Gluon fragmentation into spin-triplet S-wave quarkonium.

نویسندگان

  • Braaten
  • Yuan
چکیده

The leading color-singlet contribution to the fragmentation function for a gluon to split into spin-triplet S-wave quarkonium is presented. In the case of charmonium, we find that this color-singlet term is always negligible compared to the leading color-octet contribution. The dominant mechanism for the production of heavy quarkonium at sufficiently large transverse momentum is parton fragmentation [1]. In Ref. [1], we calculated the fragmentation functions for gluons to split into S-wave quarkonium states to leading order in αs and to leading order in the nonrelativistic expansion. The fragmentation function for the S0 state was given in analytic form, but only numerical results were presented for the S1 state due to the lengthy and cumbersome expression for the fragmentation function. In this Brief Report, we present the detailed formula for the gluon fragmentation function into the S1 state. A rigorous theory of the inclusive production of heavy quarkonium has been developed recently by Bodwin, Braaten, and Lepage [2]. This approach is based on the use of nonrelativistic QCD (NRQCD) to factor the production rate into short-distance coefficients that can be computed in perturbation theory and long-distance factors that are expressed as NRQCD matrix elements. Using this formalism, the fragmentation function for a gluon to split into a quarkonium state X with longitudinal momentum fraction z can be written as Dg→X(z, μ) = ∑ n dn(z, μ)〈O n 〉 , (1) where OX n are local 4-fermion operators in NRQCD. The short-distance coefficients dn(z, μ) are independent of the quarkonium state X. For a fragmentation scale μ of order of the heavy quark mass mQ, they can be computed using perturbative theory in αs(2mQ). The dependence on the quarkonium state X appears in the long-distance factors 〈OX n 〉. The relative magnitude of the various matrix elements for a given state X can be estimated by how they scale with mQ and with the typical relative velocity v of the heavy quark inside the quarkonium. Thus, the factorization formula (1) for the gluon fragmentation function is a double expansion in αs and v. To determine the relative importance of the terms in this formula, one should take into account both the scaling in v of the matrix elements and the order in αs of their coefficients. We now consider the fragmentation function for a S1 state which we denote by V . In the color-singlet model for quarkonium production [3], only a single term in the expansion (1) for the fragmentation function is retained. In the notation of Ref. [2], the matrix element

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عنوان ژورنال:
  • Physical review. D, Particles and fields

دوره 52 11  شماره 

صفحات  -

تاریخ انتشار 1995