CKM OVERVIEW. Luca Silvestrini. TU-München & INFN Rome

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1 CKM OVERVIEW TU-München & INFN Rome Member of the Collaboration: M. Bona, M. Ciuchini, E. Franco, V. Lubicz, G. Martinelli, F. Parodi, M. Pierini, P. Roudeau, C. Schiavi, L. S., A. Stocchi, V. Vagnoni Motivation Standard Fit in the Standard Model New Constraints and New Physics CKM fits beyond the Standard Model Conclusions Page 1

2 MOTIVATION The SM works beautifully up to a few hundred GeV's, but it must be an effective theory valid up to a scale Λ Mplanck: EW scale NP contribution to g-2, b s, etc NP contribution to EW precision, FCNC processes, CPV, etc. Page 2

3 How can we explore NP with processes involving only SM particles? EW gauge symmetry spontaneously broken tree-level relations between EW observables (masses, couplings,...) quantum corrections computable and sensitive to higher-dim operators The LEP glorious legacy of precision EW fits: Λ > 2-10 TeV!! No tree-level FCNC (GIM mechanism) quantum corrections computable and sensitive to higher-dim operators the UT in the B-factory era: Λ > 4-6 TeV!! Page 3

4 The CP violation mechanism of the SM is very peculiar CP symmetry is explicitly broken by the Yukawa couplings CP is not an approximate symmetry of the model. CP violation is suppressed by mixing angles, but there are O(1) effects A single source of CP violation in the weak interactions of quarks (but leptons wait behind the corner with more sources) Three-generations unitarity: CP violation from the measurement of CP conserving observables All these features, if experimentally confirmed, provide strong constraints on New Physics Page 4

5 The Unitarity Triangle: radiative decays Xsγ,Xdγ, Xsll B ππ, ρπ, ρρ... theo. clean? B DK Charm Physics (Dalitz) +other charmonium +from Penguins 5

6 STD FIT The Standard UTfit Parameter Value Error(Gaussian) λ Vcb ( 10-3) (excl.) Vcb ( 10-3) (incl.) Vub ( 10-4) (excl.) Vub ( 10-4) (incl.) md (ps-1) ms (ps-1) > 14.5 ps-1 95%CL sens.18.3 ps-1 95% CL mt (GeV) mc (GeV) 1.3 mb (GeV) (MeV) ξ BK εk (10-3) sin2β f Bs ^ B Bs Error(Flat) 0.1 6

7 / 1 / 2 = V ub /V cb circle (0,0) C M B s f 2B 2 A2 6 [ ]= M B s d circle (1,0) C B K [ 1 A C tt C tc C cc ]= K hyperbola M B 2 2 M B 2 2 [ 1 ]= MB M B disc (1,0) d d s s 2 1 t =sin 2 A CP J / K S angle Page 7

8 Progress of the UT analysis End of parameter determination era, begin of precision test era: redundant determination of the triangle with new measurements from B-factories and test of new physics Page 8

and =0.190±0.044 =0.349±0.024 [ 0.100, 0.

9 and =0.190±0.044 =0.349±0.024 [ 0.100, prob. [ 0.303, prob. Page 9

10 Testing the Standard Model: CPC vs CPV sides only Spectacular agreement between direct and indirect measurements sin 2 sides=0.732±0.044 sin 2 ind =0.729±0.042 sin 2 dir =0.725±0.037 sin 2 =0.728±0.028 Page 10

11 B s B s mass difference ms = 20.4 ± 2.8 ps-1 not using the limit on ms using the limit on ms ms = 18.6 ± 1.7 ps 1 ms > 31(38) ps 1 is new First NP signal from hadron colliders? Page 11

12 Many other results of the SM standard analysis see *just updated! Page 12

13 BEYOND THE STANDARD UTfit: NEW INGREDIENTS TO THE UT ANALYSIS & NEW PHYSICS Page 13

14 α from ρρ/ρπ and SU(2) flavour symmetry Parametrization of the ρρ (ππ) amplitudes (neglecting EWP) i Gronau, London, PRL65 (1990) 3381 i P = T e P e 1 i i 0 A = e T T c e 6 unknowns: T, Tc, P, δp, δc, α 2 6 observables: 3xBRave, C+-, S+-, C A =A A 2 + time-dependent Dalitz plot study of (ρπ)0 à la Snyder-Quinn A C Snyder, Quinn, PRD48 (1993) 2139 (106 ± 8)o U (170 ± 9)o Page 14

