Standard Model and Beyond · Problem 2.6

Lie Groups, Lie Algebras, and Symmetries

Physics — Particle Physics · charge-non-conserving-scalar-interaction

Problem

Suppose that the interaction potential for a complex scalar field were

V_I = \sigma_4\left(\phi^4 + \phi^{\dagger 4}\right)

(rather than

\lambda(\phi^\dagger\phi)^2/4

), which is not

U(1)

invariant. Show that charge is not conserved and calculate the lowest order amplitude for

\pi^+(\vec{p}_1)\,\pi^+(\vec{p}_2) \to \pi^-(\vec{p}_3)\,\pi^-(\vec{p}_4)