Addendum: New approach to the resummation of logarithms in Higgs-boson decays to a vector quarkonium plus a photon [Phys. Rev. D 95, 054018 (2017)

Geoffrey T Bodwin,Hee Sok Chung,Jungil Lee,June-Haak Ee

doi:10.1103/physrevd.96.116014

Abstract

In this addendum to Phys.\ Rev.\ D {\bf 95}, 054018 (2017) we recompute the rates for the decays of the Higgs boson to a vector quarkonium plus a photon, where the vector quarkonium is $J/\psi$, $\Upsilon(1S)$, $\Upsilon(2S)$, or $\Upsilon(3S)$. We correct an error in the Abel-Pad\'e summation formula that was used to carry out the evolution of the quarkonium light-cone distribution amplitude in Phys.\ Rev.\ D {\bf 95}, 054018 (2017). We also correct an error in the scale of quarkonium wave function at the origin in Phys.\ Rev.\ D {\bf 95}, 054018 (2017) and introduce several additional refinements in the calculation.

Highlights

In Ref. [1], φVðxÞ, the heavy-quarkonium light-cone distribution amplitude at light-cone momentum fraction x, was evolved from the initial scale μ0, which is of order the heavy-quark mass, to the final scale μ, which is of order the Higgs-boson mass mH, by making use of the Abel-Pademethod
Because the evolution matrix in leading logarithmic (LL) order is diagonal, this change affects the expression for the light-cone amplitude only at next-to-leading logarithmic (NLL) order and higher
In Ref. [1], only the light-cone distribution amplitude (LCDA) at leading order in αs and v was evolved at NLL order. (Here, αs is the QCD running coupling and v is the velocity of the Q or Qin the quarkonium rest frame.) Because the sums in Eq (1) are not absolutely convergent, it is not obvious that the correction in Eq (1) would not affect the results

Summary

Introduction

In Ref. [1], φVðxÞ, the heavy-quarkonium light-cone distribution amplitude at light-cone momentum fraction x, was evolved from the initial scale μ0, which is of order the heavy-quark mass, to the final scale μ, which is of order the Higgs-boson mass mH, by making use of the Abel-Pademethod. Addendum: New approach to the resummation of logarithms in Higgs-boson decays to a vector quarkonium plus a photon [Phys. We correct an error in the Abel-Padesummation formula that was used to carry out the evolution of the quarkonium light-cone distribution amplitude in Phys.

Results

Conclusion