SM parameters and heavy quarks on the lattice

Transcription

1 SM parameters and heavy quarks on the lattice Michele Della Morte CERN Lattice 2007, Regensburg Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 1 / 34

2 What is the required precision... to hope to see New Physics in B-flavor? 1 B X s γ γ γ γ t t ~ t ~ t b s b C ~ s W b t H + t s SM B( B X s γ) = (3.55 ± ± 0.03) 10 4, E γ > 1.6 GeV [exp] = (3.15 ± 0.23) 10 4 [theory] [Misiak et al., Becher and Neubert, 2007] 2 maybe more room in D 0 D 0 mixing [BABAR-SLAC] but it is not clear if lattice can contribute there 3 Contributions from charged Higgs exchange in B τν not ruled out (theory and exp errors > 20%). B s µ + µ? (among LHCb goals) 4 in the end the required precision is set by the experiment eg 50 ab 1 at Super-B B(B τν) exp = 3% V ub = 4.4% with F B at 5% Beauty2006] Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 2 / 34 MSSM

3 What is the required precision... to hope to see New Physics in B-flavor? 1 B X s γ γ γ γ t t ~ t ~ t b s b C ~ s W b t H + t s SM B( B X s γ) = (3.55 ± ± 0.03) 10 4, E γ > 1.6 GeV [exp] = (3.15 ± 0.23) 10 4 [theory] [Misiak et al., Becher and Neubert, 2007] 2 maybe more room in D 0 D 0 mixing [BABAR-SLAC] but it is not clear if lattice can contribute there 3 Contributions from charged Higgs exchange in B τν not ruled out (theory and exp errors > 20%). B s µ + µ? (among LHCb goals) 4 in the end the required precision is set by the experiment eg 50 ab 1 at Super-B B(B τν) exp = 3% V ub = 4.4% with F B at 5% Beauty2006] Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 2 / 34 MSSM

4 What is the required precision... to hope to see New Physics in B-flavor? 1 B X s γ γ γ γ t t ~ t ~ t b s b C ~ s W b t H + t s SM B( B X s γ) = (3.55 ± ± 0.03) 10 4, E γ > 1.6 GeV [exp] = (3.15 ± 0.23) 10 4 [theory] [Misiak et al., Becher and Neubert, 2007] 2 maybe more room in D 0 D 0 mixing [BABAR-SLAC] but it is not clear if lattice can contribute there 3 Contributions from charged Higgs exchange in B τν not ruled out (theory and exp errors > 20%). B s µ + µ? (among LHCb goals) 4 in the end the required precision is set by the experiment eg 50 ab 1 at Super-B B(B τν) exp = 3% V ub = 4.4% with F B at 5% Beauty2006] Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 2 / 34 MSSM

5 What is the required precision... to hope to see New Physics in B-flavor? 1 B X s γ γ γ γ t t ~ t ~ t b s b C ~ s W b t H + t s SM B( B X s γ) = (3.55 ± ± 0.03) 10 4, E γ > 1.6 GeV [exp] = (3.15 ± 0.23) 10 4 [theory] [Misiak et al., Becher and Neubert, 2007] 2 maybe more room in D 0 D 0 mixing [BABAR-SLAC] but it is not clear if lattice can contribute there 3 Contributions from charged Higgs exchange in B τν not ruled out (theory and exp errors > 20%). B s µ + µ? (among LHCb goals) 4 in the end the required precision is set by the experiment eg 50 ab 1 at Super-B B(B τν) exp = 3% V ub = 4.4% with F B at 5% Beauty2006] Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 2 / 34 MSSM

6 From these examples it is clear that heavy flavor physics has to become high precision physics. The required precision is O(5%). Lattice computations must start from first principles and all systematics (unquenching, renormalization, continuum limit, chiral extrapolations) must be kept below that 5% level. Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 3 / 34

7 Outline B and D mesons decay constants [V ub, V cd ] B B(s) and ξ [V td, V ts ] B semileptonic decays (B π, B D) [V ub, V cb ] b quark mass in HQET Conclusions V* ud Vub A (ρ,η) α V* td V tb C γ V* cd V cb β B I ll (try to) present the most recent lattice results ordered by N f and give intermediate conclusions for each point. For time reasons the review cannot be complete, sorry for that. Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 4 / 34

