Lattice QCD and flavour physics

Transcription

1 Lattice QCD and flavour physics Vittorio Lubicz Workshop on Indirect Searches for New Physics at the time of LHC 15/02/ /03/2010 OUTLINE: The accuracy of LQCD in the flavour sector the past (the quenched era) the present the future (LHCb, superb)

2 Lattice QCD and flavour physics Quark masses V ub /V cb ε K Δm d Δm d /Δm s 1/2 f +,F, B K f B B B ξ b u/b c K 0 K 0 B d -B d B s -B s UTA CKM matrix elements Beyond SM physics K π π More difficult problems Covered in this talk

3 Accuracy of Lattice QCD The past

4 For many years, uncertainties in lattice calculations have been dominated by the quenched approximation History of lattice errors (before 2006) J.Flynn Latt 96 C.Bernard Latt 00 L.Lellouch Ichep 02 Hashimoto Ichep 04 N.Tantalo CKM 06 fb [MeV] 175(25) 14% 200(30) 15% 193(27)(10) 15% 189(27) 14% 223(15)(19) 11% f Bs (46) 17% 276(38) 14% 262(35) 13% B [MeV] s 246(16)(20) 10% ξ (5) 4% 1.24(4)(6) 6% 1.23(6) 5% 1.21(2)(5) 4% QUENCHED UNQUENCHED

5 In spite of the relatively large lattice uncertainties, important results for flavour physics have been achieved CKM PARADIGM OF CP CP-conserving and CP-violating processes determine the same CKM phase UTfit, today Ciuchini et al.,2000 sin2β UTsizes ε K

6 Ciuchini et al.,1995: Sin2β UTA = 0.65 ± 0.12 PREDICTION OF Sin2β Ciuchini et al.,2000: Sin2β UTA = ± sin 2β Predictions exist since 1995 UTfit today: Sin2β UTA = ± Measurements year Direct measurement today: Sin2β J/ψ K0 = ± 0.027

7 SM PREDICTION OF Δm s LOOKING FOR NEW PHYSICS EFFECTS Ciuchini et al.,2000: Δm s = (16.3 ± 3.4) ps -1 The predicted range was very large in the frequentistic CKMFitter approach UTfit today: Δm s = (16.8 ± 1.6) ps -1 Direct measurement today Δm s = (17.77 ± 0.12) ps -1

8 The present

9 PRECISION FLAVOUR PHYSICS Experiments 2010 Lattice V us f + (0) ± % f + (0) 0.5% 0.9% V us F K V ud F π ε K ± % (2.228 ± 0.011) x % Δm (0.507 ± 0.005) ps -1 d 1% 0.7% F K /F π 0.9% B K 5% 5% Δm s (17.77 ± 0.12) ps -1 f B B B 5% 1.1% 11% 13% f Bs B Bs 13% Sin2β ± %

10 KAON AND B PHYSICS ON THE LATTICE Collaboration Quark action Nf a [fm] (M π ) min [MeV] Observables MILC + FNAL, HPQCD, Improved staggered f K,B K, f B, B B, B D/π lν PACS-CS Clover (NP) f K RBC/UKQCD DWF f + (0), f K, B K, K ππ BMW Clover smeared f K JLQCD Overlap 2 [2+1] B K ETMC Twisted mass 2 [2+1+1] f + (0), f K, B K, f B QCDSF Clover (NP) f + (0), f K

11 THE PRECISION ERA OF LATTICE QCD: WHY NOW 1) Increasing of computational power Unquenched simulations The Moore s Law For Lattice QCD today: ~5 30TFlops ~ (like (like the the # in in the the TOP500 list) list) TeraFlops machines are required to perform unquenched simulations. Available only since few years. CPU cost for Nf=2 Wilson fermions: [Del Debbio et al. 2006] TFlops-years Nconf Ls L t fm fm 2Ls mˆ / m s a 6

