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