8 B and D mesons decay constants B and D mesons decay constants 0 A µ P = F P p µ describes leptonic decays of the pseudoscalar P Experimentally B(B τ ν τ ) = (1.36 ± 0.48) 10 4 av. Belle and Babar [Faccini, 2006] V ub excl = (3.47 ± 0.29 ± 0.03) 10 3 [J. Flynn and J. Nieves, after HPQCD revision] F B = 254(50) MeV B s leptonic decays not yet observed. F Bs = 229 ± 9 MeV ± granum salis from UT angles fits. F Ds = 274 ± 13 ± 7 MeV and F Ds /F D = 1.23 ± 0.11 ± 0.04 [CLEO-c, 2007] Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 5 / 34

9 B and D mesons decay constants Φ[GeV 3/2 ] a=0.12 fm NRQCD 20 3 x64 a=0.09 fm Fermilab 28 3 x96 N f = 3 Fermilab, HPQCD F B =216(9)(19) m (4)(6) MeV F Bs /F B = 1.20(3) stat+χ (1) = 1.27(2)(6) χ valence m q /m s [m q =m l ] m sea down to about m s /10 much better agreement with χpt compared to few years ago (some sensitivity to logs in Fermilab data) same SχPT formulae used cutoff effects visible perturbative renormalization only also for power divergent subtractions in NRQCD NP renormalization in Fermilab approach ongoing[poster by A. El Khadra] and computation at two coarser lattice resolutions [poster by J. Simone] Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 6 / 34

10 B and D mesons decay constants N f = 2 NP ren. of static axial current in SF [MDM, P. Fritzsch, J. Heitger, 2007] PT applicable for µ 4 GeV!! but no sign within PT!! PT off by 5% at the hadronic scale Preliminary result: F stat B s = 297(14) = 0.08 fm and m sea = m s more work to be done, ongoing ALPHA project Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 7 / 34

11 B and D mesons decay constants N f = 0 ALPHA updated (a 0.05 fm, static) static + rel@m charm F Bs = 191(5) MeV Preliminary result for 1/M corrections in HQET, more later and [talk by N. Garron] Phenomenological remark on F Bs : it is the matrix element entering B s µ + µ. In the SM B O(10 9 ), exp bound at 10 7 level [D0, 2005]. In the MSSM non holomorphic terms [Hall, Rattazzi, Sarid, 1994] produce an enhancement tan(β) 6, tan(β) H u / H d [Babu and Kolda, 1999]. 0.02k events per year expected at LHCb [Barsuk, 2006]. Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 8 / 34

12 B and D mesons decay constants F Ds and F D HPCQD + UKCQD, arxiv: N f = 3 HISQ m l down to m s /10 V a am c fm fm fm fm 0.43 F Ds =241(3)MeV, F Ds /F D =1.162(9) This could be state of the art if: effect of rooting completely clarified [talks by M. Creutz and A. Kronfeld] Discussion of the errors based on more details, in particular on: Bayesian fits Chiral (and continuum limit) fits Algorithmic details (missing for m sea < 0.2m s and largest a) Autocorrelation of these quantities [longer publication announced, talk by E. Follana] Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 9 / 34

13 B and D mesons decay constants Preliminary N f = 2, ETMC maximal twist: automatic O(a) improvement, no Z factors needed for F PS m sea down to m s /5, V = , a 0.09 fm [ , a 0.07 fm], LW gauge action F Ds = 287(4)(3)(3) a MeV (quite large) and F Ds /F D = 1.36(4)(2)(7) χ. [talk by B. Blossier] a 3/2 f PS m PS 1/ /am 1/am PS D f Ds [MeV] QCDSF 07 ALPHA 03 ALPHA 05 UKQCD 01 Chiu et al a 2 [GeV -2 ] N f = 0, QCDSF Clover quarks, a 0.04 fm, V = linear chiral extrap from m π 500 MeV: F Ds = 220(6)(5)(11) a MeV and F Ds /F D = 1.068(18)(20). [talk by A. Ali-Khan] including also preliminary results on D πlν form factors. Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 10 / 34

14 B and D mesons decay constants Decay constants are now measured at experiments and the precision will improve in the future. In lattice computations the quenched approximation has been almost removed. Also small quark masses have been reached and better agreement with NLO χpt formulae is found. In most cases continuum limit extrapolations are missing (in some cases, like for NRQCD, not even possible in theory). NP renormalization (when needed) done only in few cases. F Ds is one of the quantities best measured experimentally and on the lattice. Quenching effects (N f = 3 vs N f = 0) do not appear to be large after continuum limit extrapolation. Still the lattice result lie at the lower end of the experimental ones from CLEO-c and BaBar. For F B(s) the unquenched results tend to give larger values than the quenched ones Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 11 / 34

