1. Standard Model and Higgs Physics SLAC SUMMER INSTITUTE, 2009 Sally Dawson, BNL
Introduction to the Higgs Sector
Review of the SU(2) x U(1) Electroweak theory
Constraints from Precision Measurements
Searching for the Higgs Boson
Theoretical problems with the Standard Model

2. Lecture 1 Introduction to the Standard Model My favorite references:
Just the SU(2) x U(1) part (See Petriello lecture)
My favorite references:
A. Djouadi, The Anatomy of Electroweak Symmetry Breaking, hep-ph/
Chris Quigg, Gauge Theories of the Strong, Weak, and Electromagnetic Interactions
Michael Peskin, An Introduction to Quantum Field Theory
Sally Dawson, Trieste lectures, hep-ph/
David Rainwater, TASI2006, hep-ph/

3. What we know The photon and gluon are massless
The W and Z gauge bosons are heavy
MW=  GeV
MZ =  GeV
There are 6 quarks
Mt=173.11.3 GeV
Mt >> all the other quark masses
There are 3 distinct neutrinos with small but non-zero masses
The pattern of fermions appears to replicate itself 3 times

4. Standard Model Synopsis
Group: SU(3) x SU(2) x U(1)
Gauge bosons:
SU(3): Gi, i=1…8
SU(2): Wi, i=1,2,3
U(1): B
Gauge couplings: gs, g, g
SU(2) Higgs doublet: 
QCD
Electroweak
Gauge bosons are massless
Massless gauge bosons have 2 transverse degrees of freedom

5. Fermions come in generations
Except for masses, the generations are identical

6. Masses for Gauge Bosons
Why are the W and Z boson masses non-zero?
U(1) gauge theory with single spin-1gauge field, A
U(1) local gauge invariance:
Mass term for A would look like:
Mass term violates local gauge invariance
We understand why MA = 0
Gauge invariance is guiding principle

7. Abelian Higgs Model Add a scalar to U(1) gauge theory Case 1: 2>0
QED with MA=0 and m=
Unique minimum at =0
By convention,  > 0

8. Abelian Higgs Model Case 2: 2 < 0 Minimum energy state at:
Vacuum breaks U(1) symmetry
Aside: What fixes sign (2)?

9. Abelian Higgs Model Rewrite L becomes: Theory now has:
Photon of mass MA=ev
Scalar field H with mass-squared –22 > 0
Gauge invariant mechanism to give mass to spin-1 boson

10. SM Higgs Mechanism Standard Model includes complex Higgs SU(2) doublet
With SU(2) x U(1) invariant scalar potential
If 2 < 0, then spontaneous symmetry breaking
Minimum of potential at:
Choice of minimum breaks gauge symmetry

11. More on SM Higgs Mechanism
Couple  to SU(2) x U(1) gauge bosons (Wi, i=1,2,3; B)
Gauge boson mass terms from:

12. SM Higgs Mechanism Massive gauge bosons:
Orthogonal combination to Z is massless photon:

13. Higgs Mechanism in a Nutshell
Higgs doublet had 4 free parameters
3 are absorbed to give longitudinal degrees of freedom to W+, W-, Z
1 scalar degree of freedom remains
This is physical Higgs boson, H
Necessary consequence of Higgs mechanism
Smoking gun for Higgs mechanism:
WWH coupling requires non-zero v!

14. Muon Decay  Consider  e e Fermi Theory: EW Theory:    W e
For k<< MW, 22GF=g2/2MW2

15. Higgs Parameters GF measured precisely
Higgs potential has 2 free parameters, 2, 
Trade 2,  for v2, MH2
Large MH  strong Higgs self-coupling
A priori, Higgs mass can be anything

16. What about Fermion Masses?
Forbidden by SU(2)xU(1) gauge invariance
Fermion mass term:
Left-handed fermions are SU(2) doublets
Scalar couplings to fermions:
Effective Higgs-fermion coupling
Mass term for down quark 

17. Fermion Masses Mu from c=i2* (not allowed in SUSY)
For 3 generations, , =1,2,3 (flavor indices)
Diagonalizing mass matrix also diagonalizes Higgs-fermion couplings: No FCNCs from Higgs

18. Review of Higgs Couplings
Higgs couples to fermion mass
Largest coupling is to heaviest fermion
Top-Higgs coupling plays special role?
No Higgs coupling to neutrinos
Higgs couples to gauge boson masses
Only free parameter is Higgs mass!
Everything is calculable….testable theory
No coupling to photon or gluon at tree level

