Constraints on Nonrelativistic-QCD Long-Distance Matrix Elements from $J/\psi$ Plus $W$/$Z$ Production at the LHC

TL;DR

This paper constrains nonrelativistic QCD long-distance matrix elements using LHC data on prompt J/psi plus W/Z production, highlighting the importance of color octet mechanisms and challenging existing LDME sets.

Contribution

It provides the first stringent constraints on charmonium LDMEs from associated J/psi plus W/Z production at the LHC, testing the universality of these nonperturbative parameters.

Findings

One LDME set is marginally compatible with data.

Two LDME sets violate cross section positivity.

Large J/psi plus W production supports color octet mechanism.

Abstract

We study the associated production of prompt $J/\psi$ mesons and $W$ or $Z$ bosons within the factorization approach of nonrelativistic QCD (NRQCD) at next-to-leading order in $\alpha_s$, via intermediate color singlet ${^3}S_1^{[1]}$ and ${^3}P_J^{[1]}$ and color octet ${^1S}_0^{[8]}$, ${^3S}_1^{[8]}$ and ${^3P}_J^{[8]}$ 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 $J/\psi$ inclusive production, we find that one is marginally compatible with the data, with central predictions typically falling short by a factor of three, one is unfavored, the factor of shortfall being about one order of magnitude, and two violate cross section positivity for direct $J/\psi+W/Z$ production. The large rate of prompt $J/\psi$ 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 $\mathcal{O}(G_F\alpha_s^4)$, beyond the order considered here.