12. Beyond the Standard Model - University of Cambridge

12. Beyond the Standard ModelParticle and Nuclear Physics

Dr. Tina Potter

Dr. Tina Potter 12. Beyond the Standard Model 1

In this section...

Summary of the Standard Model

Problems with the Standard Model

Neutrino oscillations

Supersymmetry


The Standard Model (2012)

Matter: point-like spin 12

Dirac fermions

+ antiparticles

Fermion Charge [e] Mass

1st

gen.

Electron e− −1 0.511 MeV

Electron neutrino νe 0 ∼ 0

Down quark d −1/3 4.8 MeV

Up quark u +2/3 2.3 MeV

2nd

gen.

Muon µ− −1 106 MeV

Muon neutrino νµ 0 ∼ 0

Strange quark s −1/3 95 MeV

Charm quark c +2/3 1.3 GeV

3rd

gen.

Tau τ− −1 1.78 GeV

Tau neutrino ντ 0 ∼ 0

Bottom quark b −1/3 4.7 GeV

Top quark t +2/3 173 GeV


The Standard Model (2012)Forces: mediated by spin 1 bosons

Force Particle Mass

Electromagnetic Photon γ 0

Strong 8 gluons g 0

Weak (CC) W± 80.4 GeV

Weak (NC) Z 91.2 GeV

The Standard Model also predicts the existence of a spin-0Higgs boson which gives all particles their masses via itsinteractions. Evidence from LHC confirms this, withmH ∼ 125 GeV.

The Standard Model successfully describes all existing particle physics data,with the exception of one

⇒ Neutrino Oscillations ⇒ Neutrinos have mass

In the SM, neutrinos are treated as massless; right-handed states do notexist ⇒ indication of physics Beyond the Standard Model


Problems with the Standard ModelThe Standard Model successfully describes all existing particle physics data(though question marks over the neutrino sector).

But: many (too many?) input parameters:Quark and lepton massesQuark chargeCouplings αEM, sin2 θW , αs

Quark (+ neutrino) generation mixing – VCKM

and: many unanswered questions:Why so many free parameters?Why only three generations of quarks and leptons?Where does mass come from? (Higgs boson probably OK)Why is the neutrino mass so small and the top quark mass so large?Why are the charges of the p and e identical?What is responsible for the observed matter-antimatter asymmetry?How can we include gravity?

etcDr. Tina Potter 12. Beyond the Standard Model 5

Beyond the Standard Model – further unification??

Grand Unification Theories (GUTs) aim to unite the strong interaction withthe electroweak interaction. Underpins many ideas about physics beyond theStandard Model.The strength of the interactions depends on energy:

Suggests unification of all forces at ∼ 1015 GeV?Strength of Gravity only significant at the Planck Mass ∼ 1019 GeV


Neutrino OscillationsIn 1998 the Super-Kamiokande experiment announcedconvincing evidence for neutrino oscillations implyingthat neutrinos have mass.

π → µνµ↪→ eνµνe

ExpectN(νµ)

N(νe)∼ 2

Super-Kamiokande results indicate a deficit of νµ fromthe upwards direction. Upward neutrinos createdfurther away from the detector.

Interpreted as νµ→ ντ oscillationsImplies neutrino mixing and neutrinos have mass


Detecting NeutrinosNeutrinos are detected by observing the lepton produced in charged currentinteractions with nuclei. e.g. νe + N → e− + X νµ + N → µ+ + XSize Matters:

Neutrino cross-sections on nucleons are tiny; ∼ 10−42(Eν/ GeV)m2

Neutrino mean free path in water ∼ light-years.

Require very large mass, cheap and simple detectors.

