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arXiv · 0704.1201

Evaluation of the Axial Vector Commutator Sum Rule for Pion-Pion Scattering

Stephen L. Adler·F. J. Yndurain
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Abstract

We consider the sum rule proposed by one of us (SLA), obtained by taking the expectation value of an axial vector commutator in a state with one pion. The sum rule relates the pion decay constant to integrals of pion-pion cross sections, with one pion off the mass shell. We remark that recent data on pion-pion scattering allow a precise evaluation of the sum rule. We also discuss the related Adler--Weisberger sum rule (obtained by taking the expectation value of the same commutator in a state with one nucleon), especially in connection with the problem of extrapolation of the pion momentum off its mass shell. We find, with current data, that both the pion-pion and pion-nucleon sum rules are satisfied to better than six percent, and we give detailed estimates of the experimental and extrapolation errors in the closure discrepancies.

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Stephen L. Adler, F. J. Yndurain. 2007-06-01. Evaluation of the Axial Vector Commutator Sum Rule for Pion-Pion Scattering. https://doi.org/10.1103/physrevd.75.116002

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