Why do photons behave differently than particles in scattering processes?

[CassiopeiaA]

Why do particles scatter in particle-particle collision while photons don't in photon-photon collisions, assuming that photons don't have enough energy to create particle anti-particle pairs?

 

[BvU]

What force would do the scattering ?

 

[Winkkin]

ie.. they have no mass

 

[jtbell]

Why do particles scatter in particle-particle collision while photons don't in photon-photon collisions,

Photons can in fact scatter off each other "indirectly", via intermediate virtual electron-positron pairs. See e.g. page 4 (problem 3) of this document:

http://faculty.ucmerced.edu/dkiley/Physics161Fall2011HW2solns.pdf

The cross-section (i.e. the probability) is very small because the Feynman diagram has four vertices as opposed to only two in electron-electron scattering.

 

[CassiopeiaA]

I have very little knowledge of QED, but can you tell me what dictates exchange of bosons (particle-particle interaction) or electrons (in case of photon-photon interaction) in scattering processes? It will be helpful if you provide some links to further illustrate the point.