Water Cerenkov detection

Cerenkov radiationLight is emitted when a charged particle traverses a dielectric medium

A coherent wavefront forms when the velocity of a charged particle exceeds c/n (n =

refractive index)

Cerenkov radiation is emitted in a cone i.e. at fixed angle with respect to the particle.

cos θC =c

nv=

1

nβ


Super-Kamiokande

Super-Kamiokande is a Water Cerenkov detector sited in Kamioka, Japan

50, 000 tons of water

Surrounded by 11, 146 × 50 cm diameter, photo-multiplier tubes


Super-Kamiokande Examples of events

νµ + N → µ− + X νe + N → e− + X


Super-Kamiokande ν deficit

Expect

Isotropic (flat)distributions in cos θN(νµ) ∼ 2N(νe)

Observe

Deficit of νµ from belowWhereas νe look as expected

Interpretation

νµ→ ντ oscillations⇒ neutrinos have mass

e-like

μ-like

No oscillationsWith oscillationsData


Neutrino MixingThe quark states which take part in the weak interaction (d ′, s ′) are related tothe flavour (mass) states (d , s)

Weak Eigenstates(d ′

s ′

)=

(cos θC sin θC− sin θC cos θC

)(d

s

)Mass Eigenstates

Cabibbo angle θC ∼ 13◦

Suppose the same thing happens for neutrinos. Consider only the first twogenerations for simplicity.

Weak Eigenstates= flavour eigenstates

(νeνµ

)=

(cos θ sin θ− sin θ cos θ

)(ν1

ν2

)Mass Eigenstates

Mixing angle θ

e.g. in π+ decay produce µ+ and νµ i.e. the neutrino state that couples to theweak interaction.

The νµ corresponds to a linear combinationof the states with definite mass, ν1 and ν2

νe = +ν1 cos θ + ν2 sin θ

νµ = −ν1 sin θ + ν2 cos θ

or expressing the mass eigenstatesin terms of the weak eigenstates

ν1 = +νe cos θ − νµ sin θ

ν2 = +νe sin θ + νµ cos θDr. Tina Potter 12. Beyond the Standard Model 12

Neutrino Mixing


Neutrino Mixing


Neutrino Mixing


Neutrino Mixing

Suppose a muon neutrino with momentum ~p is produced in a weak decay, e.g.π+ → µ+νµ

At t = 0, the wavefunctionψ(~p, t = 0) = νµ(~p) = ν2(~p) cos θ − ν1(~p) sin θ

The time evolution of ν1 and ν2 will be different if they have different masses

ν1(~p, t) = ν1(~p)e−iE1t ; ν2(~p, t) = ν2(~p)e−iE2t

After time t, state will in general be a mixture of νe and νµψ(~p, t) = ν2(~p)e−iE2t cos θ − ν1(~p)e−iE1t sin θ

= [νe(~p) sin θ + νµ(~p) cos θ] e−iE2t cos θ − [νe(~p) cos θ − νµ(~p) sin θ] e−iE1t sin θ

= νµ(~p)[cos2 θe−iE2t + sin2 θe−iE1t

]+ νe(~p)

[sin θ cos θ

(e−iE2t − e−iE1t

)]= cµνµ(~p) + ceνe(~p)


Neutrino MixingProbability of oscillating into νe

P(νe) = |ce|2 =∣∣sin θ cos θ


)∣∣2=

1

4sin2 2θ


) (eiE2t − eiE1t

)=

1

4sin2 2θ

(2− ei(E2−E1)t − e−i(E2−E1)t

)= sin2 2θ sin2

[(E2 − E1)t

2

]

But E =√~p 2 + m2 = ~p

√1 +

m2

~p 2∼ ~p +

m2

2~pfor m� E

1 + x ∼ (1 + x/2)2

when x is small, can ignore x2 term

⇒ E2(~p)− E1(~p) ∼ m22 −m2

1

2~p∼ m2

2 −m21

2E

⇒ P(νµ → νe) = sin2 2θ sin2[

(m22 −m2

1)t

4E

]Dr. Tina Potter 12. Beyond the Standard Model 14

Neutrino MixingFor νµ→ ντ P(νµ → ντ) = sin2 2θ sin2

[(m2

3 −m22)t

4E

]= sin2 2θ sin2

[1.27∆m2L

Eν

]where L is the distance travelled in km,

∆m2 = m23 −m2

2 is the mass difference in ( eV)2

and Eν is the neutrino energy in GeV.

