# Virtuality of a nearly on-shell photon

1. Aug 27, 2013

### muppet

Hi all,

It was recently pointed out to me that the finite electron mass puts a lower bound on the Mandelstam variable t describing the square of the transferred momentum in the centre-of-mass frame, $t_{min}=m_{e}^{2}$.

This solved a problem I was worrying about (the finiteness of the tree-level approximation to elastic scattering), but gave me a new one to worry about.

I've often heard it said that whenever a photon leaves a radio-transmitter to be received by my radio, it must be slightly off-shell, simply by virtue of the fact that it's emitted and absorbed. But apparently the minimal virtuality of the photon is set by the electron mass, which corresponds to an energy in the gamma ray spectrum, right?

So if all of this is true, then why does classical electrodynamics describe radio waves well when the virtuality of a photon is vastly larger than its 3-momentum?

2. Aug 27, 2013

### Staff: Mentor

In which process? I doubt that this is true for all processes.

All low-energetic scattering processes have a small t.

3. Aug 27, 2013

### muppet

Dammit... the claim was that this followed from the kinematics, recalling that $t=(p_1-p_3)^2$ and putting the external momenta on shell. However, checking the argument again, it looks as if the mass terms end up cancelling out. This is what I thought was the case originally, but the (quite senior) lecturer I was speaking to managed to convince me otherwise at the time. So now I'm back where I started with my original problem -namely, why does the cross-section you obtain from the t-channel Born approximation to the elastic scattering of two fermions (say) diverge?

4. Aug 27, 2013

### Staff: Mentor

smin>=me (as soon as an electron or positron is involved) is the only similar statement I see.

5. Aug 28, 2013

### muppet

Yes, thanks for taking the time to reply.