15 B (s) B (s) mixing B (s) B (s) mixing m q = G 2 F m2 W 6π 2 V tqv tb 2 ηs 0 (x t )m Bq F 2 B q B Bq B q O VV +AA B q = 8 3 F 2 B q B Bq m 2 B q Experiments: m d = ± 0.005ps 1 [PDG] m s = ± 0.25ps 1 [CDF,D0] Exp. errors here are at the percent level! In Effective theories (eg HQET): O QCD VV +AA (m b) = C L (m b, µ) O HQET VV +AA (µ)+ C S(m b, µ) O HQET SS+PP (µ)+o(1/m b) Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 12 / 34

16 B (s) B (s) mixing N f = 3 : AsqTad, m l /m s = 0.5, 0.25, NRQCD, a 0.12 fm, V = No dep. on m l visible:f Bs B RGI B s =281(21) m+stat MeV 2l B Bs (m b )=0.76(11) Results also for Γ s and preliminary estimates of B B [poster by C. Davies] Operators of dim 7 are included in the matching between NRQCD and QCD power divergent contributions have to be subtracted the way this is done is critical, with the 1 loop coeff the subtraction is 10% of the final number for B Bs! Staying in PT the problem will only get worse when decreasing a N f = 2 : [Gadiyak and Loktik, 05]Domain wall (RBC), V = ( 12), m π 500 MeV, APE-static action, a 0.12 fm 1 B Bs B B = 1.06(6)(4) F Bs F B = 1.29(4)(6) B Bq m 2 PS [GeV2 ] Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 13 / 34

17 B (s) B (s) mixing N f = 0, 2 : With Wilson fermions (in the static approximation) the mixings with operators of wrong chirality can be removed by using tmqcd [MDM, 2004, Palombi et al., 2005]. NP renormalization for the relevant parity odd operators completed in the SF scheme PT seems to work for µ 1 GeV for both N f = 0, 2 [talks by M. Papinutto and C. Pena] Also preliminary quenched results for the matrix elements [talk by F. Palombi] Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 14 / 34

18 B (s) B (s) mixing Experimental numbers are very precise. Errors on CKM parameters extracted from m q are dominated by uncertainties on the hadronic matrix elements. It is important to reduce them, although it seems difficult to do better than 10% on F 2 B q B Bq Not many new lattice results, especially for B B Anyway the quenched approximation is being removed and rather small sea quark masses reached No results in the continuum limit In the static approximation the NP renormalization has been completed for the twisted mass approach and for N f = 0, 2 No clear expectation about 1/M corrections Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 15 / 34

19 Semileptonic B decays Semileptonic B decays prototype: B πlν, q = lepton pair momentum, m 2 = (m 2 B m2 π)/q 2 dγ dq 2 = G F 2 V ub 2 192π 3 mb 3 [κ(q 2 )] 3/2 f + (q 2 ) 2 π( k) V µ B( p) = f + (q 2 )(p + k q m 2) µ + f 0 (q 2 )q µ m 2 1 for PS V transitions 4 form factors. 2 In the heavy heavy case, HQET gives relations among them valid up to O(1/M). In the static limit the Isgur-Wise function ξ(v v ) describes all the form factors. 3 Experiments measure in the small q 2 region (dγ p 3 π), lattice can access the large q 2 one (a eff.). Also, HQET is applicable only there. 4 The kinematical factor in front of f + vanishes at q max =(m B m π, 0). 5 Lattice results cover a small region of q. Parameterization of the form factors are then used (which include kin. constraints, HQET scaling and disp. rel.) [D. Becirevic and A. Kaidalov, 99] Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 16 / 34

20 Semileptonic B decays Semileptonic B decays prototype: B πlν, q = lepton pair momentum, m 2 = (m 2 B m2 π)/q 2 dγ dq 2 = G F 2 V ub 2 192π 3 mb 3 [κ(q 2 )] 3/2 f + (q 2 ) 2 π( k) V µ B( p) = f + (q 2 )(p + k q m 2) µ + f 0 (q 2 )q µ m 2 1 for PS V transitions 4 form factors. 2 In the heavy heavy case, HQET gives relations among them valid up to O(1/M). In the static limit the Isgur-Wise function ξ(v v ) describes all the form factors. 3 Experiments measure in the small q 2 region (dγ p 3 π), lattice can access the large q 2 one (a eff.). Also, HQET is applicable only there. 4 The kinematical factor in front of f + vanishes at q max =(m B m π, 0). 5 Lattice results cover a small region of q. Parameterization of the form factors are then used (which include kin. constraints, HQET scaling and disp. rel.) [D. Becirevic and A. Kaidalov, 99] Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 16 / 34

