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More conservation laws and sum rules in the heavy quark limit

Chow, Chi-Keung and Pirjol, Dan (1996) More conservation laws and sum rules in the heavy quark limit. Physical Review D, 53 (7). pp. 3998-4005. ISSN 2470-0010. doi:10.1103/PhysRevD.53.3998.

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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 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. This sum rule allows a model-independent estimate of this matrix element, with results in good agreement with those obtained from the factorization approximation. The general case of the higher order moments is also discussed.

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Additional Information:©1996 The American Physical Society. (Received 11 September 1995; revised manuscript received 7 November 1995) C.K.C. would like to thank Mark Wise for valuable discussions. His work was supported by the U.S. Department of Energy under Grant No. DE-FG03-92-ER 40701. D.P. is grateful to Arkady Vainshtein for an interesting conversation, and acknowledges a grant from the Deutsche Forschungsgemeinschaft (DPG). We thank Nikolai Uraltsev for clarifying discussions.
Subject Keywords:MESON DECAYS
Issue or Number:7
Record Number:CaltechAUTHORS:CHOprd96b
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4249
Deposited By: Tony Diaz
Deposited On:09 Aug 2006
Last Modified:08 Nov 2021 20:15

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