### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 710-714 |

Number of pages | 5 |

Journal | Physical Review D |

Volume | 5 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1972 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

## Fingerprint Dive into the research topics of 'Isovector spectral function and Kl3 decays'. Together they form a unique fingerprint.

## Cite this

Langacker, P. (1972). Isovector spectral function and Kl3 decays.

*Physical Review D*,*5*(3), 710-714. https://doi.org/10.1103/PhysRevD.5.710