More Conservation Laws and Sum Rules in the Heavy Quark Limit

Abstract

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.

16 pages in REVTeX, no figures

References in corpus (9)

• On the Motion of Heavy Quarks inside Hadrons: Universal Distributions and Inclusive Decays
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• Measurement of the B -> D^* l nu Branching Fractions and |Vcb|
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• Renormalized sum rules for structure functions of heavy mesons decays
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Cited by in corpus (8)

• Aspects Of Heavy Quark Theory
• Non-Abelian Dipole Radiation and the Heavy Quark Expansion
• Spectator Effects in the Heavy Quark Effective Theory
• Semileptonic Lambda_b decay to excited Lambda_c baryons at order Lambda_{QCD}/m_Q
• Four-fermion heavy quark operators and light current amplitudes in heavy flavor hadrons
• Quantum mechanical sum rules for two model systems
• A Few Aspects of Heavy Quark Expansion
• Quark-hadron duality at work: lifetimes of bottom baryons