15 Likelihood cos2β from ACP(B J/ψ K*(KS )) using the prior cos2β 1 cos2β > prob. Page 15

16 γ from B D(*)K no penguins four different flavours many modes XCPES=Ks π, Ks ρ, Ks π+ π-,... XCPNES=K+ π-, K+* π,... K+* K-, π+ ρ-,... Charged B: CP violation in the decay γ + GGSZ: Dalitz plot analysis of D0 3-body modes, ex. Ksπ+π Neutral B: CP violation in the interference between mixing and decay sin(2β+γ) Page 16

17 (64.0±18.2)o U (-116.0±18.2)o Page 17

18 and : angles only =0.246±0.063 =0.325±0.030 [ 0.123, prob. [ 0.265, prob. Page 18

19 and : all together sin(2β) ± sin(2α) ± 0.17 γ[ ] 58.1 ± 5.0 _ ρ _ η Excellent agreement with CKMfitter group: _ ± ± ρ _ η Page 19

20 New physics in the UT analysis (1) 3-generations unitarity Assumptions: (2) no new physics in tree-level processes ρ = η = sin2β = α = (95 15)o U ( 43 15)o Any model of new physics must satisfy these constraints Page 20

21 A more ambitious strategy: 1. Add most general NP to all sectors 2. Use all available info 3. Constrain simultaneously and NP contributions UTfit coll., hep-ph/0506xxx Only possible thanks to the new measurements of CKM angles!!! Page 21

22 General parametrization of the mixing amplitudes 2 i q SM Bq SM K B q B q mixing: A B =C q e K K mixing: Im A K =C Im A q A (3) assume NP in B=1 decays is SU(2) invariant Use: sin 2 cos 2 and Laplace, Ligeti, Nir & Perez Exploiting the redundancy of the fit, we look for bounds on 3 additional real parameters: d d C, {C, } Page 22

23 Using: md, sin 2 Page 23

24 Using: md, sin 2 Page 24

25 Using: md, sin 2 ASL Page 25

26 Using: md, sin 2 cos 2 Page 26

27 Using: md, sin 2 Page 27

28 Using: md, sin 2 cos 2 ASL Page 28

29 Page 29

The most important message of this talk: New Physics in B=2 and S=2 can be up to ~50% of the SM only if NP has the same phase of the SM, otherwise it has to be at most ~ 10%.

30 The most important message of this talk: New Physics in B=2 and S=2 can be up to ~50% of the SM only if NP has the same phase of the SM, otherwise it has to be at most ~ 10%. This is a completely general result. Only two ways out: Minimal Flavour Violation or new CP violation only in b s transitions. CBd = 1.29 ± 0.47 Bd = 0.1 ± 3.2 C = 1.07 ± 0.26 Page 30

31 The Universal Unitarity Triangle Buras et al., hep-ph/ (4) Minimal Flavour Violation: all FV in the Yukawa couplings UUT determined by processes insensitive to NP contributions: no εk Md/ Ms only valid in any MFV model Page 31

32 UUT starting point for MFV studies of rare decays Results of a model-independent MFV analysis of rare K & B decays C. Bobeth et al., hep-ph/ Page 32

33 MFV: an effective theory approach D'Ambrosio et al., hep-ph/ classification of the dim-6 operators built with the SM fields and 1 or 2 Higgs doublets under the assumption that the flavour violation dynamics is determined by ordinary Yukawa couplings 1H: Universal NP effect in the F=2 Inami-lim function of the top S 0 x t S 0 x t S 0, S 0 =O 4 We can bound the NP scale 02 2, 0 ~2.4 TeV Λ: Λ > 6.0 prob. for positive δs0 Λ > 4.6 prob. for negative δs0 Page 33

34 2H + large tanβ: terms proportional to the bottom Yukawa coupling are enhanced and cannot be neglected any more B 0 S S K 0 δs0b K 0 δs Λ > 3.6 prob. for δs0 > 0 Λ > 4.6 prob. for δs0 < 0 Λ > 5.0 prob. for δs0 > 0 Λ > 4.3 prob. for δs0 < 0 Page 34

35 Where does NP hide? NP in s d and/or b d transitions is strongly constrained by the UT fit unnecessary, given the great success and consistency of the fit NP in b s transitions is much less (un-) constrained by the UT fit natural in many flavour models, given the strong breaking of family SU(3) Pomarol, Tommasini; Barbieri, Dvali, Hall; Barbieri, Hall; Barbieri, Hall, Romanino; Berezhiani, Rossi; Masiero, Piai, Romanino Silvestrini; hinted at by ν s in SUSY-GUTs Baek, Goto, Okada, Okumura; Moroi; Akama, Kiyo, Komine, Moroi; Chang, Masiero, Murayama; Hisano, Shimizu; Goto, Okada, Shimizu, Shindou, Tanaka; Page 35

