Fermilab/MILC CKM Physics from B, D, and K Mesons

USQCD Collaboration Project

A. Bazavov, C. Bernard, C. DeTar, Daping Du, A. X. El-Khadra, J. Foley, E. D. Freeland, E. Gamiz, S. Gottlieb, U. M. Heller, J. Hetrick, A. S. Kronfeld, J. Laiho, L. Levkova, P. B. Mackenzie, D Mohler, E. Neil, J. N. Simone, R. Sugar, D. Toussaint, R. S. Van de Water, and Ran Zhou.

Great opportunities exist for improving the power of the search for BSM effects in flavor physics by improving lattice QCD calculations. Lattice QCD calculations will greatly improve the bounds on the CKM CP violating parameters ρ and η from B and Bs mixing (green band), K mixing (blue band), and B leptonic decay (salmon band and light yellow band). http://latticeaverages.org


Large new computing resources and vastly improved methods will make possible in the coming decade calculations that are dramatically more precise than have been achieved in the previous decade. This dramatic progress comes at a crucial time for particle physics, because much more is now demanded of lattice QCD than ever before. Lattice QCD calculations have made critical contributions to determinations of CKM matrix elements and to searches for beyond-the-standard-model effects in flavor physics. In Fig. 1), several of the constraints on the CKM parameters ρ and η dominated by lattice uncertainties. The experimental results for K mixing (light blue band in Fig. 1) and for the ratio B mixing/Bs mixing (green band in Fig. 1) have achieved 0.5% precision, far beyond the precisions of current lattice calculations. Future experiments will demand even more from lattice calculations. New leptonic and semileptonic B decay results expected from Belle-2 will demand improved lattice calculations. For example, better measurements of B meson leptonic decay will require better calculations of fB. The uncertainty in Vcb is the crucial bottleneck in present and future rare K decay experiments. This project aims to attack all of these.


The K semileptonic decay form factor f+(0) provides the CKM matrix element Vus.

Project Goals.

This project aims at a comprehensive analysis of the physics of B, D, and K mesons with particular emphasis on physics relevant to determinations of CKM matrix elements and quark masses. It uses the unquenched,highly improved staggered (HISQ) fermion 2+1+1 flavor gauge configurations of the MILC collaboration, HISQ valence quarks for the u, d, s, and c quarks, and clover heavy quarks for the b quark. Ultimately, we aim at determinations of B, D, and K meson decay constants, semileptonic form factors, and B B bar mixing parameters on the full MILC data set.

2013/14 Goals.

Abstract of 2013 proposal: We propose to continue with the HISQ phase of our broad flavor physics program of determining CKM matrix elements and searching for the effects of new physics in flavor physics. We focus on the leptonic and semileptonic decays and meson mixings of mesons containing a heavy b, c or s quark using highly improved staggered quarks (“HISQ” quarks) for the light valence and sea quarks. Our calculations have influenced, and will continue to influence, flavor-physics studies in the experiments BaBar, Belle, CDF, CLEO-c, D0, LHCb, BES, KLOE, NA62, and ORKA. We have brought our long standing program on the “asqtad” ensembles to a close, and are analyzing the last of asqtad data whose data-taking finished last year. The HISQ ensembles now being generated have 2+1+1 flavors of sea quark, with the first 2+1 masses as before, and the fourth at the physical charm mass. This library of ensembles includes light quarks at the physical mass, and these ensembles are increasingly dominating our analysis. We propose to compute D and K meson leptonic and semileptonic decays using HISQ for all valence quarks and to begin a new set of calculations of B physics with Fermilab b quarks.

In 2013/14, we plan to focus on the physical light quark mass ensembles with lattice spacing a = 0.12 and 0.09 fm. For B meson leptonic decay constant, semileptonic decay, and B mixing, we plan to analyze 16,000 time-sources on the a = 0.12 fm ensemble, and 12, 000 time-sources on the a=0.09 fm ensemble. For D and K semileptonic decay, we plan to bring our analyzed data set to 19,000 time-sources on the a=0.12 fm ensemble, and to 4,000 time-sources on the 0.09 fm ensemble.



Selected References

  • Neutral B-meson mixing from three-flavor lattice QCD: Determination of the SU(3)-breaking ratio ξ, Α. Bazavov et al., Phys.Rev. D86 (2012) 034503, arXiv:1205.7013.
  • Bs to Ds over B to D Semileptonic Form-Factor Ratios and Their Application to BR(Bs to muons). Jon A. Bailey et al., Phys.Rev. D85 (2012) 114502, arXiv:1202.6346.
  • B and D meson decay constants from three-flavor lattice QCD, A. Bazavov et al., Phys.Rev. D85 (2012) 114506, arXiv:1112.3051.
  • The B -> πlν semileptonic form factor from three-flavor lattice QCD: A model-independent determination of |V(ub)|. J. Bailey et al. FERMILAB-PUB-08-541-T, Nov 2008, arXiv:0811.3640 [hep-lat], Phys.Rev. D79 (2009) 054507.
  • The Anti-B -> D* l anti-ν form factor at zero recoil from three-flavor lattice QCD: A Model independent determination of |V(cb)|, C. Bernard et al. FERMILAB-PUB-08-316-T, Phys.Rev. D79 (2009) 014506, arXiv:0808.2519 [hep-lat].
  • Charmed meson decay constants in three-flavor lattice QCD. C. Aubin et al. FERMILAB-PUB-05-257-T, Jun 2005. 4pp. Published in Phys.Rev.Lett.95:122002,2005
  • Mass of the B(c) meson in three-flavor lattice QCD. By HPQCD Collaboration and Fermilab Lattice Collaboration and UKQCD Collaboration (Ian F. Allison et al.). FERMILAB-PUB-04-349-T, Nov 2004. 4pp. Published in Phys.Rev.Lett.94:172001,2005
  • Semileptonic decays of D mesons in three-flavor lattice QCD. By Fermilab Lattice Collaboration and MILC Collaboration and HPQCD Collaboration (C. Aubin et al.). FERMILAB-PUB-04-195-T, Aug 2004. 4pp. Published in Phys.Rev.Lett.94:011601,2005
  • High precision lattice QCD confronts experiment. C.T.H. Davies et al. FERMILAB-PUB-03-297-T, Apr 2003. 4pp. Published in Phys.Rev.Lett.92:022001,2004 e-Print Archive: hep-lat/0304004.