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

B介子的光锥波函数（WF）和形状函数（SF）是理论计算B介子衰变率所必需的。我们在QCD的基础上对WF和SF进行了系统的研究，包括B介子内部动力学胶子引起的效应。我们分别计算了WF和SF的QCD辐射修正，将相应的算子插入到离壳层绿色函数中。我们的结果再现了文献中注意到的奇异行为，并揭示：奇异行为不仅出现在壳层上，也出现在离壳层的情况下;紫外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，作为局部算子的矩阵元.基于这一观察，我们进行了分解的WF，SF到短距离和长距离的组件，使用运营商的产品扩展。短距离威尔逊系数计算到单圈精度， 关于我们 在MS-方案的acy，而长距离的组件表示的一套完整的本地运营商。利用QCD运动方程，五维和六维的算符可以精确地用显式动力学胶子重新表示，即，作为夸克-反夸克-胶子算符，其矩阵元已经由QCD求和规则估计。Wilson系数包含了重整化标度的双重性质，即考虑动力学胶子效应时，WF，SF受重整化群演化的“两步”控制，与尖点反常维数和局域算符反常维数有关。（在完成研究之前，科代拉教授突然去世。由于这一巨大损失，其中一些研究尚未发表或未解决。这些将由首席研究员填写。）就像其他动力学胶子扮演重要角色的模型一样。我们关注与极化强子束硬过程中动力学胶子相关的机制，并发展了相应的QCD预言。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 Because of this great loss, some of this research are yet unpublished or unsolved.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