Hypercharge Conservation,CPInvariance and the Possible Existence of a Zero-Mass Zero-Spin Field

Abstract

It is shown that by introducing a neutral zero-mass zero-spin field $\phi$, the Lagrangian density of all interactions (including weak interactions) can be made invariant under the hypercharge gauge transformation. Consequently, there exists a hypercharge current density $J_{\mu }$ that is absolutely conserved. The current density $J_{\mu }$ is related to the usual hypercharge current density $j_{\mu }$ of all the presently known particles by $J_{\mu }=j_{\mu }-{\lambda }^{-1\mathrm{}}\left(\frac{\partial \phi }{\partial x_{\mu }}\right),$ where $\lambda$ is a coupling parameter. The same Lagrangian density is invariant under $\mathrm{CP}$ transformation, time-reversal transformation, and Lorentz transformation. It turns out that if the conserved quantity $\int J_4{d}^{3}r\ne 0$, then there exists an energy difference between any hypercharged particle and its antiparticle with the same momentum. Such an energy difference would induce decays such as ${K_2}^0\to 2\pi$, and the decay rate is proportional to the square of the $K$-meson energy.