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Title: B - and D -meson leptonic decay constants from four-flavor lattice QCD

Abstract

Here, we calculate the leptonic decay constants of heavy-light pseudoscalar mesons with charm and bottom quarks in lattice quantum chromodynamics on four-flavor QCD gauge-field configurations with dynamical $u$, $d$, $s$, and $c$ quarks. We analyze over twenty isospin-symmetric ensembles with six lattice spacings down to $$a\approx 0.03$$~fm and several values of the light-quark mass down to the physical value $$\frac{1}{2}(m_u+m_d)$$. We employ the highly-improved staggered-quark (HISQ) action for the sea and valence quarks; on the finest lattice spacings, discretization errors are sufficiently small that we can calculate the $B$-meson decay constants with the HISQ action for the first time directly at the physical $b$-quark mass. We obtain the most precise determinations to-date of the $D$- and $B$-meson decay constants and their ratios, $$f_{D^+} = 212.7(0.6)$$~MeV, $$f_{D_s} = 249.9(0.4)$$~MeV, $$f_{D_s}/f_{D^+} = 1.1749(16)$$, $$f_{B^+} = 189.4 (1.4)$$~MeV, $$f_{B_s} = 230.7(1.3)$$~MeV, $$f_{B_s}/f_{B^+} = 1.2180(47)$$, where the errors include statistical and all systematic uncertainties. Our results for the $B$-meson decay constants are three times more precise than the previous best lattice-QCD calculations, and bring the QCD errors in the Standard-Model predictions for the rare leptonic decays $$\overline{\mathcal{B}}(B_s \to \mu^+\mu^-) = 3.64(11) \times 10^{-9}$$, $$\overline{\mathcal{B}}(B^0 \to \mu^+\mu^-) = 1.00(3) \times 10^{-11}$$, and $$\overline{\mathcal{B}}(B^0 \to \mu^+\mu^-)/\overline{\mathcal{B}}(B_s \to \mu^+\mu^-) = 0.00264(8)$$ to well below other sources of uncertainty. As a byproduct of our analysis, we also update our previously published results for the light-quark-mass ratios and the scale-setting quantities $$f_{p4s}$$, $$M_{p4s}$$, and $$R_{p4s}$$. We obtain the most precise lattice-QCD determination to date of the ratio $$f_{K^+}/f_{\pi^+} = 1.1950(^{+16}_{-23})$$~MeV.

