FLAG: LATTICE FLAVOUR PHYSICS AND WORLD

Transcription

1 FLAG: LATTICE FLAVOUR PHYSICS AND WORLD AVERAGES A. Vladikas INFN - TOR VERGATA Trento - ECT* 14th January 2013 Lattice QCD and Hadron Physics LPHA ACollaboration

2 OUTLINE FLAG description and summary of results Quality criteria and colour coding Quark masses (up, down strange) Conclusions

3 The Collaboration FLAG: Flavour Lattice Averaging Group

4 FLAG: the collaboration Flavour Physics important as LHC probes new energies; precision measurements may lead to signatures of new Physics Major theoretical limitation: low energy QCD effects in SM (quantified by lattice computations) are not always quantified to a satisfactory precision. Lattice simulations performed by different groups involve different choices both at the level of formalism (lattice actions, number of sea flavours etc.) and at the level of resources (lattice volumes, quark masses etc.) often this amounts to making different compromises which in turn introduces different systematic effects not all lattice results of a given quantity are directly comparable Aim: answer the question What is currently the best lattice value for a particular quantity? in a way which is readily accessible to non-experts extrapolation of precise lattice results guided by Chiral Perturbation Theory (χpt) close collaboration between lattice and χpt experts

5 FLAG - phase 1 ( ): operated within the European Network on Flavour Physics (Flavianet) First FLAG report limited to important quantities in pion and Kaon Physics Light and strange quark masses decay constants fk / fπ Kaon decay form factor f+(0) FLAG: first phase Neutral Kaon oscillation bag parameter BK SU(2) and SU(3) low energy constants Σ, F, l3, l4, l6, L4, L5, L6, L8, L9, L10 Quenched results (Nf = 0) were not discussed; limited to Nf = 2+1 and Nf = end of phase 1: G. Colangelo et al., Review of Lattice Results Concerning Low-Energy Particle Physics, Eur. Phys. J. C (2011) 71:1695

6 FLAG: second phase Extension of the project by adding new physical quantities with heavy flavours: mlight, mstrange --- now add Charm, Bottom (not mcharm, mbottom), αstrong Geographical extension: Europe --- now add USA, Japan New collaborations: before Alpha, BMW, ETMC, RBC/UKQCD; now add CLS, Fermilab, HPQCD, JLQCD, PACS-CS, SWME; new FLAG members: were12, now 28 Introduction of rules regulating the decision taking (consensus is preferred to voting and/or vetoing!) and trying to avoid conflicts of interest G. Colangelo et al., Review of Lattice Results Concerning Low-Energy Particle Physics, arxiv: [hep-lat]; to appear in Eur. Phys. J. C Cutoff: published papers until (extension in updated 2014 version, which will also include αstrong) Publish a review approximately every two years Upgrade and update the web pages:

7 Advisory Board: S. Aoki (Japan), C. Bernard (USA), C. Sachrajda (UK) Editorial Board: G.Colangelo (Bern), H.Leutwyler (Bern), A.V. (Rome-2), U. Wenger (Bern) WORKING GROUPS: Light quark masses: L. Lellouch, T. Blum, V. Lubicz fk, fk/fπ, f+ Kπ (0) Vus, Vud: A. Jüttner, T. Kaneko, S. Simula LEC: S. Dürr, H. Fukaya, S. Necco BK: H. Wittig, J. Laiho, S. Sharpe FLAG structure αs: R. Sommer, R. Horsley,T. Onogi fd, BD, fb, BB: A. El Khadra, Y. Aoki, M. Della Morte, J. Shigemitsu D --> H l ν,b --> H l ν: R. van de Water, E. Lunghi, C. Pena

8 FLAG results NB: Quark masses & condensate are in the MS-bar scheme at μ= 2 GeV NB: Results are Nf = 2, Nf = 2+1 and Nf = Quenched results are omitted except for the (imminent) review of αstrong NB: Few papers make it to the averages and should be cited (not just FLAG)

9 Quality Criteria FLAG: Flavour Lattice Averaging Group

10 Quality Criteria Two distinct goals: 1. Describe the state of the art. Show tables and use quality criteria (colour coding). This must be generally accepted by the lattice community. 2. Give FLAG results, staying on the conservative side. This is sometimes subjective (see below) Several lattice regularizations provide compatible results (typically in light flavours) and this confirms solidity of lattice approach. In heavy flavours several approaches are used in the discretization of the c- and b-quark fields. Publication status: only peer-reviewed, published papers are included in the averages (exception: obvious updates of published results in conference proceedings) systematic error estimated in a satisfactory manner and under control a reasonable attempt at estimating systematic error; can be improved no attempt or unsatisfactory attempt at controlling a systematic error