21 Semileptonic B decays Semileptonic B decays prototype: B πlν, q = lepton pair momentum, m 2 = (m 2 B m2 π)/q 2 dγ dq 2 = G F 2 V ub 2 192π 3 mb 3 [κ(q 2 )] 3/2 f + (q 2 ) 2 π( k) V µ B( p) = f + (q 2 )(p + k q m 2) µ + f 0 (q 2 )q µ m 2 1 for PS V transitions 4 form factors. 2 In the heavy heavy case, HQET gives relations among them valid up to O(1/M). In the static limit the Isgur-Wise function ξ(v v ) describes all the form factors. 3 Experiments measure in the small q 2 region (dγ p 3 π), lattice can access the large q 2 one (a eff.). Also, HQET is applicable only there. 4 The kinematical factor in front of f + vanishes at q max =(m B m π, 0). 5 Lattice results cover a small region of q. Parameterization of the form factors are then used (which include kin. constraints, HQET scaling and disp. rel.) [D. Becirevic and A. Kaidalov, 99] Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 16 / 34

22 Semileptonic B decays Semileptonic B decays prototype: B πlν, q = lepton pair momentum, m 2 = (m 2 B m2 π)/q 2 dγ dq 2 = G F 2 V ub 2 192π 3 mb 3 [κ(q 2 )] 3/2 f + (q 2 ) 2 π( k) V µ B( p) = f + (q 2 )(p + k q m 2) µ + f 0 (q 2 )q µ m 2 1 for PS V transitions 4 form factors. 2 In the heavy heavy case, HQET gives relations among them valid up to O(1/M). In the static limit the Isgur-Wise function ξ(v v ) describes all the form factors. 3 Experiments measure in the small q 2 region (dγ p 3 π), lattice can access the large q 2 one (a eff.). Also, HQET is applicable only there. 4 The kinematical factor in front of f + vanishes at q max =(m B m π, 0). 5 Lattice results cover a small region of q. Parameterization of the form factors are then used (which include kin. constraints, HQET scaling and disp. rel.) [D. Becirevic and A. Kaidalov, 99] Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 16 / 34

23 Semileptonic B decays Semileptonic B decays prototype: B πlν, q = lepton pair momentum, m 2 = (m 2 B m2 π)/q 2 dγ dq 2 = G F 2 V ub 2 192π 3 mb 3 [κ(q 2 )] 3/2 f + (q 2 ) 2 π( k) V µ B( p) = f + (q 2 )(p + k q m 2) µ + f 0 (q 2 )q µ m 2 1 for PS V transitions 4 form factors. 2 In the heavy heavy case, HQET gives relations among them valid up to O(1/M). In the static limit the Isgur-Wise function ξ(v v ) describes all the form factors. 3 Experiments measure in the small q 2 region (dγ p 3 π), lattice can access the large q 2 one (a eff.). Also, HQET is applicable only there. 4 The kinematical factor in front of f + vanishes at q max =(m B m π, 0). 5 Lattice results cover a small region of q. Parameterization of the form factors are then used (which include kin. constraints, HQET scaling and disp. rel.) [D. Becirevic and A. Kaidalov, 99] Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 16 / 34

24 B πlν Semileptonic B decays N f = 3 HPQCD, same set as for B Bs but m l /m s down to p π = (000, 001, 011, 111) 2π L f (GeV -1/2 ) Staggered Chiral perturbation theory fit linear fit E π =0.8 GeV E π =1.0 E π =1.1 E π = f 0 (q 2 ) HPQCD f + (q 2 ) HPQCD source of error size of error (%) statistics + chiral extrapolations 10 two-loop matching 9 discretization 3 relativistic 1 Total m q /m s q 2 in GeV 2 - g B Bπ varies in the SχPT fits as a function of E π (required for large E π ) - Stat. errors grow at large q 2. Statistic is being accumulated 1 q 2 max dγ V ub 2 dq 2 dq2 = 2.07(41)(39)ps 1HFAG V ub = 3.55(25)(50) GeV 2 the tension with the inclusive value (4.49(33) 10 3 [Lubicz, 2007]) is still there Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 17 / 34