Interpretation of Super-Kamiokande ResultsFor E (νµ) = 1 GeV (typical of atmospheric neutrinos)

Results are consistent with νµ → ντ oscillations:

|m23 −m2

2| ∼ 2.5× 10−3 eV2; sin2 2θ ∼ 1Dr. Tina Potter 12. Beyond the Standard Model 15

Neutrino Mixing – Comments

Neutrinos almost certainly have mass

Neutrino oscillation only sensitive to mass differences

More evidence for neutrino oscillationsSolar neutrinos (SNO experiment)Reactor neutrinos (KamLand)

suggest |m22 −m2

1| ∼ 8× 10−5 eV2.

More recent experiments use neutrino beams from accelerators or reactors;observe energy spectrum of neutrinos at a distant detector.

At fixed L, observation of the values of Eν at which minima/maxima areseen determines ∆m2, while depth of minima determine sin2 2θ.

Note all these experiments only tell us about mass differences.

Best constraint on absolute mass comes from the end point in Tritiumβ-decay, m(νe) < 2 eV.


Three-flavour oscillationsThis whole framework can be generalised...

νeνµντ

= UPNMS

ν1

ν2

ν3

where UPNMS =

1 0 0

0 c23 s230 −s23 c23

c12 0 s13e−iδ

0 1 0

−s23eiδ 0 c13

c12 s12 0

−s12 c12 0

0 1

defining cos θ12 = c12 etc.

This is an active field!Current status...

sin2 θ12 = 0.304± 0.014

sin2 θ23 = 0.51± 0.06

sin2 θ13 = 0.0219± 0.0012


Supersymmetry (SUSY)A significant problem is to explain why the Higgs boson is so light.

The effect of loop corrections on the Higgs mass should be to

drag it up to the highest energy scale in the problem (i.e.

unification, or Planck mass).

f

f

H H

One attractive solution is to introduce a new space-time symmetry, “supersymmetry”

which links fermions and bosons (the only way to extend the Poincare symmetry of special relativity

and respect quantum field theory.)

Each fermion has a boson partner, and vice versa, with the same couplings. Boson and

fermion loops contribute with opposite sign, giving a natural cancellation in their effect on

the Higgs mass. f

f

H H

f

f

H H+

Must be a broken symmetry, because we clearly don’t see bosons and fermions of the

same mass.

However, this doubles the particle content of the model, without any direct evidence (yet),

and introduces lots of new unknown parameters.


The Supersymmetric Standard Model

SM : W±, W 0, Bmixing−−−→ W±, Z , γ

SUSY : H0u , H

0d , W

0, B0 mixing−−−→ χ01, χ

02, χ

03, χ

04

H+u , H

−d , W

+, W− mixing−−−→ χ±1 , χ±2


SUSY and UnificationIn the Standard Model, the interaction strengths are not quite unified atvery high energy.Add SUSY, the running of the couplings is modified, because sparticleloops contribute as well as particle loops.Details depend on the version of SUSY, but in general unification muchimproved.


SUSY and cosmology

SUSY, or any unified theory, tends to have potential problems with explaining the

non-observation of proton decay.

For this reason, many versions of SUSY introduce a conserved quantity “R-parity”, which

means that sparticles have to be produced in pairs.

A consequence is that the lightest sparticle would have to be stable. In many scenarios

this would be a “neutralino” χ01 (a mixture of neutral “gauginos” and “Higgsinos”).

Cosmologists tell us that ∼ 25% of the mass in the

universe is in the form of “dark matter”, which interacts

gravitationally, but otherwise only weakly.

The lightest sparticle could be a candidate for the

“WIMPs” (Weakly Interacting Massive Particles) which

could comprise dark matter.

68.3% Dark Energy

26.8% Dark Matter

4.9% Atoms

? ??

So there are several different reasons why SUSY is attractive.


However, no sign of supersymmetry yet...On general grounds, some sparticles ought to be seen at energies around 1 TeVor lower. So LHC ought to be able to see them, especially squarks+gluinos(high σ @LHC).

