The simplest Extension of the Standard Model

Transcription

1 The simplest Extension of the Standard Model Alexander Lenz (TU München) in collaboration with Markus Bobrowski, Otto Eberhardt (KIT Karlsruhe), Johann Riedl, Jürgen Rohrwild (RWTH Aachen) MPIK Heidelberg, June 2, 211

2 Contents Introduction Flavor constraints Electro-weak constraints Results Alexander Lenz The simplest Extension of the Standard Model ( ) 2 / 43

3 Introduction What is the fourth family Dichtung und Wahrheit History Arguments against the fourth family in detail Arguments in favour of the fourth family Quark mixing Fitting the SM4 parameters Alexander Lenz The simplest Extension of the Standard Model ( ) 3 / 43

4 What is the new family? Another sequential generation of fermions Leptons: ( νe e ), ( νµ µ ), ( ντ τ ), ( ν4 l 4 ) Quarks: ( u d ), ( c s ), ( t b ), ( t b ) Alexander Lenz The simplest Extension of the Standard Model ( ) 4 / 43

5 Dichtung und Wahrheit History of the investigation of the SM4 Classical Period: Soni, Hou, et al Alexander Lenz The simplest Extension of the Standard Model ( ) 5 / 43

6 Dichtung und Wahrheit History of the investigation of the SM4 Classical Period: Soni, Hou, et al Decline: LEP: N ν and S,T,U Langacker und Erler Alexander Lenz The simplest Extension of the Standard Model ( ) 5 / 43

7 Dichtung und Wahrheit History of the investigation of the SM4 Classical Period: Soni, Hou, et al Decline: LEP: N ν and S,T,U Langacker und Erler Resurrection: Kribs et al 27; Vysotsky, Okun, et al Electro-weak Observables do not exclude a fourth family! ( m t m b = 1 1 ) 5 ln m H 5GeV 115GeV Alexander Lenz The simplest Extension of the Standard Model ( ) 5 / 43

8 Dichtung und Wahrheit History of the investigation of the SM4 Classical Period: Soni, Hou, et al Decline: LEP: N ν and S,T,U Langacker und Erler Resurrection: Kribs et al 27; Vysotsky, Okun, et al Electro-weak Observables do not exclude a fourth family! ( m t m b = 1 1 ) 5 ln m H 5GeV 115GeV Precision analyses: Scans over the CKM4 parameter regions : Bobrowski, A.L., Riedl, Rohrwild - very large effects : Chanowitz - S,T,U shrinks the allowed region : Soni,... - more Observables also : Buras et al. also Charm; Leptons : Eberhardt, A.L., Rohrwild - full CKM-dependence of S,T,U Complete Fit: with H. Lacker (CKMfitter) and U. Nierste Kick-off Workshop: TU Dortmund see also: : Alok, Dighe, London Alexander Lenz The simplest Extension of the Standard Model ( ) 5 / 43

9 Main arguments against the fourth family Number of light neutrinos from LEP N ν = 2.984±.82 [LEP 6] Alexander Lenz The simplest Extension of the Standard Model ( ) 6 / 43

10 Main arguments against the fourth family Number of light neutrinos from LEP N light ν = 2.984±.82 [LEP 6] But neutrinos do have a mass. [Super-Kamiokande 98] Alexander Lenz The simplest Extension of the Standard Model ( ) 6 / 43

11 Main arguments against the fourth family Number of light neutrinos from LEP N light ν = 2.984±.82 [LEP 6] But neutrinos do have a mass. [Super-Kamiokande 98] Astronomy: N eff ν = [7y WMAP 1] WMAP +Baryon acoustic oscillations +H measurements WMAP Alexander Lenz The simplest Extension of the Standard Model ( ) 6 / 43

12 Main arguments against the fourth family History of the PDG reviews 1994: one heavy generation of ordinary fermions is allowed at 95% CL Alexander Lenz The simplest Extension of the Standard Model ( ) 7 / 43

