1. LHC Physics
Alan Barr UCL

2. This morning’s stuff… Higgs – why we expect it, how to look for it, …
Supersymmetry – similar questions!
Smorgasbord of other LHC physics

3. Physics at TeV-scale
Dominated by the physics of Electroweak 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

4. 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

5. 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

6. Pictorial representation
Excitations in this direction produce physical Higgs boson
Quartic term  self- coupling positive
Excitations in this direction = gauge transformation - Global transformations unobserved - Local transformations give mass to gauge bosons
Quadratic coupling term negative
Degenerate minimum Vacuum (field strength≠0)
If you don’t understand this, study Phys.Lett.12: ,1964
Scalar field strength = 0

7. Higgs field “eats Goldstone boson”φ φ
Flat direction in potential usually represents zero-mass particle
“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'
Gauge boson
Example of a Feynman diagram showing a contribution to the gauge boson 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

8. Constraints on the Higgs mass
Higgs boson mass is the remaining unpredicted parameter in Standard Model:
Higgs self-couplings not predicted
So Higgs mass not 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

9. 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

10. Indirect Higgs bounds: LEP Electroweak data
W (and Z) mass depends on mHiggs
Logarithmic loop corrections to masses
Also depends on top mass
Measurements
Prediction as a function of mH

11. Direct bounds: Higgs searches @ LEP
Higgsstrahlung – dominant production
No discovery
Direct lower bound at GeV
ALEPH: Candidate vertex:
Phys.Lett. B565 (2003) 61-75

12. 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: GeV < mSM Higgs < 199 GeV

14. The Large Hadron Collider
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
Proton on Proton at √s = 14 TeV Design luminsoity ~
~100 fb-1 / expt / year

15. General Purpose Detectors
Similarities:
Tracker
Calorimeter
Muon chambers
ATLAS
Differences: Size : CMS “compact”
Magnetic-field configuration ATLAS has muon toroids Electromagnetic-Calorimeter:
CMS crystals. ATLAS Liquid Argon Outer tracker technology
CMS all-silicon. ATLAS straw tubes

16. Definitions * * *prove these! y φ Particle x θ Beam pipe proton proton
η = -1
η = 0
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 conserved under Lorentz boosts in the z-direction
Rapidity: *
Pseudorapidity:
Good approximation to rapidity if E>>m *
pT = (px, py)
“Transverse”
|pT| = √(px2, py2)
*prove these!

17. Making particles in hadron colliders
proton
proton
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

18. LHCb Asymmetric detector for B-meson physics
For more information see Lazzeroni talk at:

19. LHCb Physics VCKM must be unitary: V.V† = V †.V = 1
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!

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

21. ALICE
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
Signals for QGP:
Jet quenching
Quarkonim (e.g. J/ψ) suppression (“melt bound states”)
QGP
Jet
No Jet c _
J/ψ c

23. Couplings of the SM Higgs
Couplings proportional to mass
What does this mean for the Higgs-hunter?

24. Producing a Higgs Higgs couplings  mass
u-ubar  H has very small cross-section
Dominant production via vertices coupling Higgs to heavy quarks or W/Z bosons

25. Production cross-sections

26. Decay of the SM Higgs Width becomes large as WW mode opens
Branching ratios change rapidly as new channels become kinematically accessible

27. Needle in a haystack…
QCD jet production at high energy
Higgs production
Need to use signatures with small backgrounds:
Leptons
High-mass resonances
Heavy quarks to avoid being overwhelmed

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

29. H  ZZ CMS H  ZZ  e+e- e+e-
Electrons have track (green ) & energy deposit (pink)

30. H  ZZ  e+e- e+e- q _ H Z e+ e-
mH=150
background
mH=130
mH=170
Find events consistent with above topology (four electrons)
Add together the four electron 4-vectors
Find the mass of the resultant 4-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!)

31. Example (2): H  γγ No direct coupling of H to photon
However allowed at loop level
Branching ratio: ~ (at low mHiggs)
Important at low mass
Actually a very clean way of looking for Higgs
Small backgrounds
Production and decay of Higgs through ‘forbidden’ direct couplings

32. γ γ
H γγ CMS simulation. Physics TDR, 2006

33. H  γγ
Higgs signal scaled up by factor 10!
Invariant mass of the pair of photons
Simulation by CMS for different Higgs masses for early LHC data (1 fb-1)

34. H  γγ … backgrounds γ π0 “Irreducible” 2 real photons “Born” “Box”
e.g. fake photons γ q
Need v. good calorimeter segmentation to separate these γ q _ γ π0
gluon

35. Recent find – vector boson fusion
Tagging Jet
Smaller production cross-section
Weak couplings
But low backgrounds
Tagging Jet
No QCD COLOUR exchange between q and qbar So no QCD irradiation into central part of detector

36. Significance
Significance is a measure of the answer to the question “What is the probability that a background fluctuation would produce what I am seeing”
H->ZZ
5- means “probability that background fluctuation does this is less than 2.85·10-7 ”
5- is usually taken as benchmark for “discovery”

37. 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!

