An Introduction To Quantum Field Theory - M. Peskin, D. Schroeder (Perseus, 1995) · Problem 4.2

Interacting Fields and Feynman Diagrams — M. Peskin, D. Schroeder (Perseus, 1995)

Physics — QFT · interacting-fields-feynman-diagrams

Problem

Decay of a scalar particle. Consider the following Lagrangian, involving two real scalar fields

\Phi

and

\phi

\mathcal{L} = \tfrac{1}{2}(\partial_\mu\Phi)^2 - \tfrac{1}{2}M^2\Phi^2 + \tfrac{1}{2}(\partial_\mu\phi)^2 - \tfrac{1}{2}m^2\phi^2 - \mu\Phi\phi\phi.

The last term is an interaction that allows a

\Phi

particle to decay into two

\phi

's, provided that

M > 2m

. Assuming that this condition is met, calculate the lifetime of the

\Phi

to lowest order in

\mu