13 Main arguments against the fourth family History of the PDG reviews 1994: one heavy generation of ordinary fermions is allowed at 95% CL 1998: an extra generation of ordinary fermions is now excluded at the 99.2% CL Alexander Lenz The simplest Extension of the Standard Model ( ) 7 / 43

14 Main arguments against the fourth family History of the PDG reviews 1994: one heavy generation of ordinary fermions is allowed at 95% CL 1998: an extra generation of ordinary fermions is now excluded at the 99.2% CL 22: an extra generation of ordinary fermions is excluded at the 99.8% CL on the basis of the S parameter alone. [...] This result assumes [...] that any new families are degenerate. This restriction can be relaxed [...] to 95%. Alexander Lenz The simplest Extension of the Standard Model ( ) 7 / 43

15 Main arguments against the fourth family History of the PDG reviews 1994: one heavy generation of ordinary fermions is allowed at 95% CL 1998: an extra generation of ordinary fermions is now excluded at the 99.2% CL 22: an extra generation of ordinary fermions is excluded at the 99.8% CL on the basis of the S parameter alone. [...] This result assumes [...] that any new families are degenerate. This restriction can be relaxed [...] to 95%. 21: an extra generation of ordinary fermions is excluded at the 6 σ level on the S parameter alone. This result assumes [...] that any new families are degenerate. [...] a fourth family is disfavored but not excluded by current data. [Erler/Langacker] Alexander Lenz The simplest Extension of the Standard Model ( ) 7 / 43

16 Some arguments in favour of the fourth family Softening of the Higgs mass bounds [Novikov et al. 2, 9, Frere et al. 4, Kribs et al. 7] Alexander Lenz The simplest Extension of the Standard Model ( ) 8 / 43

17 Some arguments in favour of the fourth family Softening of the Higgs mass bounds [Novikov et al. 2, 9, Frere et al. 4, Kribs et al. 7] Solution to certain flavour physics problems [Hou 6, Soni 9, Buras 1, Lenz 1,...] Alexander Lenz The simplest Extension of the Standard Model ( ) 8 / 43

18 Some arguments in favour of the fourth family Softening of the Higgs mass bounds [Novikov et al. 2, 9, Frere et al. 4, Kribs et al. 7] Solution to certain flavour physics problems [Hou 6, Soni 9, Buras 1, Lenz 1,...] Baryogenesis (CP-violation and phase transition) [Hou 8, Carena et al. 4, Fok & Kribs 8, Kikukawa et al. 9, Murayama et al ] Alexander Lenz The simplest Extension of the Standard Model ( ) 8 / 43

19 Some arguments in favour of the fourth family Softening of the Higgs mass bounds [Novikov et al. 2, 9, Frere et al. 4, Kribs et al. 7] Solution to certain flavour physics problems [Hou 6, Soni 9, Buras 1, Lenz 1,...] Baryogenesis (CP-violation and phase transition) [Hou 8, Carena et al. 4, Fok & Kribs 8, Kikukawa et al. 9, Murayama et al ] Nonperturbative effects due to large Yukawa couplings - DSB [Hung 1, Wise 11,Holdom,...] Alexander Lenz The simplest Extension of the Standard Model ( ) 8 / 43

20 Some arguments in favour of the fourth family Softening of the Higgs mass bounds [Novikov et al. 2, 9, Frere et al. 4, Kribs et al. 7] Solution to certain flavour physics problems [Hou 6, Soni 9, Buras 1, Lenz 1,...] Baryogenesis (CP-violation and phase transition) [Hou 8, Carena et al. 4, Fok & Kribs 8, Kikukawa et al. 9, Murayama et al ] Nonperturbative effects due to large Yukawa couplings - DSB [Hung 1, Wise 11,Holdom,...] Unification of the gauge couplings [Hung 97] Alexander Lenz The simplest Extension of the Standard Model ( ) 8 / 43

21 Quark mixing The CKM matrix In the electroweak Lagrangian, the unitary transformation q L = Uq L q L and q R = Uq R q R from electroweak to mass eigenstates vanishes in all terms, except for: g 2 W + µ ūi L γµ d i L +h.c. Alexander Lenz The simplest Extension of the Standard Model ( ) 9 / 43

