The leading twist light-cone distribution amplitudes for the S-wave and P-wave quarkonia and their applications in single quarkonium exclusive productions

Abstract

In this paper, we calculate twist-2 light-cone distribution amplitudes (LCDAs) of the S-wave and P-wave quarkonia (namely 1 S 0 state η Q , 3 S 1 state J/ψ(Υ), 1 P 1 state h Q and 3 P J states χ QJ with J = 0, 1, 2 and Q = c, b) to the next-leading order of the strong coupling α s and leading order of the velocity expansion v in the non-relativistic QCD (NRQCD). We apply these LCDAs to some single quarkonium exclusive productions at large center-of-mass energy, such as γ * → η Q γ, χ QJ γ (J = 0, 1, 2), Z → η Q γ, χ QJ γ (J = 0, 1, 2), J/ψ(Υ)γ, h Q γ and h → J/ψγ, by adopting the collinear factorization. The asymptotic behaviors of those processes obtained in NRQCD factorization are reproduced.

The leading twist light-cone distribution amplitudes for the S-wave and P-wave Bc mesons

“…However, in this paper, we will perform the matching procedure by adopting the threshold expansion developed in [28], as in [24,26].…”

“…Note that the normalization conditions forφ 1A (x),φ ⊥ 3A (x) andφ S (x) in (2.4b) are different from the ones for quarkonia [26]. This is due to the fact that we have no C-parity constraints on the LCDAs for B c mesons.…”

“…In this paper, we extend the computation of the leading twist LCDA for the S-wave pseudo-scalar B c meson in [24] to all the ten twist-2 LCDAs for S-wave and P-wave B c mesons, up to the NLO of α s and leading order of v. This can also be regarded as a succeeding work of [25,26], in which the LCDAs for quarkonia are calculated in the same manner.…”

“…We adopt the same notations as in [26]: the momentum of B c meson is P µ = m Bc v µ where v µ is the velocity four-vector of B c satisfying v 2 = 1. A 4-vector a can be decomposed as a µ = v · av µ + a µ ⊤ where v · a ⊤ ≡ 0.…”

“…Note that (2.17) has an extra term proportional to the spin structure [ ✁ ✁ q, ✚ n + Γ] compared with (2.43) in [26]. This extra term will make some LCDAs for the P-wave B c mesons more complicated than the ones for quarkonia.…”