The branching fraction of leptonic decays of pseudo-scalar mesons
that proceed via the annihilation of the initial quark-antiquark pair (cs
in the case of Ds+ meson) into a virtual W+ that finally materializes as an antilepton-neutrino pair (lν, where l = e, μ, or τ) is
given in the Standard Model by
Mode | Branching Fraction | fDs|Vcs| (MeV) | Experiment | Source |
---|---|---|---|---|
μ+ ν | (5.65 ± 0.44 ± 0.20) × 10-3 | 250.8 ± 9.8 ± 4.4 ± 1.8 | CLEO | J. P. Alexander et al. (CLEO Collaboration), Phys. Rev. D 79, 052001 (2009) |
(6.02 ± 0.37 ± 0.32) × 10-3 | 258.9 ± 8.0 ± 6.9 ± 1.8 | BaBar | P. del Amo Sanchez et al. (BaBar Collaboration), Phys. Rev. D 82, 091103 (2010) | |
(5.31 ± 0.28 ± 0.20) × 10-3 | 243.1 ± 6.4 ± 4.6 ± 1.7 | Belle | A. Zupanc et al. (Belle Collaboration), JHEP 1309, 139 (2013) | |
(5.57 ± 0.20 ± 0.14) × 10-3 | 249.0 ± 4.5 ± 3.1 ± 1.7 | HFAG Average | ||
τ+(e+) ν | (5.31 ± 0.47 ± 0.22) × 10-2 | 246.1 ± 10.9 ± 5.1 ± 1.7 | CLEO | P. U. E. Onyisi et al. (CLEO Collaboration), Phys. Rev. D 79, 052002 (2009) |
τ+(π+) ν | (6.46 ± 0.80 ± 0.23) × 10-2 | 271.4 ± 16.8 ± 4.8 ± 1.9 | J. P. Alexander et al. (CLEO Collaboration), Phys. Rev. D 79, 052001 (2009) | |
τ+(ρ+) ν | (5.50 ± 0.54 ± 0.24) × 10-2 | 250.4 ± 12.3 ± 5.5 ± 1.8 | P. Naik et al. (CLEO Collaboration), Phys. Rev. D 80, 112004 (2009) | |
τ+ ν | (5.57 ± 0.32 ± 0.15) × 10-2 | 252.0 ± 7.2 ± 3.4 ± 1.8 | CLEO | |
τ+(e+) ν | (5.08 ± 0.52 ± 0.68) × 10-2 | 240.7 ± 12.3 ± 16.1 ± 1.7 | BaBar | P. del Amo Sanchez et al. (BaBar Collaboration), Phys. Rev. D 82, 091103 (2010) |
τ+(μ+) ν | (4.90 ± 0.46 ± 0.54) × 10-2 | 236.4 ± 11.1 ± 13.0 ± 1.7 | ||
τ+ ν | (4.95 ± 0.36 ± 0.58) × 10-2 | 237.6 ± 8.6 ± 13.8 ± 1.7 | BaBar | |
τ+(e+) ν | (5.37 ± 0.33 +0.35-0.31) × 10-2 | 247.4 ± 7.6 +8.1-7.1 ± 1.7 | Belle | A. Zupanc et al. (Belle Collaboration), JHEP 1309, 139 (2013) |
τ+(μ+) ν | (5.86 ± 0.37 +0.34-0.59) × 10-2 | 258.5 ± 8.2 +7.5-13.0 ± 1.8 | ||
τ+(π+) ν | (6.04 ± 0.43 +0.46-0.40) × 10-2 | 262.4 ± 9.3 +10.0-8.7 ± 1.8 | ||
τ+ ν | (5.70 ± 0.21 ± 0.31) × 10-2 | 254.9 ± 4.7 ± 6.9 ± 1.8 | Belle | |
τ+ ν | (5.55 ± 0.18 ± 0.17) × 10-2 | 251.5 ± 4.1 ± 3.9 ± 1.8 | HFAG average | |
μ+ ν τ+ ν |
250.6 ± 3.1 ± 2.8 ± 1.8 | HFAG average | ||
e+ ν | < 8.3 × 10-5 at 90% C.L. | Belle | A. Zupanc et al. (Belle Collaboration), JHEP 1309, 139 (2013) |
We use measurements of the branching fraction Br(Ds+→ μ+ν) from CLEO, BaBar and Belle and obtain its world average (WA) value of
From the average values of branching fractions of muonic and tauonic decays we determine from the equation on top of this page the product of Ds meson decay constant and the |Vcs| CKM matrix element to be (figure)
Assuming unitarity of the CKM matrix, the value of the element relevant in the case of leptonic Ds+ decays
is known from the global fit of the CKM matrix, |Vcs| = 0.973395+0.000095-0.000176. This value can be used to extract
the Ds meson decay constant from the experimentally measured product fDs|Vcs|.
This leads to the experimentally measured Ds meson decay constant to be:
GF /(ℏc)3 =
(1.1663787 ± 0.0000006) × 10-5 GeV-2
Mμ = (0.1056583715 ± 0.0000000035) GeV/c2
Mτ = (1.77682 ± 0.00016) GeV/c2
MDs = (1.96850 ± 0.00032) GeV/c2
τDs = (500 ± 7) × 10-15 s
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A. Zupanc
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