Flavor Physics and Lattice QCD An emblematic study: the Unitarity Triangle Analysis. Cecilia Tarantino Università Roma Tre

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1 Flavor Physics and Lattice QCD An emblematic study: the Unitarity Triangle Analysis Cecilia Tarantino Università Roma Tre 1

2 Flavor Physics is complementary, in NP searches, to the direct production of NP particles e.g. In SM suppressed Flavor processes NP effects may be visible It is crucial to have accurate theoretical predictions in order to reveal possible NP effects Lattice QCD has a primary role as it allows to compute the (non-perturbative) long-distance QCD contributions from first principles Lattice QCD: non-perturbative approach based on the path-integral formalism QCD simulated on discrete space and finite volume QCD parameters only 2

3 We are in the era of PRECISION LATTICE QCD 1) Increasing of computational power (Several machines of O( PetaFlops)) Unquenched simulations QUENCHED UNQUENCHED N f =2 (u,d) N f =2+1 (u,d,s) N f =2+1+1 (u,d,s,c) 2) Algorithmic improvements: Light quark masses in the ChPT regime

4 Systematic Uncertainties: The state of the art is evident from the color code introduced by FLAG for Pion and Kaon Physics (Flavor Lattice Averaging Group) 2013: FLAG2 updates + heavy-flavor Physics (preliminary) First N f =2+1+1 results appear

5 An emblematic study showing the important role of Lattice QCD is the accurate determination of the parameters of the Cabibbo-Kobayashi-Maskawa mixing matrix Weak eigenstates Mass eigenstates d' s' b' s W + V CKM V us u d s b The Wolfenstein parameterization (A, l, r, h) V V V ud cd td V V V up to O(l 3 ) with l sin θ Cabibbo 0.2 us cs ts V V V ub cb tb Aλ 3 λ 1 2 λ 2 (1 ρ iη) λ λ 1 2 Aλ Aλ (ρ iη) 2 Aλ 1 (O(l 5 ) corrections are required by the present accuracy) 5

6 The expansion parameter l=v us from Lattice QCD Unitarity ( V V CKM CKM ) provides 9 conditions on the CKM parameters 1 1 st row: the most stringent unitarity test V ud 2 + V us 2 + V ub 2 = 1 Source: Nuclear β-dec. Kl3,Kl2 b u semil. Abs. error: ~10-6 Pseudoscalar decay constant f K and vector form factor f + (q 2 =0) from Lattice QCD FLAG V us =0.2254(9) N f =2+1 V us =0.2251(18) N f =2 less than 0.5% uncert. 6

7 Isospin Breaking Effects The lattice determinations are usually obtained in the limit of exact ISOSPIN SYMMETRY, i.e. m u = m d and Q u = Q d = 0 Though small, isospin breaking effects are becoming important at the current level of precision in flavor physics. Their typical size is: Q u Q d : O(a e.m. ) 1/100 electromagnetic m u m d : O[(m d -m u )/Λ QCD ] 1/100 strong The strong IB corrections to f K /f p and to f + (0) have been calculated on the Lattice by using a strategy based on a m d -m u expansion [P. Dimopoulos et al., ] More recently: em corrections have been evaluated for M 2 p+ - M 2 p0 and M 2 K+ - M 2 K0 strong+em corrections have been evaluated for the octet baryon mass splittings [BMW ], Sea em charge effects have been studied [PACS-CS, ] [G.de Divitiis et al ], 7

8 The Unitarity Triangle Analysis (UTA) Among the 9 unitarity conditions V V CKM CKM λ λ ρ ρ 1, η η V ub V ud V cb V 0 is of great phenomenological interest V cd tb V td Unitarity Triangle (UT) 8

9 UTA by UTfit : Summer2013 (post-eps) fit Collaboration of Theorists and Experimentalists Adrian Bevan Queen Mary, University of London Marcella Bona Queen Mary, University of London Marco Ciuchini INFN Sezione di Roma Tre Denis Derkach Oxford University Enrico Franco University of Roma "La Sapienza Vittorio Lubicz University of Roma Tre Guido Martinelli SISSA, Trieste Fabrizio Parodi University of Genova Maurizio Pierini CERN Carlo Schiavi University of Genova Luca Silvestrini INFN Sezione of Roma Viola Sordini IPNL-IN2P3 Lyon Achille Stocchi LAL-IN2P3 Orsay Cecilia Tarantino University of Roma Tre Vincenzo Vagnoni INFN Sezione of Bologna Other UT analyses exist, by: CKMfitter ( Laiho&Lunghi&Van de Water ( 9

10 Great Accuracy achieved in the UTA Experimental Constraints NEW: Averages of recent LHCb+CMS measurements For a significant comparison between exp. measurements and theor. predictions, hadronic uncertainties must be well under control ε K Δm Δm Δm V V Obs. ub cb d d s Br(B ) 20% Br(B Br(B s d sin2β Accuracy 0.5% 1% 1% 15% ) 25% ) 40% 3% cos2β 15% α 7% γ 10% (2β γ) 50% 10

