standard model and higgs physics slac summer institute, 2009 sally dawson, bnl introduction to the...
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Standard Model and Higgs PhysicsSLAC 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)
• 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:
ElectroweakQCD
Gauge bosons are massless
Massless gauge bosons have 2 transverse degrees of freedom
Fermions come in generations
R
L
RR
L
ee
dud
u,, ,
R
L
RR
L
scs
c
,, ,
R
L
RR
L
btb
t
,, ,
Except for masses, the generations are identical
2
1 5,
RL
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
AAF
FFL
4
1
)()()( xxAxA
AAmFFL 2
2
1
4
1
Gauge invariance is guiding principle
• Case 1: 2>0
– QED with MA=0 and m=– Unique minimum at =0
Abelian Higgs Model Add a scalar to U(1) gauge theory
)(4
1 2
VDFFL
2222)(
V
ieAD
By convention, > 0
Abelian Higgs Model• Case 2: 2 < 0
• Minimum energy state at:
2222)( V
22
2 v
Vacuum breaks U(1) symmetry
Aside: What fixes sign (2)?
Abelian Higgs Model
• Rewrite
• L becomes:
• Theory now has:
– Photon of mass MA=ev
– Scalar field H with mass-squared –22 > 0
Hv 2
1
)nsinteractioself(22
1
24
1 2222
HHHHAAve
FFL
Gauge invariant mechanism to give mass to spin-1 boson
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
043
21
2
1
i
i
22 )( V
Hv
e vi jj 0
2
/
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:
Bg
iWg
iD
VDDL
ii
S
22
)()()('
...)()()(8
...
...0
))((,08
1...)(
232222122
BggWWgWgv
vBggWBggWvDD bbaa
SM Higgs Mechanism
• Massive gauge bosons:
• Orthogonal combination to Z is massless photon:
Z
WW M
M
gg
g
2'2cos
2
22'2 vgg
M
gvM
Z
W
2'2
30 '
gg
gBWgA
2'2
30
21
'2
gg
BggWZ
WWW
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:
22222
4
1HvHvWWgD
WWH coupling requires non-zero v!
Muon Decay
Consider e e
• Fermi Theory:
e
e
• EW Theory:
eF uuuugGie
2
1
2
122 55
eW
uuuugMk
ige
2
1
2
11
255
22
2
For k<< MW, 22GF=g2/2MW2
e
e
W
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
22 )( V
42
23
22
2
822H
v
MH
v
MH
MV HHH
22
22
2
2
vM
v
H
22
2
2
1
82 vM
gG
W
F 212 )246()2( GeVGv F
What about Fermion Masses?• Fermion mass term:
• Left-handed fermions are SU(2) doublets
• Scalar couplings to fermions:
• Effective Higgs-fermion coupling
• Mass term for down quark
LRRLmmL
..chdQL RLdd
L
L d
uQ
..0
),(2
1chd
HvduL RLLdd
v
M dd
2
Forbidden by SU(2)xU(1) gauge invariance
Fermion Masses
• Mu from c=i2* (not allowed in SUSY)
• For 3 generations, , =1,2,3 (flavor indices)
0
chcuQL RcLu v
M uu
2
,
..2
)(chdduu
HvL RLdRLuY
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
– 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
Hffffv
mfHf
v
mL LRRL
ff
....cos
HZZgM
HWWgMLW
ZW
No coupling to photon or gluon at tree level
Higgs Searches at LEP2
• 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=Ph
2=MH2
– s-2 s EZ+MZ2= MH
2 LEP2 : MH > 114.1 GeV
ZHee
• 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
SM Parameters
22
22
2
1282
WZ
WW
F
MM
MM
gG
Predicts MW
Radiative Corrections and the SM
• Tree level predictions aren’t adequate to explain data
– SM predicts MW
– 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
1
2
2
2
4112
ZFFW
MGGM
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
pppBpgp )()()( 222
Taylor expand around p2=MZ2 and keep first 2 terms
S,T,U
22
2
2
22
2
22
22
)0()(
4
)0()(
4
)0()0(
W
newWW
W
WnewWW
W
Z
newZZ
Z
ZnewZZ
WW
Z
newZZ
W
newWW
MM
MUS
s
MM
MS
cs
MMT
Advantages: Easy to calculate
Valid for many models
aka
• Calculate in unitary gauge and in n=4-2 dimensions
Higgs and Top Contributions to T
222
)2(2
1)()(
Hn
n
VVHHVVA
Mk
ikdgigpi
)1(4
11
32 2
2
2
2
H
HVVHH M
Mgig
2222222
)(
11
)2()()(
HVVn
n
VVHVVB
MpkM
kkg
Mk
kdigpi
2
2
2
2
2
2
22
4121
11
4
3)1(
4
16 V
H
VHVVH M
M
M
p
M
igg
H
V=W,Z
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
4
3)1(
4
cos16)0(
2
2
22
222
HW
ZZZ M
Mgp
1
4
3)1(
4
16)0(
2
2
2
222
H
WWW M
Mgp
2
2
222log
1
cos16
3)0()0(
HWZ
ZZ
W
WW
MMMT
WW
eg
22
22
sin
4
sin
)log(1 aa
1/ cancelled by contributions from W, Z loops, etc
• Top quark contributions to T
2
114
42)0(
4
cos42)0(
22
2
2
2
2
2
2
22
2
tt
cWFWW
t
tW
cWFZZ
MM
NMG
M
M
NMG2
282t
cF MNG
T
Quadratic dependence on Mt
Top Quark Contribution to T
Limits on S & T
• A model with a heavy Higgs requires a source of large (positive) T
• Fit assumes MH=150 GeV
T
Loops Modify Tree Level Relations
W
WtFt MGr
2
2
2
2
sin
cos
28
3
6
5ln
224
112
2
2
2
W
HWFH
M
MMGr
•Contributions to r from top and Higgs loops