11 Quality Criteria for Light Flavours chiral extrapolation: Mπ,min < 200 MeV NB: was 250 MeV 200 MeV Mπ,min 400 MeV 400 MeV Mπ,min NB: at least 3 points requested (otherwise there is a special mention ) NB: for tmqcd fermions we assume that Mπ+ may be used for chiral extrapolation (even if Mπ+ > Mπ0); for staggered fermions we identify Mπ with the RMS of the pion mass of all taste partners continuum extrapolation: at least 3 lattice spacings, at least two below 0.1 fm 2 or more lattice spacings, at least one below 0.1 fm otherwise NB: theory should be O(a)-improved; for non-improved theories an extra point is needed for each criterion

12 finite volume effects: (p-regime) [Mπ L ]min > 4 or at least 3 volumes [ Mπ L ]min > 3 and at least 2 volumes otherwise, and in any case if L < 2 fm NB: for tmqcd fermions we assume that Mπ+ may be used for chiral extrapolation (even if Mπ+ > Mπ0); for staggered fermions we identify Mπ with the RMS of the pion mass of all taste partners for fk, fπ, f+ Kπ (0), BK and the lightest pion for mq and LECs renormalization (where applicable): non perturbative Quality Criteria for Light Flavours 1-loop perturbation theory or higher with reasonable estimation of truncation errors otherwise NB: was 2-loop NB: different criteria were used for heavy flavours

13 Quality Criteria Averages: there are several independent results for some physical quantities; averaging them gives the lattice estimate for this quantity Which results are dropped from averaging? We drop data with If we have several good results (typically in light flavours), we do a weighted average, eventually taking correlations into account Sometimes averaging does not appear to cover all uncertainties. Sometimes a single result dominates the averages overwhelmingly. In such cases we may opt for an estimate which we feel is a fair assessment of our knowledge to-date. If there is a single result (typically in heavy flavours) we quote it, but beware! average Nf = 2, Nf = 2+1 and Nf = results separately

14 Quark Masses up, down, strange

15 Quark masses fundamental parameters of Standard Model X-sections & decay rates expressed in formulae with mcharm and mbottom knowing the quark mass values with good precision for all flavours is an important ingredient of the flavour structure of the Standard Model cannot be measured experimentally can be calculated theoretically, using some input from hadronic physics quark masses are quantities which run with the renormalization scale FLAG is centered on mud = 1/2 ( mup + mdown ) and mstrange 3 fundamental QCD quantities ( αs, mud, mstrange ) and lattice spacing a fix them through, say, mπ, fπ, mn, mk all results are presented in MeV at renormalization scale 2 GeV in the MS

16 pass quality criteria Quark masses Nf = 2

17 Quark masses Nf = 2 pass quality criteria average ALPHA12 and ETM10B for ms only quote ETM10B for mud m s = 101(3)MeV m ud =3.6(2)MeV m s m ud = 28.1(1.2)

18 Quark masses Nf = 2 special case Dürr11 follow a novel approach by HPQCD first compute mc/ms = 11.27(30)(26) combined with lattice & phenom. determination of mc (2GeV) = 1.093(13)GeV to give ms PDG value for mc (2GeV) = 1.094(21)GeV would have given compatible result then compute mud by combining their ms with the Nf = 2+1 BMW result for ms/mud

19 pass quality criteria Quark masses Nf = 2+1

20 Quark masses Nf = 2+1 pass quality criteria updated

21 Quark masses Nf = 2+1 pass quality criteria HPQCD merits special discussion HPQCD accurately computes mc/ms = 11.85(16) this is combined with mc(mc) = 1.273(6)GeV to give ms high-precision mc from lattice moments of charm-quark PS correlator (no renormalization) they compute mud by combining their ms with the MILC09 result for ms/mud

22 Quark masses Nf = 2+1 pass quality criteria HPQCD merits special discussion instead of HPQCD mc(mc) = 1.273(6)GeV, use the less accurate PDG value mc(mc) = 1.277(25)GeV to get ms = 92.3(2.2) MeV very promising method, but we prefer to postpone its inclusion in the averages, until we review mc for the moment this stays an important cross-check