11 THE UTA CONSTRAINTS Relying on LATTICE calculations Dm d Dm d/ Dm s Br(B ) B K f +,F, f Bs B 1/2 Bs /f B B 1/2 f B B 1/2 B B f B UT-ANGLES B J/Ψ K 0 B J/Ψ K* 0 B ππ,ρρ B D ( * ) K B D ( * ) π,dρ 11

12 SM analysis The UTA within the Standard Model The experimental constraints overconstrain the CKM parameters consistently r h ~18% ~ 4% The UTA has established that the CKM matrix is the dominant source of flavor mixing and CP violation 12

13 From a closer look From the UTA (excluding its exp. constraint) Prediction Measurement Pull sin2b 0.75± ± g 70 ±4 70 ±7 <1 a 86 ±4 91 ±8 <1 V cb ± ±1.0 <1 V ub ± ±0.46 <1 e K ± ± BR(B ) ± ± BR(B s ) ± ± BR(B d ) ± ±

14 e K ( B K ) K K ˆ (B K ) Nf=2+1 =0.766(10) BMW and RBC/UKQCD results are obtained with pion masses close to the physical point 14 First N f =2+1+1 computation is in progress (ETMC)

15 Looking for an explanation for the B excess (1.4s) within the Standard Model BR(B ) exp prefers a large value for V ub (f B well under control) But a shift in the central value of V ub would not solve the (1.5s) b tension the debate on V ub (exclusive vs inclusive determination) is not enough to explain all

16 Hadronic parameters on the Lattice, with B-Physics playing a fundamental role in the UTA Br(B ) Dm d Dm d/ Dm s B K f Bs B 1/2 Bs /f B B 1/2 f B B 1/2 B B f B f +,F, 16

17 Decay constants: f Bs and f Bs /f B (N f =2+1) f Bs = 228(5) MeV f Bs /f B = 1.202(22) f B =191(4) MeV New accurate analyses are in progress by FNAL/MILC, RBC/UKQCD, ETMC 17

18 f Bs and f B also enter the important rare decays: B d,s Highly sensitive to NP (loop FCNC: Z-penguin dominated) Theoretically clean (purely leptonic) LHCb+CMS (integrated) measurement : Br(B s )=(2.9 ±0.7) 10-9 SM prediction (corrected for B s -B s oscillation) : Br(B s )=(3.6 ±0.2) 10-9 [Buras et al ] SM prediction (corrected for B s -B s oscillation) from the UTA: Br(B s )=(3.9 ±0.2) 10-9 LHCb+CMS (integrated) measurement : Br(B d )=(3.7 ±1.5) SM prediction (corrected for B d -B d oscillation) : Br(B d )=(1.07 ±0.10) [Buras et al ] SM prediction (corrected for B d -B d oscillation) from the UTA: Br(B d )=(1.15 ±0.07)

19 B-parameters: B Bs and B Bs /B B (Nf=2+1) ˆ B Bs = 1.202(22) B Bs /B B = 1.06(11) Unquenched (2+1 and 2+1+1) calculations of the beyond-sm B-parameters are in progress by FNAL/MILC, ETMC 19

20 V ub : exclusive (Lattice form factor) vs inclusive (OPE) B pl B X u l Theoretically clean Lattice calculations but only two modern results exist so far Experimental cuts introduce some model dependence in treating long-distance contributions at threshold V ub excl = (34.2 ± 2.2) s V ub incl = (44.0 ± 2.5)

21 Conservative combination for the UTA V ub input = (37.5 ± 4.6) 10-4 The UTA output is close to the (lower) exclusive result: V ub UTA = (36.1 ± 1.2) 10-4 Further Lattice calculations are looked forward and are in progress [by RBC/UKQCD, Alpha and HPQCD] 21

22 V cb : exclusive (Lattice form factors) vs inclusive (OPE based global fit) Theoretically clean Lattice calculations but only one modern result exists so far Some model dependence affects the global fit V cb excl = (40.0 ± 0.8) s V cb incl = (41.9 ± 0.7) 10-3 Conservative combination for the UTA: V cb input = (40.9 ± 1.0) 10-3 The UTA output is close to the (higher) inclusive result: V cb UTA = (42.1 ± 0.7) 10-3 Further Lattice calculations are looked forward and are in progress (by FNAL/MILC) 22

23 Bounds on the NP scale L e.g. for K-K SM/MFV The high scale coefficients C i (L) can be extracted from the data (switching on one operator per time) C( Λ ) i LFi 2 Λ L LFi C( Λ ) i Tree/strong inter. NP: L~1 Perturbative NP: L ~a s 2, a W 2 23

