactified

• Gravity is free to propagate in the extra dimensions

• Gravity is as strong as the electroweak interaction, but appears weak on the brane

• TeV-scale experiments probe the `strong’ gravity sector

there is new physics at a TeV

There is no hierarchy problem

Large extra dimensions

• There are 2 or more compact dimensions of size as large as ~ 100 m

• The wavefunction of the ‘strongly’-interacting graviton spreads out in all the dimensions: only a small part intersects the brane

• Gravitons produced in a collision can fly off into the extra dimensions, carrying energy-momentum which would seem to disappear from the brane (missing energy-momentum signatures)

• Virtual graviton exchanges can look like neutral current interactions

R

Open strings Gauge fields

Closed strings MasslessGravitons

FLAT GEOMETRY

3-brane

2 2 2 2ds dt dx dy

Einstein-Hilbert action in 4+d dimensions

4

4

4

1( , )

16

( )16

1( )

16

ˆ ˆˆ

ˆ

ˆ

N

dB

B

B

B

S d y g yG

V

G

d x x

d x g x

d x g xG

B

+...

+...R

R

R

ˆ

ˆ

N

d

N d

N

N

G

V

G V

G

G

Integrate over bulk for large objects

can be large if

is large

ˆNG

dV

Cis-Planckian regime

/( ) 1Nm

rG mr e

r

For ||~1

< 150 m

2003 data

Eventually

< 60 m

Compare with29~ 10 mP

Eöt-Wash experiment

Bulk scale versus Planck scale

2

2

2

2 P

d

d

dCR

M

on a d-torus

Possible to have TeV effects if d > 2

2

2

2

2

2 2 ; ;

ˆ ˆˆ

ˆ

N N BdP

d

NP

B

N

PP

G G VM

M

G GM

V

M

Eöt-Wash experiment

Han, Lykken and Zhang, Phys Rev D59, 105006

Feynman Rules for the ADD model

all scalars

all gauge bosons

all fermions

4int (

( ) ( )) ( )2 SM SM

n

n nd x hS T T

2 2 221 2

2

...

22

dn

CC

n n nnM

RR

Tower of Kaluza-Klein states :( ) ( )nG x

Spacing between states :

1~

~ if ~

~ 0.01 eV if ~ 0.001 cm

nC

P C P

C

MR

M R

R

On the brane…

No of contributing states : 13100 GeV~ ~ 10

0.01 eVn

s

M

A massless bulk graviton is like a huge swarm of massive graviton fields on the brane — quasicontinuum

Sum over KK states can be done using the quasi-continuum approach

0

2

/ 2

( ) ( )

( )

( )4 ( /

2)

d d

d

s

nn

C

M

R MM

M dM M

d

2

2 4 4

1( , )ˆ

n n P S

d s

Ms M i M

Sum over propagators…

reduces to a contact interaction…

Collider physics with gravitons/dilatons:

Graviton tower couples to every particle-antiparticle pair

Blind to all quantum numbers except energy-momentum

Each Kaluza-Klein mode couples equally, with strength

Tower of Kaluza-Klein modes builds up collectively to an observable effect

Individual graviton modes escape detection missing Tp

TransPlanckian phenomenon: Laboratory Black Holes

1

12

8 11ˆ 2ˆ

d d

S

PP

mR

dMM

S.B. Giddings, S. Thomas, PRL 65 (2002) 056010 S. Dimopoulos, G. Landsberg, PRL 87 (2001) 161602

Hawking radiation

2 2BH ~ ~ TeV ~ 400 pbSR

Only semi-classical treatment possible

About 107 micro black holes per year @LHC

(3 1)( 1)

251 2 10 s

nn

S S

m

M M

Rapid evaporation by Hawking radiation

All possible particles are produced in the black hole decay… one just looks for such events with a huge number of uncorrelated particles shooting out in all directions….

