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

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 ${}^3{P}_1^{[1]}$ and color-octet ${}^3{S}_1^{[8]}$ $c\bar{c}$ Fock states as well as the mixing of the latter with the ${}^3{D}_1^{[8]}$ 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 $X(3872)\equiv {\chi }_{c1}(2P)$.

Comments: 5 pages, 1 figure, 1 table; three-parameter fit included, reference updated; accepted for publication as Rapid Communication in Physical Review D