Fragmentation contributions to $J\mathrm{/}\psi$ photoproduction at HERA

We compute leading-power fragmentation corrections to $J\mathrm{/}\psi$ photoproduction at DESY HERA, making use of the nonrelativistic QCD factorization approach. Our calculations include parton production cross sections through order ${\alpha }_s^3$, fragmentation functions though order ${\alpha }_s^2$, and leading logarithms of the transverse momentum divided by the charm-quark mass to all orders in ${\alpha }_s$. We find that the leading-power fragmentation corrections, beyond those that are included through next-to-leading order in ${\alpha }_s$, are small relative to the fixed-order contributions through next-to-leading order in ${\alpha }_s$. Consequently, an important discrepancy remains between the experimental measurements of the $J\mathrm{/}\psi$ photoproduction cross section and predictions that make use of nonrelativistic-QCD long-distance matrix elements that are extracted from the $J\mathrm{/}\psi$ hadroproduction cross-section and polarization data.