Lattice QCD determination of the radiative decay rates hc → ηcγ and hb → ηbγ

We present the results of our lattice QCD computation of the hadronic matrix elements relevant to the hc → ηcγ and hb → ηbγ decays by using the gauge configurations produced by the Extended Twisted Mass Collaboration with Nf ¼ 2 þ 1 þ 1 dynamical Wilson-Clover twisted mass fermions at five different lattice spacings with physical dynamical u, d, s and c quark masses (except for the coarsest lattice for which the lightest sea quark corresponds to a pion with mπ ≃ 175 MeV). While the hadronic matrix element for hc → ηcγ is obtained directly, the one relevant to hb → ηbγ is reached by working with heavy quark masses mHðnÞ ¼ λn−1mc, with λ ∼ 1.24 and n ¼ 1; 2; …; 6, and then extrapolated to mb by several judicious Ansätze. In the continuum limit we obtain Γðhc → ηcγÞ ¼ 0.604ð24Þ MeV, which is by a factor of 2.3 more accurate than the previous lattice estimates, and in good agreement with the experimental measurement. In the b-quark case we obtain Γðhb → ηbγÞ ¼ 46.0ð4.8Þ keV.