Abstract
We present results for the decay constants of the D and D s mesons computed in lattice QCD with N f = 2 + 1 dynamical flavours. The simulations are based on RBC/UKQCD’s domain wall ensembles with both physical and unphysical light-quark masses and lattice spacings in the range 0.11-0.07 fm. We employ the domain wall discretisation for all valence quarks.
The results in the continuum limit are f D = 208.7(2.8)stat( + 2.1− 1.8 )sysMeV and \( {f}_{D_s}=246.4{(1.3)}_{\mathrm{stat}}{\left({}_{-1.9}^{+1.3}\right)}_{\mathrm{sys}}\mathrm{M}\mathrm{e}\mathrm{V} \) and \( {f}_{D_s}={f}_D=1.667{(77)}_{\mathrm{stat}}{\left({}_{-43}^{+57}\right)}_{\mathrm{sys}} \). Using these results in a Standard Model analysis we compute the predictions |V cd | = 0.2185(50)exp( + 35− 37 )lat and |V cs | = 1.011(16)exp( + 4− 9 )lat for the CKM matrix elements.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
CLEO collaboration, M. Artuso et al., Improved measurement of B(D + → μ + ν) and the pseudoscalar decay constant f (D +), Phys. Rev. Lett. 95 (2005) 251801 [hep-ex/0508057] [INSPIRE].
CLEO collaboration, M. Artuso et al., Measurement of the decay constant \( f\left({D}_{{}^S}^{+}\right) \) using D + S → ℓ + ν, Phys. Rev. Lett. 99 (2007) 071802 [arXiv:0704.0629] [INSPIRE].
CLEO collaboration, B.I. Eisenstein et al., Precision measurement of B(D + → μ + ν) and the pseudoscalar decay constant f (D +), Phys. Rev. D 78 (2008) 052003 [arXiv:0806.2112] [INSPIRE].
CLEO collaboration, J.P. Alexander et al., Measurement of BD + s → ℓ + ν and the decay constant f(D + s ) from 600 pb −1 of e ± annihilation data near 4170 MeV, Phys. Rev. D 79 (2009)052001 [arXiv:0901.1216] [INSPIRE].
CLEO collaboration, P. Naik et al., Measurement of the pseudoscalar decay constant f (D s ) using \( {D}_s^{+}\to {\tau}^{+}\nu, {\tau}^{+}\to {\rho}^{+}\overline{\nu} \) decays, Phys. Rev. D 80 (2009) 112004 [arXiv:0910.3602] [INSPIRE].
CLEO collaboration, K.M. Ecklund et al., Measurement of the absolute branching fraction of D + s → τ + ν τ decay, Phys. Rev. Lett. 100 (2008) 161801 [arXiv:0712.1175] [INSPIRE].
CLEO collaboration, P.U.E. Onyisi et al., Improved measurement of absolute branching fraction of D + s → τ + ν τ , Phys. Rev. D 79 (2009) 052002 [arXiv:0901.1147] [INSPIRE].
BESIII collaboration, M. Ablikim et al., Precision measurements of B(D + → μ + ν μ ), the pseudoscalar decay constant f (D +) and the quark mixing matrix element |V cd|, Phys. Rev. D 89 (2014)051104 [arXiv:1312.0374] [INSPIRE].
Belle collaboration, A. Zupanc et al., Measurements of branching fractions of leptonic and hadronic D + s meson decays and extraction of the D + s meson decay constant, JHEP 09 (2013) 139 [arXiv:1307.6240] [INSPIRE].
BaBar collaboration, P. del Amo Sanchez et al., Measurement of the absolute branching fractions for \( {D}_s^{+}\to {\ell}^{-}{\overline{\nu}}_{\ell } \) and extraction of the decay constant f (D s ), Phys. Rev. D 82 (2010) 091103 [arXiv:1008.4080] [INSPIRE].
Particle Data Group collaboration, C. Patrignani et al., Review of particle physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
S. Aoki et al., Review of lattice results concerning low-energy particle physics, Eur. Phys. J. C 74 (2014) 2890 [arXiv:1310.8555] [INSPIRE].
J. Charles et al., Current status of the standard model CKM fit and constraints on ΔF = 2 new physics, Phys. Rev. D 91 (2015) 073007 [arXiv:1501.05013] [INSPIRE].
M. Bona et al., Unitarity Triangle analysis in the standard model from UTfit, talk given at 2016 International Conference on High Energy Physics (ICHEP 2016), August 3-10, Chicago, U.S.A. (2016).
