Renormalization of heavy quark effective field theory: Quantum action principles and equations of motion

Abstract

We discuss the quantum action principles and equations of motion for Heavy Quark Effective Field Theory. We prove the so-called equivalence theorem for HQEFT which states that the physical predictions of HQEFT are independent from the choice of interpolating fields. En passant we point out that HQEFT is in fact more subtle than the quantum mechanical Foldy-Wouthuysen transformation. *

Renormalization in reparametrization invariance

“…I then prove that the renormalized transformation determined by the matching conditions (13) can be written as the same form with the transformation (4) and (5) with the covariant derivative substituted by the operator which may be called as the generalized covariant derivative. It means that the result presented in this paper is consistent with that given in [7]. Finally, I will show that the renormalized effective lagrangian is reparameterization invariant under the renormalized transformation.…”

“…In this section, I compare the renormalized transformation determined by the matching condition (13) with those given in [7]. I show that their results can easily be understood by constructing the effective lagrangian in an alternative way, in which an effective theory in four-component field is constructed first, followed by its reduction to the effective theory in two-component field.…”

“…Thus renormalized transformation determined by the matching conditions presented in this paper is consistent with Kilian and Ohl's result. [7] The remainder of the paper is organized as follows. In section II, after a brief review on the tree level transformation, I argue that the renormalized transformation of the heavy quark field is attributed to the renormalization of the small component field.…”

“…[7]. Then I shown that the remormalized effective lagrangian is reparameterization invariant under the renormalized transformation.…”

“…Kilian and Ohl [7] proposed a renormalized transformation. The form is exactly the same with Chen's transformation except that the covariant derivative D µ in Chen's transformation is substituted by another operator which they called as the general covariant derivative.…”