How Does a New Lagrangian Term Affect the Fine Structure Constant?

[LCSphysicist]

Homework Statement

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Relevant Equations

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If we add to the Lagrangian of SM a term $$\frac{{\phi}F_{\mu v}F^{\mu v}}{F_{\phi}}$$

How does the fine structure constant $\alpha$ changes as $$\phi = A_\phi cos(m_{\phi} t)$$?

I am having some hard time to finding out where i should start. I remember see the strucutre constant arrising when we evaluate vertices on feynman diagrams for QED interactions... But i am too ignorant to know how to proceed..

 

[malawi_glenn]

What is Fphi and Aphi?

Is phi a field?

 

[LCSphysicist]

What is Fphi and Aphi?

Is phi a field?

"What is Fphi and Aphi?" I assume they are just constants... But the question says nothing about it.
Yes, phi is a field.

 

[malawi_glenn]

"What is Fphi and Aphi?" I assume they are just constants... But the question says nothing about it.
Yes, phi is a field.

Where did you find the problem? This is a non renormalizeable term