Lessons for New Physics from CKM studies

Lessons for New Physics from CKM studies Indiana University Flavor Physics and CP violation, 010 Università di Torino, May 5-8, 010

Outline Flavor violation in the Standard Model Inputs to the unitarity triangle analysis Status of CKM fits: role of Vub, Vcb and B τν Parametrization of NP in K/B-mixing and B τν and fit Interpretation in terms of complex NP coefficients Super-B/LHCb prospects Conclusions

The Cabibbo -Kobayashi -Maskawa matrix Gauge interactions do not violate flavor: L Gauge = ψ,a,b ψ a (i / ga/ δ ab )ψ b Yukawa interactions (mass) violate flavor: L Yukawa = ψ,a,b ψ La H Y ab ψ Rb = Q L HY U u R + Q L HY D d R + L L HY E E R The Yukawas are complex 3x3 matrices: Y U = U L Y diag U U R, Y D = D L Y diag D D R, Y E = E L Y diag From Gauge to Mass eigenstates neutral currents: ū 0 LZ/ u 0 L = ū L Z/ U L U L u L = ū L Z/ u L E E R huge potential for NP effects (MFV?) charged currents: ū 0 LW/ d 0 L = ū L W/ U L D L d L = ū L W/ V CKM d L 3 = Virtual Nobel Laureate = Real Nobel Laureate

The Cabibbo -Kobayashi -Maskawa matrix λ: β-decay, K πlν, D (π,k)lν, νn μx,... V ud V us V ub ρ,η: B πlν, B Xulν CP violation V cd V cs V cb A: B D (*) lν, B Xclν V td V ts V tb =1: t Wb (single top) A: no direct meas. (B Xsγ, ΔMBs,...) ρ,η: no direct meas. (ΔMBd, CP violation, K mixing) Wolfenstein parametrization: 1 λ / λ Aλ 3 (ρ iη) λ 1 λ / Aλ Aλ 3 (1 ρ iη) Aλ 1 4 = Virtual Nobel Laureate = Real Nobel Laureate

Treatment of lattice inputs and errors Lattice QCD presently delivers +1 flavors determinations for all the quantities that enter the fit to the UT Results from different lattice collaborations are often correlated MILC gauge configurations: fbd, fbs, ξ, Vub, Vcb, fk use of the same theoretical tools: BK, Vcb experimental data: Vub It becomes important to take these correlation into account when combining saveral lattice results We assume all errors to be normally distributed [Laiho,EL,Van de Water, 0910.98] Updated averages at: http://www.latticeaverages.org 5

Determining A Can be extracted from tree-level processes (b clν) ΔMBs is conventionally used only to normalize ΔMBd but it should be noted that it provides an independent determination of A (that might be subject to NP effects): M Bs f B s ˆBBs A λ 4 Other processes are very sensitive to A but also display a strong ρ-η and NP dependence and are therefore usually discussed in the framework of a Unitarity Triangle fit: ε K ˆB K κ ε A 4 λ 10 η(ρ 1) BR(B τν) f BA λ 6 (ρ + η ) 6

Observables included in the fit Vub and Vcb from inclusive and exclusive semileptonic decays Bd and Bs mass differences: ξ and f ˆB1/ Bs s α and γ from B (ππ, ρρ, ρπ,d ( ) K ( ) ) BR(B τν) ˆB f Bd = f ˆB1/ Bs s /(ξ ˆB d d ) S ψk = sin β : ( ) ε K : ˆB K, κ ε Note on ε K : ε K = e iφ ε sin φ ε ( ImM K 1 M K + ImA 0 ReA 0 ) from experiment 7 mostly short distance + χpt κ ε long distance ε ) {(use /ε

Inputs to the fit: summary ˆB K =0.70 ± 0.05 κ ε =0.94 ± 0.017 ξ =1.37 ± 0.03 f Bs ˆB s = (75 ± 13) MeV ˆB d =1.6 ± 0.11 V cb excl = (39.0 ± 1.) 10 3 (40.43 ± 0.86) 10 3 V cb incl = (41.31 ± 0.76) 10 3 V ub excl = (30.9 ± 3.3) 10 4 V ub incl = (40.1 ±.7 ± 4.0) 10 4 } 1.7σ tension (error rescaled) } (33.0 ± 3.7) 10 4 1.6σ tension (error rescaled) additional theory uncertainty m Bd = (0.507 ± 0.005) ps 1 m Bs = (17.77 ± 0.10 ± 0.07) ps 1 α = (89.1 ± 4.4) o γ = (78 ± 1) o η 1 =1.51 ± 0.4 m t,pole = (17.4 ± 1.) GeV η =0.5765 ± 0.0065 m c (m c ) = (1.68 ± 0.009) GeV η 3 =0.47 ± 0.04 ε K = (.9 ± 0.01) 10 3 η B =0.551 ± 0.007 λ =0.55 ± 0.0007 S ψks =0.67 ± 0.04 f K = (156.1 ± 1.) MeV BR(B τν) = (1.74 ± 0.35) 10 4 8