22 Quark mixing The CKM matrix In the electroweak Lagrangian, the unitary transformation q L = Uq L q L and q R = Uq R q R from electroweak to mass eigenstates vanishes in all terms, except for: g ) ijd W µ + ūl i γµ( (UL u ) UL d j 2 }{{} L +h.c. V CKM Alexander Lenz The simplest Extension of the Standard Model ( ) 9 / 43

23 Quark mixing The CKM matrix V CKM3 = V CKM3 ud V CKM3 cd V CKM3 td V CKM3 us V CKM3 cs V CKM3 ts 1 c 23 s 23 s 23 c 23 V CKM3 ub V CKM3 cb V CKM3 tb c 13 s 13e iδ 13 1 s 13e iδ 13 c 13 c ij cosθ ij s ij sinθ ij c 12 s 12 s 12 c 12 1 = c 12c 13 s 12c 13 s 13e iδ 13 s 12c 23 c 12s 23s 13e iδ 13 c 12c 23 s 12s 23s 13e iδ 13 s 23c 13 s 12s 23 c 12c 23s 13e iδ 13 c 12s 23 s 12c 23s 13e iδ 13 c 23c 13 Alexander Lenz The simplest Extension of the Standard Model ( ) 1 / 43

24 The unitarity triangle The Wolfenstein parametrisation η V CKM λ2 λ Aλ 3 (ρ iη) λ λ2 Aλ 2 Aλ 3 (1 ρ iη) Aλ 2 1 V ud V ub V cd V cb α V td V tb V cd V cb γ β 1 ρ Alexander Lenz The simplest Extension of the Standard Model ( ) 11 / 43

25 The unitarity triangle The Wolfenstein parametrisation V CKM λ2 λ Aλ 3 (ρ iη) λ λ2 Aλ 2 Aλ 3 (1 ρ iη) Aλ 2 1 η excluded area has CL >.95 sin 2β ε K γ m d α & m s m d ε K V ub τ ν CKM f i t t e r ICHEP 1 sol. w/ cos 2β < (excl. at CL >.95) α.1 V ub γ SL α β ρ Alexander Lenz The simplest Extension of the Standard Model ( ) 11 / 43

26 Notation The 4 4 CKM matrix V CKM4 = 1 1 c 34 s 34 s 34 c 34 1 c 24 s 24e iδ 24 1 s 24e iδ 24 c 24 c 14 s 14e iδ s 14e iδ 14 c 14 1 VCKM3 c ij cosθ ij s ij sinθ ij Alexander Lenz The simplest Extension of the Standard Model ( ) 12 / 43

27 Notation The 4 4 CKM matrix V CKM4 = c 12 c 13 c 14 c 13 c 14 s 12 c 14 s 13 e iδ 13 s 14 e iδ 14 c 23 c 24 s 12 c 12 c 23 c 24 c 13 c 24 s 23 c 14 s 24 e iδ 24 c 12 c 24 s 13 s 23 e iδ 13 c 24 s 12 s 13 s 23 e iδ 13 s 13 s 14 s 24 e i(δ 13 +δ 24 δ 14 ) c 12 c 13 s 14 s 24 e i(δ 14 δ 24 ) c 13 s 12 s 14 s 24 e i(δ 14 δ 24 ) c 12 c 23 c 34 s 13 e iδ 13 c 12 c 34 s 23 c 13 c 23 c 34 c 14 c 24 s 34 +c 34 s 12 s 23 c 23 c 34 s 12 s 13 e iδ 13 c 13 s 23 s 24 s 34 e iδ 24 c 12 c 13 c 24 s 14 s 34 e iδ 14 c 12 c 23 s 24 s 34 e iδ 24 c 24 s 13 s 14 s 34 e i(δ 14 δ 13 ) +c 23 s 12 s 24 s 34 e iδ 24 c 13 c 24 s 12 s 14 s 34 e iδ 14 +c 12 s 13 s 23 s 24 s 34 e i(δ 13 +δ 24 ) +s 12 s 13 s 23 s 24 s 34 e i(δ 13 +δ 24 ) c 12 c 13 c 24 c 34 s 14 e iδ 14 c 12 c 23 c 34 s 24 e iδ 24 c 13 c 23 s 34 c 14 c 24 c 34 +c 12 c 23 s 13 s 34 e iδ 13 +c 12 s 23 s 34 c 13 c 34 s 23 s 24 e iδ 24 +c 23 c 34 s 12 s 24 e iδ 24 c 13 c 24 c 34 s 12 s 14 e iδ 14 c 24 c 34 s 13 s 14 e i(δ 14 δ 13 ) s 12 s 23 s 34 +c 23 s 12 s 13 s 34 e iδ 13 +c 12 c 34 s 13 s 23 s 24 e i(δ 13 +δ 24 ) +c 34 s 12 s 13 s 23 s 24 e i(δ 13 +δ 24 ) c ij cosθ ij s ij sinθ ij Alexander Lenz The simplest Extension of the Standard Model ( ) 12 / 43

