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 My favorite references: 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) 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:  QCD Electroweak Gauge bosons are massless Massless gauge bosons have 2 transverse degrees of freedom

Fermions come in generations Except for masses, the generations are identical

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 Gauge invariance is guiding principle

Abelian Higgs Model Add a scalar to U(1) gauge theory Case 1: 2>0 QED with MA=0 and m= Unique minimum at =0 By convention,  > 0

Abelian Higgs Model Case 2: 2 < 0 Minimum energy state at: 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 –22 > 0 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

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:

SM Higgs Mechanism Massive gauge bosons: Orthogonal combination to Z is massless photon:

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: WWH coupling requires non-zero v!

Muon Decay  Consider  e e Fermi Theory: EW Theory:    W e For k<< MW, 22GF=g2/2MW2

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

What about Fermion Masses? Forbidden by SU(2)xU(1) gauge invariance Fermion mass term: Left-handed fermions are SU(2) doublets Scalar couplings to fermions: Effective Higgs-fermion coupling Mass term for down quark 

Fermion Masses Mu from c=i2* (not allowed in SUSY) For 3 generations, , =1,2,3 (flavor indices) 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 No coupling to photon or gluon at tree level

Higgs Searches at LEP2 LEP2 : MH > 114.1 GeV 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=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  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

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 Taylor expand around p2=MZ2 and keep first 2 terms

S,T,U aka  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 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/ cancelled by contributions from W, Z loops, etc

Top Quark Contribution to T Top quark contributions to T Quadratic dependence on Mt

Limits on S & T A model with a heavy Higgs requires a source of large (positive) T Fit assumes MH=150 GeV

Loops Modify Tree Level Relations r is a physical quantity which incorporates 1-loop corrections Contributions to r from top and Higgs loops Extreme sensitivity to Mt

Top Quark Mass Restricts Higgs Mass Data prefer a light Higgs Assumes SM MW (GeV) Mt (GeV)

Precision Measurements Limit MH 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) 2 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 Higgs limit including Tevatron and LEP direct searches: 2 MH (GeV) Gfitter, March 2009

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 |F1/2|2 4Mq2/MH2 Light Quarks: F1/2(Mb/MH)2log(Mb/MH) Heavy Quarks: F1/2 -4/3 |F1/2|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: 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: Outgoing jets are mostly forward and can be tagged Peaks at small  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

Higgs Decays Hff proportional to Mf2 H Branching Ratios Identifying b quarks important for Higgs searches H Branching Ratios MH (GeV) For MH<2MW, decays to bb most important

Higgs Decays to Photons Dominant contribution is W loops Contribution from top is small W top

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 H W- f W+ f' H W-

Higgs decays to gauge bosons H W+W- ffff has sharp threshold at 2 MW, but large branching ratio even for MH=130 GeV H Branching Ratios 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) Cross sections involving longitudinal gauge bosons grow with energy H→WL+WL- As Higgs gets heavy, decays are longitudinal

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 H Decay Width (GeV) MH (GeV)

Producing the Higgs at the Tevatron Aside: Tevatron analyses now based on 4 fb -1  (pb) 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 MH (GeV) Luminosity/experiment (fb-1) Projections assume improvements in analysis/detector

Production Mechanisms at LHC Bands show scale dependence  (pb) 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- 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 Events/7.5 GeV MH (GeV)

Data-driven methods to estimate backgrounds 5σ discovery with less than 30 fb-1 No systematic errors Preliminary CMS Significance Significance 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: 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 5σ 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 Measure spin/parity Measure self interactions 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