36 The last resort: NP in b s modes Obs. #1: These modes should not be averaged in the SM They measure the same S=S(ccK) only if one amplitude is dominant Obs. #2: These modes should not be averaged beyond SM They do not get in general the same NP contribution THESE MODES SHOULD NOT BE AVERAGED Page 36

37 Conclusions The SM is (surprisingly enough) extremely successful in reproducing all available data Thanks to the recent progress, NP in B=2 and S=2 transitions is strongly constrained, testing scales above the TeV Hadron colliders will tell us whether SM, MFV or New Flavour & CPV in b s... Page 37

38 BACKUP SLIDES Page 38

39 Ciuchini et al., hep-ph/ Buras, Silvestrini, hep-ph/ For example, with the charming penguins parametrization: A(B0 φ Κ0) = - Vts Vtb* P1'(c) - Vus Vub* {P1' GIM(u-c)} A(B0 Κ0 π0) = - Vts Vtb* P1(c) - Vus Vub* {E2+P1GIM(u-c)} S= S= small deviations from SccK (model-dependent) Page 39

40 B fb fb = 0.20 ± 0.10 GeV from UTfit fb = ± ± GeV Lattice QCD B not competitive yet Page 40

41 Vcb - Inclusive Method ν l c b Vcb Moments of distributions HADRONIC mass, LEPTON Momentum, Photon energy b s γ 2% Γsl = (0.434 (1 ± 0.018)) MeV Γsl (b cl ν ) Brsl Vcb = τb = f(µ2π, mb,, mc αs, ρd(or 1/mb3)) mb ( also named Λ) µ2π (λ1 Fermi movement) 2 F Based on OPE Mb,kin(1GeV) = 4.59 ± 0.08 ± 0.01GeV 4.23(mb(mb)) mc,kin. (1GeV) = 1.13 ± 0.13 ± 0.03GeV µπ2 = 0.31 ± 0.07 ± 0.02GeV2 ρd2 = 0.05 ± 0.04 ± 0.01GeV2 terms 1/mb3 (under control?)/small! Vcb(inclusive)= ( 41.4 ± 0.6 ± 0.7(theo.) ) 10-3 Exp + (µ2π, mb,, ρd.absorbed!) Pert. QCD. αs, terms 1/mb4 hep-ph/ C.Bauer,Z.Ligeti,M.Luke,A.Manohar hep-ph/ , M.Battaglia et al. (P.Gambino,N.Uraltsev) hep-ph/ D. Benson,I.Bigi,T.Mannel,N.Uralstev 41

42 Vcb-Exclusive Method Based on HQET dγ dw G 2F 48 π 2 V cb 2 F w 2 G w F(1) Vcb At zero recoil (w=1), as MQ F(1) 1 ρ2 F(1) ~ 0.91 ± 0.04 Vcb(exclusive)= ( 41.5± 1.0 ± 1.8 )

43 Vub Inclusive methods Vub = ( 4.7 ± 0.44) 10-3 B Xu l+ ν 43

44 Exclusive methods B (π,ρ,ω) l ν Common to all analyses Vub = ( 3.30 ± 0.24 ± 0.46) 10-3 Error : dominated by form factor errors as F(1) in Vcb 44

45 Oscillations in B0d system : md B0d,s b W t,c,u d, s d,s + W Vtd md t,c,u b Vts 2 f B2d BBd Vcb λ2 Vtd P B0 B0 B0 q q q 1 t /τ q e 1±cos Δmq t 2 ( today dominated by Belle-BaBar ) f Bd BBd Vcb λ ((1 ρ ) + η ) md = ± ps-1 LEP/SLD/CDF/B-factories Precise measurement (1.2%) 45

46 Oscillations in B0s system : ms m s f B2s B B s V td Δm d Δm s 2 f 2 Bd BB f 2 Bs BB d f B2s B B s V cb λ 2 1 ρ 2 η 2 s 1/ξ2 ms > 14.4 ps-1 at 95% CL Sensitivity at 19.3 ps-1 LEP/SLD/CDF-I 2 46

47 ξ Calculation partially unquenched (Nf=2 or 2+1) in agreement 1.02±0.02 f Bs f Bd = 1.18 ± , BBs BBd = 1.00 ± 0.03 ξ= ^ f Bs B Bs f Bd ^ = 1.24 ± 0.04 ± 0.06 B Bd Chiral extrapolation : light quarks simulated typically in a range [ms/2 - ms ] 47