28 Fitting the SM4 parameters The old parameters Quarks: m u,m d,m s,m c,m b,m t, θ 12,θ 13,θ 23, δ 13 Leptons: m νe,m νµ,m ντ,m e,m µ,m τ, θ l 12,θl 13,θl 23, δl 13 Alexander Lenz The simplest Extension of the Standard Model ( ) 13 / 43

29 Fitting the SM4 parameters The old parameters Quarks: m u,m d,m s,m c,m b,m t, θ 12,θ 13,θ 23, δ 13 Leptons: m νe,m νµ,m ντ,m e,m µ,m τ, θ12 l,θl 13,θl 23, δl 13 The new parameters Quarks: m b,m t, θ 14,θ 24,θ 34, δ 14,δ 24 Leptons: m ν4,m l4, θ14 l,θl 24,θl 34, δl 14,δl 24 Alexander Lenz The simplest Extension of the Standard Model ( ) 13 / 43

30 Fitting the SM4 parameters The old parameters Quarks: m u,m d,m s,m c,m b,m t, θ 12,θ 13,θ 23, δ 13 Leptons: m νe,m νµ,m ντ,m e,m µ,m τ, θ12 l,θl 13,θl 23, δl 13 The new parameters Quarks: m b,m t, θ 14,θ 24,θ 34, δ 14,δ 24 Leptons: m ν4,m l4, θ14 l,θl 24,θl 34, δl 14,δl free parameters Alexander Lenz The simplest Extension of the Standard Model ( ) 13 / 43

31 Fitting the SM4 parameters Our two approaches Scatter plots Alexander Lenz The simplest Extension of the Standard Model ( ) 14 / 43

32 Fitting the SM4 parameters Our two approaches Scatter plots.6 CKMfitter plots 1 θ θ 23 Alexander Lenz The simplest Extension of the Standard Model ( ) 14 / 43

33 Fitting the SM4 parameters Our two approaches Scatter plots.6 CKMfitter plots 1 θ θ 23 Scatter: Create 1 1 parameter points for the SM4: test if bounds from V CKM, FCNC and electro-weak precision observables are fulfilled Fit: Full combined CKM-,(PMNS)- and electro-weak fit - Work in progress Alexander Lenz The simplest Extension of the Standard Model ( ) 14 / 43

34 Constraints on the SM4 Direct constraints Mass constraints (quarks, leptons, Higgs) Direct measurements of CKM elements Phase constraints on the CKM matrix Alexander Lenz The simplest Extension of the Standard Model ( ) 15 / 43

35 Constraints on the SM4 Direct constraints Mass constraints (quarks, leptons, Higgs) Direct measurements of CKM elements Phase constraints on the CKM matrix Indirect constraints FCNC Lepton observables Electro-weak precision observables Alexander Lenz The simplest Extension of the Standard Model ( ) 15 / 43