25 Semileptonic B decays Alternative approach for large q 2 by Heavy flavor χpt f + (q 2 ) = F [ ( B g B 2F Bπ π 1 1 v k π m B + m B m B ) + F ] B F B [F B ] = 2 In the static approx. B (0) A µ B(0) = 2m B ĝɛ µ = g B BπF π ɛ µ + O(1/M) -New N f =0 result using all to all propagators with 100 ev [J. Foley et al., 2005] for 2 and 3 pt functions on 32 confs at β =6, (Clover, HYP1) and m π 650 MeV ĝ = 0.517(16) [Negishi, Matsufuru and Onogi, 2006] 0.65 Preliminary N f = 2 result [talk by H. Ohki] 0.55 Our result (n f =2) 0.5 Becirevic et al. (n a 0.2 fm, HYP1, 200 ev, PT ren f =2) Negishi et al. (n f =0) 0.45 Abada et al. (n ĝ = 0.54(3)(3) χ (3) PT (6) f =0) disc g Towards a computation of f + (q 2 ) in HQET: 0.6 m PS 2 (GeV 2 ) scale independent ratio Z V stat computed NP for N ZA stat f = 0 and various static actions (EH, APE, HYP) using WI [Palombi, 2007] Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 18 / 34

26 Semileptonic B decays Heavy heavy transitions B Dlν [ V cb ] in the Rome II SSF approach [talk by N. Tantalo] this work CLEO BELLE G B --> D V cb w 1 The computation is done in quenched QCD starting in small volumes (0.4 fm, where b and c quark are accessible) 2 (3 times) Larger volumes are reached through 2 SSF: σ i f (w, L 0, L 1 ) = F i f (w, L 1 ) F i f (w, L 0 ) idea: FSE might be large but depend mildly on m heavy and can be extrapolated in 1/M from masses, in the last step, around the charm 3 Results in the continuum limit, although using two lattice resolutions for the ssf 4 Momenta injected by twisted boundary conditions 5 Chiral limit by extrapolating from m m s /4 Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 19 / 34

27 Semileptonic B decays Heavy heavy transitions B Dlν [ V cb ] in the Rome II SSF approach [talk by N. Tantalo] this work CLEO BELLE G B --> D V cb w 1 The computation is done in quenched QCD starting in small volumes (0.4 fm, where b and c quark are accessible) 2 (3 times) Larger volumes are reached through 2 SSF: σ i f (w, L 0, L 1 ) = F i f (w, L 1 ) F i f (w, L 0 ) idea: FSE might be large but depend mildly on m heavy and can be extrapolated in 1/M from masses, in the last step, around the charm 3 Results in the continuum limit, although using two lattice resolutions for the ssf 4 Momenta injected by twisted boundary conditions 5 Chiral limit by extrapolating from m m s /4 Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 19 / 34

28 Semileptonic B decays Heavy heavy transitions B Dlν [ V cb ] in the Rome II SSF approach [talk by N. Tantalo] this work CLEO BELLE G B --> D V cb w 1 The computation is done in quenched QCD starting in small volumes (0.4 fm, where b and c quark are accessible) 2 (3 times) Larger volumes are reached through 2 SSF: σ i f (w, L 0, L 1 ) = F i f (w, L 1 ) F i f (w, L 0 ) idea: FSE might be large but depend mildly on m heavy and can be extrapolated in 1/M from masses, in the last step, around the charm 3 Results in the continuum limit, although using two lattice resolutions for the ssf 4 Momenta injected by twisted boundary conditions 5 Chiral limit by extrapolating from m m s /4 Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 19 / 34

29 Semileptonic B decays Heavy heavy transitions B Dlν [ V cb ] in the Rome II SSF approach [talk by N. Tantalo] this work CLEO BELLE G B --> D V cb w 1 The computation is done in quenched QCD starting in small volumes (0.4 fm, where b and c quark are accessible) 2 (3 times) Larger volumes are reached through 2 SSF: σ i f (w, L 0, L 1 ) = F i f (w, L 1 ) F i f (w, L 0 ) idea: FSE might be large but depend mildly on m heavy and can be extrapolated in 1/M from masses, in the last step, around the charm 3 Results in the continuum limit, although using two lattice resolutions for the ssf 4 Momenta injected by twisted boundary conditions 5 Chiral limit by extrapolating from m m s /4 Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 19 / 34

30 Semileptonic B decays Heavy heavy transitions B Dlν [ V cb ] in the Rome II SSF approach [talk by N. Tantalo] this work CLEO BELLE G B --> D V cb w 1 The computation is done in quenched QCD starting in small volumes (0.4 fm, where b and c quark are accessible) 2 (3 times) Larger volumes are reached through 2 SSF: σ i f (w, L 0, L 1 ) = F i f (w, L 1 ) F i f (w, L 0 ) idea: FSE might be large but depend mildly on m heavy and can be extrapolated in 1/M from masses, in the last step, around the charm 3 Results in the continuum limit, although using two lattice resolutions for the ssf 4 Momenta injected by twisted boundary conditions 5 Chiral limit by extrapolating from m m s /4 Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 19 / 34

