M W M Z correlation µ W ν µ e ν e G F 2 = 2M 2 W πα ( 1 M 2 W /MZ) 2
with loop contributions G F 2 = 2M 2 W (1+ r) πα ( 1 M 2 W /MZ) 2 1-loop examples ØÓÔ ÕÙ Ö r : quantum correction r = r(m t,m H ) Ï Ø Ï À Ó ÓÒ r = α c2 W s 2 W ρ+ Ï Ï À ρ m2 t M 2 W Ï Ù ¹ Ó ÓÒ Ð ¹ÓÙÔÐ Ò Ï determines W mass Ï Ï M W = M W (α,g F,M Z,m t,m H ) complete at 2-loop order full structure of SM
http://lepewwg.web.cern.ch/lepewwg/ m W 80.5 80.4 March 2012 LHC excluded LEP2 and Tevatron LEP1 and SLD 68% CL 80.3 m H α 114 300 600 1000 155 175 195 m t
Z resonance cross section [nb] 30 20 LEP: ALEPH DELPHI L3 OPAL data 2ν 3ν 4ν e + f 10 Z 0 86 88 90 92 94 cms energy e - f effective Z boson couplings with higher-order g V,A v f g f V = v f + g f V, a f g f A = a f + g f A effective ew mixing angle (for f = e): sin 2 θ eff = 1 ( ) 1 Re ge V = κ 4 ga e ( 1 M2 W M 2 Z )
importance of two-loop calculations 0.2325 0.232 sin 2 Θeff 0.2315 0.231 0.2305 1loop QCD lead.3loop 2loop exp 200 400 600 800 1000 M H GeV lowest order: sin 2 θ W = 1 M2 W = 0.22290 ± 0.00029 MZ 2 exp. value: sin 2 θ eff = 0.23153±0.00016
Global analysis within the SM 200 March 2012 High Q 2 except m t 68% CL m t 180 m t (Tevatron) 160 Excluded 10 10 2 10 3 M H
before the top quark was discovered (< 1995): indirect mass determination m t = 178±8 +17 20 GeV 40 LEP + SLD + Colliders + νn Data 35 30 χ 2 25 20 m H = 1 TeV m H = 300 GeV Preliminary top discovery: Tevatron 1995 today: m H = 60 GeV 100 150 200 250 m t m t = 180±12GeV m t = 173.2±0.9GeV
The way to the Higgs boson development of bounds from direct and indirect searches 800 600 Higgs mass 400 200 0 1995 1996 1997 1998 1999 2000 2001 year
Global fit to the Higgs boson mass 6 5 4 July 2011 Theory uncertainty α had = α (5) 0.02750±0.00033 0.02749±0.00010 incl. low Q 2 data m Limit = 161 GeV blueband: Theory uncertainty χ 2 3 2 1 Excluded 0 30 100 300 M H Precision Calculations at the Z Resonance CERN 95-03 [Bardin, WH, Passarino (eds.)] M H < 161 GeV (at 95% C.L.)
χ 2 6 5 4 3 2 1 0 March 2012 LEP excluded Theory uncertainty α had = α (5) 0.02750±0.00033 0.02749±0.00010 incl. low Q 2 data 40 100 200 M H m Limit = 152 GeV LHC excluded after the 2011 results from the LHC on the Higgs boson mass M H < 152 GeV (95%C.L.) M H = 94 +29 24 GeV
The direct search for the Higgs boson Higgs production at LEP: À excluded M H < 114GeV Higgs production at the Tevatron: t t t H W,Z H W,Z
Higgs production at the LHC ggf VBF VBF VH tth tth VH Handbook of Higgs Cross sections, arxiv:1101.0593, arxiv:1201.3084
Higgs boson decay channels branching ratios BR(H X) = Γ(H X) Γ(H all) Higgs BR + Total Uncert 1 10 ττ cc bb gg WW ZZ LHC HIGGS XS WG 2011-2 10 γγ Zγ -3 10 100 120 140 160 180 200 M H γ(z) γ(z) H W + H F γ γ loop-induced (rare) decays