36 Direct mass limits Up-type Quarks u c t t Down-type Quarks d s b b Charged Leptons e µ τ l 4 Neutrinos τ ν µ ν e ν 4 1 ev 1 kev 1 MeV 1 GeV 1 TeV m m q > O(3GeV): D, CDF, CMS m ν4 > O(5GeV): LEP m l4 > O(1GeV): LEP m H / [137 GeV,27GeV]:D, CDF, CMS Alexander Lenz The simplest Extension of the Standard Model ( ) 16 / 43

37 Tree level constraints f W f V CKM4 = V ud V us V ub V ub V cd V cs V cb V cb V td V ts V tb V tb V t d V t s V t b V t b Alexander Lenz The simplest Extension of the Standard Model ( ) 17 / 43

38 Tree level constraints β decays V ud V us V ub V ub V cd V cs V cb V cb V td V ts V tb V tb V t d V t s V t b V t b Alexander Lenz The simplest Extension of the Standard Model ( ) 17 / 43

39 Tree level constraints β decays semileptonic meson decays V ud V us V ub V ub V cd V cs V cb V cb V td V ts V tb V tb V t d V t s V t b V t b Alexander Lenz The simplest Extension of the Standard Model ( ) 17 / 43

40 Tree level constraints β decays semileptonic meson decays V ud V us V ub V ub V cd V cs V cb V cb V td V ts V tb V tb V t d V t s V t b V t b (single) top production Alexander Lenz The simplest Extension of the Standard Model ( ) 17 / 43

41 Tree level constraints β decays semileptonic meson decays V ud V us V ub V ub V cd V cs V cb V cb V td V ts V tb V tb V t d V t s V t b V t b (single) top production The latest PDG value for V tb is.88±.7. Alexander Lenz The simplest Extension of the Standard Model ( ) 17 / 43

42 Tree level constraints alone CL.5 1-CL V tb θ 34 Still huge mixing with a fourth familiy possible! include also loop observables! Alexander Lenz The simplest Extension of the Standard Model ( ) 18 / 43

43 Further constraints: FCNC Flavour observables: W b s d u,c,t,t b u,c,t,t B d W W B d b u,c,t,t d q γ q Alexander Lenz The simplest Extension of the Standard Model ( ) 19 / 43

44 FCNC - in the SM CKM picture works very - Corrections should be small Calculation of the box diagram gives transition rate between the flavor eigenstates B s and B s : M 12 and Γ 12 The mass difference of the Mass eigenstates B H and B L is given by M s = m BH m BL 2 M 12 Performing the loop in the box diagram gives ( ) M 12 (V tb Vts) 2 S x t = m2 t MW 2 fb 2 s B Bs We have no direct information on V td and V ts. Indirect information is obtained from FCNCs, if we assume the unitarity of the 3x3 CKM matrix Alexander Lenz The simplest Extension of the Standard Model ( ) 2 / 43

45 FCNC in the SM4 Analysis: still huge corrections possible! There are two effects that change the value of M 12 in the SM4 t running in the loop The t loop is also changed, because now the CKM elements from the 3x3 fit can not be use anymore! This was overseen many times! Huge cancellations between these two effects are possible ,15.355: Parameter sets with O(3%) effects found Alexander Lenz The simplest Extension of the Standard Model ( ) 21 / 43

46 Bounds from FCNC Observables used as bounds M s, M d, M D ǫ K : CP violation in K decays b sγ, B s µµ sin2β from B d ψk s Observables not yet used B K ( ) ll Rare K decays Semileptonic asymmetries, Dimuonasymmetry sin2β s from B s ψφ Alexander Lenz The simplest Extension of the Standard Model ( ) 22 / 43

47 Bounds on the CKM element V td Im V td vs. Re V td Eberhardt, A.L., Rohrwild: Alexander Lenz The simplest Extension of the Standard Model ( ) 23 / 43

48 Bounds on the CKM element V ts Im V ts vs. Re V ts Eberhardt, A.L., Rohrwild: Alexander Lenz The simplest Extension of the Standard Model ( ) 24 / 43

