Transcript Document 7205029

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
Lecture 1
• Introduction to the Standard Model
– Just the SU(2) x U(1) part (See Petriello lecture)
• My favorite references:
– A. Djouadi, The Anatomy of Electroweak Symmetry
Breaking, hep-ph/0503172
– 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/9901280
– David Rainwater, TASI2006, hep-ph/0702124
What we know
• The photon and gluon are massless
• The W and Z gauge bosons are heavy
– MW=80.399  0.025 GeV
– MZ =91.1875  0.0021 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
Standard Model Synopsis
• Group: SU(3) x SU(2) x U(1)
QCD
Electroweak
• Gauge bosons:
– SU(3): Gi, i=1…8
– SU(2): Wi, i=1,2,3
– U(1):
B
Gauge bosons
are massless
• Gauge couplings: gs, g, g
• SU(2) Higgs doublet: 
Massless gauge bosons have 2
transverse degrees of freedom
Fermions come in generations
u 
  u R , d R ,
 d L
 
  , eR
 e L
c
 
  cR , s R ,   ,  R
 s L
  L
t 
 
  t R , bR ,   ,  R
 b L
  L
Except for
masses, the
generations
are identical
 L,R
1  5

2
Masses for Gauge Bosons
• Why are the W and Z boson masses non-zero?
• U(1) gauge theory with single spin-1gauge field, A
1
L   F F 
4
F   A    A
• U(1) local gauge invariance:
A ( x)  A ( x)    ( x)
• Mass term for A would look like:
1
1
L   F F   m 2 A A
4
2
• Mass term violates local gauge invariance
• We understand why MA = 0
Gauge invariance is guiding principle
Abelian Higgs Model
Add a scalar to U(1) gauge theory
2
1

L   F F  D   V ( )
4
D     ieA
 
V ( )      
2
2
2 2
• Case 1: 2>0
– QED with MA=0 and m=
– Unique minimum at =0
By convention,  > 0
Abelian Higgs Model
• Case 2: 2 < 0
 
V ( )       
2
2
2 2
• Minimum energy state at:
2
v
   

2
2
Vacuum breaks U(1) symmetry
Aside: What fixes sign (2)?
Abelian Higgs Model
• Rewrite
1
v  H 

2
• L becomes:


1
e 2v 2 
1

L   F F 
A A    H  H  2 2 H 2  ( H self  interactio ns )
4
2
2
• 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
SM Higgs Mechanism
• Standard Model includes complex Higgs SU(2)
doublet
1 1  i2    

   0 

2 3  i4    
• With SU(2) x U(1) invariant scalar potential
V   2     (  ) 2
• If 2 < 0, then spontaneous symmetry breaking
i  / v
• Minimum of potential at:
0

e

j
j
2


v  H 
– Choice of minimum breaks gauge symmetry
More on SM Higgs Mechanism
• Couple  to SU(2) x U(1) gauge bosons (Wi,
i=1,2,3; B)
LS  ( D  )  ( D   )  V ()
g i i
g'
D     i  W   i B
2
2
• Gauge boson mass terms from:
1
a a
b b
  0
( D ) D   ...  0, v ( gW   g B )( gW   g B )   ...
8
v 


v2 2 1 2
 ...  g (W )  g 2 (W2 ) 2  ( gW3  g B ) 2   ...
8
SM Higgs Mechanism
• Massive gauge bosons:
W 
gv
MW 
2
g 2  g '2 v
MZ 
2
Z 0 
W1  W2
2
gW3  g ' B
g 2  g '2
• Orthogonal combination to Z is massless
photon:
g 'W  gB
3
A 
0
g g
2
'2
cos W 
g
g 2  g '2
MW

MZ
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:

1 2   2
D   g W W v  2vH  H 2
4
2

WWH coupling requires non-zero v!
Muon Decay
Consider  e e
• Fermi Theory:
• EW Theory:




W
e
e
1  5 
 1  5 
 i 2 2GF g  u   
u  u e  
ue
 2 
 2 

e
e
ig 2
1
 1  5 
 1  5 
g
u

u
u




ue




2
2

e
2 k  MW
 2 
 2 
For k<< MW, 22GF=g2/2MW2
Higgs Parameters
• GF measured precisely
GF
g2
1