H γγ Events / 2 GeV Events - Fitted bkg 10000 8000 6000 4000 2000 500 400 300 200 100 0 00-200 s = 7 TeV, Ldt = 4.8 fb s = 8 TeV, Ldt = 20.7 fb Selected diphoton sample Data 2011+2012 Sig+Bkg Fit (m =126.8 GeV) H Bkg (4th order polynomial) ATLAS Preliminary H γγ 100 110 120 130 140 150 160 m γγ S/(S+B) Weighted Events / 1.5 GeV 5000 CMS Preliminary Data 4000 3000 2000 1000 0 s = 7 TeV, L = 5.1 fb (MVA) s = 8 TeV, L = 19.6 fb (MVA) S+B Fit Bkg Fit Component ±1 σ ±2 σ 110 120 130 140 150 (GeV) m γγ
Å À Å À Higgs decays into 4 fermions also below VV threshold with one or two V off-shell a) H V V b) H V f f c) H f 1 f 2 f 3 f 4 ½ Ê À Ï Ï µ Ê À µ ¼º½ ¼º½ ß Ó Ý ß Ó Ý ¾ß Ó Ý ¼º¼½ ß Ó Ý ß Ó Ý ¼º¼½ ¾ß Ó Ý ¼º¼¼½ ¼º¼¼½ ½ ¼ ½ ¼ ½ ¼ ½ ¼ ½¾¼ ½ ¼ ½¼¼ ½¾¼ ½¼¼ ¾¼¼ ½ ¼ [Djouadi] Î Î
H ZZ l + l l + l Events/2.5 GeV 30 25 20 Data (*) Background ZZ Background Z+jets, tt Signal (m =125 GeV) H Syst.Unc. ATLAS Preliminary (*) H ZZ 4l s = 7 TeV: Ldt = 4.6 fb s = 8 TeV: Ldt = 20.7 fb Events / 3 GeV 35 30 25 20 CMS Preliminary s = 7 TeV, L = 5.1 fb ; s = 8 TeV, L = 19.6 fb Data Z+X * Zγ,ZZ m H =126 GeV 15 15 10 10 5 5 0 80 100 120 140 160 m 4l 0 80 100 120 140 160 180 m 4l signal + background
A Standard Model Higgs boson at the LHC? ATLAS Preliminary W,Z H bb s = 7 TeV: Ldt = 4.7 fb s = 8 TeV: Ldt = 13 fb H ττ s = 7 TeV: Ldt = 4.6 fb s = 8 TeV: Ldt = 13 fb (*) H WW H γγ s = 7 TeV: Ldt = 4.8 fb s = 8 TeV: Ldt = 20.7 fb (*) H ZZ lνlν s = 7 TeV: Ldt = 4.6 fb s = 8 TeV: Ldt = 20.7 fb 4l s = 7 TeV: Ldt = 4.6 fb s = 8 TeV: Ldt = 20.7 fb m H = 125.5 GeV Combined s = 7 TeV: Ldt = 4.6-4.8 fb s = 8 TeV: Ldt = 13-20.7 fb µ = 1.30 ± 0.20 0 +1 Signal strength (µ) H mass ATLAS (GeV) H mass CMS (GeV) 125.5 ± 0.2 ± 0.6 125.7 ± 0.3 ± 0.3 Theory: σ(pp H) BR(H X)
Landau pole Higgs self coupling is scale dependent, λ(q) À À À À variation with scale Q described by RGE solution: Q 2 dλ dq 2 = β(λ) = 3 4π 2 λ2 λ(q) = λ(v) 1 3 λ(v)log Q2 4π 2 v 2 with λ(v) = M2 H 2v 2 diverges at scale Q = Λ C (Landau pole) ( 4π 2 v 2 ) Λ C = v exp 3M 2 H
self-coupling diverges at Λ C = v exp ( 4π 2 v 2 ) 3M 2 H maximum Higgs mass by condition Λ C > M H M H < 800GeV
vacuum stability top-quark Yukawa coupling g t m t contributes to the running Higgs self coupling λ(q) through top loop g 4 t À À À À variation with scale Q described by RGE approximate solution: Q 2 dλ dq 2 = 3 4π 2 ( λ 2 m4 t v 4 ) λ(q) = λ(v) 3m4 t 2π 2 v 4 log Q v λ(q) < 0 for Q > Λ C vacuum not stable high value of Λ C needs M H large enough
combined effects, RGE in two-loop order: dλ dt = 1 16π 2 ( 12λ 2 3g 4 t +6λg 2 t + )
M H 350 300 λ = π λ = 2π Perturbativity bound Stability bound Finite-T metastability bound Zero-T metastability bound Shown are 1σ error bands, w/o theoretical errors 250 200 Tevatron exclusion at >95% CL 150 LEP exclusion at >95% CL 100 4 6 8 10 12 14 16 18 log (Λ / GeV) 10 [Espinosa et al. 2009]
10 18 10 18 10 16 1Σbandin M t 173.1±0.7GeV Α s M Z 0.1184±0.0007 10 16 1Σbandsin Α s M Z 0.1184±0.0007 Instability scale in GeV 10 14 10 12 Instability scale in GeV 10 14 10 12 Mh 124GeV Mh 126GeV 10 10 10 10 10 8 115 120 125 130 135 10 8 170 171 172 173 174 175 176 HiggsmassM h ingev TopmassM t ingev [Degrassi et al. 2012]