| Research Abstract |
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
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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 Because of this great loss, some of this research are yet unpublished or unsolved.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
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