Beyond the static limit for quarkonium decays

Abstract

We examine the problems of calculating the leading relativistic corrections to heavyquarkonium decays [relative O(v2)] within the context of QCD. The incorporation of constituent motion in a consistent manner poses nontrivial problems associated with gauge invariance and multiple counting with higher-order contributions in the coupling constant. Although we were unable to resolve these questions in a completely satisfactory manner, we present an improved static limit where the kinematic relativistic corrections are included through binding effects. Our results are gauge invariant and in qualitative agreement with the relative size of relativistic corrections suggested in the analysis of the branching ratio of r(3g)/r(~T) in the $ / J and ' Y systems in QCD.

Heavy quarkonium effective theory

“…0 1/m 2 correction in (92) has also been discussed by BBL [5] and by Keung and Muzinich (KM) [18]. It is in fact the only correction that occurs in either approach.…”

“…(83). Kinematical corrections of type (i) have been discussed by Keung and Muzinich some time ago [18] for S-wave decays and more recently applied also to J/ψ photo- [25] and hadroproduction [7]. The prescription is to evaluate the amplitude A( q 2 , ǫ), (107), at q 2 = mǫ rather than at q 2 = 0.…”

Color singlet relativistic correction inJ/ψphotoproduction

“…(5). Secondly, the correction calculated in [13], is based on the model proposed in [18], in which the contribution of the momentum q to the energy of the heavy quark is neglected-that is the energy is taken to be M J/ψ /2, in the quarkonium rest frame; it really should be √ m 2 + q 2 . This implies that our result cannot be obtained from that presented in [13] by setting M J/ψ = 2m, and the parameter ǫ proportional to P H/ψ ( 3 S (1) 1 ) .…”

“…Previously, models have been constructed to describe such an order v 2 effect. The one parameter model presented in [18] has been used to examine quarkonia photoproduction by Jung et al [13]; a two parameter model has also been proposed [14]. The O(v 2 ) contribution has not been computed within NRQCD.…”

Inclusive charm production inΥ(nS)decay

“…(1). The order-v 2 and order-v 4 relativistic corrections to the color-singlet contributions were calculated by Keung and Muzinich [6] and by Bodwin and Petrelli [7], respectively.…”