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### LHC Physics

Alan Barr UCL

This morning’s stuff…

Higgs – why we expect it, how to look for it, …

Supersymmetry – similar questions!

Smorgasbord of other LHC physics

Physics at TeV-scale

- Dominated by the physics ofElectroweak Symmetry Breaking
- Answering the question:
- “Why do the W and Z bosons have mass?”
- Standard Model suggests: Higgs mechanism
- However Higgs boson predicted by SM not yet observed

Higgs mechanism - history

- 1964 Demonstration that a scalar field with appropriate interactions can give mass to gauge bosons
- Peter Higgs (Edinburgh, previously UCL)
- Independently discovered by Francois Englert and Robert Brout (Brussels)
- Not until 1979 that Salam, Weinberg and Glashow use this in a theory of electroweak symmetry breaking
- For a biographic article on P. Higgs see http://physicsweb.org/articles/world/17/7/6

Higgs mechanism: why needed?

- Example of P. Higgs – give mass to a U(1) boson (heavy “photon” in a QED-like theory)

Start with QED Lagrangian:

where

Which is invariant under the local U(1) gauge transformation

(*)

Adding a gauge boson mass term could be attempted with a term like:

But this isn’t invariant under gauge transformation (*) so is not allowed

Instead add a complex scalar field which couples to the gauge boson

Pictorial representation

Excitations in this direction produce physical Higgs boson

Quartic term self-couplingpositive

Excitations in this direction = gauge transformation- Globaltransformationsunobserved- Local transformations give mass to gauge bosons

Quadratic coupling termnegative

Degenerate minimumVacuum (field strength≠0)

If you don’t understand this, study Phys.Lett.12:132-133,1964

Scalar field strength = 0

Higgs field “eats Goldstone boson”

- Flat direction in potential usually represents zero-massparticle
- “Goldstone boson”
- But in Higgs theory this direction is coupled to the gauge boson
- No massless Goldstone boson
- Instead mass term generated for gauge boson

φ

φ

φ'

Gauge boson

Example of a Feynmandiagram showing a contribution to the gaugeboson mass term

N.B. Our example here was for a single complex scalar and for a U(1) field.

In the Standard Model the Higgs is an electroweak SU(2) doublet field, with 4 degrees of freedom. 3 of these are ‘eaten’ by W±, Z0, mass terms leaving a single scalar for the physical Higgs boson. For full SU(2) treatment see e.g. Halzen & Martin section 14.9

Constraints on the Higgs mass

- Higgs boson mass is the remaining unpredicted parameter in Standard Model:
- Higgs self-couplings not predicted
- So Higgs massnot predicted by Electroweak theory
- However there are:
- Bounds from theory:
- Perterbative unitarity of boson-boson scattering
- Indirect bounds
- Loop effects on gauge boson masses
- Direct bounds
- Searches

Perturbative limit

Vector Boson scattering

Without other new physics the Higgs boson must exist & have mass < 1 TeV

Phys.Rev.D16:1519,1977

Halzen & Martin section 15.6

W (and Z) mass depends on mHiggs

Logarithmic loop corrections to masses

Also depends on top mass

Indirect Higgs bounds: LEP Electroweak dataMeasurements

Prediction as a function of mH

http://lepewwg.web.cern.ch/LEPEWWG/

Direct bounds:Higgs searches @ LEP

- No discovery
- Direct lower bound at 114.4 GeV

Higgsstrahlung – dominant production

ALEPH:Candidate vertex:

Phys.Lett. B565 (2003) 61-75

Higgs-Hunter Situation Report

- Something very much like the Higgs must exist with:~100 GeV < m < ~1 TeV
- No discovery as yet
- If it is a Standard Model Higgs the constraints are tighter:114.4 GeV < mSM Higgs <199 GeV

Large

27 km circumference

Built in LEP tunnel

Hadron

Mostly protons

Can also collide ions

Collider

~ 7 x higher collision energy

~ 100 x increase in luminosity

Compared to Tevatron

The Large Hadron ColliderProton on Protonat √s = 14 TeVDesign luminsoity ~

~100 fb-1 / expt / year

General Purpose Detectors

- Similarities:
- Tracker
- Calorimeter
- Muon chambers

ATLAS

Differences:Size : CMS “compact”

Magnetic-field configurationATLAS has muon toroidsElectromagnetic-Calorimeter:

CMS crystals. ATLAS Liquid ArgonOuter tracker technology

CMS all-silicon. ATLAS straw tubes

Definitions

φ

x

Particle

η = 0

η = -1

η = +1

η = -2

η = +2

η = -3

η = +3

θ

Beam pipe

proton

proton

z

Endcap“Forward”

Barrel“Central”

Endcap“Forward”

Differences in rapidity are conservedunder Lorentz boosts in the z-direction

*

Rapidity:

Good approximation to rapidity if E>>m

Pseudorapidity:

*

pT = (px, py)

*prove these!

