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- W2029942896 abstract "Symmetries which are not exact but which leave the vacuum invariant cannot be implemented locally. In this note we consider simple nonlocal symmetries. For the in- and out-fields, the nonlocality involved can be simply some trivial scale transformations that accompany the internal-symmetry index transformations. In particular, with proper relative normalizations, a set of in-fields ${stackrel{^}{ensuremath{varphi}}}_{ensuremath{alpha}}^{mathrm{in}}(0)$ will transform irreducibly under the nonlocal group. If one assumes that the vector currents ${V}_{ensuremath{alpha}}^{ensuremath{mu}}(0)$ behave like vector-meson fields $ensuremath{square}{stackrel{^}{ensuremath{varphi}}}_{ensuremath{alpha},mathrm{in}}^{ensuremath{mu}}(0)$, as far as the vacuum to one-vector-meson matrix elements are concerned, one finds $tan{ensuremath{theta}}_{Y}=tan{ensuremath{theta}}_{B}{(frac{{m}_{ensuremath{varphi}}}{{m}_{ensuremath{omega}}})}^{2} mathrm{and} frac{1}{3}{m}_{ensuremath{rho}}ensuremath{Gamma}(ensuremath{rho}ensuremath{rightarrow}ee)={m}_{ensuremath{omega}}ensuremath{Gamma}(ensuremath{omega}ensuremath{rightarrow}ee)+{m}_{ensuremath{varphi}}ensuremath{Gamma}(ensuremath{varphi}ensuremath{rightarrow}ee)$, both previously derived from Weinberg's first sum rule. If one assumes that the weak axial-vector currents behave like the pseudoscalar meson fields ${ensuremath{partial}}_{ensuremath{mu}}{stackrel{^}{ensuremath{varphi}}}_{ensuremath{alpha}}^{mathrm{in}}(0)$, as far as the vacuum to one-pseudoscalar-meson matrix elements are concerned, one finds $frac{{m}_{ensuremath{pi}}}{{m}_{K}}=(frac{{f}_{K}}{{f}_{ensuremath{pi}}})tan{ensuremath{theta}}_{A}$." @default.
- W2029942896 created "2016-06-24" @default.
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- W2029942896 date "1971-07-15" @default.
- W2029942896 modified "2023-09-26" @default.
- W2029942896 title "Nonlocal Symmetry Operations, the Cabibbo Angle, and the Leptonic Decays of Vector Mesons" @default.
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- W2029942896 doi "https://doi.org/10.1103/physrevd.4.393" @default.
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