NLO NRQCD disfavors the interpretation of X(3872) as $\chi_{c1}(2P)$

TL;DR

This paper investigates the production of the charmonium state $ ext{X}(3872)$ under the assumption it is $ ext{chi}_{c1}(2P)$, and finds that NLO NRQCD calculations do not support this interpretation due to inconsistencies with experimental data and theoretical expectations.

Contribution

The study provides a detailed NLO NRQCD analysis of $ ext{X}(3872)$ production assuming it is $ ext{chi}_{c1}(2P)$, and demonstrates the incompatibility of this hypothesis with empirical and theoretical constraints.

Findings

NLO NRQCD fits yield high $ ext{chi}^2$ values.

Incompatible $|R_{2P}^ ext{'}(0)|$ with potential models.

Violation of NRQCD velocity scaling rules.

Abstract

We study $\chi_{c1}(2P)$ inclusive hadroproduction at next-to-leading order (NLO), both in $\alpha_s$ and $v^2$, within the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD), including the color-singlet $^3P_1^{[1]}$ and color-octet $^3S_1^{[8]}$ $c\bar c$ Fock states as well as the mixing of the latter with the $^3D_1^{[8]}$ state. Assuming the recently discovered X(3872) hadron to be the $J^{PC}=1^{++}$ charmonium state $\chi_{c1}(2P)$, we perform a fit to the cross sections measured by the CDF, CMS, and LHCb Collaborations. We either obtain an unacceptably high value of $\chi^2$, a value of $|R_{2P}^\prime(0)|$ incompatible with well-established potential models, or an intolerable violation of the NRQCD velocity rules. We thus conclude that NLO NRQCD is inconsistent with the hypothesis $X(3872)\equiv\chi_{c1}(2P)$.