 2
2
2v
2 8M W
v 2  ( 2GF ) 1  (246 GeV ) 2
• Higgs potential has 2 free parameters, 2, 
V   2     (  ) 2
2

2
2
2
• Trade  ,  for v , MH
v2  
2
V
2
2
MH
M
M
H 2  H H 3  H2 H 4
2
2v
8v
MH
2
2
 2v 2 
– Large MH  strong Higgs self-coupling
– A priori, Higgs mass can be anything
What about Fermion Masses?
• Fermion mass term:
L  m  mL R  R L  
Forbidden by
SU(2)xU(1) gauge
invariance
• Left-handed fermions are SU(2) doublets
u 
QL   
 d L
• Scalar couplings to fermions:
Ld  d QL d R  h.c.
• Effective Higgs-fermion coupling
Ld  d
 0 
1
d R  h.c.
(u L , d L )
2
v  H 
• Mass term for down quark
d  
Md 2
v
Fermion Masses
• Mu from c=i2* (not allowed in SUSY)
L  u QL  cu R  hc
 0 
 c    
 
Mu 2
u  
v
• For 3 generations, , =1,2,3 (flavor indices)
(v  H )
  
  
LY  

u
u



u
L R
d d L d R  h.c.
2  ,


Diagonalizing mass matrix also diagonalizes
Higgs-fermion couplings: No FCNCs from Higgs
Review of Higgs Couplings
• Higgs couples to fermion mass
– Largest coupling is to heaviest fermion
mf
mf
L
ffH  
fL fR  fR fL H
v
v
– Top-Higgs coupling plays special role?
– No Higgs coupling to neutrinos


• Higgs couples to gauge boson masses
gM Z 
No coupling to photon
L  gM W W W H 
Z Z  H  ....
or gluon at tree level
cos W


• Only free parameter is Higgs mass!
• Everything is calculable….testable theory
Higgs Searches at LEP2
• LEP2 searched for e+e-ZH
• Rate turns on rapidly after
threshold, peaks just above
threshold, 3/s
 
e e  ZH
• 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 > 114.1 GeV
SM Parameters
• Four free parameters in gauge-Higgs sector
– Conventionally chosen to be
• =1/137.0359895(61)
• MZ=91.1875  0.0021 GeV
• GF =1.16637(1) x 10-5 GeV -2
• MH
– Express everything else in terms of these
parameters
GF
g2



2
 M W2
2 8M W
21  2
 MZ
 2
 M W

 Predicts MW
Radiative Corrections and the SM
• Tree level predictions aren’t adequate to
explain data
 
2
– SM predicts MW M W   2 1  1  4
GF 
– Plug in numbers:
• MW (predicted) = 80.939 GeV
• MW(experimental) =80.399 0.025 GeV
– Need to calculate beyond tree level
• Loop corrections sensitive to MH, Mt


2GF M Z2 
1
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
  ( p 2 )  g  ( p 2 )  B( p 2 ) p p
Taylor expand around p2=MZ2 and keep first 2 terms
S,T,U
WnewW (0)  new
ZZ (0)
T 

2
MW
M Z2
aka 

2
new
 new
(
M
)

ZZ
Z
ZZ (0)
S

2 2
2
4sW cW
MZ
M Z2

WnewW ( M W2 ) WnewW (0)
S  U  

2
2
4sW
MW
M W2
Advantages: Easy to calculate
Valid for many models
Higgs and Top Contributions to T
• Calculate in unitary gauge and in n=4-2
dimensions
H
i
A
VV
1 d nk
i
( p )  (igVVHH g ) 
2 (2 ) n k 2  M H2

2

V=W,Z
 ig VVHH g

M H2  1  42 
 (1   )
  1
2 
32 2  
M
 H 
  k  k
d nk
1
g 
i VV ( p )  (igVVH ) 
n
2
2 
(2 ) k  M V 
M V2
B
2
2
 g
2
VVH
g

i  4
 2
2 
16  M H
2


1

2
2
 (k  p)  M H
 3 1  1  p 2

M H2 

 (1   )
   1

2
2 

 4     12M V 4M V 
Higgs Contribution to T
• For Z: gZZHH=g2/(2 cos2 W), gZZH=gMZ/cos W
 4
g M
 2
 ZZ ( p  0)  
2
16 cos W  M H
2
2
2
Z
2
2