“Transverse”

|pT| = √(px2, py2)

Making particles in hadron colliders

- Hadron-Hadron collisions complicated
- See lectures by Mark Lancaster(“Hadron Collider Physics”)
- QCD Lots of background events with jets
- QCD Lots of hadronic “rubbish” in signal events
- Hard scatters are largely from q-qbar or glue-glue
- Proton structure is important – See lectures by Robert Thorne
- But they provide the highest energies available
- Often these are the discovery machines

proton

proton

LHCb

- Asymmetric detector for B-meson physics

For more information see Lazzeroni talk at:

http://indico.cern.ch/conferenceDisplay.py?confId=5426

LHCb Physics

Quark flavour e-states are not the same as mass e-states: mixing:

- VCKM must be unitary: V.V† = V †.V = 1
- Multiply out rows & columns:

Do this!

LHCb Physics

- Measurements of decay rates and kinematics tell us about squark mixings
- Over-constraining triangles gives sensitivity to new physics through loop effects

Signals for QGP:

Jet quenching

Quarkonim (e.g. J/ψ) suppression(“melt bound states”)

Designed to examine collisions of heavy ions(e.g. lead-lead or gold-gold)

Theorised to produce a new state of matter – a quark-gluon plasma

Quarks no longer confined inside colourless baryons

ALICEQGP

Jet

No Jet

c

_

J/ψ

c

Couplings of the SM Higgs

- Couplings proportional to mass
- What does this mean for the Higgs-hunter?

Producing a Higgs

- Higgs couplings mass
- u-ubar Hhas very small cross-section
- Dominant production via vertices coupling Higgs to heavy quarks or W/Z bosons

Decay of the SM Higgs

- Width becomes large as WW mode opens
- Branching ratios change rapidly as new channels become kinematically accessible

QCD jet productionat high energy

Higgs production

- Need to use signatures with small backgrounds:
- Leptons
- High-mass resonances
- Heavy quarksto avoid being overwhelmed

e-

Z

q

_

H

q

e+

Z

e-

Example 1 : H ZZ- Only works when mHiggs >~ 2.MZ
- When the Z decays to leptons there are small backgrounds

e-

Z

q

_

H

q

e+

Z

e-

H ZZ e+e- e+e-mH=150

background

mH=130

mH=170

- Find events consistent with above topology(four electrons)
- Add together the fourelectron 4-vectors
- Find the mass of the resultant4-vector ( mass of the Higgs)

Plot shows simulated distributions of [invariant mass of four electrons] for 3 different values of mHiggs(We wouldn’t see all of these together!)

Example (2): H γγ

- No direct coupling of H to photon
- However allowed at loop level
- Branching ratio: ~ 10 -3(at low mHiggs)
- Important at low mass
- Actually a very clean way of looking for Higgs
- Small backgrounds

Production and decay of Higgsthrough ‘forbidden’ direct couplings

H γγ

- Simulation by CMS for different Higgs massesfor early LHC data (1 fb-1)

Higgs signalscaled up by factor 10!

Invariant mass of the pair of photons

q

H γγ … backgrounds“Irreducible”2 real photons

“Born”

“Box”

“Reducible”

e.g. fake photons

γ

q

Need v. good calorimetersegmentationto separate these

γ

γ

π0

gluon

Significance

Significance is a measureof the answer to the question“What is the probabilitythat a backgroundfluctuation would producewhat I am seeing”

H->ZZ

5- means “probabilitythat backgroundfluctuation does this is less than 2.85·10-7 ”

5- is usually takenas benchmarkfor “discovery”

After discovery of Higgs?

- Measure Higgs mass
- The remaining unconstrained parameter of the Standard Model
- Measure Higgs couplings to fermions and vector bosons
- All predicted by Standard Model
- Check Higgs mechanism
- Couplings very important since there may be more than one Higgs boson
- Theories beyond the Standard Model (such as Supersymmetry) predict multiple Higgs bosons.
- In such models the couplings would be modified
- Do direct searches for further Higgs bosons!

If no Higgs found?

- Arguably more exciting than finding Higgs
- Look at WW scattering process
- Look for whatever is “fixing” the cross-section
- E.g. exotic resonances

Nature permits only particular types of symmetry:

Space & time

Lorentz transforms

Rotations and translations

Gauge symmetry

Such as Standard Model force symmetries

SU(3)c x SU(2)L x U(1)

Supersymmetry

Anti-commuting (Fermionic) generators

Changes Fermions into Bosons and vice-versa

Consequences?

