Lattice QCD and Vittorio Lubicz flavour physics OUTLINE: OUTLINE: Workshop on The accuracy of LQCD in the “Indirect Searches for flavour sector New Physics at the • the past (the quenched era) time of LHC” • the present 15/02/2010 - 26/03/2010 • the future (LHCb, superB)
Lattice QCD and flavour physics Quark masses ε K Δ m d Δ m d / Δ m s |V ub /V cb | CKM matrix elements 1/2 f B B B ξ B K f + ,F,… Beyond SM UTA physics K 0 –K 0 b → u/b → c B d -B d B s -B s π More difficult Covered in K problems π this talk
Accuracy of Lattice QCD The past
For many years, uncertainties in lattice calculations have been dominated by the quenched approximation History of lattice errors (before 2006) f f B ξ B s Bs [MeV] [MeV] J.Flynn 175(25) ---- ---- 14% Latt’96 C.Bernard 200(30) 267(46) 1.16(5) QUENCHED 15% 17% 4% Latt’00 L.Lellouch 193(27)(10) 276(38) 1.24(4)(6) 15% 14% 6% Ichep’02 Hashimoto 189(27) 262(35) 1.23(6) 14% 13% 5% Ichep’04 N.Tantalo UNQUENCHED 223(15)(19) 246(16)(20) 1.21(2)(5) 11% 10% 4% CKM’06
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 UTfit, today processes determine the same CKM phase Ciuchini et al.,2000 sin2 β UTsizes ε K
PREDICTION OF Sin2 β Ciuchini et al.,1995: Sin2 β UTA = 0.65 ± 0.12 Predictions exist since 1995 Ciuchini et al.,2000: Sin2 β UTA = 0.698 ± 0.066 sin 2 β UTfit today: Sin2 β UTA = 0.751 ± 0.035 Measurements year Direct measurement today: Sin2 β J / ψ K 0 = 0.655 ± 0.027
SM PREDICTION OF Δ m s LOOKING FOR NEW PHYSICS EFFECTS Ciuchini et al.,2000: The predicted range was very large in the frequentistic CKMFitter approach Δ m s = (16.3 ± 3.4) ps -1 UTfit today: Δ m s = (16.8 ± 1.6) ps -1 Direct measurement today Δ m s = (17.77 ± 0.12) ps -1
The present
PRECISION FLAVOUR PHYSICS Lattice 2010 Experiments 2010 2006 0.2% 0.21661 ± 0.00047 |V us |f + (0) 0.5% 0.9% f + (0) |V us | F K 0.2% 0.27599 ± 0.00059 0.9% 1.1% F K /F π |V ud |F π 5% 11% 0.5% (2.228 ± 0.011) x 10 -3 B K ε K 5% 13% 1% (0.507 ± 0.005) ps -1 f B √ B B Δ m d 5% 13% 0.7% f Bs √ B Bs (17.77 ± 0.12) ps -1 Δ m s 4% 0.655 ± 0.027 Sin2 β
KAON AND B PHYSICS ON THE LATTICE Quark (M π ) min Collaboration Nf a [fm] Observables action [MeV] f K , B K , f B , B B , MILC Improved ≥ 0.045 2+1 230 staggered B → D/ π l ν + FNAL, HPQCD,… PACS-CS Clover (NP) 2+1 0.09 156 f K f + (0), f K , B K , ≥ 0.08 RBC/UKQCD DWF 2+1 290 K → ππ Clover ≥ 0.07 f K BMW 2+1 190 smeared 2 B K JLQCD Overlap 0.12 290 [2+1] f + (0), f K , B K , 2 Twisted ≥ 0.07 ETMC 260 mass [2+1+1] f B ≥ 0.06 f + (0), f K QCDSF Clover (NP) 2 300
THE “PRECISION ERA” OF LATTICE QCD: WHY NOW 1) Increasing of computational power Unquenched simulations For Lattice QCD For Lattice QCD today: ~ 5–30TFlops The Moore’s Law today: ~ 5–30TFlops (like the # 500 in the (like the # 500 in the TOP500 list) TOP500 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] 5 6 ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ N L L ⎛ ⎞ 0.15 0.08 fm TFlops-years � 0.1 5 conf s t ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ˆ ⎝ 1 0 0 ⎠ ⎝ 3 fm ⎠ 2L / ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ m m a s s
2) Algorithmic improvements: Light quark masses in the ChPT regime 2001 Today CPU cost (for Nf=2 Wilson fermions): Ukawa 2001 ( The Berlin wall ): 3 5 7 ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ N L L ⎛ ⎞ 0.2 0.1 f m conf s t TFlops-years � 3.1 ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ˆ 1 00 3 fm 2 L / ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ m m a s s Del Debbio et al. 2006: 5 ⎛ ⎞ ⎛ ⎞ 6 ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ N L L 0.2 0.1 fm � conf s t TFlops-years 0.0 3 ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ˆ / 100 3 fm 2 L ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ m m a s s ( ) Today: ≈ − ≈ − ChPT ˆ 200 300 MeV / 1 / 6 1 / 12 latt latt M m m π ud s ( ) ≈ ≈ ˆ Few years ago: latt 500 MeV latt / 1 / 2 M m m π ud s
