We study the associated production of prompt $J/\mathrm{<ruby><rb>\psi </rb><rt>ぷさい</rt></ruby>}$ mesons and $W$ or $Z$ bosons within the factorization approach of nonrelativistic QCD (NRQCD) at next-to-leading order in ${\mathrm{<ruby><rb>\alpha </rb><rt>あるふぁ</rt></ruby>}}_s$, via intermediate color singlet ${{}^{3}S}_1^{[1]}$ and ${{}^{3}P}_J^{[1]}$ and color octet ${{}^1\mathrm{S}}_0^{[8]}$, ${{}^3\mathrm{S}}_1^{[8]}$, and ${{}^3\mathrm{P}}_J^{[8]}$ states. Requiring for our predictions to be compatible with recent ATLAS measurements yields stringent new constraints on charmonium long-distance matrix elements (LDMEs) being nonperturbative, process-independent input parameters. Considering four popular LDME sets fitted to data of single $J/\mathrm{<ruby><rb>\psi </rb><rt>ぷさい</rt></ruby>}$ inclusive production, we find that one is marginally compatible with the data, with central predictions typically falling short by a factor of 3, one is unfavored, the factor of shortfall being about 1 order of magnitude, and two violate cross section positivity for direct $J/\mathrm{<ruby><rb>\psi </rb><rt>ぷさい</rt></ruby>}+W/Z$ production. The large rate of prompt $J/\mathrm{<ruby><rb>\psi </rb><rt>ぷさい</rt></ruby>}$ plus $W$ production observed by ATLAS provides strong evidence for the color octet mechanism inherent to NRQCD factorization, the leading color singlet contribution entering only at $\mathcal{O}(G_F{\mathrm{<ruby><rb>\alpha </rb><rt>あるふぁ</rt></ruby>}}_s^4)$, beyond the order considered here.

• Received 22 July 2022
• Accepted 21 December 2022

DOI:https://doi.org/10.1103/PhysRevLett.130.041901

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Published by the American Physical Society