31
 (1   )
4

• MH2 pieces cancel!
• For W: gWWHH=g2/2 , gWWH=gMW

2


g
M
4

31
2
 2  (1   )
W W ( p  0)  
16  M H 
4
2
2
W
2
W W (0)  ZZ (0)
3
T 


2
2
MW
MZ
16 cos 2 W
1
 2
  log  2
M

 H


 


e2
4
g 

2
sin W sin 2 W
2
a  1   log( a)
1/ cancelled by contributions from W, Z loops, etc
Top Quark Contribution to T
• Top quark contributions to T
 ZZ (0) 
W W (0) 
GF M
2
2
W
GF M
2
2
W

 42  M t2
Nc


2
2 
2 
4 cos W  M t  
N c  4

2 
4  M t2
2

T 

1 1
 M t2   
 2

Quadratic dependence on Mt
GF N c
2
M
t
2
2 8
Limits on S & T
• A model with a heavy
Higgs requires a
source of large
(positive) T
T  
• Fit assumes MH=150
GeV
Loops Modify Tree Level Relations
GF
g2



2
 M W2  2
2 8M W
21  2  M W 1  r 
 MZ 
•r is a physical quantity which incorporates 1-loop
corrections
•Contributions to r from top and Higgs loops
11GF M W2
r 
24 2 2
H
 M H2 5 
 ln 2  
 MW 6 
2
2

3
G
M
cos
W
t
F
t

r  
2
8 2 2  sin W



Extreme sensitivity to Mt
Top Quark Mass Restricts Higgs Mass
• Data prefer a light Higgs
MW (GeV)
Assumes SM
Mt (GeV)
Precision Measurements Limit MH
LEP EWWG (March, 2009):
2
• Mt=173.1  1.3 GeV
• MH=90+36-27 GeV (68% CL)
• MH < 163 GeV (one-sided 95%
CL)
• MH < 191 GeV (Precision
measurements plus direct search
limit)
MH (GeV)
Best fit in region excluded by direct searches
Limits move with top quark mass/ inclusion of different data
Tevatron Limits Have Impact on MH
2
Higgs limit including Tevatron and LEP direct searches:
Gfitter, March 2009
MH (GeV)
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
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
Gluon Fusion
• Lowest order cross section
 4M
q F1/ 2  M

2
q
2
H
Light Quarks:
F1/2(Mb/MH)2log(Mb/MH)
Heavy Quarks: F1/2 -4/3
2

  ( M H 2  sˆ)


|F1/2|2
 ( )
ˆ 0 ( gg  H )  s R 2
1024v
2
4Mq2/MH2
• Rapid approach to heavy quark limit
• NNLO corrections calculated in heavy top limit
Vector Boson Fusion
•
W+W-
X is a real process:  ppW W X (s)   dz
dL
dz
 W W X ( zs )
pp / W W
• 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:
d
d

 (k 2  MW 2 )2  (2EE' (1  cos )  MW 2 )2
Peaks at small 
• Outgoing jets are mostly forward and can be tagged
H
k=W,Z momentum
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
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1.3-1.4
Electroweak corrections known (-5%)
Small scale dependence (3-5%)
Small PDF uncertainties
Improved scale dependence at NNLO
• Hff proportional to Mf2
 M b2 
BR ( H  bb )
 N c  2 
 
BR ( H    )
 M 
• Identifying b quarks
important for Higgs
searches
H Branching Ratios
Higgs Decays
MH (GeV)
For MH<2MW, decays to bb most important
Higgs Decays to Photons
• Dominant contribution is W loops
• Contribution from top is small
 3 M H3
16
( H   ) 
7   ...
2 2
2
256 s M W
9
W
top
2
Higgs Decays to W/Z
W+
• Tree level decay


