Finding the Higgs boson

Sally Dawson, BNL

XIII Mexican School of Particles and Fields

Lecture 1, Oct, 2008

Properties of the Higgs boson

Higgs production at the Tevatron and LHC

Discovery vs spectroscopy

Tevatron LHC LHC L Upgrade ILC

2007 2008 2015

Collider Physics Timeline

Planned shut-down in 2010

First collisions in Spring, 2009

e+e- @ 500 GeV, earliest possible date, 202x

15+ billion $’s

Large Hadron Collider (LHC)

• proton-proton collider at CERN (2008)

• 14 TeV energy– 7 mph slower than the

speed of light– cf. 2 TeV @ Fermilab

( 307 mph slower than the speed of light)

• Typical energy of quarks and gluons 1-2 TeV

Detectors of Unprecedented Scale

• Two large multi-purpose detectors

• CMS is 12,000 tons (2 x’s ATLAS)

• ATLAS has 8 times the volume of CMS

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 symmetry forbids gauge boson masses

The Problem of Mass

• Why are the W and Z boson masses non-zero?

• U(1) gauge theory with spin-1gauge field, A

• U(1) local gauge invariance:

AAF

FFL

4

1

)()()( xxAxA

The Problem of Masses

• Mass term for A would look like:

• Mass term violates local gauge invariance

• We understand why MA = 0

AAmFFL 2

2

1

4

1

Gauge invariance is guiding principle

SM Higgs Mechanism

• Standard Model includes complex Higgs SU(2) doublet

• With SU(2) x U(1) invariant scalar potential

2 > 0, boring….. (Minimum at =0, gauge bosons stay massless)

043

21

2

1

i

i

22 )( V

SM Higgs Mechanism

• If 2 < 0, then spontaneous symmetry breaking

• Minimum of potential at:– Choice of minimum breaks gauge symmetry– Why is 2 < 0?

v

0

2

1

22 )( V

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

v

0

2

1

Higgs mechanism gives gauge bosons mass

More on SM Higgs Mechanism

• Massive gauge bosons:

W = (W

1 W2) /2

Z 0 = (g W3 - g'B )/ (g2+g'2)

• Orthogonal combination to Z is massless photon

A 0 = (g' W3+gB )/ (g2+g'2)

MW=gv/2MZ=(g2+g'2)v/2

More on SM Higgs Mechanism

• Weak mixing angle defined

• Z = - sin WB + cosWW3

• A = cos WB + sinWW3

MW=MZ cos W

2222sincos

gg

g

gg

gWW

Natural relationship in SM—Provides stringent restriction on Beyond the SM models

Recap

• Generate mass for W,Z using Higgs mechanism

– Higgs VEV breaks SU(2) x U(1)U(1)em

– Single Higgs doublet is minimal case• Before spontaneous symmetry breaking:

– Massless Wi, B, Complex • After spontaneous symmetry breaking:

– Massive W,Z; massless ; physical Higgs boson H

Exercise: Count degrees of freedom

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

e

e

W

22

2

2

1

82 vM

gG

W

F GF=1.16637 x 10-5 GeV-2

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

mdd

2

Forbidden by SU(2)xU(1) gauge invariance

Fermion Masses, 2

• Mu from c=i2* (not allowed in SUSY)

• For 3 generations, , =1,2,3 (flavor indices)

0

chcuQL RcLu v

muu

2

,

..2

)(chdduu

HvL RLdRLuY

Fermion masses, 3• Unitary matrices diagonalize mass matrices

– Yukawa couplings are diagonal in mass basis– Neutral currents remain flavor diagonal– Not necessarily true in models with extended

Higgs sectors

mRdR

mRuR

mLdL

mLuL

dVduVu

dUduUu

Exercise: Prove this!

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

Review of Higgs Boson Feynman Rules

• Higgs couples to heavy particles

• No tree level coupling to photons () or gluons (g)

• MH2=2v2large MH is

strong coupling regime

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

Higgs Decays to Gluons

2

3

22

2

72)(

W

Hs

M

M

sggH

tt mmk

kd 1

)( 3

4

•Top quark contribution most important

•Doesn’t decouple for large mt

•Decoupling theorem doesn’t apply to particles which couple to mass (ie Higgs!)

