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