C.T.H. Davies, C. McNeile, E. Follana, G.P. Lepage, H. Na and J. Shigemitsu, Update: Precision D s decay constant from full lattice QCD using very fine lattices, Phys. Rev. D 82 (2010) 114504 [arXiv:1008.4018] [INSPIRE].
Fermilab Lattice, MILC collaborations, A. Bazavov et al., B- and D-meson decay constants from three-flavor lattice QCD, Phys. Rev. D 85 (2012) 114506 [arXiv:1112.3051] [INSPIRE].
H. Na, C.T.H. Davies, E. Follana, G.P. Lepage and J. Shigemitsu, |V cd | from D meson leptonic decays, Phys. Rev. D 86 (2012) 054510 [arXiv:1206.4936] [INSPIRE].
Y.-B. Yang et al., Charm and strange quark masses and fD s from overlap fermions, Phys. Rev. D 92 (2015) 034517 [arXiv:1410.3343] [INSPIRE].
N. Carrasco et al., Leptonic decay constants f K , f D , and f (D s ) with N f = 2 + 1 + 1 twisted-mass lattice QCD, Phys. Rev. D 91 (2015) 054507 [arXiv:1411.7908] [INSPIRE].
Fermilab Lattice, MILC collaborations, A. Bazavov et al., Charmed and light pseudoscalar meson decay constants from four-flavor lattice QCD with physical light quarks, Phys. Rev. D 90 (2014) 074509 [arXiv:1407.3772] [INSPIRE].
S. Aoki et al., Review of lattice results concerning low-energy particle physics, Eur. Phys. J. C 77 (2017) 112 [arXiv:1607.00299] [INSPIRE].
HPQCD/UKQCD collaboration, E. Follana et al., Highly improved staggered quarks on the lattice, with applications to charm physics, Phys. Rev. D 75 (2007) 054502 [hep-lat/0610092] [INSPIRE].
A.X. El-Khadra, A.S. Kronfeld and P.B. Mackenzie, Massive fermions in lattice gauge theory, Phys. Rev. D 55 (1997) 3933 [hep-lat/9604004] [INSPIRE].
H. Neuberger, Exactly massless quarks on the lattice, Phys. Lett. B 417 (1998) 141 [hep-lat/9707022] [INSPIRE].
K. Osterwalder and E. Seiler, Gauge field theories on the lattice, Annals Phys. 110 (1978) 440 [INSPIRE].
ALPHA collaboration, A. Juttner and J. Rolf, A precise determination of the decay constant of the D s meson in quenched QCD, Phys. Lett. B 560 (2003) 59 [hep-lat/0302016] [INSPIRE].
J. Heitger, G.M. von Hippel, S. Schaefer and F. Virotta, Charm quark mass and D-meson decay constants from two-flavour lattice QCD, PoS(LATTICE 2013)475 [arXiv:1312.7693] [INSPIRE].
S.L. Glashow, J. Iliopoulos and L. Maiani, Weak interactions with lepton-hadron symmetry, Phys. Rev. D 2 (1970) 1285 [INSPIRE].
RBC/UKQCD collaboration, N. Christ et al., Calculating the K L − K S mass difference and ϵ K to sub-percent accuracy, PoS(LATTICE2013)397 [arXiv:1402.2577] [INSPIRE].
Z. Bai, N.H. Christ, T. Izubuchi, C.T. Sachrajda, A. Soni and J. Yu, K L -K S mass difference from lattice QCD, Phys. Rev. Lett. 113 (2014) 112003 [arXiv:1406.0916] [INSPIRE].
RBC/UKQCD collaboration, N.H. Christ et al., Prospects for a lattice computation of rare kaon decay amplitudes: K → πℓ + ℓ − decays, Phys. Rev. D 92 (2015) 094512 [arXiv:1507.03094] [INSPIRE].
N.H. Christ, X. Feng, A. Juttner, A. Lawson, A. Portelli and C.T. Sachrajda, First exploratory calculation of the long-distance contributions to the rare kaon decays K →πℓ + ℓ −, Phys. Rev. D 94 (2016) 114516 [arXiv:1608.07585] [INSPIRE].
RBC/UKQCD collaboration, N.H. Christ et al., Prospects for a lattice computation of rare kaon decay amplitudes II \( K\to \pi \nu \overline{\nu} \) decays, Phys. Rev. D 93 (2016) 114517 [arXiv:1605.04442] [INSPIRE].
Y.-G. Cho et al., Improved lattice fermion action for heavy quarks, JHEP 05 (2015) 072 [arXiv:1504.01630] [INSPIRE].
