Algebra of Currents andKe3Decay

Chiral symmetry breaking and meson-nucleon sigma commutators: A review

“…Finally, let us mention another low-energy theorem, namely the Callan -Treiman -Mathur -Okubo -Pandit relation for E&3 decays, which reads (Callan and Treiman, 1966;Mathur, Okubo, and Pandit, 1966) f+(mlt2) + f (mrt') = f~/f (2 45) where the semileptonic decay constants f and fz are again given by Eq. (2.9) and the scalar form factors are defined by (~'t U, +~(0)~K+)…”

The theory of weak interactions in particle physics

“…Thus However, since SU, is not exact we must retain both form factors. As before, we may obtain a soft-pion theorem, known as the C T M O P relation (Callan and Treiman 1966, Mathur et al 1966) f$(mH) +f YmH) = fKiV'2fT (3.152) wheref: are the form factors f, for zero-mass pions (v2 = 0). Thus the soft-pion theorem relates the K,, decay to the K,, decay.…”

Precision dispersive approaches versus unitarized chiral perturbation theory for the lightest scalar resonances $$\sigma /f_0(500) $$ and $$\kappa /K_0^*(700) $$

“…But the κ name stuck. The need for a near-threshold κ state besides the K * observed above 1.3 GeV was also required from attempts to saturate the Adler-Weisberger Axial-charge sum rule for πK scattering, although the mass predictions were very crude, ranging from 0.85-1.2 MeV [39] or 500-740 MeV [40]. This predicted state was much wider than 30 MeV, even reaching a 450 MeV width 3 .…”