More Conservation Laws and Sum Rules in the Heavy Quark Limit

Details More Conservation Laws and Sum Rules in the Heavy Quark Limit More Conservation Laws and Sum Rules in the Heavy Quark Limit

1995-08-31

arxiv.org/abs/hep-ph/9508412v1

Phys.Rev.D53:3998,1996; Erratum-ibid.D55:1699,1997

Physics

High Energy Physics

High Energy Physics - Phenomenology

16 pages in REVTeX, no figures

Scientific paper

10.1103/PhysRevD.53.3998 10.1103

This is the continuation of a previous article, in which the Bjorken and Voloshin sum rules were interpreted as statements of conservation of probability and energy. Here the formalism is extended to higher moments of the Hamiltonian operator. From the conservation of the second moment of the Hamiltonian operator one can derive a sum rule which, in the small velocity limit, reduces to the Bigi--Grozin--Shifman--Uraltsev--Vainshtein (BGSUV) sum rule. On the other hand, the conservation of the third moment of the Hamiltonian operator gives a new sum rule, which is related to the matrix element of the heavy quark counterpart of the Darwin term in atomic physics. The general case of the higher order moments is also discussed.

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