TY - JOUR
T1 - More conservation laws and sum rules in the heavy quark limit
AU - Chow, Chi Keung
AU - Pirjol, Dan
PY - 1996
Y1 - 1996
N2 - 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.
AB - 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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U2 - 10.1103/PhysRevD.53.3998
DO - 10.1103/PhysRevD.53.3998
M3 - Article
AN - SCOPUS:0001198921
SN - 1550-7998
VL - 53
SP - 3998
EP - 4005
JO - Physical Review D - Particles, Fields, Gravitation and Cosmology
JF - Physical Review D - Particles, Fields, Gravitation and Cosmology
IS - 7
ER -