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

VL - 5

SP - 710

EP - 714

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 3

ER -