Physics beyond the Standard Model:Higgs and Supersymmetry –

Why, what, where and how?

Nanyang Technological UniversitySingapore, January 2012

John Ellis, King’s College London & CERN

Plan of the Lectures

• The Standard Model and issues beyond it

• Origin of particle masses: Higgs boson or?

• Supersymmetry

• Searches for supersymmetry: LHC & dark matter

Summary of the Standard Model

• Particles and SU(3) × SU(2) × U(1) quantum numbers:

• Lagrangian: gauge interactions

matter fermions

Yukawa interactions

Higgs potential

Gauge Interactions of the Standard Model

• Three separate gauge group factors:– SU(3) × SU(2) × U(1)

– Strong × electroweak

• Three different gauge couplings:– g3, g2, g ́

• Mixing between the SU(2) and U(1) factors:

• Experimental value: sin2θW = 0.23120 ± 0.00015

Clue for Grand Unification and supersymmetry

Weak Interactions

• Interactions of lepton doublets:

• Charged-current interactions:

• Neutral-current interactions:

• Mixing between quark flavours:

Status of the Standard Model

• Perfect agreement with all confirmed accelerator data

• Consistency with precision electroweak data (LEP et al) only if there is a Higgs boson

• Agreement seems to require a relatively light Higgs boson weighing < ~ 180 GeV

• Raises many unanswered questions:

mass? flavour? unification?

Precision Tests of the Standard Model

Lepton couplings Pulls in global fit

Parameters of the Standard Model

• Gauge sector:– 3 gauge couplings: g3, g2, g ́– 1 strong CP-violating phase

• Yukawa interactions:– 3 charge-lepton masses– 6 quark masses– 4 CKM angles and phase

• Higgs sector:– 2 parameters: μ, λ

• Total: 19 parameters

Unification?

Flavour?

Mass?

Open Questions beyond the Standard Model

• What is the origin of particle masses?due to a Higgs boson? + other physics?solution at energy < 1 TeV (1000 GeV)

• Why so many types of matter particles?matter-antimatter difference?

• Unification of the fundamental forces?at very high energy ~ 1016 GeV?probe directly via neutrino physics, indirectly via masses, couplings

• Quantum theory of gravity?(super)string theory: extra space-time dimensions?

Susy

Susy

Susy

Why do Things Weigh?

0

Where do the masses come from?

Newton:Weight proportional to Mass

Einstein:Energy related to Mass

Neither explained origin of Mass

Are masses due to Higgs boson? (the physicists’ Holy Grail)

Think of a Snowfield

Skier moves fast:

Like particle without mass

e.g., photon = particle of light

Snowshoer sinks into snow,

moves slower:

Like particle with mass

e.g., electron

Hiker sinks deep,

moves very slowly:

Particle with large mass

The LHC looks for

the snowflake:

the Higgs Boson

The Higgs Boson and Cosmology

• Changed the state of the Universe when it was about 10-12 seconds old

• May have generated then the matter in the Universe

• Contributes (too much) to today’s dark energy

• A related inflaton might have expanded the Universe when it was about 10-35 seconds old

The Higgs Mechanism

• Postulated effective Higgs potential:

• Minimum energy at non-zero value:

• Non-zero masses:

• Components of Higgs field:

• π massless, σ massive:

Masses for Gauge Bosons

• Kinetic terms for SU(2) and U(1) gauge bosons:

where

• Kinetic term for Higgs field:

• Expanding around vacuum:

• Boson masses:

The Seminal Papers

The Englert-Brout-Higgs Mechanism

• Vacuum expectation value of scalar field

• Englert & Brout: June 26th 1964

• First Higgs paper: July 27th 1964

• Pointed out loophole in argument of Gilbert if gauge theory described in Coulomb gauge

• Accepted by Physics Letters

• Second Higgs paper with explicit example sent on July 31st 1964 to Physics Letters, rejected!

