Order v4 corrections to Higgs boson decay into J/ψ+γ

Abstract

The process H → J/ψ + γ, where H is the Higgs particle, provides a way to probe the size and the sign of the Higgs-charm coupling. In order to improve the theoretical control of the decay rate, we compute order v 4 corrections to the decay rate based on the nonrelativistic QCD factorization formalism. The perturbative calculation is carried out by using automated computer codes. We also resum logarithms of the ratio of the masses of the Higgs boson and the J/ψ to all orders in the strong coupling constant α s to next-to-leading logarithmic accuracy. In our numerical result for the decay rate, we improve the theoretical uncertainty, while our central value is in agreement with previous studies within errors. We also present numerical results for H → Υ(nS) + γ for n = 1, 2, and 3, which turn out to be extremely sensitive to the Higgs bottom coupling. PACS numbers:Recently there have been many efforts to improve the theoretical prediction of the decay rate within the Standard Model [4][5][6][7][8]. Especially, approaches based on nonrelativistic effective field theories allow a systematic improvement of theoretical accuracy [4,5,7,8]. In the nonrelativistic QCD (NRQCD) effective field theory [9], decay and production processes involving a heavy quarkonium are given by a double series in α s and v, where v is the typical velocity of a heavy quark Q in a heavy quarkonium; for charmonium, v 2 ≈ 0.3, and for bottomonium, v 2 ≈ 0.1. Currently, the decay rates Γ(H → V +γ) for V = J/ψ or Υ(nS) for n = 1, 2, and 3 have been computed to relative order α s v 0 and v 2 accuracy [5,7,8,10]. In Refs. [5,7,8], the large logarithms of m 2 H /m 2 V that appear in higher order corrections in α s , where m H is the Higgs mass and m V is the mass of the quarkonium V , have been resummed to all orders in α s by combining the NRQCD and the light-cone formalisms [11][12][13].

FeynOnium: using FeynCalc for automatic calculations in Nonrelativistic Effective Field Theories

“…FeynOnium's capability of handling nonrelativistic objects can be combined with the built-in 4-dimensional algebra of FeynCalc to perform nonrelativistic expansion of QCD hadronic matrix elements that involve lightlike collinear momenta. In this section, we show how FeynOnium can be used to compute light-cone distribution amplitudes (LCDAs) of J P C = 1 −− heavy quarkonia in NRQCD to relative order v 4 accuracy at leading order in α s , which was first done in [139]. Following [139], we compute the LCDA for the J/ψ state with momentum P , which is defined by the matrix element…”

“…In this section, we show how FeynOnium can be used to compute light-cone distribution amplitudes (LCDAs) of J P C = 1 −− heavy quarkonia in NRQCD to relative order v 4 accuracy at leading order in α s , which was first done in [139]. Following [139], we compute the LCDA for the J/ψ state with momentum P , which is defined by the matrix element…”

“…To relative order v 4 accuracy, the sum over n involves the NRQCD operators with J P C = 1 −− of dimensions up to 7 that are listed in eqs. (4) and (6) of [139]. Additionally, NRQCD operators with J P C = 1 +− of dimensions up to 7 can be found in appendix C of [139].…”

“…(4) and (6) of [139]. Additionally, NRQCD operators with J P C = 1 +− of dimensions up to 7 can be found in appendix C of [139].…”

“…(6.44) to obtain the quarkonium LCDAs. In [139], the J/ψ and Υ(nS) LCDAs were computed to relative order v 4 accuracy using FeynOnium, and the LCDAs were then used to compute Higgs boson decays to a heavy quarkonium plus a photon.…”