TY - JOUR
T1 - Isovector spectral function and Kl3 decays
AU - Langacker, Paul
N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 1972
Y1 - 1972
N2 - An inequality relating the parameter λ+ of Kl3 decays to the spectral function of the isovector electromagnetic current is derived, assuming only Weinberg's first spectral-function sum rule. It is shown that a large value for λ+ (e.g., λ+=0.045) is not compatible with ρ saturation of the isovector spectral function. Since the principal tests of the sum rule have relied on the additional assumption that such resonance saturations are possible, some doubt is cast on the validity, or at least on the previous applications, of the sum rule. Implications for the Weinberg mass relations, c-number Schwinger terms, and the e+e - annihilation cross section are discussed.
AB - An inequality relating the parameter λ+ of Kl3 decays to the spectral function of the isovector electromagnetic current is derived, assuming only Weinberg's first spectral-function sum rule. It is shown that a large value for λ+ (e.g., λ+=0.045) is not compatible with ρ saturation of the isovector spectral function. Since the principal tests of the sum rule have relied on the additional assumption that such resonance saturations are possible, some doubt is cast on the validity, or at least on the previous applications, of the sum rule. Implications for the Weinberg mass relations, c-number Schwinger terms, and the e+e - annihilation cross section are discussed.
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U2 - 10.1103/PhysRevD.5.710
DO - 10.1103/PhysRevD.5.710
M3 - Article
AN - SCOPUS:35949032051
SN - 1550-7998
VL - 5
SP - 710
EP - 714
JO - Physical review D: Particles and fields
JF - Physical review D: Particles and fields
IS - 3
ER -