Model e, µ, τ, γ Jets EmissT

∫L dt[fb−1] Mass limit Reference

Incl

usiv

eS

earc

hes

3rdge

n.g

med

.3rd

gen.

squa

rks

dire

ctpr

oduc

tion

EW

dire

ctLo

ng-li

ved

part

icle

sR

PV

Other

qq, q→qχ01 0 2-6 jets Yes 36.1 m(χ0

1)<200 GeV, m(1st gen. q)=m(2nd gen. q) 1712.023321.57 TeVq

qq, q→qχ01 (compressed) mono-jet 1-3 jets Yes 36.1 m(q)-m(χ0

1)<5 GeV 1711.03301710 GeVq

gg, g→qqχ01 0 2-6 jets Yes 36.1 m(χ0

1)<200 GeV 1712.023322.02 TeVg

gg, g→qqχ±1→qqW±χ01 0 2-6 jets Yes 36.1 m(χ0

1)<200 GeV, m(χ±)=0.5(m(χ01)+m(g)) 1712.023322.01 TeVg

gg, g→qq(ℓℓ)χ01

ee, µµ 2 jets Yes 14.7 m(χ01)<300 GeV, 1611.057911.7 TeVg

gg, g→qq(ℓℓ/νν)χ01 3 e, µ 4 jets - 36.1 m(χ0

1)=0 GeV 1706.037311.87 TeVg

gg, g→qqWZχ01 0 7-11 jets Yes 36.1 m(χ0

1) <400 GeV 1708.027941.8 TeVg

GMSB (ℓ NLSP) 1-2 τ + 0-1 ℓ 0-2 jets Yes 3.2 1607.059792.0 TeVgGGM (bino NLSP) 2 γ - Yes 36.1 cτ(NLSP)<0.1 mm ATLAS-CONF-2017-0802.15 TeVgGGM (higgsino-bino NLSP) γ 2 jets Yes 36.1 m(χ0

1)=1700 GeV, cτ(NLSP)<0.1 mm, µ>0 ATLAS-CONF-2017-0802.05 TeVg

Gravitino LSP 0 mono-jet Yes 20.3 m(G)>1.8 × 10−4 eV, m(g)=m(q)=1.5 TeV 1502.01518F1/2 scale 865 GeV

gg, g→bbχ01 0 3 b Yes 36.1 m(χ0

1)<600 GeV 1711.019011.92 TeVg

gg, g→ttχ01 0-1 e, µ 3 b Yes 36.1 m(χ0

1)<200 GeV 1711.019011.97 TeVg

b1b1, b1→bχ01 0 2 b Yes 36.1 m(χ0

1)<420 GeV 1708.09266950 GeVb1

b1b1, b1→tχ±1 2 e, µ (SS) 1 b Yes 36.1 m(χ01)<200 GeV, m(χ±1 )= m(χ0

1)+100 GeV 1706.03731275-700 GeVb1

t1 t1, t1→bχ±1 0-2 e, µ 1-2 b Yes 4.7/13.3 m(χ±1 ) = 2m(χ01), m(χ0

1)=55 GeV 1209.2102, ATLAS-CONF-2016-077t1 117-170 GeV 200-720 GeVt1

t1 t1, t1→Wbχ01 or tχ0

1 0-2 e, µ 0-2 jets/1-2 b Yes 20.3/36.1 m(χ01)=1 GeV 1506.08616, 1709.04183, 1711.11520t1 90-198 GeV 0.195-1.0 TeVt1

t1 t1, t1→cχ01 0 mono-jet Yes 36.1 m(t1)-m(χ0

1)=5 GeV 1711.0330190-430 GeVt1

t1 t1(natural GMSB) 2 e, µ (Z) 1 b Yes 20.3 m(χ01)>150 GeV 1403.5222t1 150-600 GeV