Warped gravity

• There need be only one extra dimension, but it is compactified on SS1/Z2

• There are two branes at the orbifold fixed points

• The Standard Model lives on one brane; `strong’ gravity on the other

• The graviton wavefunction is exponentially damped across the extra dimension a ratio of about

1/12 enough to reproduce the electroweak-Planck scale hierarchy

• On our brane gravitons appear like spin-2 WIMPs

WARPED GEOMETRY

Planck brane

TeV brane

AdS5 ‘throat’

Metric contracts exponentially along AdS5 ‘throat’

Gravitons acquire TeV masses

R

2 2 2 2kyds e dt dx dy

Modulus stabilization and the radion:

16~ 10 if 11.7CkRCe kR

Warping is extremely sensitive to RC

( ) 222 2(( ))T xk T xds e g x d

Consider the radius of the extra dimension as a dynamical object :

( )T xModulus field :3ˆ2 ( )4( ) kM

k

T xex Radion field :

34 2 ˆ1 1 22 12

( )gravMk

S d x g x

Radion is a free field i.e. it can assume any value same for modulus Need for modulus stabilization

Goldberger-Wise mechanism :

Assume a bulk scalar field ( , )B x y

Write down a B4 theory in the bulk and on the two branes…

Solving the equation of motion for (x) and integrating over y leads to potential with a steep minimum at

20

2

v4( ) log

vCB

kkR k T x

M

Can assume the desired value (≈ 11.7) without assuming any large/small numbers…

Undetermined parameters: radion mass & radion vev

M

k T

( )V ky

Radion couplings are very Higgs-like…

Extra dimensions are an exciting idea

Provide an intimate link with structure of spacetime and technical problems in particle physics

• None of the models is completely free from fine-tuning

• There is no way to determine the number of the extra dimensions

• We do not understand dynamically why some of the dimensions are

compact

• Phenomenology is highly model-dependent –only spin-2 graviton is universal

Little Higgs models

Grew out of extra dimensions and borrowed many ideas from technicolour theories

Simplest theory is the littlest Higgs model

• Above about 10 TeV there is a global SU(5) gauge symmetry, with a locally gauged subset

10 TeV

1 2

10 TeV

(2) (1) (2) (1) (2) (1)

(5) (5)

L YSU U SU U SU U

SU SO

• Global symmetry breaking produces 14 Goldstone bosons

12/100 3,2,3,1

Higgs mass is protected

The Higgs is actually a pseudo-Goldstone boson

• There are massive gauge bosons W’ and B’ at the TeV scale ─ radiative corrections generate (negative) Higgs mass terms (Coleman-

Weinberg mechanism)

• Quadratic divergences in the Higgs mass generated by W and B cancel with those generated by W’ and B’ (negative signs are generated by group-theoretic factors)

• Top quark generates a large Higgs mass correction; this is cancelled by a heavy pair of vectorlike fermions

Hierarchy problem disappears: lots of TeV physics

Little Higgs models are ingenious

Provide a non-supersymmetric way to cancel quadratic divergences

• Too clever by half

• The gauge symmetry is completely ad hoc

• New fields, interactions and symmetries have been thrown in as and when

required…

• Experience shows that Nature is generally simple

String Theory

Strings naturally live in more than 1+3 dimensions (26, 10, …)

If some of these dimensions are large, in the ADD sense, we could have strong gravity at a few TeV, (maybe) grand unification at a few TeV, and stringy effects at a few TeV

Could the LHC then see stringy effects?

CME PM

Landscape of string theoretic vacua

Proposed as a solution to the cosmological constant problem

Limited number of these vacua can lead to structure formation

Choice of compactification scheme is limited,

e.g. KKLT: modulus mediation, mirage mediation

Construct a low-energy spectrum and ensure that it is consistent with

Compare different signatures at the LHC…

Kane, Kumar, Shao 2007

Y.G.Kim 2007

Y.G.Kim 2007

Landscape ideas (anthropic principle) are still controversial

New ideas, model variants, etc. are coming thick and fast…

Most of them essentially propose a new sparticle spectrum

A particular sparticle spectrum does not necessarily imply a particular compactification scheme

More phenomenological study is required…

How to search for New Physics at the LHC…