The BESIII Collaboration has reported the most precise D_s⁺ decay constant f_Ds+ in a newly published Physical Review Letters paper [Phys. Rev. Lett. 127 (2021) 171801].

In the D_s⁺ leptonic decays, the f_Ds+ describes the amplitude for the quark and antiquark within the D_s⁺ meson to have zero separation, a condition necessary for them to annihilate into the virtual W⁺ boson that produces the l⁺ν (l= e, μ, τ) pair. High precision charm data enables us to calibrate the lattice quantum chromodynamics (LQCD) calculations of f_Ds+ and helps to guide the development of LQCD calculation techniques for better understanding of non-perturbative QCD effects.

This measurement was performed with the data samples corresponding to an integrated luminosity of 6.32 fb^-1 collected at center-of-mass energies between 4.178 and 4.226 GeV. The absolute branching fraction of D_s⁺→τ⁺ν has been determined to be BF(D_s⁺→τ⁺ν)= (5.27±0.10±0.12)×10^-2, where τ⁺ →e⁺νν. Taking the CKM matrix element |V_cs|=0.97320±0.00011 from the CKMfitter group as an input, the f_Ds+ is extracted to be (251.1±2.4±3.0) MeV. Combining the recent measurements of BF(D_s⁺→τ⁺ν) based on τ⁺→ π⁺ν and τ⁺→ π⁺π⁰ν from the BESIII Collaboration and the world average value, the relative sensitivity of f_Ds+ achieves to be 1.1%, of which about 50% contribution is from our measurement. Subsequently, combining the above updated world average BF(D_s⁺→τ⁺ν) and the world average BF(D_s⁺→μ⁺ν), a ratio of 9.67±0.34 is obtained, which is consistent with the Standard Model expectation of lepton flavor universality, 9.75±0.01 within the experimental uncertainty.

Further reading:

The PRL publication: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.127.171801

The INSPIRE entry:https://inspirehep.net/literature/1867208