Long-distance Matrix Elements And Relativitic Corrections In The Production Of P-wave Heavy Quarkonium

Heavy quarkonium physics is an important platform to study perturbative QCD and non-perturbative QCD. Non-relativistic quantum chromodynamics(NRQCD) deriving from QCD first principles, is the most widely-used theoretical framework for heavy quarkonium production and decay at present. NRQCD has achieved great success since it was proposed. Especially, in recent years, the introduction of higher-order corrections greatly alleviated the sharp contradictions between the experimental date and the theoretical predictions in the excess production of J/?(?') at the hadron colliders and in the inclusive and exclusive production for charmonium at the B factories. But there are still some challenges that could not be avoided for NRQCD. These challenges include the convergence problem in the perturbation expansion and the universality for the Long-distance matrix elements,etc In this thesis, the Long-distance matrix elements in the production for the P-wave heavy quarkonium are studied, and the universality of the matrix elements are also discussed.Under the framework of NRQCD, the calculations on the production of P-wave heavy quarkonium involve more Long-distance matrix elements with very large uncertainties in the theoretical predictions. In this thesis, the Long-distance matrix elements<0|P(3S1[8])|0>?<0|P(3P0[1])|0>?<0|P(3P2[1])|0> in the production of P-wave heavy quarkonium are extracted from the combined analysis in the di-photon and light hadron decay modes with some proper approximations. The numerical results imply that the relations between these matrix elements and Leading-order matrix elements satisfy the condition, <v2)?(0|P|0>/m2<0|O|0>?O(v2), which is consistent with the velocity-scaling rules. It suggests that the values of the Long-distance matrix elements in the relativistic corrections can be obtained using velocity-scaling rules at a rough eatimate. Meanwhile, the results of this thesis show that the Long-distance matrix elements of relativity corrections can be negative. It should be given special attention when investigating the magnitude of the relativistic correction in the P-wave heavy quarkonium production using the velocity-scaling rules.Subsequently, the relativistic corrections to ?cJ exclusive production associated with J/?(?1) in electron-positron annihilation are investigated in this thesis. For the exclusive J/?/+ ?c production at B factories, experimental data are about one order of magnitude larger than the leading-order predictions that was used to one of the worst crisis which NRQCD encountered. The introduction of next-to-leading order corrections make theoretical predictions reach the lower bound of the experiment, and the discrepancy is largely removed. Similarly, for the exclusive J/???cJ production,the discrepancy is also shown between the experiment and the leading-order predictions. On the experimental aspect, the measured cross sections are very large for the J/???c0, production, and meanwhile, there is no clear signals for the J/?+?c1,2 production. On the theoretical aspect, the cross section of the J/?+?c0 production are only about twice as large as that of the J/?+?c1,2 production at Leading-order level. As well, the higher-order corrections are significant for these processes. The next-to-leading order correction in ?s enhances the cross sections by the factor of 1.57 for the J / /?+?c0 production,and meanwhile,it suppresses the cross sections by the factors of 0.91?0.78 for th J//?+?c1,2 production, respectively. These results alleviate the contradiction between theoretical predictions and experimental data. At the same time, it still leave room for the theoretical analysis. In this thesis, the relativistic corrections for the exclusiveJ/?+?cJ production are considered. The K-factors given by the relativitic corrections are about 1-2.2<v2>?1-1.5<v2>?1-2.3<v2),respectively, for the J/?+?c0,1,2 production. The relativistic corrections are about 30-60% of leading-order cross sections when the matrix elements were estimated using velocity-scaling rules and it implies the relativistic corrections play a very important role. In addition, the effects of different parameters are also investigated in this thesis.Combined with the next-to-leading order QCD correction, the discrepancy is found between the total cross sections at the next-to-leading order and the experimental data.Note that the below reasons, such as experimental statistical samples are small, the central values are not consistent between the data measured by the Belle and BaBar collaborations and the theoretical predictions have large uncertainties, the clear conclusion cannot be given and it should be further clarified.