19. Higgs Searches at LEP2 LEP2 : MH > 114.1 GeV
LEP2 searched for e+e-ZH
Rate turns on rapidly after threshold, peaks just above threshold, 3/s
Measure recoil mass of Higgs; result independent of Higgs decay pattern
Pe-=s/2(1,0,0,1)
Pe+=s/2(1,0,0,-1)
PZ=(EZ, pZ)
Momentum conservation:
(Pe-+Pe+-PZ)2=Ph2=MH2
s-2 s EZ+MZ2= MH2
LEP2 : MH > GeV

20. SM Parameters Four free parameters in gauge-Higgs sector
Conventionally chosen to be
=1/ (61)
MZ=  GeV
GF = (1) x 10-5 GeV -2 MH
Express everything else in terms of these parameters
 Predicts MW

21. Radiative Corrections and the SM
Tree level predictions aren’t adequate to explain data
SM predicts MW
Plug in numbers:
MW (predicted) = GeV
MW(experimental) = 0.025 GeV
Need to calculate beyond tree level
Loop corrections sensitive to MH, Mt

22. S,T,U formalism
Suppose “new physics” contributes primarily to gauge boson 2 point functions
Also assume “new physics” is at scale M>>MZ
Two point functions for  , WW, ZZ, Z
Taylor expand around p2=MZ2 and keep first 2 terms

23. S,T,U
aka 
Advantages: Easy to calculate
Valid for many models

24. Higgs and Top Contributions to T
Calculate in unitary gauge and in n=4-2 dimensions H
V=W,Z

25. Higgs Contribution to T
For Z: gZZHH=g2/(2 cos2 W), gZZH=gMZ/cos W
MH2 pieces cancel!
For W: gWWHH=g2/2 , gWWH=gMW
1/ cancelled by contributions from W, Z loops, etc

26. Top Quark Contribution to T
Top quark contributions to T
Quadratic dependence on Mt

27. Limits on S & T
A model with a heavy Higgs requires a source of large (positive) T
Fit assumes MH=150 GeV

28. Loops Modify Tree Level Relations
r is a physical quantity which incorporates 1-loop corrections
Contributions to r from top and Higgs loops
Extreme sensitivity to Mt

29. Top Quark Mass Restricts Higgs Mass
Data prefer a light Higgs
Assumes SM
MW (GeV)
Mt (GeV)

30. Precision Measurements Limit MH
LEP EWWG (March, 2009):
Mt=173.1  1.3 GeV
MH= GeV (68% CL)
MH < 163 GeV (one-sided 95% CL)
MH < 191 GeV (Precision measurements plus direct search limit)
2
MH (GeV)
Best fit in region excluded by direct searches
Limits move with top quark mass/ inclusion of different data

31. Tevatron Limits Have Impact on MH
Higgs limit including Tevatron and LEP direct searches:
2
MH (GeV)
Gfitter, March 2009

32. Higgs production at Hadron Colliders
Many possible production mechanisms; Importance depends on:
Size of production cross section
Size of branching ratios to observable channels
Size of background
Importance varies with Higgs mass
Need to see more than one channel to establish Higgs properties and verify that it is a Higgs boson

33. Production Mechanisms in Hadron Colliders
Gluon fusion
Largest rate for all MH at LHC and Tevatron
Gluon-gluon initial state
Sensitive to top quark Yukawa t
Largest contribution is top loop
In SM, b-quark loops unimportant

34. Gluon Fusion Lowest order cross section |F1/2|2 4Mq2/MH2
Light Quarks: F1/2(Mb/MH)2log(Mb/MH)
Heavy Quarks: F1/2 -4/3
|F1/2|2
4Mq2/MH2
Rapid approach to heavy quark limit
NNLO corrections calculated in heavy top limit

35. Vector Boson Fusion W+W- X is a real process:
Rate increases at large s: (1/ MW2 )log(s/MW2)
Integral of cross section over final state phase space has contribution from W boson propagator:
Outgoing jets are mostly forward and can be tagged
Peaks at small  H
k=W,Z momentum

36. Vector Boson Fusion
Idea: Tag 2 high-pT jets with large rapidity gap in between
No color flow between tagged jets – suppressed hadronic activity in central region

37. W(Z)-strahlung W(Z)-strahlung (qqWH, ZH) important at Tevatron
Same couplings as vector boson fusion
Rate proportional to weak coupling
Theoretically very clean channel
NNLO QCD corrections: KQCD
Electroweak corrections known (-5%)
Small scale dependence (3-5%)
Small PDF uncertainties
Improved scale dependence at NNLO

38. Higgs Decays Hff proportional to Mf2 H Branching Ratios
Identifying b quarks important for Higgs searches
H Branching Ratios
MH (GeV)
For MH<2MW, decays to bb most important

39. Higgs Decays to Photons
Dominant contribution is W loops
Contribution from top is small W
top

40. Higgs Decays to W/Z Tree level decay
Below threshold, H→WW* with branching ratio W* →ff' implied
Final state has both transverse and longitudinal polarizations H W- f W+ f' H W-