t2 t2, t2→t1 + Z 3 e, µ (Z) 1 b Yes 36.1 m(χ01)=0 GeV 1706.03986290-790 GeVt2

t2 t2, t2→t1 + h 1-2 e, µ 4 b Yes 36.1 m(χ01)=0 GeV 1706.03986320-880 GeVt2

ℓL,R ℓL,R, ℓ→ℓχ01 2 e, µ 0 Yes 36.1 m(χ0

1)=0 ATLAS-CONF-2017-03990-500 GeVℓ

χ+1 χ−1 , χ+1→ℓν(ℓν) 2 e, µ 0 Yes 36.1 m(χ0

1)=0, m(ℓ, ν)=0.5(m(χ±1 )+m(χ01 )) ATLAS-CONF-2017-039750 GeVχ±

1

χ±1 χ∓1 /χ

02, χ+1→τν(τν), χ0

2→ττ(νν) 2 τ - Yes 36.1 m(χ01)=0, m(τ, ν)=0.5(m(χ±1 )+m(χ0

1)) 1708.07875760 GeVχ±1

χ±1 χ02→ℓLνℓLℓ(νν), ℓνℓLℓ(νν) 3 e, µ 0 Yes 36.1 m(χ±1 )=m(χ0

2), m(χ01)=0, m(ℓ, ν)=0.5(m(χ±1 )+m(χ0

1)) ATLAS-CONF-2017-0391.13 TeVχ±1 , χ

02

χ±1 χ02→Wχ0

1Zχ01 2-3 e, µ 0-2 jets Yes 36.1 m(χ±1 )=m(χ0

2), m(χ01)=0, ℓ decoupled ATLAS-CONF-2017-039580 GeVχ±

1 , χ02

χ±1 χ02→Wχ0

1h χ01, h→bb/WW/ττ/γγ e, µ, γ 0-2 b Yes 20.3 m(χ±1 )=m(χ0

2), m(χ01)=0, ℓ decoupled 1501.07110χ±

1 , χ02 270 GeV

χ02χ

03, χ0

2,3 →ℓRℓ 4 e, µ 0 Yes 20.3 m(χ02)=m(χ0

3), m(χ01)=0, m(ℓ, ν)=0.5(m(χ0

2)+m(χ01)) 1405.5086χ0

2,3 635 GeVGGM (wino NLSP) weak prod., χ0

1→γG 1 e, µ + γ - Yes 20.3 cτ<1 mm 1507.05493W 115-370 GeVGGM (bino NLSP) weak prod., χ0

1→γG 2 γ - Yes 36.1 cτ<1 mm ATLAS-CONF-2017-0801.06 TeVW

Direct χ+1 χ−1 prod., long-lived χ±1 Disapp. trk 1 jet Yes 36.1 m(χ±1 )-m(χ0

1)∼160 MeV, τ(χ±1 )=0.2 ns 1712.02118460 GeVχ±1

Direct χ+1 χ−1 prod., long-lived χ±1 dE/dx trk - Yes 18.4 m(χ±1 )-m(χ0

1)∼160 MeV, τ(χ±1 )<15 ns 1506.05332χ±1 495 GeV

Stable, stopped g R-hadron 0 1-5 jets Yes 27.9 m(χ01)=100 GeV, 10 µs<τ(g)<1000 s 1310.6584g 850 GeV

Stable g R-hadron trk - - 3.2 1606.051291.58 TeVgMetastable g R-hadron dE/dx trk - - 3.2 m(χ0

1)=100 GeV, τ>10 ns 1604.045201.57 TeVg

Metastable g R-hadron, g→qqχ01 displ. vtx - Yes 32.8 τ(g)=0.17 ns, m(χ0

1) = 100 GeV 1710.049012.37 TeVg

GMSB, stable τ, χ01→τ(e, µ)+τ(e, µ) 1-2 µ - - 19.1 10<tanβ<50 1411.6795χ0

1 537 GeVGMSB, χ0

1→γG, long-lived χ01 2 γ - Yes 20.3 1<τ(χ0

1)<3 ns, SPS8 model 1409.5542χ01 440 GeV

gg, χ01→eeν/eµν/µµν displ. ee/eµ/µµ - - 20.3 7 <cτ(χ0

1)< 740 mm, m(g)=1.3 TeV 1504.05162χ01 1.0 TeV

LFV pp→ντ + X, ντ→eµ/eτ/µτ eµ,eτ,µτ - - 3.2 λ′311=0.11, λ132/133/233=0.07 1607.080791.9 TeVντ

Bilinear RPV CMSSM 2 e, µ (SS) 0-3 b Yes 20.3 m(q)=m(g), cτLS P<1 mm 1404.2500q, g 1.45 TeVχ+1 χ