Current fit to the unitarity triangle [sin β] fit =0.774 ± 0.038. σ [BR(B τν)] fit = (0.773 ± 0.095) 10 4.7 σ [ ˆB K ] fit =0.918 ± 0.086.4 σ 9

Current fit to the unitarity triangle [sin β] fit =0.774 ± 0.038. σ [BR(B τν)] fit = (0.773 ± 0.095) 10 4.7 σ [ ˆB K ] fit =0.918 ± 0.086.4 σ 10

Removing Vub [Lunghi,Soni 0803.4340 and 0903.5059] Vub is the \begin{personal opinion} most controversial \end{personal opinion} input [sin β] fit =0.86 ± 0.045 3.3 σ [BR(B τν)] fit = (0.784 ± 0.098) 10 4.6 σ [ ˆB K ] fit =0.914 ± 0.086.4 σ 11

Removing Vub [Lunghi,Soni 0803.4340 and 0903.5059] Vub is the \begin{personal opinion} most controversial \end{personal opinion} input [sin β] fit =0.86 ± 0.045 3.3 σ [BR(B τν)] fit = (0.784 ± 0.098) 10 4.6 σ [ ˆB K ] fit =0.914 ± 0.086.4 σ disturbing 1.7σ problem 1

Removing Vub and Vcb? [Lunghi,Soni 091.00] The use of Vcb seems to be necessary in order to use K mixing to constrain the UT: M Bs = χ s f B s ˆBBs A λ 4 ε K =χ ε ˆBK κ ε ηλ 6( A 4 λ 4 (ρ 1)η S 0 (x t )+A ( η 3 S 0 (x c,x t ) η 1 S 0 (x c ) )) BR(B τν)=χ τ f BA λ 6 (ρ + η ) The interplay of these constraints allows to drop Vcb while still constraining new physics in K mixing: ε K ˆB K (f ˆB1/ Bs s ) 4 f(ρ, η) ε K ˆB K BR(B τν) f 4 B g(ρ, η) 13

Removing Vcb! [Lunghi,Soni 091.00] The use of Vcb seems to be necessary in order to use K mixing to constrain the UT: ρ-η topology of the constraint makes it relevant despite large errors on B τν X : ˆBK V cb f ˆB1/ Bs s BR(B τν) f B δx : 3.7%.5% 4.7% 1% 5% δε K : 3.7% 10% 18.9% 4% 0% 14

Removing Vcb! [Lunghi,Soni 091.00] [sin β] fit =0.863 ± 0.051.8 σ [BR(B τν] fit = (0.763 ± 0.098) 10 4.7 σ [ ˆB K ] fit =0.970 ± 0.17 1.6 σ V cb fit = (4.6 ± 0.8) 10 3 1.7 σ 15

Model Independent Interpretation The tension can be interpreted as NP in Bd/K mixing or B τν: For NP in Bd mixing: For NP in B τν: M 1 = M1 SM rd e iφ d ε K = ε SM K C ε BR(B τν) = BR(B τν) SM r H a ψks = sin (β + φ d ) sin α eff = sin (α φ d ) X sd = X SM sd BR(B τν) NP = BR(B τν) (1 SM tan β m B + m H (1 + ɛ + 0 tan β) }{{} r H 16 r d )

Model Independent Interpretation NP in B mixing (marginalizing over rd): (θ d ) fit = (3.8 ± 1.9) o (8.8 ± 3.1) o (10.5 ± 3.5) o (.1σ,p= 11%) complete fit (3.σ,p= 68%) no V ub (3.0σ,p= 76%) no V qb p SM =.3% p no V ub SM =1.4% p no V qb SM =.6% NP in K mixing: (C ε ) fit = 1.8 ± 0.13 (.4σ,p= 1%) complete fit 1.7 ± 0.13 (.4σ,p= 7%) no V ub 1.35 ± 0.3 (1.6σ,p= 4%) no V qb NP in B τν: (r H ) fit =.30 ± 0.53 (.7σ,p= 19%) complete fit.7 ± 0.53 (.7σ,p= 1%) no V ub.33 ± 0.55 (.7σ,p= 30%) no V qb Hard to reconcile with H + effects: in natural configurations rh<1 (see also B Dτν) 17