41. Higgs decays to gauge bosons
H W+W- ffff has sharp threshold at 2 MW, but large branching ratio even for MH=130 GeV
H Branching Ratios
MH (GeV)
For any given MH, not all decay modes accessible

42. Higgs Decays to W+ W-, ZZ
The action is with longitudinal gauge bosons (since they come from the EWSB)
Cross sections involving longitudinal gauge bosons grow with energy
H→WL+WL-
As Higgs gets heavy, decays are longitudinal

43. Total Higgs Width Small MH, Higgs is narrower than detector resolution
As MH becomes large, width also increases
No clear resonance
For MH 1.4 TeV,
tot  MH
H Decay Width (GeV)
MH (GeV)

44. Producing the Higgs at the Tevatron
Aside: Tevatron analyses now based on 4 fb -1
 (pb)
MH/2 <  < MH/4
NNLO or NLO rates
MH (GeV)
New cross section calculations affect Tevatron Higgs bound: See Petriello lecture

45. Higgs at the Tevatron
Largest rate, ggH, H bb, is overwhelmed by background
(ggH)1 pb << (bb)
MH (GeV)

46. Looking for the Higgs at the Tevatron
MH (GeV)
High mass: Look for HWWll
Large ggH production rate
Low Mass: Hbb, Huge QCD bb background
Use associated production with W or Z
Analyses use more than 70 channels

47. SM Higgs Searches at Tevatron
MH (GeV)

48. SM Higgs Searches at Tevatron
Assumes SM!!!!

49. How Far Will Tevatron Go?
Now have 6 fb -1; expect 10 fb -1 by 2010
MH (GeV)
Luminosity/experiment (fb-1)
Projections assume improvements in analysis/detector

50. Production Mechanisms at LHC
Bands show scale dependence
 (pb)
All important channels calculated to NLO or NNLO
MH (GeV)
See Petriello lecture

51. Search Channels at the LHC
ggHbb has huge QCD background: Must use rare decay modes of H
ggH
Small BR (10-3 – 10-4)
Only measurable for MH < 140 GeV
Largest Background: QCD continuum production of 
Also from -jet production, with jet faking , or fragmenting to 0
Fit background from data

52. H→: A Few Years Ago….
MH=120 GeV; L=100 fb-1

53. H→: Today’s Reality Aside: CMS slightly more optimistic
ATL-PHYS-PROC

54. Golden Channel: H→ZZ→4 leptons
Need excellent lepton ID
Below MH 130 GeV, rate is too small for discovery

55. H→ZZ→(4 leptons)
CMS:
Possible discovery with < 10 fb-1

56. Heavy Higgs in 4-lepton Mode
H  ZZ  l+l- l+l-
200 GeV < MH < 600 GeV:
- Discovery in H  ZZ  l+l- l+l-
Background smaller than signal
Higgs width larger than experimental resolution (MH > 300 GeV)
Confirmation in H  ZZ  l+l- jj
Events/7.5 GeV
MH (GeV)

57. Data-driven methods to estimate backgrounds
5σ discovery with less than 30 fb-1
No systematic errors
Preliminary
CMS
Significance
Significance
MH (GeV)
MH (GeV)

58. Vector Boson Fusion Important channel for extracting couplings
Need to separate gluon fusion contribution from VBF
Central jet veto
Azimuthal distribution of 3rd hardest jet
VBF
QCD H

59. CMS SM Higgs, 2008 Improvement in  channel from earlier studies
Note: no tth discovery channel

60. ATLAS SM Higgs, 2008 Observation: VBF H, HWWll, and HZZ4l
ATLAS preliminary
MH(GeV)

61. ATLAS SM Higgs, 2008 Discovery: Need ~20 fb-1 to probe MH=115 GeV
10 fb-1 gives 5σ discovery for 127< MH< 440 GeV
3.3 fb-1 gives 5σ discovery for 136< MH 190 GeV 5σ
Luminosity numbers include estimates of systematic effects and uncertainties
Herndon, ICHEP 2008

62. ATLAS SM Higgs, 2008 Exclusion:
2.8 fb-1 excludes at 95% CL MH = 115 GeV
2 fb-1 gives exclusion at 95% CL for 121< MH < 460 GeV
Herndon, ICHEP 2008

63. Early LHC Data

64. What if the LHC Energy is Lower?

65. Is it the Higgs? Measure couplings to fermions & gauge bosons
Measure spin/parity
Measure self interactions
Need good ideas here!

66. Higgs Couplings Difficult
Extraction of couplings requires understanding NLO QCD corrections for signal & background
Ratios of couplings easier
Logan et al, hep-ph/ ; LaFaye et al, hep-ph/