The infrared divergence in chi_cJ to e+e- decays is canceled by adding the next-to-leading Fock component, yielding finite, scale-independent leptonic width predictions expressed through Bethe logarithms.
NLO NRQCD disfavors the interpretation of X(3872) as $\chi_{c1}(2P)$
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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 $X(3872)\equiv\chi_{c1}(2P)$.
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A tale of Bethe logarithms: leptonic widths of $\chi_{cJ}$ and Lamb shift
The infrared divergence in chi_cJ to e+e- decays is canceled by adding the next-to-leading Fock component, yielding finite, scale-independent leptonic width predictions expressed through Bethe logarithms.