Non-vanishing Vacuum Expectation Value Research Articles

Spontaneous Symmetry Breakdown in a Nonlinear Boson Field: a Model forCViolation

A boson field with quartic self-coupling is discussed in the BCS approximation. For certain values of the coupling constant the transition from simple products to normal ordered products by a Bogolyubov transformation implies a spontaneous breakdown of the original symmetries in the Lagrangian. In a real scalar field a discrete symmetry can be broken; in more complex fields mass splitting also occurs. If the boson is characterized by the assignment ${0}^{+\ensuremath{-}}$, the nonvanishing vacuum expectation value of its field operator may result in tadpole diagrams, which offer an explanation of the $C$-violating transitions. The experimental consequences of different coupling schemes between the ${0}^{+\ensuremath{-}}$ meson and other particles are discussed in detail. The role of the $\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\eta}$ and $\ensuremath{\rho}\ensuremath{\pi}X$ matrix elements is emphasized in explaining different $C$-violating transitions in $\mathrm{SU}(2)$- and $\mathrm{SU}(3)$-symmetric ways, respectively.