Abstract
We study the production of heavy quarkonium states in high energy proton-nucleus collisions. Following earlier work of Blaizot, Fujii, Gelis, and Venugopalan, we systematically include both small $x$ evolution and multiple scattering effects on heavy quark pair production within the Color Glass Condensate (CGC) framework. We obtain for the first time expressions in the Non-Relativistic QCD (NRQCD) factorization formalism for heavy quarkonium differential cross sections as a function of transverse momentum and rapidity. We observe that the production of color singlet heavy quark pairs is sensitive to both "quadrupole" and "dipole" Wilson line correlators, whose energy evolution is described by the Balitsky-JIMWLK equations. In contrast, the color octet channel is sensitive to dipole correlators alone. In a quasi-classical approximation, our results for the color singlet channel reduce to those of Dominguez et. al. [1]. We compare our results to those obtained combining the CGC with the color evaporation model and point to qualitative differences in the two approaches.
Highlights
Counting to organize this complexity, and there has been a tremendous amount of work since in making this a quantitative framework–for recent summaries of the state of the art, see for example [3,4,5]
We study the production of heavy quarkonium states in high energy protonnucleus collisions
We should point to recent next-to-leading order studies which find that the yield of all quarkonia states in proton-proton collisions can be described in Non-Relativistic QCD (NRQCD) factorization, including the J/ψ [6, 7], ψ [8], χcJ [9] and Υ(nS) [10, 11] states
Summary
In the CGC formalism, the proton-nucleus collision is described as a collision of two classical fields originating from color sources representing the large x degrees of freedom in the proton and the nucleus. Where MF (q⊥, p⊥) is the amputated time-ordered quark propagator in the presence of the classical field generated by the sources The expression, as it stands, is not gauge invariant. The multiple scattering effects are included in i) the classical field obtained from solving the Yang-Mills equation in eq (2.1) with the current in eq (2.2), ii) in the propagator of the quark in this classical field, as well as iii) in the small x renormalization group evolution of the color source distribution of the nucleus. A Gaussian distribution of sources is equivalent to the QCD Glauber model of independent multiple scattering [28] We shall address this point further later in our discussion of the quasi-classical limit of quarkonium production. We will discuss the Balitsky-JIMWLK hierarchy further
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