23 Quark masses Nf = 2+1 pass quality criteria HPQCD merits special discussion we are left with three results to average and HPQCD as a cross-check average gives ms = 92.3(2.2) MeV including HPQCD in the average gives ms = 93.8(1.5) MeV average gives mud = 3.42(6) MeV including HPQCD in the average gives mud = 3.41(5) MeV

24 pass quality criteria Quark masses Nf = 2+1

25 Quark masses Nf = 2+1 we need a rough estimate of the errors due to neglecting heavy flavours BMW: when scale is set by MΞ, then MΛ agrees with experiment to 2.3% as these masses have strongly correlated error, we expect a 2% accuracy for M Ξ -MΛ mc-mud this is a crude upper bound of a second (systematic) error due to neglecting heavy flavours m s = 93.8(1.5)(1.9)MeV m ud =3.42(6)(7)MeV m s m ud = 27.46(15)(41) also includes the neglect of isospin breaking (see below)

26 Quark masses Plots have their own colour coding: results based on PT renorm results based on NP renorm. results based on SR FLAG estimates PDG estimate

27 Quark masses Plots have their own colour coding: results based on PT renorm results based on NP renorm. results based on SR FLAG estimates PDG estimate

28 Quark masses Plots have their own colour coding: results based on PT renorm results based on NP renorm. results based on SR FLAG estimates PDG estimate

29 Quark masses and E/M effects we are entering an era where E/M effects in meson masses, though small, cannot be entirely ignored need to account for such effects in the meson masses used for quark mass determination use two definitions for the E/M self-energy: M P M P ˆMP P M 2 P ˆM 2 P physical (observed) meson mass pure-qcd meson mass define a physical pion mass split Δπ: M 2 + M 2 0 express neutral meson E/M self energies and the pure-qcd pion (isospin) split in terms of Δπ: 0 0 K 0 K 0 ˆM 2 + ˆM 2 0 m derive charged meson E/M self energies: + =(1+ 0 m ) K + =(1+ + K 0 m ) Dashen s theorem (LO χpt): 0 = K 0 =0 + = K + ε parametrizes violation of Dashen s theorem: K + K

30 Quark masses and E/M effects FLAG combined a plethora of (mostly) lattice, χpt and phenomenological analyses to obtain the following conservative estimates: Dashen violation is dominant generous errors self energies: pure-qcd masses:

31 Quark masses and isospin breaking most lattice computations are performed in the isospin limit isospin symmetry (u d) implies π - π + and K 0 K + ˆM 2 + f[(m u m d ) even ] 1 2 ( ˆM 2 K + + ˆM 2 K 0 ) g[(m u m d ) even ] χpt implies that the isospin symmetric masses are very close to the pure-qcd ones: ˆM 2 + M 2 = O[(m u m d ) 2 (m u + m d )] << ˆM 2 + ˆM 2 0 =0.2(1)MeV isospin symmetric meson mass 1 2 ( ˆM 2 K + + ˆM 2 K 0 ) M 2 K h(2l 8 L 5 ) Numerically the isospin breaking effects are negligible compared to E/M self energies

32 Quark mass ratio, E/M & isospin breaking effects from LO χpt we have expressing this in terms of the E/M and isospin-breaking ε-parameters: using the FLAG estimates for these ε-parameters: the green lattice values for the same q-mass ratio differ from the above by 3-10%; this is a measure of NLO χpt effects; compared to FLAG average it is a 6% shift the above LO result implies that E/M and isospin breaking effects are small (central value stays the same for ε=0 and ε 0) but not irrelevant (there is a small but visible error of 0.4%) assign a 1.5% uncertainty due to these E/M and isospin breaking effects and also for omitting c-/bquark loops m s m ud = 27.46(15)(41) FLAG average lack of EM, NLO χpt and of c-/bquark loop effects

33 Isospin breaking Different groups use very different methods in order to measure mup and mdown (rather than mud) Need a new physical input (e.g. K-meson mass split) Again the estimate of E/M self energy effects needs careful analysis

34 Isospin breaking

35 Isospin breaking

36 Conclusions Lattice is now credible and as accurate as experiment (2%-5% ---> 1%) It is the responsibility of the lattice community to provide experimentalists and non-lattice theorists with a review of phenomenologically relevant lattice results FLAG rates lattice output according to some quality criteria, performs averages or proposes estimates and is sometimes trying to push the analysis beyond that FLAG has entered its second phase with a larger group and a wider Physics scope The initiative is gaining momentum and the support of the lattice community Future: new quantities? new people! new policies?!?!?!