# $B$- and $D$-meson leptonic decay constants from four-flavor lattice QCD

## Abstract

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, $$f_{D^+} = 212.6 (0.5)$$~MeV, $$f_{D_s} = 249.8(0.4)$$~MeV, $$f_{D_s}/f_{D^+} = 1.1749(11)$$, $$f_{B^+} = 189.4(1.4)$$~MeV, $$f_{B_s} = 230.7(1.2)$$~MeV, $$f_{B_s}/f_{B^+} = 1.2180(49)$$, 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 $$\overline{\mathcal{B}}(B_s \to \mu^+\mu^-) = 3.65(11) \times 10^{-9}$$, $$\overline{\mathcal{B}}(B^0 \to \mu^+\mu^-) = 1.00(3) \times 10^{-11}$$, and $$\overline{\mathcal{B}}(B^0 \to \mu^+\mu^-)/\overline{\mathcal{B}}(B_s \to \mu^+\mu^-) = 0.00264(7)$$ 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 $$f_{K^+}/f_{\pi^+} = 1.1950(^{+15}_{-22})$$~MeV.

- Authors:

- Michigan State U.
- Washington U., St. Louis
- Utah U.
- Fermilab
- Granada U., Theor. Phys. Astrophys.
- Indiana U.
- APS, New York
- TUM-IAS, Munich
- Syracuse U.
- RIKEN BNL
- UC, Santa Barbara
- Glasgow U.

- 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)

- OSTI Identifier:
- 1423226

- Report Number(s):
- FERMILAB-PUB-17-491-T; arXiv:1712.09262

1644910

- DOE Contract Number:
- AC02-07CH11359

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: TBD

- 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, D., and Van De Water, R. S..
```*$B$- and $D$-meson leptonic decay constants from four-flavor lattice QCD*. United States: N. p., 2017.
Web.

```
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, D., & Van De Water, R. S..
```*$B$- and $D$-meson leptonic decay constants from four-flavor lattice QCD*. United States.

```
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, D., and Van De Water, R. S.. Tue .
"$B$- and $D$-meson leptonic decay constants from four-flavor lattice QCD". United States.
doi:. https://www.osti.gov/servlets/purl/1423226.
```

```
@article{osti_1423226,
```

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, D. and Van De Water, R. S.},

abstractNote = {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, $f_{D^+} = 212.6 (0.5)$~MeV, $f_{D_s} = 249.8(0.4)$~MeV, $f_{D_s}/f_{D^+} = 1.1749(11)$, $f_{B^+} = 189.4(1.4)$~MeV, $f_{B_s} = 230.7(1.2)$~MeV, $f_{B_s}/f_{B^+} = 1.2180(49)$, 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 $\overline{\mathcal{B}}(B_s \to \mu^+\mu^-) = 3.65(11) \times 10^{-9}$, $\overline{\mathcal{B}}(B^0 \to \mu^+\mu^-) = 1.00(3) \times 10^{-11}$, and $\overline{\mathcal{B}}(B^0 \to \mu^+\mu^-)/\overline{\mathcal{B}}(B_s \to \mu^+\mu^-) = 0.00264(7)$ 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 $f_{K^+}/f_{\pi^+} = 1.1950(^{+15}_{-22})$~MeV.},

doi = {},

journal = {TBD},

number = ,

volume = ,

place = {United States},

year = {Tue Dec 26 00:00:00 EST 2017},

month = {Tue Dec 26 00:00:00 EST 2017}

}