• Revised version (Aug. 31st 1964) accepted by PRL

• Guralnik, Hagen & Kibble (Oct. 12th 1964)

The Englert-Brout-Higgs Mechanism

•Englert & Brout •Guralnik, Hagen & Kibble

• •

The Higgs Boson

• Higgs pointed out a massive scalar boson

• “… an essential feature of [this] type of theory … is the prediction of incomplete multiplets of vector and scalar bosons”

• Englert, Brout, Guralnik, Hagen & Kibble did not comment on its existence

• Discussed in detail by Higgs in 1966 paper

Nambu, EB, GHK and Higgs

Spontaneous breaking of symmetry

A Phenomenological Profile of the Higgs Boson

• Neutral currents (1973)

• Charm (1974)

• Heavy lepton τ (1975)

• Attention to search for W±, Z0

• For us, the Big Issue: is there a Higgs boson?

• Previously ~ 10 papers on Higgs bosons

• MH > 18 MeV

• First attempt at systematic survey

• Higgs decay modes and searches in 1975:

A Phenomenological Profile of the Higgs Boson

• Couplings proportional to mass:– Decays into heavier particles favoured

• But: important couplings through loops:– gluon + gluon → Higgs → γγ

Higgs Decay Branching Ratios

Constraints on Higgs Mass

• Electroweak observables sensitive via quantum loop corrections:

• Sensitivity to top, Higgs masses:

• Preferred Higgs mass: mH ~ 80 ± 30 GeV• Compare with lower limit from direct searches:

mH > 114 GeV

• No conflict!

The State of the Higgs in Mid-2011

• High-energy search:– Limit from LEP:

mH > 114.4 GeV

• High-precision electroweak data:– Sensitive to Higgs mass:

mH = 96+30–24 GeV

• Combined upper limit:

mH < 161 GeV, or 190 GeV including direct limit

• Exclusion from high-energy search at Tevatron:

mH < 158 GeV or > 173 GeV

Combining the Information from Previous Direct Searches and Indirect Data

mH = 125 ± 10 GeV •Gfitter collaboration

Latest Higgs Searches @ Tevatron

Exclude (100,109); (156,177) GeV

Standard Model

prediction

Experimental

upper limit

Higgs Production at the LHC

A la recherche du Higgs perdu …

Higgs Hunting @ LHC: Status reported on Dec. 13th, 2011

Exclude 112.7 GeV to 115.5 GeV,

131 GeV to 237 GeV,

251 GeV to 453 GeV

Exclude 127 to 600 GeV

Has the Higgs Boson been Discovered?

Interesting hints around Mh = 125 GeV ?

CMS sees broad

enhancement

ATLAS prefers

125 GeV

Has the Higgs Boson been Discovered?

Interesting hints around 125 GeV in both experiments

- but could also be 119 GeV ?

ATLASSignals

• γγ: 2.8σ• ZZ: 2.1σ• WW: 1.4σ• Combined: 3.6σ

CMS Signals

Combined: 2.6σ

Has the Higgs Boson been Discovered?

Unofficial blogger’s combination

NOT ENDORSED BY EXPERIMENTS

but he was right last time !

Combining the Information from Previous Direct Searches and Indirect Data

mH = 125 ± 10 GeVErler: arXiv:1201.0695

mH = 124.5 ± 0.8 GeV

Assuming the Standard Model

The Spin of the Higgs Boson @ LHC

Higher mass: angular correlations in H → ZZ decays

Low mass: if H →γγ,It cannot have spin 1

Do we already know the ‘Higgs’ has Spin Zero ?

• Decays into γγ, so cannot have spin 1

• 0 or 2?

• If it decays into ττ or b-bar: spin 0 or 1 or orbital angular momentum

• Can diagnose spin via angular correlations of leptons in WW, ZZ decays

For Mh = 120 GeV

Higgs Measurements @ LHC & ILC

•

• • Precision

Electroweak

data??

Higgs

coupling

blows up!!

Higgs

potential

collapses Higgs coupling less

than in Standard Model

•viXra Blogger’s Combination

•of Dec.13th Data

There must be New Physics

Beyond the Standard Model

Heretical Interpretation of EW Data

Do all the data

tell the same story?

e.g., AL vs AH

What attitude towards LEP, NuTeV?

