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Fragmentation contributions to $J/ψ$ photoproduction at HERA

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