Speaker: Andrey GROZIN
Title
Renormalization of HQET at three loops
Abstract
Recently, calculations of perturbative corrections in Heavy Quark Effective Theory reached a new level. An algorithm of calculation of arbitrary three-loop propagator diagrams in HQET has been constructed and implemented: A.G.Grozin, JHEP 03 (2000) 013 Until this work, the only known three-loop algorithm was the classical Chetyrkin-Tkachov algorithm for massless propagator diagrams. In HQET, there are 10 generic three-loop topologies instead of 3 in the massless case. Simultaneously with this HQET work, an algorithm for single-mass on-shell three-loop propagator diagrams was also constructed by Melnikov and van Ritbergen. The HQET algorithm is implemented as a package Grinder - 3000 lines of REDUCE code. Its debugging required more than 1 CPU-month on good workstations. Using this package, I have calculated the heavy-quark propagator in HQET at 3 loops. Now I am calculating the 3-loop anomalous dimension of the heavy-light bilinear quark current. The 2-loop anomalous dimension of this operator was obtained by myself and David Broadhurst and, independently, by Ji and Musolf in 1991. In 1995, I and David Broadhurst have found 2-loop matching of heavy-light currents in QCD and HQET (see also some clarification by myself in 1998). However, in order to use this result, say, for improving the accuracy of f_B extraction from lattice simulations, the 3-loop anomalous dimension is also required. Another interesting application is extraction of f_B from HQET sum rules. As observed by myself and Broadhurst in 1992, the 2-loop correction is about +100% of the leading perturbative contribution. We concluded that reliable extraction of f_B from QCD sum rules is impossible. However, there is a hope that, though the 2-loop correction is large, the 3-loop and higher corrections are moderate (this hope was expressed by Bagan, Ball, Braun, Dosch in 1992). The only way to resolve this long-standing mystery is to calculate this 3-loop correction.