24 Updated lower bound on the NP scale w.r.t From (the most constraining) K-K sector, i with the new unquenched Lattice results for the NP B-parameters, by ETMC ( , with N f =2 and 3 lattice spacings) Generic Flavor Structure Compatible with recent results by RBC/UKQCD ( , N f =2+1, ONE lattice spacing) MS at 2 GeV B 2 B 3 B 4 B (02) 0.89(05) 0.78(03) 0.57(04) OLD NEW L LFi C( Λ ) Tree/strong inter. NP: L~1 From B d -B d and B s -B s (N f =2 ETMC B-parameters) [ ] (preliminary N f =2+1 results by FNAL/MILC ) 24

25 D-D mixing It is sensitive to a different sector of New Physics (NP) with respect to K and B, being the charm an up-type quark It is affected by large long-distance effects (internal d and s quarks) which dominate over the short-distance contribution Only order of magnitude estimates exist for the long-distance contributions and are at the level of the experimental constraints, preventing from revealing an unambiguous sign of NP Still, barring accidental cancellations between SM and NP contributions, significant constraints can be put on the NP parameter space NP scale from D-D (N f =2 ETMC B-parameters) [PRELIMINARY] 25

26 HOT TOPIC in charm Physics DA CP =A KK -A pp Naive SM expectation: O(0.1%) World average (HFAG13) 1/mc expansion can have large corrections Penguin contractions can be larger than naively expected [Brod et al. 2012, Franco et al. 2012] A SM explanation is possible (though there is room for NP effects) 26

27 First unquenched Lattice results for b s l + l - transitions (recently measured by BaBar, Belle, CDF, LHCb, ) B K*l + l - significant constraints on the Wilson coefficients C 7, C 9, C 10 of the NP effective Hamiltonian (C.Bobeth et al ,hambrock&hiller ) [preliminary results for the form factors by Cambridge/Edinburgh Coll.] L b Ll + l - NP sensitive (baryonic analogue) [first computation of the form factors by Cambridge/Edinburgh Coll. ( )] B Kl + l - complementary constraints to B s (Becirevic&Kosnik&Mescia&Schneider ) Lattice unquenched results for the three form factors f +, f 0 and f T are looked forward [preliminary results by FNAL/MILC and by Cambridge/Edinburgh Coll.] 27

28 HOT TOPIC in B-Physics P 5 of B K* Several observables are measured from the angular distribution There is a general compatibility to the SM predictions BUT There is a 3.7s discrepancy in on P 5 bin (q 2 ϵ[4.3,8.7]gev 2 ) [LHCb] It decreases to 2.5s for q 2 ϵ[1,6]gev 2 We look forward the inclusion of 2012 data (1/fb 2/fb) 28

29 The challenging K p p has been computed for the first time on the Lattice in , by RBC/UKQCD [ , , , ] A 0 A(K (p p) I=0 ) [DI=1/2] Very hard computation due to power divergences disconnected diagrams Computed, so far, only with unphysical kinematics (i.e. unphysical K and p masses such that m K =2m p ) A 2 A(K (p p) I=2 ) [DI=3/2] Computed also with physical kinematics (i.e. physical K and p masses with p p 0) Preliminary studies towards a computation with physical kinematics are in progress 29

30 The DI=1/2 rule (Re(A 0 )/Re(A 2 ) 22.5) emerges already with the unphysical kinematics from a cancellation of two large contributions in Re(A 2 ), which are instead of the same sign in Re(A 0 ) An exploratory study of the long-distance contribution o DM K has been recently preformed (N.Christ et al ) 30

31 Looking at the next decade In the next years there will be a great experimental activity, not only in the direct NP search at LHC, but also in the Flavor Sector In particular, LHCb and Belle II (SuperB): aim at improving the accuracy of the B-factories by a factor 5-10 will test the CKM matrix at 1% level 31

32 Role of B-factories in constraining the UT After B-factories Before B-factories After SuperB-factories? The CKM matrix will be tested at 1% level 32

33 On the Lattice side: Ten Years Ago Today Hadronic parameter L.Lellouch ICHEP 2002 [hep-ph/ ] UTA Lattice inputs 2013 [ Bˆ K 0.86(15) [17%] 0.76(1) [1%] f Bs 238(31) MeV [13%] 228(5) MeV [2%] f Bs /f B 1.24(7) [6%] 1.20(2) [1.5%] Bˆ Bs 1.34(12) [9%] 1.33(6) [5%] B Bs /B B 1.00(3) [3%] (quenched, l >m s /2, ) 1.06(11) [10%] F D* (1) 0.91(3) [3%] 0.92(2) [2%] F + B p -- [20%] -- [11%] The last 10 years teach us that Lattice QCD has made important progresses (quenched->unquenched, higher computational power, better algorithms) More recently further improvements are being realized: simulations at the physical point, discretization effects well under control (in the light and heavy sectors), N 33 f =2+1+1,

34 Conclusion: We expect significant improvements in the next years 34