QCD sum rules in the effective heavy quark theory

E. Bagan, Patricia Ball, V.M. Braun, H.G. Dosch
1992 Physics Letters B  
We derive sum rules for the leptonic decay constant of a heavy-light meson in the effective heavy quark theory. We show that the summation of logarithms in the heavy quark mass by the renormalization group technique enhances considerably radiative corrections. Our result for the decay constant in the static limit agrees well with recent lattice calculations. Finite quark mass corrections are estimated. I. In this paper we give a consistent framework for the construction of QCD sum rules [ 1 ]
more » ... r heavy-light quark systems in the heavy quark limit (HQL), which in that approach has first been discussed by Shuryak [ 2 ] and has been further studied by several authors [ 3, 4 ] . Although for the heavy quark mass mQ below 10 GeV both the logarithmic and nonlogarithmic contributions are numerically of the same size, for the consistent treatment of the limit mQ~oV it is necessary to sum all corrections of the type [as(mQ)lnmQ] n, as (m o) [ as (mQ) In mQ ] n, etc. by the renormalization group technique. This "mass factorization" has become one of the most actively discussed topics in the literature, and we find it important to formulate the sum rule approach in such a way that all the scaling laws inherent to the heavy quark expansion (HQE) are automatically fulfilled. This task is interesting for several reasons. First, the sum rules formulated in this way exhibit explicit Isgur-Wise symmetries [ 5 ] and so do the physical quantities extracted as their output. Second, quantitative estimates can be made for the finite heavy quark mass corrections. In addition, such a formulation of sum rules facilitates the comparison to the results of lattice calculations [6, 7 ] . A convenient framework for systematically factorizing out the large-mass physics is provided by the effective field theory [ 5 ] . The key issue there is the introduction of a separate heavy quark and antiquark field h ~ for each four-velocity v in order to implement the velocity superselection rule: the velocity of the heavy quark cannot be changed by the radiation of gluons since it would correspond to infinitely large momentum transfers 8pu = m o ~v~. Hence, the part of the lagrangian associated with heavy quarks becomes f d3v (ih-f~+ v~ DUh + -ih~ v~ DUh~ ) ( 1 ) from which Feynman rules can be derived for the heavy quark propagator i ( 1 + ~)/(2vk) and the heavy quarkgluon vertex -igvut a. For each composite operator of the full theory we can write an expansion in operators of the effective theory (see refs. [5, 8] ) ~ ~ The sign "g" reminds that the the operator on the LHS of (2) must be sandwiched between hadron states of the full theory, while the operators on the RHS are taken between states of the effective theory, cf. ref. [8]. 0370-2693/92/$ 05.00
doi:10.1016/0370-2693(92)90585-r fatcat:imfyzxmwdbgxtcvtagwpwsvbtu