Model Independent Interpretation NP in B mixing ( dimensional [θd,rd] contours) 1.0 full fit: no Vub no Vqb 1.0 1.0 r d 1.15 1.10 1.05 1.00 0.95 3Σ Σ 1Σ r d 1.15 1.10 1.05 1.00 0.95 3Σ Σ 1Σ r d 1.15 1.10 1.05 1.00 0.95 3Σ Σ 1Σ 0.90 0.90 0.90 0.85 0.85 0.85 0.80 0.4 0.3 0. 0.1 0.0 Θ d 0.80 0.4 0.3 0. 0.1 0.0 p = 11% p = 68% p = 76% pno V ub p no V qb p SM =.3% SM =1.4% SM =.6% Θ d 0.80 0.4 0.3 0. 0.1 0.0 Θ d One dimensional r d ranges compatible with r d =1 18

Super-B expectations Reducing uncertainties on Bs mixing and B τν : δ τ δ s p SM θ d ± δθ d p θd θ d /δθ d 0% 4.6%.6% (10.6 ± 3.5) o 75% 3.0σ 0%.5% 0.6% (10. ± 3.3) o 71% 3.4σ 0% 1% 3 10 % (9.9 ± 3.0) o 69% 3.9σ 10% 4.6% 6 10 3 % (10.9 ±.4) o 74% 4.7σ 3% 4.6% 4 10 5 % (11.0 ±.0) o 74% 5.6σ 10%.5% 1.4 10 3 % (10.7 ±.4) o 69% 4.8σ 10% 1% 1. 10 4 % (10.5 ±.4) o 64% 5.1σ 3%.5% 1.1 10 5 % (10.9 ±.0) o 68% 5.7σ 3% 1% 4 10 6 % (10.8 ±.0) o 6% 5.8σ δ τ = δbr(b τν) Even modest improvements on B τν have tremendous impact on the UT fit (10/50 ab -1 δτ = 10/3% ) 19 δ s = δ(f Bs Bs ) Interplay between Bs mixing and B τν can result in a 5σ effect

Operator Level Analysis Effective Hamiltonian for Bd mixing: H eff = G F m W 16π (V tb V td) ( 5 i=1 C i O i + 3 i=1 C i Õ i ) O 1 =( d L γ µ b L )( d L γ µ b L ) O =( d R b L )( d R b L ) Õ 1 =( d R γ µ b R )( d R γ µ b R ) Õ =( d L b R )( d L b R ) O 3 =( d α R bβ L )( d β R bα L ) O 4 =( d R b L )( d L b R ) Õ 3 =( d α L bβ R )( d β L bα R ) O 5 =( d α R bβ L )( d β L bα R ). Parametrization of New Physics effects: H eff = G F m4 W 16π (V tb Vtd) C1 SM ( 1 m W eiϕ Λ ) O 1 Analogue expressions for K mixing 0

Operator Level Analysis: Mixing The contribution of the LR operator O4 to K mixing is strongly enhanced ( µ L GeV,µ H m t ): C 1 (µ L ) K O 1 (µ L ) K 0.8 C 1 (µ H ) 1 3 f Km K B 1 (µ L ) C 4 (µ L ) K O 4 (µ L ) K 3.7 C 4 (µ H ) 1 ( 4 m K m s (µ L )+m d (µ L ) O(1) ) f Km K B 4 (µ L ) running from μh to μl chiral enhancement C 4 (µ L ) K O 4 (µ L ) K C 1 (µ L ) K O 1 (µ L ) K (65 ± 14) B 4(µ L ) B 1 (µ L ) C 4 (µ H ) C 1 (µ H ) No analogous enhancement in Bq mixing 1

Operator Level Analysis: Bd Mixing dimensional [Λ,φ] contours: 3 full fit: no Vub no Vqb 3 3 1 1Σ Σ 3Σ 1 1Σ Σ 3Σ 1 1Σ Σ 3Σ φ rad 0 φ rad 0 φ rad 0 1 1 1 p SM =.3% pno V ub SM =1.4% p no V qb SM =.6% 3 100 00 300 400 500 GeV 3 100 00 300 400 500 GeV 3 100 00 300 400 500 GeV Lower limit on Λ induced by M Bs / M Bd Projections of contours yield the one-dimensional nσ regions Fit points to Λ in the few hundred GeV range and O(1) phase

dimensional [Λ,φ] contours (O1): full fit: no Vub no Vqb 3 3 3 1 1 1 Σ 0 "1 1Σ Σ 0 "1 3Σ $!rad" 1Σ $!rad" $!rad" Operator Level Analysis: K Mixing "1 3Σ " " "3 "3 "3 #!GeV" 00 300 psm =.3% 400 500 100 #!GeV" Vub pno = 1.4% SM 00 300 400 Σ 0 " 100 1Σ 500 3Σ 100 #!GeV" no Vqb psm =.6% 00 300 400 No lower limit on Λ: fitting one parameter only (Cε) Fit points to Λ in the few hundred GeV range and O(1) phase; fine tuning allow lower masses 3 500

dimensional [Λ,φ] contours (O4): full fit: no Vub no Vqb 3 3 3 1 1 1 Σ 0 "1 1Σ Σ $!rad" 1Σ $!rad" $!rad" Operator Level Analysis: K Mixing 0 "1 3Σ "1 3Σ " " "3 "3 "3 #!TeV" 3 psm =.3% 4 1 #!TeV" Vub pno = 1.4% SM 3 Σ 0 " 1 1Σ 4 3Σ 1 #!TeV" no Vqb psm =.6% 3 4 No lower limit on Λ: fitting one parameter only (Cε) Fit points to Λ in the few TeV range and O(1) phase; fine tuning allow lower masses 4