Supersymmetric theory has a Boson for every Fermion and vice-versa

Doubles the particle content

Partners to Standard Model particles not yet observed

Examples of Supersymmetric partner-states

What is supersymmetry?(S)Particles

StandardModel

Supersymmetricpartners

quarks (L&R)leptons (L&R) neutrinos (L&?)

squarks (L&R)sleptons (L&R)sneutrinos (L&?)

Spin-1/2

Spin-0

AfterMixing

Z0W±

gluon

BinoWino0Wino±

gluino

BW0

Spin-1

4 x neutralino

Spin-1/2

gluino

~

h0

H0

A0

H±

H0H±

~

2 x chargino

Spin-0

(Higgsinos)

Extended higgs sector 2 cplx doublets 8-3 = 5 Higgs bosons!

Higgs mass

Quantum corrections to mH

Would make “natural” mass near cut-off (Unification or Planck scale)

But we know mH <~ 1 TeV

mH = mH bare + DmH

Severe fine tuning required between two very big numbers

Enter Supersymmetry (SUSY)

Scalar partner of quarks also provide quantum corrections

Factor of -1 from Feynman rules

Same coupling, λ

Quadratic corrections cancel

mH now natrually at electroweak scale

stop

top

λ

λ

λ

λ

higgs

higgs

higgs

higgs

Δm2(h) Λ2cutoff

Why Supersymmetry?Quantum correction to mHiggs

Cancelling correction to mHiggs

Further advantages

Big Bang relic abundance calculations are in good agreement with WMAP microwave background observations in regions of SUSY parameter space

- Lightest SUSY particle is:
- Light
- Weakly interacting
- Stable
- Massive
- Good dark matter candidate
- Predicts gauge unification
- Extra particles modify running of couplings
- Step towards “higher things”

1/α

1/α

+SUSY

miss

Hit!

SM

Log10 (μ / GeV)

Log10 (μ / GeV)

R-parity

- Multiplicative discrete quantum number
- RP= (-1)2s+3B+L
- S=spin, B=baryon number, L=lepton number
- Standard Model particles have RP = +1
- SUSY Model particles have RP = -1
- If RP is conserved then SUSY particles must be pair-produced
- If RP is conserved then the Lightest Supersymmetric Particle (LSP) is stable

Example of a Feynmandiagram for proton decaywhich is allowed if the RP-violating couplings (λ) are not zero

How is SUSY broken?

Weakcoupling

(mediation)

- Direct breaking in visible sector not possible
- Would require squarks/sleptons with mass < mSM
- Not observed!
- Must be strongly broken “elsewhere” and then mediated
- Soft breaking terms enter in visible sector
- (>100 parameters)

Strongly

broken

sector

Soft SUSY-breaking termsenter lagrangianin visible sector

Various models offer different mediation e.g.Gauge “GMSB”Gravity “mSUGRA” (supergravity)

Anomaly “AMSB”

Sparticle Interactions

- Interactions & couplings same as SM partners
- 2 SUSY legs for RP conservation

Largely partnerof W0 boson

Largely partnerof W0 boson

Q: Does the gluino couple to:

the quark?

the slepton?the photino?

General features

Mass/GeV

Production dominatedby squarks and gluinos

- Complicated cascade decays
- Many intermediates
- Typical signal
- Jets
- Squarks and Gluinos
- Leptons
- Sleptons and weak gauginos
- Missing energy
- Undetected Lightest Susy Particle

“typical” susy spectrum(mSUGRA)

The “real thing”(a simulation of…)

- Two high-energy jets of particles
- Visible decay products
- “Missing” momentum
- From two invisible particles
- these are the invisible Dark Matter guys

Proton beams perpendicular to screen

Example: backgroundto “4 jets + missing energy”

Measure background in control region

Extrapolate to signal region

Look for excess in signal region

m

m

n

n

Standard Model backgrounds: measure from LHC DATAμμ

With SUSY

- Measure in Z -> μμ

- Use in Z -> νν

R: Z -> nn

B: Estimated

Missing PT / GeV

Constraining SUSY masses

Frequently-

studieddecay chain

- Mass constraints
- Invariant masses in pairs
- Missing energy
- Kinematic edges

Observable:

Depends on:

Limits depend on angles betweensparticle decays

Mass determination

Measure

edges

Try various

masses in equations

C.G. Lester

- Narrow bands in ΔM
- Wider in mass scale
- Improve using cross- section information

