Veneziano Model forK-Meson Decays

Abstract

We investigate the decay amplitude of K-meson on the basis of the Veneziano model, and examine our model by comparing its result with that of the effective chiral Lagrangian. We construct the Veneziano amplitudes for nK->nKA and nK~nK* scatterings. Then, (I) the form factors in the Kt 4 decay are explicitly given by correlating them with the scattering nK->nM(M=K, KA and K*), (II) the decay amplitude for K 3 "' is also given by correlating it with the scatterings n-n, n-K, nn->nA 1 and nK~nKA and (III) there are some remarks on the K 2"' and Kt3 decays.In the approximation of the Veneziano amplitude to the :first order of s, t and u, the contributions of n-K and rc-rc scatterings to the form factors in Kt 4 and the decay amplitude for K 3 "' take the same forms as those of the chiral Lagrangian. The contributions of nK ->rcKA and rcn~nA 1 scatterings depend on the values of g<al and g<a1l which are, in principle, determined by the coupling constants, and also whether or not the cr-and K-mesons should be neglected. § l. Introduction V eneziano 1 l has recently proposed a simple and very interesting model for scattering amplitudes which satisfies crossing symmetry and Regge asymptotic behavior. Several properties of Veneziano amplitudes in the low energy (soft pion) limit have also been investigated by L,ovelace and others. 2 )-4 ) In particular it turns out that the Veneziano amplitude for meson-meson scattering in the low energy region gives results similar to those of current algebra or the effective chiral Lagrangian. 5 ) This fact prompts us to apply the Veneziano model to the vveak interactions by correlating decay amplitudes with scattering amplitudes. In this paper we will investigate the decay amplitude of K-meson on the basis of the Veneziano model, and examine our model by comparing its result with that of the effective chiral Lagrangian. 5 ) In § § 1 and 3, (I) the form factors in the decay mode K ->n + 7r + l + Vt (Kt4)

Veneziano Model forKl4andKl3Decays. II

“…(PtMPz)p, (1) where J" =J" v +J" A is the strangeness changing weak current, and the f/s are functions of s=-(p1 -Px) 2 , t=-(p1 +p2) 2 and u=-(p2 -Px) 2 The (hard meson) PCAC constraints 3 l determine the four parameters0 a, b, g<al and g<bl in the Veneziano amplitude for nK-'> nKA as follows:…”

Two-step BEC coming from a temperature dependent energy gap

“…This gap begins with a value at T = 0 which decreases as the temperature increases, becoming zero at the superconducting critical temperature. On the other hand, some properties of superfluid helium four, such as its temperature dependent specific heat exponential behavior near T = 0 was explained by London [4], suggesting that helium superfluidity is motivated by a BEC of the helium atoms with an artificial constant gap in their energy dispersion relation [5,6]. Although the exponential behavior of the isochoric specific heat is reproduced for low temperatures, the BE critical temperature (T c ) increases beyond the BE critical temperature of an ideal Bose gas of helium atoms as the energy gap magnitude increases.…”