49 Bounds on the CKM element V tb Im V tb vs. Re V tb Eberhardt, A.L., Rohrwild: Alexander Lenz The simplest Extension of the Standard Model ( ) 25 / 43

50 The oblique parameters S, T and U What are S, T and U? Explicit expressions The S-T ellipse Mass degeneracy The Higgs mass Alexander Lenz The simplest Extension of the Standard Model ( ) 26 / 43

51 What are S, T and U? a.k.a. Peskin-Takeuchi parameters a.k.a. oblique parameters a.k.a. electroweak pseudo-observables (S,T,U) full = (S,T,U) SM3 ferm +(S,T,U)SM4 ferm }{{} (S,T,U) ferm +(S,T,U) gauge +(S,T,U) Higgs }{{} (S,T,U) bos (S,T,U) = (S,T,U) SM4 ferm +(S,T,U)SM4 Higgs Alexander Lenz The simplest Extension of the Standard Model ( ) 27 / 43

52 What are S, T and U? Self-energy contributions by the fourth family Z,γ t Z,γ Z,γ b Z,γ t b W u W W c W W t W W b b b t t t W W W W W W W t d s b b Alexander Lenz The simplest Extension of the Standard Model ( ) 28 / 43

53 What are S, T and U? The S parameter S ferm = 16πs2 e 2 c cosθ W s sinθ W N c f c 2 Z f f Z + c ( s 2 p 2 c 2) γ f f s c 2 γ f f γ p 2 = Z Alexander Lenz The simplest Extension of the Standard Model ( ) 29 / 43

54 What are S, T and U? The T parameter T ferm = 4π e 2 c 2 M 2 Z f N c f W f f W 2cs γ f f c 2 Z f f Z s 2 γ f f Z γ p 2 = Alexander Lenz The simplest Extension of the Standard Model ( ) 3 / 43

55 What are S, T and U? The U parameter U ferm = 16πs2 e 2 N c W f f W c 2 Z f f p 2 f f 2cs γ f f Z s 2 γ f f Z γ p 2 = Alexander Lenz The simplest Extension of the Standard Model ( ) 31 / 43

56 Explicit expressions The exact formulae for S and T S ferm T ferm = = N c 6π (U,D) [ 1 2 ( )] 3 ln mu + 1 m D 6π N c 16πs 2 c 2 MZ πs 2 c 2 MZ 2 (ν,l) i i=u,dm 2 4 V (CKM) UD U,D i=ν,lm 2 i 4 ν,l V (PMNS) νl [ 1+2ln ( mν m l )] 2 mu 2m2 D mu 2 ln m2 D 2 mνm 2 l 2 mν 2 ln m2 l ( mu m D ( mν m l ) ) Alexander Lenz The simplest Extension of the Standard Model ( ) 32 / 43

57 The S-T ellipse We assume Gaussian distributions for S and T: 1 P(S,T) S T Alexander Lenz The simplest Extension of the Standard Model ( ) 33 / 43

58 The S-T ellipse: Experimental values S,T [PDG 94] [PDG 2] [Gfitter 9] [PDG 1] +.1 time Alexander Lenz The simplest Extension of the Standard Model ( ) 34 / 43

59 The S-T ellipse: Experimental values S,T [PDG 94] [PDG 2] [Gfitter 9] [PDG 1] +.1 time.2 T.4.6 Best fit 95%CL SM S Alexander Lenz The simplest Extension of the Standard Model ( ) 34 / 43

60 The S-T ellipse: SM4-fit T S Alexander Lenz The simplest Extension of the Standard Model ( ) 35 / 43

61 The S-T ellipse: SM4-fit T Best fit S Alexander Lenz The simplest Extension of the Standard Model ( ) 35 / 43

62 Fermion mass difference Neglecting the leptons 1 1-CL m t -m b (V CKM = 1) Alexander Lenz The simplest Extension of the Standard Model ( ) 36 / 43

63 Fermion mass difference Neglecting the leptons 1 1-CL.5 Excluded at 6σ -5 5 m t -m b (V CKM = 1) Alexander Lenz The simplest Extension of the Standard Model ( ) 36 / 43