P. Boyle et al., An exploratory study of heavy domain wall fermions on the lattice, JHEP 04 (2016) 037 [arXiv:1602.04118] [INSPIRE].
N. Carrasco et al., QED corrections to hadronic processes in lattice qcd, Phys. Rev. D 91 (2015) 074506 [arXiv:1502.00257] [INSPIRE].
RBC/UKQCD collaboration, T. Blum et al., Domain wall QCD with physical quark masses, Phys. Rev. D 93 (2016) 074505 [arXiv:1411.7017] [INSPIRE].
RBC/UKQCD collaboration, C. Allton et al., Physical results from 2 + 1 flavor domain wall QCD and SU(2) chiral perturbation theory, Phys. Rev. D 78 (2008) 114509 [arXiv:0804.0473] [INSPIRE].
Y. Aoki et al., Continuum limit of B K from 2 + 1 flavor domain wall QCD, Phys. Rev. D 84 (2011) 014503 [arXiv:1012.4178] [INSPIRE].
RBC/UKQCD collaboration, Y. Aoki et al., Continuum limit physics from 2 + 1 flavor domain wall QCD, Phys. Rev. D 83 (2011) 074508 [arXiv:1011.0892] [INSPIRE].
Y. Iwasaki and T. Yoshie, Renormalization group improved action for SU(3) lattice gauge theory and the string tension, Phys. Lett. 143B (1984) 449 [INSPIRE].
Y. Iwasaki, Renormalization group analysis of lattice theories and improved lattice action: two-dimensional nonlinear O(N) σ-model, Nucl. Phys. B 258 (1985) 141 [INSPIRE].
R.C. Brower, H. Neff and K. Orginos, Mobius fermions: improved domain wall chiral fermions, Nucl. Phys. Proc. Suppl. 140 (2005) 686 [hep-lat/0409118] [INSPIRE].
R.C. Brower, H. Neff and K. Orginos, Mobius fermions, Nucl. Phys. Proc. Suppl. 153 (2006) 191 [hep-lat/0511031] [INSPIRE].
R.C. Brower, H. Neff and K. Orginos, The Möbius domain wall fermion algorithm, Comput. Phys. Commun. 220 (2017) 1 [arXiv:1206.5214] [INSPIRE].
D.B. Kaplan, A method for simulating chiral fermions on the lattice, Phys. Lett. B 288 (1992) 342 [hep-lat/9206013] [INSPIRE].
Y. Shamir, Chiral fermions from lattice boundaries, Nucl. Phys. B 406 (1993) 90 [hep-lat/9303005] [INSPIRE].
UKQCD collaboration, M. Foster and C. Michael, Quark mass dependence of hadron masses from lattice QCD, Phys. Rev. D 59 (1999) 074503 [hep-lat/9810021] [INSPIRE].
UKQCD collaboration, C. McNeile and C. Michael, Decay width of light quark hybrid meson from the lattice, Phys. Rev. D 73 (2006) 074506 [hep-lat/0603007] [INSPIRE].
P.A. Boyle, A. Juttner, C. Kelly and R.D. Kenway, Use of stochastic sources for the lattice determination of light quark physics, JHEP 08 (2008) 086 [arXiv:0804.1501] [INSPIRE].
P.A. Boyle, Hierarchically deflated conjugate gradient, arXiv:1402.2585 [INSPIRE].
A. Juttner and M. Della Morte, Heavy quark propagators with improved precision using domain decomposition, PoS(LAT2005)204 [hep-lat/0508023] [INSPIRE].
P. Boyle, L. Del Debbio and A. Khamseh, Massive momentum-subtraction scheme, Phys. Rev. D 95 (2017) 054505 [arXiv:1611.06908] [INSPIRE].
G. Martinelli, C. Pittori, C.T. Sachrajda, M. Testa and A. Vladikas, A general method for nonperturbative renormalization of lattice operators, Nucl. Phys. B 445 (1995) 81 [hep-lat/9411010] [INSPIRE].
C. Sturm, Y. Aoki, N.H. Christ, T. Izubuchi, C.T.C. Sachrajda and A. Soni, Renormalization of quark bilinear operators in a momentum-subtraction scheme with a nonexceptional subtraction point, Phys. Rev. D 80 (2009) 014501 [arXiv:0901.2599] [INSPIRE].
P.A. Boyle, Conserved currents for mobius domain wall fermions, PoS(LATTICE2014)087 [arXiv:1411.5728] [INSPIRE].