48 ^ Calculation partially unquenched (Nf=2 or 2+1) in agreement ± = d B,B ev 0 M ± 03 2 = d B f + f Bd B Bd ^ f Bd B Bd = 223 ± 33 ± 12 MeV 1.09±0.06 ( Sum Rules f Bd = 208 ± 27 MeV, BBd = 1.67 ± 0.23) (syst not correlated ~mb) ± = K K B.04 0 ± = ) ev G (2 B BK ^ ^ 1.05±0.15 unquenching factor 1.05±0.05 SU(3) effects factor ^ B K = 0.86 ± 0.06 ± ±0.09

49 sin 2 β B0 mixing 0 B CP violation comes from interference between decays with and without mixing Af dec ay a f (t ) = CP CP f CP ay dec A f CP 0 ( t) f ) Γ( B 0phys (t) f CP) Γ( Bphys CP 0 ( t) f ) Γ( B 0phys (t) f CP) + Γ( Bphys CP = C f cos( md t) + S f sin( md t) CP CP ~ η J /ψ K sin 2β sin( mdt ) 0 S,L sin 2 β = ±

50 B AVcb u W b B λ angle γ AVub decay K s Vub = Vub e-iγ Vcb D 0 u u A( B D 0 K ) = AB 0 A( B + D K + ) = AB AB δ B = δ1 δ 2 u c s u b c strong amplitude (the same for Vub and Vcb mediated transitions strong phase difference between Vub and Vcb mediated transitions W B u D 0 K A( B D K ) = AB rb ei (δ B γ ) A( B + D 0 K + ) = A r ei (δ B +γ ) 0 B B 0 A( B D K ) rb = A( B D 0 K ) rb is a crucial parameter. It drives the sensitivity on γ 50

51 GLW (Gronau,London,Wyler) Method ACP ± angle γ Γ( B + DCP ±2rB sin γ sin δ B ± K ) Γ ( B DCP ± K ) = = Γ( B DCP ± K ) + Γ( B DCP ± K ) 1 + rb ± 2rB cosγ cosδb RCP ± = Γ( B+ DCP ± K ) + Γ ( B DCP ± K ) 0 Γ( B + D K + ) + Γ ( B D0 K ) = 1 + rb 2 ± 2rB cos γ cos δb ADS (Atwood, Dunietz, Soni) Method (only Babar) RADS Γ( B+ ( K π + ) D K + ) Γ (B (K + π ) D K ) 2 2 = = r + r + 2rB rdcs cos γ cos(δ B + δ D ) B DCS Γ( B ( K π ) D K ) + Γ( B ( K π ) D K ) rdcs + BR( D K π ) BR( D 0 K +π ) 0 (3.62 ± 0.29)

angle γ Dalitz Method - GGSZ new technique which makes use of the D0 three-body decays Plot of the weights K ρ(π π ) CP-GLW method (second derivative wrt γ) s + - D 0 K S π+ π M

52 angle γ Dalitz Method - GGSZ new technique which makes use of the D0 three-body decays Plot of the weights K ρ(π π ) CP-GLW method (second derivative wrt γ) s + - D 0 K S π+ π M 2 ( K sπ ) BaBar Interference due to the overlap of large resonances from Cabibbo allowed Vcb and Vub transitions K*+ (1430) K (892)(Κs π ) π ) ADS method *+ + - M 2 ( K sπ + ) 52

53 rdk = 0.10 ± 0.04 CL) rd*k = 0.09 ± 0.04 ([0.01, CL) = 64.0 ± % CL) = ± % CL) 53

54 angle α sin2 with SU(2) analysis Starting from the SU(2) amplitudes: Gronau-London, Phys. Rev. Lett. 65, (1990) A+- = -Te-i + Pei P A+0 = -1/ 2 e-i (T + TC ei C) A00 = -1/ 2 (TC ei C e-i + Pei P) unknowns: T, P, TC, P, TC, observables: 3x BR, C+-, S+-, C00 even if the system is not closed yet we start to have relevant information 54

55 angle α Experimental situation for the decays mode HFAG experimental inputs: ππ ρρ Observable BaBar Belle Average BaBar Belle Average C ± ± ± ± ± 0.20 S ± ± ± ± ± 0.24 BR(+-) (10-6) 4.7 ± ± ± ± ± 6.0 BR(+0) (10-6) 5.8 ± ± ± ± ± ± 6.4 fl(+0) ± ± BR(00) (10-6) 1.17 ± ± ± ± ± 0.41 fl(00) (ρπ) (assumed) BaBar result 55

56 angle α = (106 ± 8) o U (170 ± 9)o 56

Bounds on New Physics from the Unitarity Triangle fit: Summer'06 update

Bounds on New Physics from the Unitarity Triangle fit: Summer'06 update University of Wisconsin, Madison on behalf of UTfit Collaboration http://www.utfit.org M. Bona, M. Ciuchini, E. Franco, V. Lubicz,