Lattice calculation of the Ds meson radiative form factors over the full kinematical range

Abstract

We compute the structure-dependent axial and vector form factors for the radiative leptonic decays Ds→ℓνℓγ, where ℓ is a charged lepton, as functions of the energy of the photon in the rest frame of the Ds meson. The computation is performed using gauge-field configurations with 2+1+1 sea-quark flavours generated by the European Twisted Mass Collaboration and the results have been extrapolated to the continuum limit. For the vector form factor we observe a very significant partial cancellation between the contributions from the emission of the photon from the strange quark and that from the charm quark. The results for the form factors are used to test the reliability of various Anzätze based on single-pole dominance and its extensions, and we present a simple parametrization of the form factors which fits our data very well and which can be used in future phenomenological analyses. Using the form factors we compute the differential decay rate and the branching ratio for the process Ds→eνeγ as a function of the lower cut-off on the photon energy. With a cut-off of 10 MeV for example, we find a branching ratio of Br(Eγ>10MeV)=4.4(3)×10−6 which, unlike some model calculations, is consistent with the upper bound from the BESIII experiment Br(Eγ>10MeV)<1.3×10−4 at 90% confidence level. Even for photon energies as low as 10 MeV, the decay Ds→eνeγ is dominated by the structure-dependent contribution to the amplitude (unlike the decays with ℓ=μ or τ), confirming its value in searches for hypothetical new physics as well as in determining the Cabibbo-Kobayashi-Maskawa (CKM) parameters at O(αem), where αem is the fine-structure constant.

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