P. Dimopoulos et al., Pseudoscalar decay constants f K /f π , f D and \( {f}_{D_s} \) with N f = 2 + 1 + 1 ETMC configurations, PoS(LATTICE2013)314 [arXiv:1311.3080] [INSPIRE].
Fermilab Lattice, MILC collaborations, A. Bazavov et al., Charmed and strange pseudoscalar meson decay constants from HISQ simulations, PoS(LATTICE 2013)405 [arXiv:1312.0149] [INSPIRE].
Fermilab Lattice, MILC collaborations, A. Bazavov et al., Pseudoscalar meson physics with four dynamical quarks, PoS(LATTICE 2012)159 [arXiv:1210.8431] [INSPIRE].
PACS-CS collaboration, Y. Namekawa et al., Charm quark system at the physical point of 2+1 flavor lattice QCD, Phys. Rev. D 84 (2011)074505 [arXiv:1104.4600] [INSPIRE].
HPQCD/UKQCD collaboration, E. Follana et al., High precision determination of the π, K, D and D s decay constants from lattice QCD, Phys. Rev. Lett. 100 (2008)062002 [arXiv:0706.1726] [INSPIRE].
C. Aubin et al., Charmed meson decay constants in three-flavor lattice QCD, Phys. Rev. Lett. 95 (2005)122002 [hep-lat/0506030] [INSPIRE].
TWQCD collaboration, W.-P. Chen et al., Decay Constants of Pseudoscalar D-mesons in Lattice QCD with Domain-Wall Fermion, Phys. Lett. B 736 (2014) 231 [arXiv:1404.3648] [INSPIRE].
ETM collaboration, N. Carrasco et al., B-physics from N f = 2 tmQCD: the standard model and beyond, JHEP 03 (2014) 016 [arXiv:1308.1851] [INSPIRE].
ETM collaboration, P. Dimopoulos et al., Lattice QCD determination of m b , f B and \( {f}_{B_s} \) with twisted mass Wilson fermions, JHEP 01 (2012) 046 [arXiv:1107.1441] [INSPIRE].
ETM collaboration, B. Blossier et al., Pseudoscalar decay constants of kaon and D-mesons from N f = 2 twisted mass Lattice QCD, JHEP 07 (2009) 043 [arXiv:0904.0954] [INSPIRE].
T. Kinoshita, Radiative corrections to π-e decay, Phys. Rev. Lett. 2 (1959) 477 [INSPIRE].
A. Sirlin, Large m(W), m(Z) behavior of the O(α) corrections to semileptonic processes mediated by W , Nucl. Phys. B 196 (1982) 83 [INSPIRE].
H. Na, C.T.H. Davies, E. Follana, G.P. Lepage and J. Shigemitsu, The D → K, lν semileptonic decay scalar form factor and |V cs | from lattice QCD, Phys. Rev. D 82 (2010) 114506 [arXiv:1008.4562] [INSPIRE].
H. Na et al., D → π, lν semileptonic decays, |V cd | and 2 nd row unitarity from lattice QCD, Phys. Rev. D 84 (2011) 114505 [arXiv:1109.1501] [INSPIRE].
P. Boyle et al., Charm physics with domain wall fermions and physical pion masses, arXiv:1611.06804 [INSPIRE].
P.A. Boyle, The BAGEL assembler generation library, Comput. Phys. Commun. 180 (2009) 2739 [INSPIRE].
ALPHA collaboration, U. Wolff, Monte Carlo errors with less errors, Comput. Phys. Commun. 156 (2004) 143 [Erratum ibid. 176 (2007) 383] [hep-lat/0306017] [INSPIRE].
R. Hudspith, https://github.com/RJhudspith/GLU.
RBC/UKQCD collaboration, R. Arthur and P.A. Boyle, Step scaling with off-shell renormalisation, Phys. Rev. D 83 (2011) 114511 [arXiv:1006.0422] [INSPIRE].
S. Hashimoto et al., Lattice QCD calculation of \( \overline{B}\to D \) lepton anti-neutrino decay form-factors at zero recoil, Phys. Rev. D 61 (1999) 014502 [hep-ph/9906376] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Consortia
Corresponding author
Additional information
ArXiv ePrint: 1701.02644
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
The RBC/UKQCD collaboration., Boyle, P., Del Debbio, L. et al. The decay constants f D and \( {f}_{D_s} \) in the continuum limit of N f = 2 + 1 domain wall lattice QCD. J. High Energ. Phys. 2017, 8 (2017). https://doi.org/10.1007/JHEP12(2017)008
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2017)008