−1 , χ+1→Wχ0

1, χ01→eeν, eµν, µµν 4 e, µ - Yes 13.3 m(χ0

1)>400GeV, λ12k,0 (k = 1, 2) ATLAS-CONF-2016-0751.14 TeVχ±1

χ+1 χ−1 , χ+1→Wχ0

1, χ01→ττνe, eτντ 3 e, µ + τ - Yes 20.3 m(χ0

1)>0.2×m(χ±1 ), λ133,0 1405.5086χ±1 450 GeV

gg, g→qqχ01, χ0

1 → qqq 0 4-5 large-R jets - 36.1 m(χ01)=1075 GeV SUSY-2016-221.875 TeVg

gg, g→ttχ01, χ0

1 → qqq 1 e, µ 8-10 jets/0-4 b - 36.1 m(χ01)= 1 TeV, λ112,0 1704.084932.1 TeVg

gg, g→t1t, t1→bs 1 e, µ 8-10 jets/0-4 b - 36.1 m(t1)= 1 TeV, λ323,0 1704.084931.65 TeVg

t1 t1, t1→bs 0 2 jets + 2 b - 36.7 1710.07171100-470 GeVt1 480-610 GeVt1

t1 t1, t1→bℓ 2 e, µ 2 b - 36.1 BR(t1→be/µ)>20% 1710.055440.4-1.45 TeVt1

Scalar charm, c→cχ01 0 2 c Yes 20.3 m(χ0

1)<200 GeV 1501.01325c 510 GeV

Mass scale [TeV]10−1 1

√s = 7, 8 TeV

√s = 13 TeV

ATLAS SUSY Searches* - 95% CL Lower LimitsDecember 2017

ATLAS Preliminary√s = 7, 8, 13 TeV

*Only a selection of the available mass limits on new states orphenomena is shown. Many of the limits are based onsimplified models, c.f. refs. for the assumptions made.


Signs of anything else?

2015: search for new boson

decaying to two photons,

X → γγ.

Bump at 750 GeV...

In both experiments...

200 400 600 800 1000 1200 1400 1600 1800 2000

Even

ts /

20 G

eV

1−10

1

10

210

310

410 PreliminaryATLAS

Spin-2 Selection-1 = 13 TeV, 3.2 fbs

Data

Background-only fit

[GeV]γγm200 400 600 800 1000 1200 1400 1600 1800 2000

Dat

a - f

itted

bac

kgro

und

10−

5−05

1015

Eve

nts

/ ( 2

0 G

eV )

1

10

210

Data

Fit model

σ 1 ±σ 2 ±

EBEB

(GeV)γ γm400 600 800 1000 1200 1400 1600

stat

σ(d

ata-

fit)/

-2

0

2

(13 TeV, 3.8T)-12.7 fbCMS Preliminary

ATLAS 750 GeV local excess ∼ 3.5σ (global drops to 1.8σ) evidence,

CMS 750 GeV local excess ∼ 2.9σ (global drops to 1σ) not discovery

Revisited 8 TeV dataset and performed same analysis. Results are consistent...

What could this be?Extra dimensions: excitations of gravitational field in small, curled up, warped extra dimension

– gives “towers” of spin-2 resonances, gravitons.

Extended Higgs sector: add a second Higgs doublet to the SM

– gives 5 (pseudo-)scalar Higgs bosons (lightest is the 126 GeV Higgs).

Sadly, analysis of larger 2016 dataset showed no such resonance– a statistical fluctuation


Follow the results from LHC yourself!

http://atlas.chhttp://cms.web.cern.chhttp://lhcb-public.web.cern.ch/lhcb-public/


Summary

Over the past 40 years our understanding of the fundamental particles andforces of nature has changed beyond recognition.

The Standard Model of particle physics is an enormous success. It has beentested to very high precision and can model all experimental observationsso far.

The Higgs “hole” is now becoming closed, though some other aspects ofthe SM are not quite yet under as much experimental “control” as onemight wish for (the neutrino sector, the CKM matrix, etc).

Good reasons to expect that the next few years will bring many more(un)expected surprises (more Higgs or gauge bosons, SUSY?).

Up next...Section 13: Nuclear Physics, Basic Nuclear Properties


Documents

12. Beyond the Standard Model - University of Cambridge