Authors:
 [1];  [2];  [2];  [3];  [4];  [5];  [6];  [7];  [8];  [9];  [10];  [11];  [12];  [11];  [13];  [14];  [11]
  1. Michigan State Univ., East Lansing, MI (United States)
  2. Washington Univ., St. Louis, MO (United States)
  3. Univ. of Utah, Salt Lake City, UT (United States)
  4. Univ. of Illinois, Urbana, IL (United States); Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
  5. Univ. de Granada, Granada (Spain)
  6. Indiana Univ., Bloomington, IN (United States)
  7. American Physical Society, Ridge, NY (United States)
  8. Technische Univ. Munchen, Garching (Germany); Univ. of Glasgow, Glasgow (United Kingdom)
  9. Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Technische Univ. Munchen, Garching (Germany)
  10. Syracuse Univ., Syracuse, NY (United States)
  11. Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
  12. Univ. of Colorado, Boulder, CO (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
  13. Univ. of California, Santa Barbara, CA (United States)
  14. Univ. of Arizona, Tucson, AZ (United States)
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Contributing Org.:
Fermilab Lattice and MILC Collaborations
OSTI Identifier:
1479610
Alternate Identifier(s):
OSTI ID: 1423226
Report Number(s):
arXiv:1712.09262; FERMILAB-PUB-17/491-T
Journal ID: ISSN 2470-0010; PRVDAQ; 1644910
Grant/Contract Number:  
AC02-07CH11359; AC02-05CH11231; AC02-06CH11357; FG02-91ER40628; FC02-12ER41879; SC0010120; FG02-91ER40661; FG02-13ER42001; SC0015655; SC0010005; FG02-13ER41976; SC0009998; SC0012704
Resource Type:
Journal Article: Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 98; Journal Issue: 7; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Bazavov, A., Bernard, C., Brown, N., DeTar, C., El-Khadra, A. X., Gámiz, E., Gottlieb, Steven, Heller, U. M., Komijani, J., Kronfeld, A. S., Laiho, J., Mackenzie, P. B., Neil, E. T., Simone, J. N., Sugar, R. L., Toussaint, Doug, and Van de Water, R. S. B- and D-meson leptonic decay constants from four-flavor lattice QCD. United States: N. p., 2018. Web. doi:10.1103/PhysRevD.98.074512.
Bazavov, A., Bernard, C., Brown, N., DeTar, C., El-Khadra, A. X., Gámiz, E., Gottlieb, Steven, Heller, U. M., Komijani, J., Kronfeld, A. S., Laiho, J., Mackenzie, P. B., Neil, E. T., Simone, J. N., Sugar, R. L., Toussaint, Doug, & Van de Water, R. S. B- and D-meson leptonic decay constants from four-flavor lattice QCD. United States. doi:10.1103/PhysRevD.98.074512.
Bazavov, A., Bernard, C., Brown, N., DeTar, C., El-Khadra, A. X., Gámiz, E., Gottlieb, Steven, Heller, U. M., Komijani, J., Kronfeld, A. S., Laiho, J., Mackenzie, P. B., Neil, E. T., Simone, J. N., Sugar, R. L., Toussaint, Doug, and Van de Water, R. S. Mon . "B- and D-meson leptonic decay constants from four-flavor lattice QCD". United States. doi:10.1103/PhysRevD.98.074512.
@article{osti_1479610,
title = {B- and D-meson leptonic decay constants from four-flavor lattice QCD},
author = {Bazavov, A. and Bernard, C. and Brown, N. and DeTar, C. and El-Khadra, A. X. and Gámiz, E. and Gottlieb, Steven and Heller, U. M. and Komijani, J. and Kronfeld, A. S. and Laiho, J. and Mackenzie, P. B. and Neil, E. T. and Simone, J. N. and Sugar, R. L. and Toussaint, Doug and Van de Water, R. S.},
abstractNote = {Here, we calculate the leptonic decay constants of heavy-light pseudoscalar mesons with charm and bottom quarks in lattice quantum chromodynamics on four-flavor QCD gauge-field configurations with dynamical $u$, $d$, $s$, and $c$ quarks. We analyze over twenty isospin-symmetric ensembles with six lattice spacings down to $a\approx 0.03$~fm and several values of the light-quark mass down to the physical value $\frac{1}{2}(m_u+m_d)$. We employ the highly-improved staggered-quark (HISQ) action for the sea and valence quarks; on the finest lattice spacings, discretization errors are sufficiently small that we can calculate the $B$-meson decay constants with the HISQ action for the first time directly at the physical $b$-quark mass. We obtain the most precise determinations to-date of the $D$- and $B$-meson decay constants and their ratios, $f_{D^+} = 212.7(0.6)$~MeV, $f_{D_s} = 249.9(0.4)$~MeV, $f_{D_s}/f_{D^+} = 1.1749(16)$, $f_{B^+} = 189.4 (1.4)$~MeV, $f_{B_s} = 230.7(1.3)$~MeV, $f_{B_s}/f_{B^+} = 1.2180(47)$, where the errors include statistical and all systematic uncertainties. Our results for the $B$-meson decay constants are three times more precise than the previous best lattice-QCD calculations, and bring the QCD errors in the Standard-Model predictions for the rare leptonic decays $\overline{\mathcal{B}}(B_s \to \mu^+\mu^-) = 3.64(11) \times 10^{-9}$, $\overline{\mathcal{B}}(B^0 \to \mu^+\mu^-) = 1.00(3) \times 10^{-11}$, and $\overline{\mathcal{B}}(B^0 \to \mu^+\mu^-)/\overline{\mathcal{B}}(B_s \to \mu^+\mu^-) = 0.00264(8)$ to well below other sources of uncertainty. As a byproduct of our analysis, we also update our previously published results for the light-quark-mass ratios and the scale-setting quantities $f_{p4s}$, $M_{p4s}$, and $R_{p4s}$. We obtain the most precise lattice-QCD determination to date of the ratio $f_{K^+}/f_{\pi^+} = 1.1950(^{+16}_{-23})$~MeV.},
doi = {10.1103/PhysRevD.98.074512},
journal = {Physical Review D},
issn = {2470-0010},
number = 7,
volume = 98,
place = {United States},
year = {2018},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevD.98.074512

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