Conclusions Using +1 lattice QCD hint for NP in the UT fit (~3σ) We need better understanding of inclusive Vub and Vcb The tension in the UT fit could be explained by new physics in Bd mixing (preferred), K mixing or B τν As long as Vqb determinations remain problematic, removing semileptonic decays allows to cast the UT fit as a clean & highprecision tool to identify new physics Super-B precision on B τν coupled with improvements on the lattice determination of f Bs Bs can test the SM at the 5σ level Interpretation of this tension in terms of SM like new physics contribution point to masses in the few hundred GeV range and complex couplings with O(1) phases. 5

Comments on systematic uncertainties We treat all systematic uncertainties as gaussian Most relevant systematic errors come from lattice QCD (BK,ξ) and are obtained by adding in quadrature several different sources of uncertainty Gaussian treatment seems a fairly conservative choice 7

Comments on systematic uncertainties We treat all systematic uncertainties as gaussian Most relevant systematic errors come from lattice QCD (BK,ξ) and are obtained by adding in quadrature several different sources of uncertainty Gaussian treatment seems a fairly conservative choice B K 0.70 ± 0.013 stat ± 0.037 syst B K 0.70 ± 0.013 stat ± 0.037 syst 14 1 Gaussian 14 1 Flat 10 10 pdf 8 pdf 8 6 6 4 4 0 0.60 0.65 0.70 0.75 0.80 0.85 0 0.60 0.65 0.70 0.75 0.80 0.85 B K B K 8

Comments on systematic uncertainties We treat all systematic uncertainties as gaussian Most relevant systematic errors come from lattice QCD (BK,ξ) and are obtained by adding in quadrature several different sources of uncertainty Gaussian treatment seems a fairly conservative choice B K 0.70 ± 0.013 stat ± 0.037 syst 14 1 Flat Gaussian 10 pdf 8 6 4 0 0.60 0.65 0.70 0.75 0.80 0.85 B K 9

Comments on systematic uncertainties We treat all systematic uncertainties as gaussian Most relevant systematic errors come from lattice QCD (BK,ξ) and are obtained by adding in quadrature several different sources of uncertainty Gaussian treatment seems a fairly conservative choice B K 0.70 ± 0.013 stat ± 0.037 syst 14 1 10 Flat Gaussian 1.5Σ gaussian pdf 8 6 13 gaussian 0.7 flat 4 0 0.60 0.65 0.70 0.75 0.80 0.85 B K 30

Time dependent CP asymmetry in b q qs [HFAG 009] arg(v td) b$ccs rage 0.67! 0.0 { S ψks = sin (β + θ d )+O(0.1%) b s ss { # K 0 %& K 0 K S K S K S ' 0 K 0 ( 0 K S ) K S f 0 K S 0.44 + - 0 0.. 1 1 7 8 0.59! 0.07 0.74! 0.17 0.57! 0.17 0.54 + - 0 0.. 1 8 1 0.45! 0.4 0.60 + - 0. 11 0. 13 In QCDF: S f S f sin (β + θ d ) ( ) = V ub Vus a u f V cb Vcs cos β sin γ Re a c f 0.05 S φ = 0.03 ± 0.01 S η = 0.01 ± 0.05 [Beneke,Neubert] [EL, Soni] K + K - K 0 0.8! 0.07 0. 0.4 0.6 0.8 1 Other approaches find similar results [Chen,Chua,Soni; Buchalla,Hiller,Nir,Raz] We will consider the asymmetries in the A case can be made for the J/ψ, φ, η K s K s K s final state modes [Cheng,Chua,Soni] 31

K mixing ( ε K ) Buras, Guadagnoli & Isidori pointed out that also M1 K receives non-local corrections with two insertions of the ΔS=1 Lagrangian: u, c s d s u, c d K 0 K 0 d s K 0 K 0 d s Using CHPT they obtain a conservative estimate of these xxxxxxxxxxxxxeffects. π Combining the latter with our K 0 K 0 xxxxxxxxxxxxxdetermination of ImA0 we obtain: π κ ε =0.94 ± 0.017-6%! [Laiho,EL,Van de Water; Buras, Guadagnoli, Isidori] 3