•Decay sensitive to extra generations

Hg

gtm

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 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

MggMWWHA

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

Exercise: Prove this

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

Data points are e+e- at s=350 GeV with L=500 fb-1

• Bands show theory errors

• Largest source of uncertainty is b quark mass

Status of Theory for Higgs BRs

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

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

Higgs Limits From LEP2

LEP2 limit, MH > 114.1 GeV

e+e- →ZH

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: q=4Mq

2/MH2

– Light Quarks: F1/2(Mb/MH)2log(Mb/MH)

– Heavy Quarks: F1/2 -4/3

)ˆ()(1024

)()(ˆ 2

2

2/12

2

0 sMFv

Hgg Hq

qRs

• Rapid approach to heavy quark limit: Counts number of heavy fermions

• NLO/NNLO corrections calculated in heavy top limit

Gluon fusion, continued

• Integrate parton level cross section with gluon parton distribution functions

– z=MH2/S, S is hadronic

center of mass energy

• Rate depends on R, F

1

00 ),(),(ˆ)(z

FF x

zgxg

x

dxzHpp

NNLO, ggH

Bands show .5MH < < 2 MH

LO and NLO dependence bands don’t overlap

dependence used as estimate of theoretical uncertainty

Rates depend on renormalization scale, s(R), and factorization scale, g(F)

LO

NLOK Higher order corrections

computed in large Mt limit

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

Producing the Higgs at the Tevatron

NNLO or NLO rates

MH/2 < < MH/4

Aside: Tevatron analyses now based on 3 fb -1

Tevatron

Higgs at the Tevatron

• Largest rate, ggH, H bb, is overwhelmed by background

(ggH)1 pb << (bb)

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

SM Higgs Searches at Tevatron

95% CL exclusion of SM Higgs at 170 GeV

SM Higgs Searches at Tevatron

Expected sensitivity of CDF/DØ combined with 3 fb-1:

< 3.0xSM @ 115 GeV

Production Mechanisms at LHC

Bands show scale dependence

All important channels calculated to NLO or NNLO

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→

MH=120 GeV; L=100 fb-1

S/B = 2.8 to 4.3

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 > 600 GeV:

4 lepton channel statistically limitedLook for:

H ZZ l+l- H ZZ l+l- jj H WW l jj

-150 times larger BR than 4 lepton channel

Heavy Higgs

Vector Boson Fusion

• Outgoing jets are mostly forward and can be tagged– Little jet activity in central rapidity region

• Idea: Look for different H decay channels in Vector boson fusion– Ratio will have smaller errors than total rate

H

Vector Boson Fusion for light Higgs

105

1

mHiggs (GeV) 200 100 120 140 160 180 200

Sig

nal

sig

nif

ican

ce

ATLAS

qqH qq qqH qqWWAll channels

Vector boson fusion effective for measuring Higgs couplings

Higgs Discovery Reach at LHC

•Improvement in channel from earlier studies

Early Higgs Physics

ATLAS

Higgs Discovery at ATLAS

ATLAS

If we find a “Higgs-like” object, what then?

• We need to:– Measure Higgs couplings to fermions & gauge

bosons– Measure Higgs spin/parity– Reconstruct Higgs potential– Is it the SM Higgs?

• Reminder: Many models have other signatures:– New gauge bosons (little Higgs)– Other new resonances (Extra D)– Scalar triplets (little Higgs, NMSSM)– Colored scalars (MSSM)

Is it a Higgs?

• How do we know what we’ve found? • Measure couplings to fermions & gauge bosons

• Measure spin/parity

• Measure self interactions

2

2

3)(

)(

m

m

H

bbH b

0PCJ

42

23

22

822H

v

MH

v

MH

MV HHH

Absolute Measurements of Higgs Couplings

• Ratios of couplings more precisely measured than absolute couplings

• 10-40% measurements of most couplings

Can we reconstruct the Higgs potential?

4433

22

42HvHH

MV H

• Fundamental test of model!

2

2

43 2:

v

MSM H

• We have no idea how to measure 4

Reconstructing the Higgs potential

3 requires 2 Higgs production• MH<140 GeV, Hbbbb• Overwhelming QCD background

Can determine whether 3=0 at 95% cl with 300 fb-1 for 150 <MH <200 GeV

Conclusions

• If a SM Higgs exists, the LHC will find it

• But there will still be questions…..