What most

of us think

Chanowitz

Spread looks natural: no significant disagreement

Estimates of mH from different Measurements

Higgs + Higher-Order Operators

Precision EW data suggest they are small: why?

But conspiracies

are possible: mH

could be large,

even if believe

EW data …?Do not discard possibility of heavy Higgs

Corridor to

heavy Higgs?

Barbieri, Strumia

Elementary Higgs or Composite?

• Higgs field:

<0|H|0> ≠ 0• Quantum loop problems

• Fermion-antifermion condensate

• Just like QCD, BCS superconductivity

• Top-antitop condensate? needed mt > 200 GeV

• New technicolour force? heavy scalar resonance?• inconsistent with precision electroweak data?

• Cut-off Λ ~ 1 TeV with• Supersymmetry?

•Cutoff

•Λ = 10 TeV

Comparison between Weakly- and Strongly-coupled Models

Interpolating Models

• Combination of Higgs boson and vector ρ

• Two main parameters: mρ and coupling gρ

• Equivalently ratio weak/strong scale:

gρ / mρ

Grojean, Giudice, Pomarol, Rattazzi

Generic LittleHiggs Models

Loop cancellation mechanism

SupersymmetryLittle Higgs

(Higgs as pseudo-Goldstone

boson of larger symmetry)

Little Higgs Models

• Embed SM in larger gauge group• Higgs as pseudo-Goldstone boson• Cancel top loop

with new heavy T quark

new gauge bosons, Higgses• Higgs light, other new

physics heavyNot as complete as susy: more physics > 10 TeV

MT < 2 TeV (mh / 200 GeV)2

MW’ < 6 TeV (mh / 200 GeV)2

MH++ < 10 TeV

What if the Higgs is not quite a Higgs?

• Tree-level Higgs couplings ~ masses– Coefficient ~ 1/v

• Couplings ~ dilaton of scale invariance• Broken by Higgs mass term –μ2, anomalies

– Cannot remove μ2 (Coleman-Weinberg)– Anomalies give couplings to γγ, gg

• Generalize to pseudo-dilaton of new (nearly) conformal strongly-interacting sector

• Couplings ~ m/V (V > v?), additions to anomalies

A Phenomenological Profile of a Pseudo-Dilaton

• New strongly-interacting sector at scale ~ V• Pseudo-dilaton only particle with mass << V• Universal suppression of couplings to Standard

Model particles ~ v/V• Γ(gg) may be enhanced• Γ(γγ) may be suppressed• Modified self-couplings• Pseudo-baryons

as dark matter?

•Compilation

•of constraints

•Campbell, JE, Olive: arXiv:1111.4495

•Updated

•with Dec. 11

•constraints

Higgsless Models?

• Four-dimensional versions:

Strong WW scattering @ TeV, incompatible with precision data?

• Break EW symmetry by boundary conditions in extra dimension:

delay strong WW scattering to ~ 10 TeV?

Kaluza-Klein modes: mKK > 300 GeV?

compatibility with precision data?• Warped extra dimension + brane kinetic terms?

Lightest KK mode @ few 00 GeV, strong WW @ 6-7 TeV

Theorists getting Cold Feet

• Composite Higgs model?conflicts with precision electroweak data

• Interpretation of EW data?consistency of measurements? Discard some?

• Higgs + higher-dimensional operators?corridors to higher Higgs masses?

• Little Higgs models?extra `Top’, gauge bosons, `Higgses’

• Higgsless models?strong WW scattering, extra D?