Variety of edges/variables

These measurements can tell us about SUSY breaking

Other things to do with SUSY

- Measure the sparticle spins
- “prove” that it is really supersymmetric partners we are seeing
- Measuring the couplings & mixings
- Use to “predict” Dark Matter relic density
- Find the extra Higgs bosons
- Recall that SUSY predicts 5 Higgs bosons
- Now we want to find H0, h0, A0, H±
- Also measure their couplings, CP, …

Standard Model Physics

- The ATLAS and CMS experiments also potentially can measure:
- Top mass
- W mass
- Rare B-meson decay rates
- Jet physics
- To much higher precision that is currently achievable
- Large number of e.g. top quarks produced
- Small statistical errors
- Systematic errors (such as jet energy scale determination) limiting

Mass of hadronic top

Other things to look for…

- Leptoquarks
- Motivated by Grand Unified Theories
- Carry lepton and baryon number
- E.g. LQ bμ
- New heavy quarks
- Predicted by some non-SM Higgs theories
- New heavy gauge bosons
- Indications of new symmetry groups
- Extra dimensions
- Large variety of models on the market!

Extra dimensions models

- Motivated by need for ED in string theory and m-theory
- Logical a possibility for a LHC discovery
- Different models…
- Which particles are localised where (bulk/brane)
- Form of space-time metric (flat/warped)
- Geometry and size of extra dimensions
- …make different predictions
- Kalazua-Klein resonances of SM particles
- Graviton states
- Stringy resonances
- Effects of strong gravity (micro Black Holes)
- Energy loss into extra dimensions

More information:http://eps2003.physik.rwth-aachen.de/data/talks/parallel/09StringTheory/09Vacavant.ppt

General sources

- Higgs at the LHC: talk by Zeppenfeld http://whepp9.iopb.res.in/talks/zeppenfeld_WHEPP9.pdf
- Physics at the LHC: Higgs talk by Harlander:http://newton.ftj.agh.edu.pl/physLHC/
- ATLAS physics Technical Design Report (TDR)http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/TDR/access.html (1999)
- CMS physics Technical Design Report (TDR)http://cmsdoc.cern.ch/cms/cpt/tdr/ (2006)
- Supersymmetry: http://arxiv.org/abs/hep-ph/9709356

q

H

g

H

H

_

W/Z

g

q

top

g

top

q

W/Z

_

q

H

Producing a Higgs @ LHC- Higgs couplings mass
- Direct e.g. u-ubar H very small cross-section
- Dominant production via vertices coupling Higgs to heavy quarks or W/Z bosons

Higgs’ mechanism

- Add a complex scalar field
- In fact he adds 2 real scalar fields,

(fermion part of L now ignored)

This is gauge invariant when the scalars have covariant derivatives:

N.B. scalar field must couple to gauge field likethis for the Higgsmechanism to work

Now if the potential, V, has a degenerate minimum at φ≠0 we get interesting consequences…

mSUGRA – “super gravity”

1016 GeV

Unification of couplings

- A.K.A. cMSSM
- Gravity mediated SUSY breaking
- Flavour-blind (no FCNCs)
- Strong expt. limits
- Unification at high scales
- Reduce SUSY parameter space
- Common scalar mass M0
- squarks, sleptons
- Common fermionic mass M½
- Gauginos
- Common trilinear couplings A0
- Susy equivalent of Yukawas

Iterate using

Renormalisation

Group

Equations

EW scale

Correct MZ, MW, …

Programs include

e.g. ISASUSY,

SOFTSUSY

Other suggestions for SUSY breaking

- Gauge mediation
- Gauge (SM) fields in extra dimensions mediate SUSY breaking
- Automatic diagonal couplings no EWSB
- No direct gravitino mass until Mpl
- Lightest SUSY particle is gravitino
- Next-to-lightest can be long-lived (e.g. stau or neutralino)
- Anomaly mediation
- Sequestered sector (via extra dimension)
- Loop diagram in scalar part of graviton mediates SUSY breaking
- Dominates in absence of direct couplings
- Leads to SUSY breaking RGE β-functions
- Neutral Wino LSP
- Charged Wino near-degenerate with LSP lifetime
- Interesting track signatures

Not exhaustive!

If exotics can be produced singly they can decay

No good for Dark Matter candidate

If they can only be pair-produced they are stable

Only disappear on collision (rare)

standard

standard

exotic

exotic

Time

Time

exotics

standard

standard

exotics

Time

Time

Producing exotics?No RP

With RP

Require an even number of exotic legs to/from blobs

(Conserved multiplicative quantum number)If we want a good dark matter candidate

Decay part

Time

heavyexotic

lighterexotic

standard

Time

= exotic

= standard

How do they then behave?Production part

- Events build from blobs with 2 “exotic legs”
- A pair of cascade decays results
- Complicated end result

standard

2 exotics

Time

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