( H  W W ) 
 M H3
16s2 M W2
3 

1  xW 1  xW  xW2 
4 

H
A  gM W   (M
pW)    ( p )
xW  4
2
M H2
• Below threshold, H→WW* with
branching ratio W* →ff' implied
• Final state has both transverse and
longitudinal polarizations
W+
H
W-
W-
f
f'
• H W+W- ffff has
sharp threshold at
2 MW, but large
branching ratio
even for MH=130
GeV
H Branching Ratios
Higgs decays to gauge bosons
MH (GeV)
For any given MH, not all decay modes accessible
Higgs Decays to W+ W-, ZZ
• The action is with longitudinal gauge bosons
(since they come from the EWSB)

pV  ( EV ,0,0, pV )
1
0,1,i,0
T 
2
pV
1 
 pV ,0,0, EV  
L 
MV
MV
• Cross sections involving longitudinal gauge
bosons grow with energy
• H→WL+WLM H2
A( H  W W )  gM W  L ( p )   L ( p )  g
MW

L

L


• As Higgs gets heavy, decays are longitudinal
xV2
( H  VTVT )

( H  VLVL ) 2  xV2
M W2
xW  4 2
MH
H Decay Width (GeV)
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
MH (GeV)

3
MH
( H  W W ) 
16 sin 2 W M W 2


 M 
 330GeV  H 
 1TeV 
3
Producing the Higgs at the Tevatron
Tevatron
 (pb)
Aside: Tevatron
analyses now
based on 4 fb -1
MH/2 <  < MH/4
NNLO or NLO rates
MH (GeV)
New cross section calculations affect Tevatron Higgs
bound: See Petriello lecture
Higgs at the Tevatron
• Largest rate, ggH, H bb, is overwhelmed by
background
(ggH)1 pb << (bb)
MH (GeV)
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
SM Higgs Searches at Tevatron
MH (GeV)
SM Higgs Searches at Tevatron
• Assumes SM!!!!
How Far Will Tevatron Go?
Now have 6 fb -1; expect 10 fb -1 by 2010
Luminosity/experiment (fb-1)
MH (GeV)
Projections assume improvements in analysis/detector
Production Mechanisms at LHC
 (pb)
Bands show scale
dependence
All important
channels calculated
to NLO or NNLO
MH (GeV)
See Petriello lecture
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
H→: A Few Years Ago….
MH=120 GeV; L=100 fb-1
H→: Today’s Reality
Aside: CMS slightly more optimistic
ATL-PHYS-PROC-2008-014
Golden Channel: H→ZZ→4 leptons
• Need excellent lepton ID
• Below MH 130 GeV, rate is too small for discovery
H→ZZ→(4 leptons)
CMS:
Possible discovery with < 10 fb-1
Heavy Higgs in 4-lepton Mode
H  ZZ  l+l- l+l-
- 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
200 GeV < MH < 600 GeV:
MH (GeV)
H  ZZ  4l
*
• Data-driven methods to estimate backgrounds
• 5σ discovery with less than 30 fb-1
Significance
Significance
Preliminary

CMS
H  4
No systematic
errors
MH (GeV)
MH (GeV)

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
CMS SM Higgs, 2008
•Improvement in  channel from earlier studies
•Note: no tth discovery channel
ATLAS SM Higgs, 2008
• Observation: VBF H, HWWll, and
HZZ4l
ATLAS preliminary
MH(GeV)
ATLAS SM Higgs, 2008
Discovery:
5σ
• 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
Luminosity numbers include estimates of systematic effects and uncertainties
Herndon, ICHEP 2008
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
Early LHC Data
What if the LHC Energy is Lower?
Is it the Higgs?
• Measure couplings to fermions & gauge bosons
 ( H  bb )
mb

3
2
( H     )
m
2
• Measure spin/parity
J PC  0  
• Measure self interactions
2
2
2
M
M
M
V  H H 2  H H 3  H2 H 4
2
2v
8v
Need good
ideas here!
Higgs Couplings Difficult
Extraction of couplings
requires
understanding NLO
QCD corrections for
signal & background
Ratios of couplings
easier
Logan et al, hep-ph/0409026; LaFaye et al, hep-ph/0904.3866