Particle Spectrum in Simplest Model with Extra Dimensions

Lowest-lying states have flat wave functions (n = 0)

Excitations (Kaluza-Klein) have nodes (n > 0):

Mass ~ n/R (R = radius of circle)

‘Fold’ Circle: Orbifold

• Identify two halves of circle: up to a minus sign

• ‘Even’ particles include massless: odd ones all massive• A way to give masses to particles that are asymmetric

Mechanism to break Gauge Symmetry

• Identify two halves up to a group transformation U

• Unbroken part of gauge group commutes with U• Masses for asymmetric particles:

– e.g., SU(2) × U(1) U(1)

Search for Vector Resonance in Higgsless Model

Vector resonance structure in WZ scattering

Simulation of resonance structure in mWZ @ LHC

Theoretical Constraints on Higgs Mass

• Large Mh → large self-coupling → blow up at low-energy scale Λ due to renormalization

• Small: renormalization due to t quark drives quartic coupling < 0at some scale Λ→ vacuum unstable

• Vacuum could be stabilized by supersymmetry•Espinosa, JE, Giudice, Hoecker, Riotto, arXiv0906.0954

•LHC 95%

•exclusion

Vacuum Stability vs Metastability

• Dependence on scale up to which Standard Model remains

– Stable

– Metastable at non-zero temperature

– Metastable at zero temperature

What is the probable fate of the SM?Confidence Levels (CL) for different fatesConfidence Levels (CL)

without/with Tevatron exclusion

Blow-up excludedat 99.2% CL

Espinosa, JE, Giudice, Hoecker, Riotto

CL asfunction ofinstability

scale

The LHC will Tell the Fate of the SM

Espinosa, JE, Giudice, Hoecker, Riotto

Examples with LHC measurement of mH = 120 or 115 GeV

How to Stabilize a Light Higgs Boson?

• Top quark destabilizes potential: introduce introduce stop-like scalar:

• Can delay collapse of potential:• But new coupling must be

fine-tuned to avoid blow-up:• Stabilize with new fermions:

– just like Higgsinos

• Very like Supersymmetry!

•Favoured values of Mh ~ 119 GeV:

•Range consistent with evidence from LHC !

•Higgs mass

•χ2 price to pay if Mh = 125 GeV is < 2

•Buchmueller, JE et al: arXiv:1112.3564

The Stakes in the Higgs Search

• How is gauge symmetry broken?• Is there any elementary scalar field?• Would have caused phase transition in the Universe when

it was about 10-12 seconds old• May have generated then the matter in the Universe:

electroweak baryogenesis• A related inflaton might have expanded the Universe

when it was about 10-35 seconds old • Contributes to today’s dark energy: 1060 too much!

Intermediate Models

Effects on Higgs Decays

• Dependences on of Higgs branching ratios

• Standard Model recovered in limit 0

•Grojean, Giudice, Pomarol, Rattazzi

At what Energy is the New Physics?

A lot accessibleto the LHC

Some accessible only indirectly:Astrophysics & cosmology?

Dark matter

Origin of mass

Indications on the Higgs Mass

Sample observable:W mass @ LEP & Tevatron

Combined informationon Higgs mass

Summer 2008

The State of the Higgs: November 2009

• Direct search limit from LEP:

mH > 114.4 GeV

• Electroweak fit sensitive to mt

(Now mt = 173.1 ± 1.3 GeV)

• Best-fit value for Higgs mass:

mH = 89+35–26 GeV

• 95% confidence-level upper limit:

mH < 157 GeV, or 186 GeV including direct limit

• Tevatron exclusion:

mH < 162 GeV or > 166 GeV

Higgs Search @ Tevatron

Tevatron excludes Higgs between 162 & 166 GeV

Higgs Search @ Tevatron

Tevatron excludes Higgs between 162 & 166 GeV

Combining the Higgs Information

mH = 116.4+ 15.6-1.3 GeV

Progress of Tevatron

Higgs Search

Possibility of

future evidence

Past improvements

Theoretical Constraints on Higgs Mass

• Large → large self-coupling → blow up at low energy scale Λ due to renormalization

• Small: renormalization due to t quark drives quartic coupling < 0at some scale Λ→ vacuum unstable

• Bounds on Higgs mass depend on Λ

The Large Hadron Collider (LHC)

Proton- Proton Collider

7 TeV + 7 TeV

1,000,000,000 collisions/second

Primary targets: •Origin of mass•Nature of Dark Matter•Primordial Plasma•Matter vs Antimatter

Event rates in ATLAS or CMS at L = 1033 cm-2 s-1

Huge Statistics thanks to High Energy and Luminosity

LHC is a factory for anything: top, W/Z, Higgs, SUSY, etc…. mass reach for discovery of new particles up to m ~ 5 TeV

Process Events/s Events per year Total statistics collected at previous machines by 2007

W e 15 108 104 LEP / 107 Tevatron

Z ee 1.5 107 107 LEP

1 107 104 Tevatron

106 1012 – 1013 109 Belle/BaBar ?

