Amplitude-level NLO predictions for exclusive $J/\psi +\gamma$ production in ultraperipheral collisions

Abstract

Exclusive $\gamma \gamma \to J/\psi +\gamma$ production is studied in the color-singlet channel at leading order in the heavy-quark velocity. The conventional next-to-leading-order (NLO) result $B+V$, comprising Born production and its interference with the renormalized one-loop amplitude, is compared with $B+V+Q$, where $Q$ retains the complete one-loop square. At photon-photon energies $W=80\mathrm{GeV}$ and $160\mathrm{GeV}$, the conventional spectrum becomes negative over finite high-$p_T$ intervals already at renormalization scale ${\mu }_R=W$, whereas the complete square remains non-negative. In contrast, the total partonic cross section exceeds Born at the larger energies in the energy scan, owing to positive virtual contributions from other scattering directions. For $p$-$p$ collisions at $14\mathrm{TeV}$ and $Pb$-$Pb$ collisions at $\sqrt{s_{NN}}=5.52\mathrm{TeV}$, $Q$ raises the central integrated ultraperipheral rates by $11.6\%$--$18.4\%$. Their absolute scale widths over ${\mu }_R=\{W/2,W,2W\}$ decrease by $36\%$--$67\%$. Retaining the complete one-loop square changes both the predicted integrated rates and the shapes of the differential distributions.