Griffiths Introduction to Elementary Particles · Problem 7.42

Electrodynamics of Quarks and Hadrons — David J. Griffiths

Physics — QFT · scalar-photon-decay

Problem

Assuming it is heavy enough, this ``photon'' can decay. (a) Calculate the decay rate for

\gamma \to e^+ + e^-

. (b) If

m_\gamma = 300

MeV/

c^2

, find the lifetime of the ``photon,'' in seconds. [Note: Problems 42--44 pertain to the following model: What if the photon, instead of being a massless vector (spin 1) particle, were a massive scalar (spin 0) particle? Specifically, suppose the QED vertex factor were

ig_e\mathbf{1}

(where

\mathbf{1}

is the

4\times 4

unit matrix), and the ``photon'' propagator were

\dfrac{-i}{q^2-(m_\gamma c)^2}

. There is no photon polarization vector now, and hence no factor for external photon lines. Apart from this, the Feynman rules for QED are unchanged.]

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