H m=130 GeV 0.02 105 ?

m= 1 TeV 0.001 104 ---

Black holes 0.0001 103 ---m > 3 TeV (MD=3 TeV, n=4)

The LHC Physics Haystack(s)

Interesting cross sections

Higgs

Susy

• Cross sections for heavy particles

~ 1 /(1 TeV)2

• Most have small couplings ~ α2

• Compare with total cross section

~ 1/(100 MeV)2

• Fraction ~ 1/1,000,000,000,000

• Need ~ 1,000 events for signal

• Compare needle

~ 1/100,000,000 m3

• Haystack ~ 100 m3

• Must look in ~ 100,000 haystacks

The LHC’s Most Anticipated Discovery

a Higgs boson

a Higgs boson

1 fb-1

…

The LHC Roulette WheelStandard Model

Higgs boson

A Simulated Higgs Event in CMS

Higgs Production at the LHC

A la recherche du

Higgs perdu …

… not far away?

Combining direct,

Indirect information

Some Sample Higgs SignalsA la recherche du Higgs perdu …

γγ

ZZ* -> 4 leptonsττ

Some Sample Higgs Signals

ttH

bbH

γγZZ* -> llll

Measuring Higgs Self-Coupling

Heavier Higgs possible @ SLHCLight Higgs @ low-energy LC

When will ATLAS discover the Higgs boson?

Duehrssen, La Thuile 2010

When will the LHC discover the Higgs boson?

1 ‘year’ @ 1033

‘month’ @ 1033

‘month’ @ 1032

Blaising, JE et al: 2006

The Stakes in the Higgs Search

• How is gauge symmetry broken?• Is there any elementary scalar field?• Would have caused phase transition in the Universe when

it was about 10-12 seconds old• May have generated then the matter in the Universe:

electroweak baryogenesis• A related inflaton might have expanded the Universe

when it was about 10-35 seconds old • Contributes to today’s dark energy: 1060 too much!

International Linear Collider

• e+e- collisionsup to Ecm = 1 TeV

• Option for next collider

• Now subject of Global Design Effort

• Hope for decisionby 2012?

• To be constructed by2020?

Tasks for the TeV ILC

• Measure mt to < 100 MeV

• If there is a light Higgs of any kind, pin it down:

Does it have standard model couplings?

What is its precise mass?

• If there are extra light particles: Measure mass and properties

• If LHC sees nothing new below ~ 500 GeV:

Look for indirect signatures

Measuring Properties of Light Higgs

Measuring top-Higgs couplings

Other studies …LC capabilities

bb, ττ, gg, cc, WW, γγ

For Mh = 120 GeV

For Mh = 140 GeV

Higgs Measurements @ ILC & LHC

Sensitivity to Strong WW scattering

@ LHC @ 800 GeV LC

Measuring a WW Resonance

Form factor measurements@ 500 GeV LC

Resonance parameters@ LHC

Resonance parameters @ 500 GeV LC

After LHC @ CERN - CLIC?

Electron-Positron

collisions up to 3 TeV

Can measure rare decay modes …

Large Cross Section @ CLIC

H bb

Δg/g = 4% Δg/g = 2%

mH = 120 GeV mH = 180 GeV

If the Higgs boson is heavier …

Can establish its existencebeyond any doubt if < 1 TeV:

ee H ee

Find resonance in strongWW scattering if > 1 TeV:

ee H νν

Measuring Effective Higgs Potential @ Higher-Energy LC

Large cross section

for HH pair production

Accuracy in measurement of HHH coupling

MH = 240 GeV

180 GeV

140 GeV

120 GeV

11%

9%