64 Fermion mass difference Neglecting the leptons CL.5 Excluded at 6σ 1-CL m t -m b m t -m b (V CKM = 1) (V CKM 1) Alexander Lenz The simplest Extension of the Standard Model ( ) 36 / 43

65 Fermion mass difference Taking also the leptons into account: -2 m ν4 -m l4 [GeV] [GeV] - m l4 m ν th Generation M H =12 GeV B G fitter SM preliminary Aug m t -m b [GeV] (V CKM = 1) %, 95%, 99% CL fit contours (allowed) m d [GeV] u4 4 Alexander Lenz The simplest Extension of the Standard Model ( ) 37 / 43

66 Fermion mass difference Taking also the leptons into account: m ν4 -m l4 [GeV] m ν4 -m l4 [GeV] m t -m b [GeV] m t -m b [GeV] (V CKM = 1) (V CKM 1) Alexander Lenz The simplest Extension of the Standard Model ( ) 37 / 43

67 The Higgs mass Until now, m H was fixed to 116 GeV. m H > 116 GeV shift to the right: T m H = 116 GeV S T m H = 5 GeV S Alexander Lenz The simplest Extension of the Standard Model ( ) 38 / 43

68 The impact of S and T Tree-level CL.5 1-CL V tb θ 34 Alexander Lenz The simplest Extension of the Standard Model ( ) 39 / 43

69 The impact of S and T Tree-level + S and T CL.5 1-CL V tb θ 34 Alexander Lenz The simplest Extension of the Standard Model ( ) 39 / 43

70 New physics in B s mixing M 12 = M SM 12 2 excluded area has CL >.68 Γ s & τfs s 1 SM point & m s m d Im s -1-2 CKM A SL & a SL (B ) & a d (B ) SL s φ s-2β s f i t t e r New Physics in B - B s mixing Summer 1 s Re s A.L., Nierste, CKMfitter Alexander Lenz The simplest Extension of the Standard Model ( ) 4 / 43

71 New physics in B s mixing due to SM4? M 12 = M SM 12 Eberhardt, A.L., Rohrwild, Alexander Lenz The simplest Extension of the Standard Model ( ) 41 / 43

72 Outlook Future project: Prepare a combined CKM and electro-weak fit Include further flavor observables to the fits Replace S, T, U by the explicit observables Gonzalez, Rohrwild, Wiebusch, Include the whole lepton sector to the fits Lacker, Menzel ; A.L., Paes, Schalla Include new data to the fits - Summer conferences 211 New physics in B s mixing at LHCb? This kind of fit has also to be performed for other NP models Alexander Lenz The simplest Extension of the Standard Model ( ) 42 / 43

73 Outlook SM4 is not yet excluded by experimental data Perform Fits without approximations Investigate interesting theoretical aspects Lepton sector Aparici et al. 11, A.L., Paes, Schalla 11 DM candidates Soni et al 11 SM4 + other extensions of the SM, e.g. SUSY Lebed 11, Garg 11 2HDM Soni 11 DSB Wise et al 11 Non-perturbative effects Jansen et al 11 Baryogenesis Murayama et al 11, Wise et al 11 Exclude or discover the fourth family Alexander Lenz The simplest Extension of the Standard Model ( ) 43 / 43

74 Back-up slides Alexander Lenz The simplest Extension of the Standard Model ( ) 44 / 43

75 Results There are small hints at the fourth family: [WMAP 1] [CDF 1] Alexander Lenz The simplest Extension of the Standard Model ( ) 45 / 43

76 Results Alexander Lenz The simplest Extension of the Standard Model ( ) 46 / 43

77 Results LHC Alexander Lenz The simplest Extension of the Standard Model ( ) 46 / 43

78 Results LHC SUSY, Little Higgs, Warped Extra Dimensions... Alexander Lenz The simplest Extension of the Standard Model ( ) 46 / 43