31 Semileptonic B decays Preliminary N f = 2 results from tmqcd PS to PS form factors around the charm, ξ(ω) agress with N f = 0, Rome II with larger stat errors, different systematics [talk by S.Simula] B D lν at 0 recoil, Fermilab Collab. [talk by J. Laiho] Rate larger than B D, preferred for V cb At 0 recoil only 1 (h A1 ) of the 4 form factors. Matrix element of the axial current 1 double ratio (where most of the ren. constants cancel) instead of considering heavy mass dependence of 3 double ratios h A1 (1) medium coarse (0.15 fm coarse (0.12 fm) fine (0.09 fm) extrapolated value h A1 (1) = 0.924(12)(20) Same lattices as for F D(s) [N f = 3] m π (GeV ) Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 20 / 34

32 Semileptonic B decays Increasing efforts in recent times, especially in leaving the quenched approximation Still other systematics (mainly continuum limit for N f > 0) are poorly studied Many different heavy-light and heavy-heavy processes considered and with different approaches Rather satisfactory overlap with experiments concerning the choice of processes and the accessible q 2 region. Improving on the latter requires considering very small lattice spacings. Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 21 / 34

33 m b in HQET The b quark mass in HQET LPHA ACollaboration In collaboration with N. Garron, M. Papinutto and R. Sommer Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 22 / 34

34 m b in HQET Why do we like HQET[Eichten and Hill, 89]? Theoretically very sound Can be treated non-perturbatively including renormalization (and O(1/M)) [Heitger and Sommer, 2003] Subleading corrections can be computed systematically or estimated by combining with relativistic quarks around the charm The continuum limit is well defined and can be reached numerically [ALPHA, 2003] Unquenching can be included now Can be used together with other methods, eg the Rome II method [Guazzini, Sommer and Tantalo, 2006] still it might be a little involved... Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 23 / 34

35 m b in HQET A bit of notation Field content: ψ h s.t. P + ψ h = ψ h with P + = 1+γ 0 2 S HQET = a { 4 ψ h (D 0 + δm)ψ h + ω spin ψh ( σb)ψ h + ω kin ψh ( 12 ) D2 ψ h x 3 parameters (we ll get rid of one through spin-average) to be set in order to reproduce QCD up to O(1/m 2 b ). ω spin and ω kin formally O(1/m b ). Renormalization and matching! The two steps could be performed separately. In particular at leading order in 1/m b matching can be done in perturbation theory. Here we are interested in 1/m b corrections and do the two things at the same time and non-perturbatively. Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 24 / 34

36 m b in HQET We don t include the next to leading terms of the 1/m b expansion in the action, the theory would be non renormalizable. We treat them as insertions into correlation functions and consider the static action only. e (S rel +S HQET ) = e (S rel +S stat) [1 a 4 x L (1) (x, ω spin, ω kin ) +... ] and S stat = a 4 x ψ h (x)d HYP 0 ψ h (x) [spin-flavor symmetric] f 1 f 1 kin/spin Okin/spin 0 T f A, da (x ) 0 x 0 x 0 f kin/spin (x A, da 0 ) A, da O kin/spin y 0 y 0 A, da x 0 x 0 Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 25 / 34

37 m b in HQET Overview of the approach We will use a finite volume scheme (Schrödinger functional). The volume L 1 should be small enough to simulate relativistic b-quarks 1 (a<<1/m b ) but also such that L 1 m b Λ QCD m b (in the end L fm.) Considering spin-averaged quantities, we are left with two coefficients. Strategy: define two (sensible) quantities Φ k and require (in small volume) Φ HQET k = Φ QCD k k = 1, 2 Evolve these quantities in the effective theory to large volumes. There the B-meson mass expressed in terms of Φ k and large volume HQET quantities can be used to fix the b-quark mass. experiment Lattice with am q 1 m B = 5.4GeV Φ 1 (L 1,M b ),Φ 2 (L 1,M b ) L 2 = 2L 1 Φ HQET 1 (L 2 ),Φ HQET 2 (L 2 ) σ m(u 1 ) Φ HQET 1 (L 1 ),Φ HQET 2 (L 1 ) σ1 kin (u 1 ),σ2 kin (u 1 ) Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 26 / 34