38. 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

40. What is supersymmetry?
Examples of Supersymmetric partner-states
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

41. Supersymmetric partners
(S)Particles
Standard Model
Supersymmetric partners
quarks (L&R) leptons (L&R) neutrinos (L&?)
squarks (L&R) sleptons (L&R) sneutrinos (L&?)
Spin-1/2
Spin-0
After Mixing
 Z0 W±
gluon
B W0
Bino Wino0 Wino±
gluino
Spin-1
4 x neutralino
Spin-1/2
gluino h0 H0 A0 H± ~
H0 H± ~
2 x chargino
Spin-0
(Higgsinos)
Extended higgs sector 2 cplx doublets  8-3 = 5 Higgs bosons!

42. Why Supersymmetry? Higgs mass Enter Supersymmetry (SUSY)
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
top
Δm2(h)  Λ2cutoff
higgs λ
Quantum correction to mHiggs
stop
higgs λ
Cancelling correction to mHiggs

43. Further advantages Lightest SUSY particle is:
Weakly interacting
Stable
Massive
Good dark matter candidate
Predicts gauge unification
Extra particles modify running of couplings
Step towards “higher things”
Big Bang relic abundance calculations are in good agreement with WMAP microwave background observations in regions of SUSY parameter space
1/α
1/α
+SUSY
miss
Hit! SM
Log10 (μ / GeV)
Log10 (μ / GeV)

44. 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 Feynman diagram for proton decay which is allowed if the RP-violating couplings (λ) are not zero

45. How is SUSY broken? Direct breaking in visible sector not possible
Weak coupling
(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 terms enter lagrangian in visible sector
Various models offer different mediation e.g. Gauge  “GMSB” Gravity  “mSUGRA” (supergravity)
Anomaly  “AMSB”

46. Sparticle Interactions
Interactions & couplings same as SM partners
2 SUSY legs for RP conservation
Largely partner of W0 boson
Largely partner of W0 boson
Q: Does the gluino couple to:
the quark?
the slepton? the photino?

48. “typical” susy spectrum (mSUGRA)
General features
Mass/GeV
Complicated cascade decays
Many intermediates
Typical signal
Jets
Squarks and Gluinos
Leptons
Sleptons and weak gauginos
Missing energy
Undetected Lightest Susy Particle
Production dominated by squarks and gluinos
“typical” susy spectrum (mSUGRA)

49. The “real thing” (a simulation of…)
Invisible particles
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

50. Standard Model backgrounds: measure from LHC DATA
μ μ n
With SUSY
Measure in Z -> μμ
Use in Z -> νν
R: Z -> nn
B: Estimated
Example: background to “4 jets + missing energy”
Measure background in control region
Extrapolate to signal region
Look for excess in signal region
Missing PT / GeV

51. Constraining SUSY masses
Mass constraints
Invariant masses in pairs
Missing energy
Kinematic edges
Frequently-
studied decay chain
Observable:
Depends on:
Limits depend on angles between sparticle decays

52. Mass determination Try various masses in equations Measure edges
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

53. 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, …

54. 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

55. 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!

56. 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:

58. General sources
Higgs at the LHC: talk by Zeppenfeld
Physics at the LHC: Higgs talk by Harlander:
ATLAS physics Technical Design Report (TDR) (1999)
CMS physics Technical Design Report (TDR) (2006)
Supersymmetry:

59. Constraints on mHiggs No perturbative unitarity Unstable vacuum
Scale at which new physics enters

60. Producing a Higgs @ LHC Higgs couplings  mass
top H g
top H g
W/Z H q _
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
W/Z H q _

61. 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 like this for the Higgs mechanism to work
Now if the potential, V, has a degenerate minimum at φ≠0 we get interesting consequences…

62. mSUGRA – “super gravity”
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
1016 GeV
Unification of couplings
Iterate using
Renormalisation
Group
Equations
EW scale
Correct MZ, MW, …
Programs include
e.g. ISASUSY,
SOFTSUSY

63. 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!

64. Producing exotics? If exotics can be produced singly they can decay
Time
standard
exotic
Time
standard
exotic
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)
No RP
Time
standard
exotics
Time
standard
exotics
With RP
Require an even number of exotic legs to/from blobs
(Conserved multiplicative quantum number) If we want a good dark matter candidate

65. How do they then behave? Production part Complete “event” Decay part
Time
Complete “event”
standard
2 exotics
Time
Time
standard
heavy exotic
lighter exotic
Decay part
Events build from blobs with 2 “exotic legs”
A pair of cascade decays results
Complicated end result
= exotic
= standard