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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=173.11.3 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): Gi, i=1…8
– SU(2): Wi, 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 –22 > 0
Gauge invariant mechanism to give mass to spin-1 boson
SM Higgs Mechanism
• Standard Model includes complex Higgs SU(2)
doublet
1 1 i2
0
2 3 i4
• 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 (W2 ) 2 ( gW3 g B ) 2 ...
8
SM Higgs Mechanism
• Massive gauge bosons:
W
gv
MW
2
g 2 g '2 v
MZ
2
Z 0
W1 W2
2
gW3 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, 22GF=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 mL 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=i2* (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
21 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 42
(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
42 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
21 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
1024v
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: ppW 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 (qqWH, ZH) important at
Tevatron
– Same couplings as vector boson fusion
– Rate proportional to weak coupling
• Theoretically very clean channel
–
–
–
–
NNLO QCD corrections: KQCD1.3-1.4
Electroweak corrections known (-5%)
Small scale dependence (3-5%)
Small PDF uncertainties
Improved scale dependence at NNLO
• Hff 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
16s2 M W2
3
1 xW 1 xW xW2
4
H
A gM W (M
pW) ( 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, ggH, H bb, is overwhelmed by
background
(ggH)1 pb << (bb)
MH (GeV)
Looking for the Higgs at the Tevatron
MH (GeV)
• High mass: Look for HWWll
Large ggH production rate
• Low Mass: Hbb, 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
ggHbb has huge QCD background: Must use
rare decay modes of H
• ggH
– 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, HWWll, and
HZZ4l
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