Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2007-04-10
Phys.Rev.D75:116002,2007
Physics
High Energy Physics
High Energy Physics - Phenomenology
Plain TeX file;minor changes; version to be published in Pys. Rev. D; corrected refs.12,13
Scientific paper
10.1103/PhysRevD.75.116002
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.
Adler Stephen L.
Yndurain F. J.
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