Resummation of large endpoint corrections to color-octet J/ψ photoproduction

An unresolved problem in $J/\ensuremath{\psi}$ phenomenology is a systematic understanding of the differential photoproduction cross section, $d\ensuremath{\sigma}/dz[\ensuremath{\gamma}+p\ensuremath{\rightarrow}J/\ensuremath{\psi}+X$], where $z={E}_{\ensuremath{\psi}}/{E}_{\ensuremath{\gamma}}$ in the proton rest frame. In the nonrelativistic QCD (NRQCD) factorization formalism, fixed-order perturbative calculations of color-octet mechanisms suffer from large perturbative and nonperturbative corrections that grow rapidly in the endpoint region, $z\ensuremath{\rightarrow}1$. In this paper, NRQCD and soft collinear effective theory are combined to resum these large corrections to the color-octet photoproduction cross section. We derive a factorization theorem for the endpoint differential cross section involving the parton distribution function and the color-octet $J/\ensuremath{\psi}$ shape functions. A one-loop matching calculation explicitly confirms our factorization theorem at next-to-leading order. Large perturbative corrections are resummed using the renormalization group. The calculation of the color-octet contribution to $d\ensuremath{\sigma}/dz$ is in qualitative agreement with data. Quantitative tests of the universality of color-octet matrix elements require improved knowledge of shape functions entering these calculations as well as resummation of the color-singlet contribution which accounts for much of the total cross section and also peaks near the endpoint.