38 Main advantage of these SF correlators: no 1/m b terms in the HQET expansion of the boundary fields. Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 27 / 34 m b in HQET The Schrödinger functional QCD in a finite volume L 3 T with periodic boundary conditions in space and Dirichlet boundary condition is time. Periodicity up to a phase θ: ψ(x + Lˆk) = e iθ ψ(x) QCD correlations (b-quark boundary field: ζ b ) f 1 ζ l (u)γ 5ζ b (v) ζ b (y)γ 5 ζ l (z) k 1 u,v,y,z u,v,y,z,k ζ l (u)γ kζ b (v) ζ b (y)γ k ζ l (z) in HQET (b-quark boundary field: ζ h ) up to O(1/mb 2 { ). [m bare=δm+m b ] } (f 1 ) R = Zζ 2 h Zζ 2 e m baret f1 stat + ω kin f1 kin + ω spin f spin 1 { (k 1 ) R = Zζ 2 h Zζ 2 e m baret f1 stat + ω kin f1 kin 1 } 3 ω spinf spin 1 PS V

39 m b in HQET Φ 1 (L, M) = Φ 2 (L, M) = ( ) ln f1 (θ) f 1 (θ ) + 3 ln QCD ( k1 (θ) k 1 (θ ) HQET ) R1 stat = ω kin R1 kin(θ, θ ) LΓ 1 = L T ln f av 1 = L[m bare + Γ stat 1 + ω kin Γ kin 1 ] f av 1 = (f 1 k 3 1 )1/4 For the lattice spacings (ie β values) used here (L 1 ) we could determine ω kin and m bare as functions of M (implicitly we ll do that). but we don t get the relation among M and m B to fix the b-quark 1.6 fm L mass. 1 To this end we first evolve the Φ k to larger volumes Φ k (L 2, M, β) = j Σ kj (L 1, β)φ j (L 1, M, β) the SSF Σ kj are defined in HQET and have a continuum limit. Notice Φ k (L 2, M) still depend on M!! Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 28 / 34

40 m b in HQET The parameters (β) used in L 2 can be used in large volumes. There we take a phenomenological quantity to fix M b m B av = E stat + ω kin E kin + m bare, E stat = lim L Γstat 1, E kin = 1 2 B z ψ h D 2 ψ h (0, z) B rewriting ω kin and m bare in terms of Φ k (L 2, M) = Σ k jφ j (L 1, M) we get a relation between m B av and M which we solve for M b. The relation involves quantities, which have a continuum limit either in QCD or HQET. The bare parameters have disappeared (implicit above). Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 29 / 34

41 m b in HQET The static piece In this case only 1 parameter (δm, linearly divergent) to be eliminated 1: volume. Experimental input m B : m B = E stat + m bare m bare is a counter-term in the action independent from L 2: Small volume (L 1 ) matching condition M b obtained by inserting 2 in 1: Γ 1 (M b, L 1 ) = Γ stat 1 (L 1 ) + m bare m B = [E stat Γ stat 1 (L 1 )] + Γ 1 (M b, L 1 ) Each piece has a well defined continuum limit in HQET or QCD. The difference between volume ( 1.6 fm.) and L 1 ( 0.4 fm.) is too large to simulate at the same bare parameters and a fine a. We insert one SSF evolution Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 30 / 34

42 m b in HQET 2L 1 m B 2L 1 [E stat Γ stat 1 (2L 1 )] σ m (L 1 ) = 2L 1 Γ 1 (M b, L 1 ) σ m (L 1 ) = 2L 1 (Γ stat 1 (2L 1 ) Γ stat 1 (L 1 )) We also get M stat b = 6771(99) MeV S = 1 L 1 Φ 2 (L 1, M) M = 0.61(5) Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 31 / 34

43 Similarly for NLO corrections m b in HQET m B av = m stat B + m 1 B with mb 1 in terms of E kin, SSF and Φ k (L 1, MB stat ), eg (notice a/l now): and M 1 B = m1 B S In the MS scheme at the scale m b m b (m b ) = 4.350(64) 0.049(29) GeV Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 32 / 34

44 m b in HQET We tried (12) different matching conditions. All results agree, indicating very small 1/m 2 b corrections. θ 0 r 0 M (0) b r 0 M b = r 0 (M (0) b + M(1a) b + M (1b) b ) θ 1 = 0 θ 1 = 1/2 θ 1 = 1 θ 2 = 1/2 θ 2 = 1 θ 2 = (20) 17.12(22) 17.12(22) 17.12(22) (25) 17.25(28) 17.23(27) 17.24(27) 1/ (22) 17.23(28) 17.21(27) 17.22(28) (28) 17.17(32) 17.14(30) 17.15(30) For F Bs as well (now Φ needed for the matching) [talk by N. Garron] Preliminary!! FB stat s [MeV] FB stat s + F (1) B s [MeV] θ 0 θ 1 = 0 θ 1 = 0.5 θ 1 = 1 θ 2 = 0.5 θ 2 = 1 θ 2 = ± ± ± ± ± ± ± ± ± ± ± ± 12 Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 33 / 34

