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Next-to-next-to-leading-order QCD corrections to $\chi_c0,2\rightarrow \gamma\gamma$

Wen-Long Sang; Feng Feng; Yu Jia; Shuang-Ran LiangSubjects: Physics >> Nuclear Physics

We calculate the next-to-next-to-leading-order (NNLO) perturbative corrections to?P-wave quarkonia annihilation decay to two photons, in the framework of nonrelativistic QCD (NRQCD) factorization. The order-α2s?short-distance coefficients associated with each helicity amplitude are presented in a semi-analytic form, including the "light-by-light" contributions. With substantial NNLO corrections, we find disquieting discrepancy when confronting our state-of-the-art predictions with the latest \textsf{BESIII} measurements, especially fail to account for the measured?χc2→γγwidth. Incorporating the effects of spin-dependent forces would even exacerbate the situation, since it lifts the degeneracy between the nonperturbative NRQCD matrix elements of?χc0?and?χc2?toward the wrong direction. We also present the order-α2s?predictions to?χb0,2→γγ, which await the future experimental test. |

Quasi Distribution Amplitude of Heavy Quarkonia

Yu Jia; Xiaonu XiongSubjects: Physics >> Nuclear Physics

The recently-proposed quasi distributions point out a promising direction for lattice QCD to investigate the light-cone correlators, such as parton distribution functions (PDF) and distribution amplitudes (DA), directly in the?x-space. Owing to its excessive simplicity, the heavy quarkonium can serve as an ideal theoretical laboratory to ascertain certain features of quasi-DA. In the framework of non-relativistic QCD (NRQCD) factorization, we compute the order-αs?correction to both light-cone distribution amplitudes (LCDA) and quasi-DA associated with the lowest-lying quarkonia, with the transverse momentum UV cutoff interpreted as the renormalization scale. We confirm analytically that the quasi-DA of a quarkonium does reduce to the respective LCDA in the infinite-momentum limit. We also observe that, provided that the momentum of a charmonium reaches about 2-3 times its mass, the quasi-DAs already converge to the LCDAs to a decent level. These results might provide some useful guidance for the future lattice study of the quasi distributions. |

Finite volume corrections to the binding energy of the X(3872)

M. Jansen; H.-W. Hammer; Yu JiaSubjects: Physics >> Nuclear Physics

The quark mass dependence of hadrons is an important input for lattice calculations. We investigate the light quark mass dependence of the binding energy of the X(3872) in a finite box to next-to-leading order in an effective field theory for the X(3872) with perturbative pions (XEFT). At this order, the quark mass dependence is determined by a quark mass-dependent contact interaction in addition to the one-pion exchange. While there is only a moderate sensitivity to the light quark masses in the region up to twice their physical value, the finite volume effects are significant already at box length as large as 20 fm. |

Can NRQCD Explain the $\gamma\gamma^* \to \eta_c$ Transition Form Factor Data?

Feng Feng; Yu Jia; Wen-Long SangSubjects: Physics >> Nuclear Physics

Unlike the bewildering situation in the?γγ?→π?form factor, a widespread view is that perturbative QCD can decently account for the recent \textsc{BaBar} measurement of?γγ?→ηc?transition form factor. The next-to-next-to-leading order (NNLO) perturbative correction to the?γγ?→ηc,b?form factor, is investigated in the NRQCD factorization framework for the first time. As a byproduct, we obtain by far the most precise order-α2s?NRQCD matching coefficient for the?ηc,b→γγ?process. After including the substantial negative order-α2s?correction, the good agreement between NRQCD prediction and the measured?γγ?→ηc?form factor is completely ruined over a wide range of momentum transfer squared. This eminent discrepancy casts some doubts on the applicability of NRQCD approach to hard exclusive reactions involving charmonium. |

Relativistic correction to gluon fragmentation function into pseudoscalar quarkonium

Xiangrui Gao; Yu Jia; LiuJi Li; Xiaonu XiongSubjects: Physics >> Nuclear Physics

Inspired by the recent measurements of the?ηc?meson production at LHC, we investigate the relativistic correction effect for the fragmentation function of the gluon into?ηc, which constitutes the crucial nonperturbative elements to understand?ηc?production at high?pT. Employing three distinct methods, we calculate the leading relativistic correction to the?g→ηc?fragmentation function in the NRQCD factorization framework, as well as verify the existing NLO result for the?c→ηc?fragmentation function. We also study the evolution behavior of these fragmentation functions with the aid of DGLAP equation. |

[1 Pages/ 5 Totals]