New approach to the resummation of logarithms in Higgs-boson decays to a vector quarkonium plus a photon

We present a calculation of the rates for Higgs-boson decays to a vector heavy-quarkonium state plus a photon, where the heavy quarkonium states are the J/psi and the Upsilon(nS) states, with n=1, 2, or 3. The calculation is carried out in the light-cone formalism, combined with nonrelativistic QCD factorization, and is accurate at leading order in m_Q^2/m_H^2, where m_Q is the heavy-quark mass and m_H is the Higgs-boson mass. The calculation contains corrections through next-to-leading order in the strong-coupling constant alpha_s and the square of the heavy-quark velocity v, and includes a resummation of logarithms of m_H^2/m_Q^2 at next-to-leading logarithmic accuracy. We have developed a new method, which makes use of Abel summation, accelerated through the use of Pade approximants, to deal with divergences in the resummed expressions for the quarkonium light-cone distribution amplitudes. This approach allows us to make definitive calculations of the resummation effects. Contributions from the order-alpha_s and order-v^2 corrections to the light-cone distribution amplitudes that we obtain with this new method differ substantially from the corresponding contributions that one obtains from a model light-cone distribution amplitude [M. Koenig and M. Neubert, J. High Energy Phys. 08 (2015) 012]. Our results for the real parts of the direct-process amplitudes are considerably smaller than those from one earlier calculation [G. T. Bodwin, H. S. Chung, J.-H. Ee, J. Lee, and F. Petriello, Phys. Rev. D 90, 113010 (2014)], reducing the sensitivity to the Higgs-boson--heavy-quark couplings, and are somewhat smaller than those from another earlier calculation [M. Koenig and M. Neubert, J. High Energy Phys. 08 (2015) 012]. However, our results for the standard-model Higgs-boson branching fractions are in good agreement with those in M. Koenig and M. Neubert, J. High Energy Phys. 08 (2015) 012.