QCD study of B meson decays: investigation of dynamical gluon effects inside B meson

B介子的光锥波函数(WF)和形函数(SF)是理论计算B介子衰减率所不可缺少的。我们开展了基于QCD的WF和SF的系统研究，包括B介子内动力胶子诱导的效应。我们分别计算了WF和SF的QCD辐射修正，将相应的算符插入到离壳层格林函数中。我们的结果再现了文献中注意到的奇异行为，并揭示了：奇异行为不仅出现在壳层上，而且也出现在壳外情况下；紫外线发散的结构与红外发散的结构完全不同；相关的红外行为与“软模”有关，作为局域算符的矩阵元素。基于这一观察结果，我们利用算符乘积展开将WF、SF分解为短距离分量和长距离分量。将短距离威尔逊系数计算到单环精度…在MS方案中有更多的ACY，而长距离分量由一组完整的局部算子来表示。利用QCD运动方程，五维和六维算符可以精确地表示为显式动力学胶子，即夸克-反夸克-胶子算符，其矩阵元素已经根据QCD求和规则进行了估计。威尔逊系数包含重整化标度的双对数，即考虑到动力学胶子效应，WF、SF受“两步”重整化群演化的支配，与尖点反常维度和局域算符的反常维度有关。(在完成研究之前，Kodaira教授突然去世。由于这一巨大损失，这项研究中的一些尚未发表或尚未解决。这些将由首席调查员完成。)与其他动力学胶子起重要作用的模型情况一样。我们注意到了极化强子束硬过程中与胶子动力学有关的机制，并发展了相应的QCD预言。较少

The lightcone wavefunction (WF) and the shape function (SF) for B meson are indispensable for theoretical calculation of B-meson decay rates. We developed systematic investigation of WF and SF based on QCD, including effects induced by dynamical gluons inside B meson. We computed QCD radiative corrections for WF and SF, respectively, inserting the corresponding operators into off-shell Green functions. Our results reproduced the singular behavior, noticed in the literature, and revealed: the singular behavior arises not only for on-shell but also for off-shell cases; the structure of ultra-violet divergence is completely different from that of infra-red divergence; the relevant infra-red behavior is associated with "soft modes", as matrix elements of local operators. Based on this observation, we performed the decomposition of WF, SF into the short-and long-distance components, using the operator product expansion. The short-distance Wilson coefficients are calculated to one-loop accur … More acy in the MS-scheme, while the long-distance components are expressed by a complete set of local operators. Using QCD equations of motion, the operators of dimension five and six can be exactly reexpressed in terms of explicit dynamical gluon, i.e., as the quark-antiquark-gluon operators, whose matrix elements were already estimated from QCD sum rules. The Wilson coefficients contain the double logarithms of renormalization scale; namely, taking dynamical gluon effects into account, the WF, SF are governed by the "two-step" renormalization-group evolution, associated with the cusp anomalous dimension, and with the anomalous dimensions of local operators. (Before completing research, Professor Kodaira died suddenly. Because of this great loss, some of this research are yet unpublished or unsolved. These will be completed by the head investigator.) As other model cases where dynamical gluons play essential roles. we paid attention to mechanisms associated with dynamical gluons in hard processes with polarized hadron beams, and developed the corresponding QCD predictions. Less