The FLAG working group FLAG (constituted in November 2007) F lavianet L attice A veraging G roup 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 easy- to-read “color code” classification ( ) averages of lattice results (when it makes sense)
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
The FLAG colour coding
V us from kaon decays: f + (0) and f K /f π K π V us π K V us K [Marciano 04]
V us from kaon decays: f + (0) and f K /f π K π V us π 1 K V us K [Marciano 04] 2 Assuming the Standard Model and combining with nuclear β decays: Assuming the Standard Model From nuclear β decays 3 20 superallowed transitions 4 [Hardy and Towner 08] one obtains: [FLAG ] Lattice independent estimates and of the hadronic parameters
V us from kaon decays: f + (0) and f K /f π K π V us [ V.Lubicz@LATT’09 ] K π • |V us | Kl3 = 0.2252(13) • |V us | = 0.2255(10) Using unitarity and |V ud | from nuclear β decays f + (0) = 0.962 (3) (4) 0.5% Analytical model calculations tends to give larger predictions Error in 2006: 0.9% than lattice results
V us from kaon decays: f + (0) and f K /f π K π [ V.Lubicz@LATT’09 ] V us K [Marciano 04] • |V us | Kl2 = 0.2248(19) • |V us | Kl3 = 0.2252(13) f K /f π = 1.196 (1) (10) 0.8% • |V us | = 0.2255(10) Using unitarity and |V ud | from nuclear β decays The accuracy is comparable to the one reached on f + (0) [0.5%]
K 0 - K 0 mixing: B K K K * V qs V qd 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 17% ^ B K = 0.79 ± 0.04 ± 0.08 C.Dawson@Latt’05 11% ^ [VL, C.Tarantino 0807.4605] B K = 0.731 ± 0.036 Until 2008 few unquenched calculations at Until 2008 few unquenched calculations at 5% V.Lubicz@Latt’09 fixed (and rather large) lattice spacing fixed (and rather large) lattice spacing
K 0 - K 0 mixing: B K ^ B K = 0.724 (8) (28) [ Nf=2+1, ALVdW 09 ] ^ B K = 0.738 (8) (25) [ Nf=2+1, RBC/UKQCD 09 ] ^ B K = 0.730 (30) (30) [ Nf=2, ETM 09 ] 3 results with no red tags, all new No visible effect of the partial quenching ( Nf=2 ).
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) with K ε = 0.94(2), ^ B K = 0.731 (7) (35) 5% A.Buras, D.Guadagnoli, G.Isidori, arXiv:1002.3612 Error in 2006: 11%
B-mesons decay constants: f B ,f Bs Averages from J.Laiho, E.Lunghi, R.Van de Water, 0910.2928 f Bs = 238.8 ± 9.5 MeV 2% 4-5% f Bs /f B = 1.231 ± 0.027 f B = 192.8 ± 9.9 MeV Error in 2006: 14% Error in 2006: 5%
B-B mixing: B Bd/s * V tb V tq B B Only one modern calculation HPQCD [0902.1815] ^ B Bd = 1.26 ± 0.11 ^ B Bs = 1.33 ± 0.06 Combining with fB and fBs: ^ 5% 2% ξ = 1.243 ± 0.028 f Bs √ B Bs = 275 ± 13 MeV Error in 2006: 13% Error in 2006: 5%
Exclusive Vcb TWO DIFFERENT APPROACHES: - “double ratios” (FNAL) - “step scaling” (TOV) Remarkable agreement Roma-TOV Averages from VL, C.Tarantino 0807.4605 2% F(1) = 0.924 ± 0.022 Error in 2006: 4% G(1) = 1.060 ± 0.035 3%
Exclusive Vub * excl. 11% |V ub | excl. = (35.0 ± 4.0) 10 -4 V ub = (3.5 ± 0.4) 10 -3 From LQCD and QCDSR Error in 2006: 11% incl. V ub = (4.0 ± 0.4) 10 -3 MORE LATTICE Model dependent CALCULATIONS REQUIRED BLNP, DGE, GGOU, ADFR, BLL
OF LATTICE PARAMETERS UT-angles UT-lattice Assuming the validity of the Standard Model one can perform a fit of the hadronic parameters: from Δ ms 2%! B K f Bs √ B Bs (MeV) ξ UTA 0.87 ± 0.08 265 ± 4 1.25 ± 0.06 Lattice 0.73 ± 0.04 275 ± 13 1.24 ± 0.03 Lattice inputs are less relevant today for the SM analysis. But they are crucial when looking for new physics effects
K-K AND B-B MIXING BEYOND THE SM [M.Ciuchini et al., hep-lat/9808328] ! K-K ! D E D E APE 99 E N E Babich et al 06 R A S CP-PACS 06 ∗ N O I T A L U C B-B L A C W APE 01 E N JLQCD 02 HPQCD 06 The full operator basis only in the quenched approximation For K-K mixing results quite in disagreement
The future
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