r is a physical quantity which incorporates 1-loop corrections
Extreme sensitivity to Mt
rMM
MM
gG
WZ
WW
F
112
82 22
22
2
Top Quark Mass Restricts Higgs Mass• Data prefer a light Higgs
Mt (GeV)
MW
(GeV
)
Assumes SM
Precision Measurements Limit MH
Limits move with top quark mass/ inclusion of different data
Best fit in region excluded by direct searches
MH (GeV)
2
LEP EWWG (March, 2009):• 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)
Tevatron Limits Have Impact on MH Higgs limit including Tevatron and LEP direct searches:
Gfitter, March 2009MH (GeV)
2
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
• Rapid approach to heavy quark limit
• NNLO corrections calculated in heavy top limit
Gluon Fusion• Lowest order cross section
)ˆ(4
1024
)()(ˆ 2
2
2
2
2/12
2
0 sMM
MF
vHgg H
q H
qRs
Light Quarks: F1/2(Mb/MH)2log(Mb/MH)
Heavy Quarks: F1/2 -4/3 |F1/
2|2
4Mq2/MH
2
Vector Boson Fusion• W+W- X is a real process:
• Rate increases at large s: (1/ MW2 )log(s/MW
2)• Integral of cross section over final state phase space
has contribution from W boson propagator:
• Outgoing jets are mostly forward and can be tagged
22222 ))cos1('2()( WW MEE
d
Mk
d
k=W,Z momentum
Peaks at small
)()(/
zsdz
dLdzs XWW
WWppXWWpp
H
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
Higgs Decays
• Hff proportional to Mf2
• Identifying b quarks important for Higgs searches
2
2
)(
)(
M
MN
HBR
bbHBR bc
For MH<2MW, decays to bb most important
MH (GeV)H
Bra
nchi
ng R
atio
s
Higgs Decays to Photons
• Dominant contribution is W loops• Contribution from top is small
2
2
3
22
3
...9
167
256)(
W
H
M
M
sH
topW
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
)()( ppgMA W
2
2
3
2 4
311
16)( WWW
W
H xxxM
M
sWWH
2
2
4H
WW M
Mx
H
W+
W-
HW+
W-
ff'
Higgs decays to gauge bosons
• H W+W- ffff has sharp threshold at 2 MW, but large branching ratio even for MH=130 GeV
For any given MH, not all decay modes accessible
MH (GeV)H
Bra
nchi
ng R
atio
s
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
0,,1,02
1),0,0,(
i
pEp
T
VVV
W
HLLWLL M
MgppgMWWHA
2
)()()(
2
2
2)(
)(
V
V
LL
TT
x
x
VVH
VVH
2
2
4H
WW M
Mx
V
VVV
VL M
pEp
M
,0,0,1
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
3
2
3
2
1330
sin16)(
TeV
MGeV
M
MWWH
H
W
H
W
H D
ecay
Wid
th (
GeV
)MH (GeV)
Producing the Higgs at the Tevatron
NNLO or NLO rates
MH/2 < < MH/4
Aside: Tevatron analyses now based on 4 fb -1
Tevatron
MH (GeV)
(p
b)
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
• 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
MH (GeV)
SM Higgs Searches at Tevatron
MH (GeV)
SM Higgs Searches at Tevatron
• Assumes SM!!!!
How Far Will Tevatron Go?
Projections assume improvements in analysis/detector
MH (GeV)Luminosity/experiment (fb-1)
Now have 6 fb -1; expect 10 fb -1 by 2010
Production Mechanisms at LHC
Bands show scale dependence
All important channels calculated to NLO or NNLO
MH (GeV)
(p
b)
See Petriello lecture
Search Channels at the LHC
• 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
ggHbb has huge QCD background: Must use rare decay modes of H
H→: A Few Years Ago….
MH=120 GeV; L=100 fb-1
H→: Today’s Reality
ATL-PHYS-PROC-2008-014
Aside: CMS slightly more optimistic
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-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
MH (GeV)E
vent
s/7.
5 G
eV
No systematic errors
PreliminaryPreliminary
• Data-driven methods to estimate backgrounds• 5σ discovery with less than 30 fb-1
H 4
CMS
H ZZ* 4l
MH (GeV) MH (GeV)
Sig
nific
ance
Sig
nific
ance
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
VBFQCD
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)
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
ATLAS SM Higgs, 2008
5σ
Herndon, ICHEP 2008
Luminosity numbers include estimates of systematic effects and uncertainties
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
ATLAS SM Higgs, 2008
Herndon, ICHEP 2008
Early LHC Data
What if the LHC Energy is Lower?
• Measure couplings to fermions & gauge bosons
• Measure spin/parity
• Measure self interactions
2
2
3)(
)(
m
m
H
bbH b
0PCJ
42
23
22
2
822H
v
MH
v
MH
MV HHH
Is it the Higgs?
Need good ideas here!
Higgs Couplings Difficult
Logan et al, hep-ph/0409026; LaFaye et al, hep-ph/0904.3866
Ratios of couplings easier
Extraction of couplings requires understanding NLO QCD corrections for signal & background
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