12 2) Algorithmic improvements: Light quark masses in the ChPT regime Today 2001 CPU cost (for Nf=2 Wilson fermions): Ukawa 2001 (The Berlin wall): TFlops-years Nconf L s L t fm fm 2L s mˆ / m s a 3 7 Del Debbio et al. 2006: 5 Nconf Ls L t fm TFlops-years fm 2L ˆ s m/ m s a 6 Today: Few years ago: ( latt ˆ ) ud s ( latt ˆ ) MeV / 1/ 6 1/12 latt Mπ m m latt Mπ mud ms 500 MeV / 1/ 2 ChPT

13 FLAG The FLAG working group (constituted in November 2007) Flavianet Lattice Averaging Group G.Colangelo, S.Dürr, A.Jüttner, L.Lellouch, H.Leutwyler, V.Lubicz, S.Necco, C.Sachrajda, S.Simula, T.Vladikas, U.Wenger, H.Wittig A working group of: Aims: for each quantity, provide to the network s working groups and to the wider community a collection of current lattice results and references a summary of the essential aspects of each calculation, using an easyto-read color code classification ( ) averages of lattice results (when it makes sense)

14 The FLAG colour coding A number of sources of systematic errors are identified and to each calculation a colour with respect to each of these is assigned: when the systematic error has been estimated in a satisfactory manner and convincingly shown to be under control when a reasonable attempt at estimating the systematic error has been made, although this could be improved when no or a clearly unsatisfactory attempt at estimating the systematic error has been made

15 The FLAG colour coding

16 V Kπ us from kaon decays: f + (0) and f K /f π V us K π V us K [Marciano 04]

17 V Kπ us from kaon decays: f + (0) and f K /f π V us K π 1 K V us [Marciano 04] 2 Assuming the Standard Model and combining with nuclear β decays: 3 one obtains: [FLAG ] 4 From nuclear β decays 20 superallowed transitions [Hardy and Towner 08] and Lattice independent estimates of the hadronic parameters

18 V Kπ us from kaon decays: f + (0) and f K /f π [ V.Lubicz@LATT 09 ] K V us π V us Kl3 = (13) V us = (10) Using unitarity and V ud from nuclear β decays f + (0) = (3) (4) 0.5% Error in 2006: 0.9% Analytical model calculations tends to give larger predictions than lattice results

19 V Kπ us from kaon decays: f + (0) and f K /f π [ V.Lubicz@LATT 09 ] V us K [Marciano 04] V us Kl2 = (19) f K /f π = (1) (10) 0.8% The accuracy is comparable to the one reached on f + (0) [0.5%] V us Kl3 = (13) V us = (10) Using unitarity and V ud from nuclear β decays

20 K 0 -K 0 mixing: B K V qs V qd * K K K K ^ B K = 0.90 ± 0.03 ± 0.15 S.Sharpe@Latt 96 17% B ^ K = 0.86 ± 0.05 ± 0.14 L.Lellouch@Latt 00 B ^ K = 0.79 ± 0.04 ± 0.08 C.Dawson@Latt 05 17% 11% ^ B K = ± V.Lubicz@Latt 09 5% [VL, C.Tarantino ] Until 2008 few unquenched calculations at fixed (and rather large) lattice spacing

21 K 0 -K 0 mixing: B K 3 results with no red tags, all new ^ B K = (8) (28) [Nf=2+1, ALVdW 09] ^ B K = (8) (25) [Nf=2+1, RBC/UKQCD 09] ^ B K = (30) (30) [Nf=2, ETM 09] No visible effect of the partial quenching (Nf=2).

22 K 0 -K 0 mixing: B K [ V.Lubicz@LATT 09 ] V qs V qd * K K From the UT fit, assuming the Standard Model ^ B K = 0.87 (8) B ^ K = (7) (35) 5% with Kε = 0.94(2), A.Buras, D.Guadagnoli, G.Isidori, arxiv: Error in 2006: 11%

23 B-mesons decay constants: f B,f Bs Averages from J.Laiho, E.Lunghi, R.Van de Water, f Bs = ± 9.5 MeV 4-5% f B = ± 9.9 MeV f Bs /f B = ± % Error in 2006: 14% Error in 2006: 5%