45 Conclusions Conclusions 1 To keep the pace with forth-coming experiments and really help in the quest for New Physics, lattice results in Heavy Flavor Physics must aim at high precision. 2 To this end all the systematics must be kept under control. Unquenching, renormalization, continuum limit, chiral extrapolations, each of them can easily have a 5 10% uncertainty associated. 3 A great effort has been put in recent years in removing the quenched approximation, with great success. 4 In my view it is now time to tackle also the other systematics. 5 I ve given an example how this can be done discussing the b-quark mass in HQET. Almost done, it was quenched. Unquenching is ongoing [talks by P. Fritzsch and J. Heitger] 1 The approach can be extended to other quantities, eg F Bs and B B 2 The approach can be extended to other formulations, eg for the non-perturbative determinations of the parameters in Fermilab-like actions[n. Christ, Li and Lin, 2006]. Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 34 / 34

46 Conclusions Conclusions 1 To keep the pace with forth-coming experiments and really help in the quest for New Physics, lattice results in Heavy Flavor Physics must aim at high precision. 2 To this end all the systematics must be kept under control. Unquenching, renormalization, continuum limit, chiral extrapolations, each of them can easily have a 5 10% uncertainty associated. 3 A great effort has been put in recent years in removing the quenched approximation, with great success. 4 In my view it is now time to tackle also the other systematics. 5 I ve given an example how this can be done discussing the b-quark mass in HQET. Almost done, it was quenched. Unquenching is ongoing [talks by P. Fritzsch and J. Heitger] 1 The approach can be extended to other quantities, eg F Bs and B B 2 The approach can be extended to other formulations, eg for the non-perturbative determinations of the parameters in Fermilab-like actions[n. Christ, Li and Lin, 2006]. Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 34 / 34

47 Conclusions Conclusions 1 To keep the pace with forth-coming experiments and really help in the quest for New Physics, lattice results in Heavy Flavor Physics must aim at high precision. 2 To this end all the systematics must be kept under control. Unquenching, renormalization, continuum limit, chiral extrapolations, each of them can easily have a 5 10% uncertainty associated. 3 A great effort has been put in recent years in removing the quenched approximation, with great success. 4 In my view it is now time to tackle also the other systematics. 5 I ve given an example how this can be done discussing the b-quark mass in HQET. Almost done, it was quenched. Unquenching is ongoing [talks by P. Fritzsch and J. Heitger] 1 The approach can be extended to other quantities, eg F Bs and B B 2 The approach can be extended to other formulations, eg for the non-perturbative determinations of the parameters in Fermilab-like actions[n. Christ, Li and Lin, 2006]. Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 34 / 34

48 Conclusions Conclusions 1 To keep the pace with forth-coming experiments and really help in the quest for New Physics, lattice results in Heavy Flavor Physics must aim at high precision. 2 To this end all the systematics must be kept under control. Unquenching, renormalization, continuum limit, chiral extrapolations, each of them can easily have a 5 10% uncertainty associated. 3 A great effort has been put in recent years in removing the quenched approximation, with great success. 4 In my view it is now time to tackle also the other systematics. 5 I ve given an example how this can be done discussing the b-quark mass in HQET. Almost done, it was quenched. Unquenching is ongoing [talks by P. Fritzsch and J. Heitger] 1 The approach can be extended to other quantities, eg F Bs and B B 2 The approach can be extended to other formulations, eg for the non-perturbative determinations of the parameters in Fermilab-like actions[n. Christ, Li and Lin, 2006]. Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 34 / 34

49 Conclusions Conclusions 1 To keep the pace with forth-coming experiments and really help in the quest for New Physics, lattice results in Heavy Flavor Physics must aim at high precision. 2 To this end all the systematics must be kept under control. Unquenching, renormalization, continuum limit, chiral extrapolations, each of them can easily have a 5 10% uncertainty associated. 3 A great effort has been put in recent years in removing the quenched approximation, with great success. 4 In my view it is now time to tackle also the other systematics. 5 I ve given an example how this can be done discussing the b-quark mass in HQET. Almost done, it was quenched. Unquenching is ongoing [talks by P. Fritzsch and J. Heitger] 1 The approach can be extended to other quantities, eg F Bs and B B 2 The approach can be extended to other formulations, eg for the non-perturbative determinations of the parameters in Fermilab-like actions[n. Christ, Li and Lin, 2006]. Michele Della Morte (CERN) SM parameters and heavy quarks Lattice 2007, Regensburg 34 / 34