M W M Z correlation. πα 1 M G F 2 = 2M 2 W 2 W

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Piotr Urbański
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1 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

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

3 m W March 2012 LHC excluded LEP2 and Tevatron LEP1 and SLD 68% CL 80.3 m H α m t

4 Z resonance cross section [nb] LEP: ALEPH DELPHI L3 OPAL data 2ν 3ν 4ν e + f 10 Z 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 )

5 importance of two-loop calculations sin 2 Θeff loop QCD lead.3loop 2loop exp M H GeV lowest order: sin 2 θ W = 1 M2 W = ± MZ 2 exp. value: sin 2 θ eff = ±

6 Global analysis within the SM 200 March 2012 High Q 2 except m t 68% CL m t 180 m t (Tevatron) 160 Excluded M H

7 before the top quark was discovered (< 1995): indirect mass determination m t = 178± GeV 40 LEP + SLD + Colliders + νn Data χ m H = 1 TeV m H = 300 GeV Preliminary top discovery: Tevatron 1995 today: m H = 60 GeV m t m t = 180±12GeV m t = 173.2±0.9GeV

8 The way to the Higgs boson development of bounds from direct and indirect searches Higgs mass year

9 Global fit to the Higgs boson mass July 2011 Theory uncertainty α had = α (5) ± ± incl. low Q 2 data m Limit = 161 GeV blueband: Theory uncertainty χ Excluded M H Precision Calculations at the Z Resonance CERN [Bardin, WH, Passarino (eds.)] M H < 161 GeV (at 95% C.L.)

10 χ March 2012 LEP excluded Theory uncertainty α had = α (5) ± ± incl. low Q 2 data 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 = GeV

11 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

12 Higgs production at the LHC ggf VBF VBF VH tth tth VH Handbook of Higgs Cross sections, arxiv: , arxiv:

13 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 γγ Zγ M H γ(z) γ(z) H W + H F γ γ loop-induced (rare) decays

14 H γγ Events / 2 GeV Events - Fitted bkg s = 7 TeV, Ldt = 4.8 fb s = 8 TeV, Ldt = 20.7 fb Selected diphoton sample Data Sig+Bkg Fit (m =126.8 GeV) H Bkg (4th order polynomial) ATLAS Preliminary H γγ m γγ S/(S+B) Weighted Events / 1.5 GeV 5000 CMS Preliminary Data 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 (GeV) m γγ

15 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

16 H ZZ l + l l + l Events/2.5 GeV 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 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 m 4l 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.

17 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 = GeV Combined s = 7 TeV: Ldt = fb s = 8 TeV: Ldt = fb µ = 1.30 ± Signal strength (µ) H mass ATLAS (GeV) H mass CMS (GeV) ± 0.2 ± ± 0.3 ± 0.3 Theory: σ(pp H) BR(H X)

18 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

19 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

20 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

21 combined effects, RGE in two-loop order: dλ dt = 1 16π 2 ( 12λ 2 3g 4 t +6λg 2 t + )

22 M H 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 Tevatron exclusion at >95% CL 150 LEP exclusion at >95% CL log (Λ / GeV) 10 [Espinosa et al. 2009]

23 Σbandin M t 173.1±0.7GeV Α s M Z ± Σbandsin Α s M Z ± Instability scale in GeV Instability scale in GeV Mh 124GeV Mh 126GeV HiggsmassM h ingev TopmassM t ingev [Degrassi et al. 2012]

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