Higher twist effect in inclusive quarkonium photoproduction

Abstract

Abstract:We analyze higher twist effect in photoproduction of quarkonium, where the quarkonium is a spin-triplet, S-wave state. We find that the nonperturbative effect of next-toleading twist is contained in three correlation functions related to the initial hadron and some of the effect of next-to-leading twist is only suppressed by the inverse of the mass square of the quarkonium. A naive estimation indicates that the effect can be significant for charmonium. In the analysis we only take the leading order in the small velocity expansion for the nonperturbative parts related to the quarkonium. Possible corrections from higher orders, especially, corrections from color-octet states are discussed in detail.

Theory of hard photoproduction

“…Relativistic corrections to the color-singlet state have been evaluated, but there is unfortunately no agreement on their effects in the literature (Greub et al, 1993;Khan and Hoodboy, 1996;Ma, McKellar, and Paranavitane, 2000). Higher twist effects due to multiple interactions with the proton or photon remnants should be suppressed as a power of Λ Krämer, and Vänttinen, 1998) and not as a power of Λ 2 /(4m 2 c ) (Ma, 1997), since only the first result leads to the intuitively expected Λ 2 /p 2 T behavior at large p T . On the other hand, the discrepancy between the NRQCD prediction and the HERA data can clearly be reduced, if higher order effects of multi-gluon emission are approximately taken into account in the extraction of the operator matrix elements at the Tevatron (Kniehl and Kramer, 1999).…”

Color singlet relativistic correction inJ/ψphotoproduction

“…The coefficients appearing in the transition matrix are related to the ones appearing in (11). Using the identities in (9), the contraction of the Lorenz indices relates the A ij , b…”

“…As pointed out in [11], this parameter can be negative and can be defined as a matrix element in NRQCD which is different to the one appearing in Eq. (5).…”

Heavy flavour production at HERA

“…It is, however, premature to interpret the discrepancy between the theoretical predictions for colour-octet contributions and the HERA data at large z as a failure of the NRQCD approach itself, as long as not all theoretical uncertainties that reside in the calculation of the short distance cross sections have been assessed carefully. Potentially large QCD effects include higher-twist contributions [51], higher-order corrections and intrinsic transverse momentum of the partons in the proton [52]. Moreover, the peaked shape of the z-distribution is derived neglecting the energy transfer in the non-perturbative transition cc[n] → J/ψ + X.…”