24 B-B mixing: B Bd/s V tb V tq * B B Only one modern calculation HPQCD [ ] B ^ Bd = 1.26 ± 0.11 B ^ Bs = 1.33 ± 0.06 Combining with fb and fbs: f Bs B ^ Bs = 275 ± 13 MeV 5% ξ = ± % Error in 2006: 13% Error in 2006: 5%

25 Exclusive Vcb TWO DIFFERENT APPROACHES: - double ratios (FNAL) - step scaling (TOV) Remarkable agreement Roma-TOV Averages from VL, C.Tarantino F(1) = ± % G(1) = ± % Error in 2006: 4%

26 Exclusive Vub * V ub excl. = (35.0 ± 4.0) % Error in 2006: 11% MORE LATTICE CALCULATIONS REQUIRED excl. V ub = (3.5 ± 0.4) 10-3 From LQCD and QCDSR incl. V ub = (4.0 ± 0.4) 10-3 Model dependent BLNP, DGE, GGOU, ADFR, BLL

27 OF LATTICE PARAMETERS UT-angles UT-lattice Assuming the validity of the Standard Model one can perform a fit of the hadronic parameters: 2%! from Δms B K f Bs B Bs (MeV) ξ UTA 0.87 ± ± ± 0.06 Lattice 0.73 ± ± ± 0.03 Lattice inputs are less relevant today for the SM analysis. But they are crucial when looking for new physics effects

28 K-K AND B-B MIXING BEYOND THE SM [M.Ciuchini et al., hep-lat/ ] K-K APE 99 Babich et al 06 CP-PACS 06 B-B APE 01 JLQCD 02 HPQCD 06 NEW CALCULATIONS ARE NEEDED!! The full operator basis only in the quenched approximation For K-K mixing results quite in disagreement

29 The future

30 The goal of the SuperB factory is precision flavour physics for indirect New Physics searches For example: testing the CKM paradigm at the 1% level Today With a SuperB in 2015 the dream The theoretical accuracy must compete with the experimental one. Can we reach the 1% accuracy in Lattice QCD??

31 Cost of the SuperB lattice simulation Simulation parameters Nconf = 120 a = fm [ 1/a = 6.0 GeV ] m/m ˆ = 1/12 s [ M π = 200 MeV ] L s = 4.5 fm [V = ] The SuperB is running ~ 3 PFlop-years Affordable with 1-10 PFlops available for Lattice QCD in 2015!

32 Hadronic matrix element F B D/D*lν Current latt. error (2006) (26% on ξ-1) 4% (40% on 1-F) 11% 13% 6 TFlop Year [2009] (18% on ξ-1) 2% (21% on 1-F) % TFlop Year [2011 LHCb] 0.9% 0.7% 0.4% < 0.1% (22% on 1-f + ) (17% on 1-f + ) (10% on 1-f + ) (2.4% on 1-f + ) Bˆ K 11% 5% 3% 1% f B 14% % % 1 1.5% 1/2 BsB Bs 13% 4-5% 3-4% 1 1.5% ξ 5% 3% % % K π f + (0) f f,... T B π + B K */ρ 1 (9-12% on ξ-1) 1.2% (13% on 1-F) 4-5% PFlop Year [2015 SuperB] (3-4% on ξ-1) 0.5% (5% on 1-F) 2 3% 3 4%

33 Hadronic matrix element Kπ f + (0) THE 2009 STATUS REPORT Lattice error in % Bˆ K 11% 5% 5% 3% 1% f B 14% 5% % % 1 1.5% f B Bs 1/2 Bs 13% ξ 5% 2% 3% % % F B D/D*lν 4% 2% 2% 1.2% 0.5% f,... Bπ + B K*/ρ T 1 11% 13% Lattice error in % 5% 11% 13% 6 TFlop Year [2009] 0.7% 4-5% % TFlop Year 0.4% 3-4% 4-5% PFlop Year [2011 LHCb] [2015 SuperB] < 0.1% 1 1.5% 2 3% 3 4% The expected accuracy has been reached! (except for Vub)

34 The past the present η γ 1 and the 0.5 β Δm d Δm s future α ρ