Lattice QCD determination of the radiative decay rates hc→ηc γ and hb→ηb γ

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=2+1+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 mH(n)=λn-1mc, with λ∼1.24 and n=1,2,…,6, and then extrapolated to mb by several judicious Ansätze. In the continuum limit we obtain Γ(hc→ηcγ)=0.604(24) 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 Γ(hb→ηbγ)=46.0(4.8) keV.