Relativistic corrections to light-cone distribution amplitudes of S-wave Bc mesons and heavy quarkonia

Abstract

In collinear factorization, light-cone distribution amplitudes (LCDAs) are key ingredients to calculate the production rate of a hadron in high energy exclusive processes. For a doubly-heavy meson system (such as B c , J/ψ, Υ etc), the LCDAs contain perturbative scales that can be integrated out and then are re-factorized into products of perturbatively calculable distribution parts and non-relativistic QCD matrix elements. In this re-factorization scheme, the LCDAs are known at next-to-leading order in the strong coupling constant α s and at leading order in the velocity expansion. In this work, we calculate the O(v 2 ) corrections to twist-2 LCDAs of S-wave B c mesons. These results are applicable to heavy quarkonia like η c,b , J/ψ and Υ by setting m b = m c . We apply these relativistically corrected LCDAs to study their inverse moments and a few Gegenbauer moments which are important for phenomenological study. We point out that the relativistic corrections are sizable, and comparable with the next-to-leading order radiative corrections. These results for LCDAs are useful in future theoretical analyses of the productions of heavy quarkonia and B c mesons.

Study ofBc→ψ(2S)K,ηDuan1, Yu2 2018Phys. Rev. D3070View full textAdd to dashboardCite

“…In our numerical calculation, we adopt the following input parameters [12,25,32,40,41]: Table I, and in Table II we show the result of the branching fractions for B c → X cc K decays. The branching fractions for B c → ψð3770ÞK decay are displayed in Table V, which contains two sets of S-D mixing angles.…”

“…In Ref. [25], the authors have calculated the relativistic corrections of Gegenbauer moments and found that they are comparable with the next to leading order radiative corrections, and they have also given the total correction values for the first two Gegenbauer moments a 1 and a 2 , which contain leading order contribution, one-loop QCD radiative corrections, and relativistic corrections.…”

“…[25,26] ϕ B c ðuÞ ¼ 6uð1 − uÞ 1 þ X ∞ n¼1 a n ðμÞC 3=2 n ð2u − 1Þ ; ð6Þ where C 3=2 1 ðxÞ ¼ 3x, C 3=2 2 ðxÞ ¼ 3 2 ð5x 2 − 1Þ, and a n denotes the Gegenbauer moments. In Ref.…”

Heavy quark expansion for heavy-light light-cone operators

“…(16), we have (18) where the last term is the same as the one-loop correction of decay constant. By eliminating this term one will arrive at the result for LCDA, which was firstly calculated by Bell and Feldmann [19] and later further explored in NRQCD re-factorization approach [35,36].…”

Pseudoscalar quarkonium+γ production at NLL+NLO accuracy

“…On the other hand in heavy quarkonium the LCDA and short-distance part of the decay constant are perturbatively calculable by matching QCD onto NRQCD amplitude. Their one-loop correction was obtained in [14] and the relativistic correction was obtained in [26,37]. We treat v 2 and α s corrections are of the same size and expand up to the same power.…”