What is the mass of a photon?
This question falls into two parts:
Does the photon have mass? After all, it has energy and energy is equivalent to mass.
Photons are traditionally said to be massless. This is a figure of speech that physicists use to describe something about how a photon's particle-like properties are described by the language of special relativity.
Is there any experimental evidence that the photon has zero rest mass?
Alternative theories of the photon include a term that behaves like a mass, and this gives rise to the very advanced idea of a "massive photon". If the rest mass of the photon were non-zero, the theory of quantum electrodynamics would be "in trouble" primarily through loss of gauge invariance, which would make it non-renormalisable; also, charge conservation would no longer be absolutely guaranteed, as it is if photons have zero rest mass. But regardless of what any theory might predict, it is still necessary to check this prediction by doing an experiment.
It is almost certainly impossible to do any experiment that would establish the photon rest mass to be exactly zero. The best we can hope to do is place limits on it.
http://www.desy.de/user/projects/Physics/ParticleAndNuclear/photon_mass.html
So are photons massless? No, physicists are just vacillators who SAY that photons are massless, sort of, but they seem to have mass, sort of. In fact, physics cannot really handle the question of whether the energy of photons should be considered as equivalent to mass.