79 Approximative and exact Higgs contributions to S and T For free Higgs masses: T m t -m b [GeV] -1 Approximation S m l4 -m ν4 [GeV] T m t -m b [GeV] -1 Exact expression S m l4 -m ν4 [GeV] Alexander Lenz The simplest Extension of the Standard Model ( ) 47 / 43

80 Back-up:The unitarity quadrangle η V t d V t b V cd V cb α V ud Vub α V V td tb V cd Vcb γ γ β β 1 ρ Alexander Lenz The simplest Extension of the Standard Model ( ) 48 / 43

81 Back-up:The unitarity quadrangle η V t d V t b V cd V cb α V ud Vub α V V td tb V cd Vcb γ γ β β γ = π +arg(v ud V ub ) arg(v cdv cb ) 1 ρ Alexander Lenz The simplest Extension of the Standard Model ( ) 48 / 43

82 Back-up:The unitarity quadrangle η V t d V t b V cd V cb α V ud Vub α V V td tb V cd Vcb γ γ β β γ = π +arg(v ud V ub ) arg(v cdv cb ) 1 ρ C.L δ 13 Alexander Lenz The simplest Extension of the Standard Model ( ) 48 / 43

83 Back-up What is the effective number of neutrinos? The total energy density of massive neutrinos d 3 p 1 ρ ν (a) = 2 ( ) (2π) 3 p 2 +m exp p ν 2 i T ν(a) +1 i = 1 q 2 dq 1 ( a 4 π 2 q exp q T ν )+1 2 +mν 2 i a 2 i can for relativistic neutrinos be related to the photon energy density ρ ν (a) 7 ( )4 4 3 N eff 8 11 ν ρ γ (a) taking the present-day neutrino temperature T ν = ( ) T cmb. (a is the cosmic scale and q = pa the comoving momentum. It was assumed that m νi = m νj.) Alexander Lenz The simplest Extension of the Standard Model ( ) 49 / 43

84 Explicit expressions The exact formula for U U ferm = Nc 3π + 1 3π 5Nc 36π [ ( V (CKM) UD 2 2m 2 U md 2 m 2 (m 2 + U +md 2 U,D U m2 D )2 mu 2 m2 D [ ( V (PMNS) νl 2 2m 2 ν ml 2 m 2 (m 2 ν,l ν ml 2 + ν +ml 2 )2 mν 2 ml π q ν,l 2m2 U m2 D (m2 U +m2 D ) ) (mu 2 ln m2 D )3 ) 2m2 ν m2 l (m2 ν +m2 l ) (m 2 ν m 2 l )3 ( ) ] mu m D ( ) ] mν ln m l Alexander Lenz The simplest Extension of the Standard Model ( ) 5 / 43

85 Explicit expressions Fourth family contributions to S and T Sferm SM4 = 1 [ 2+ln 3π Tferm SM4 1 16πs 2 c 2 MZ 2 12 ( )] mb m ν4 m t m l4 [ 3 ( mt 2 ) +m2 b +m 2 l4 +mν 2 4 i=t,t j=b,b 4 m2 ν 4 m 2 l 4 m 2 ν 4 m 2 l 4 ln +12 m2 tmb 2 mt 2 mb 2 ln V CKM 2 mi 2m2 j i j mi 2 mj 2 ) ( mν4 m l4 ( mt m b )] ( ) mi ln m j Alexander Lenz The simplest Extension of the Standard Model ( ) 51 / 43

86 The S-T ellipse The U parameter U U S S.2 (without T) (with T) Alexander Lenz The simplest Extension of the Standard Model ( ) 52 / 43

87 The Higgs mass The exact Higgs contributions S.1.5 Exact formula Approximation T.15 m H [GeV] Exact formula m H [GeV] Approximation Alexander Lenz The simplest Extension of the Standard Model ( ) 53 / 43

88 The Higgs mass The exact Higgs contributions S.1.5 Exact formula Approximation T.15 m H [GeV] Exact formula m H [GeV] Approximation Relative errors: m H [GeV] m H [GeV] Alexander Lenz The simplest Extension of the Standard Model ( ) 53 / 43