The Photon is a (massless) particle which could be verified through various experiments, viz., Young's Double slit experiment, Photoelectric effect, etc.
Is there an experimental evidence to suggest the same for Gluons or Gravitons?
Is Young's Double slit experiment ever performed for Gravitons ? (if I could calculate required slit width, I will try an attempt)
I am certainly not an expert on this, but my very limited understanding is that the masslessness of the gluons and graviton are a result of the theory. I do not know to what extent this has been experimentally tested.
I think there have been some experiments to determine the mass (or lack thereof) of gluons but I do not know the details. As far as I know, the graviton is a hypothetical particle introduced in an attempt to add gravity into the standard model and its existence has to date not been confirmed.
Even photon rest mass is not zero experimentally! How do you determine the value of some thing as being precisely zero? The photon rest mass is less than a very small number ~ 10-58 kg and thus it is assumed to be zero. Refer to the particle data group's booklet.
In the context of condensed matter physics, phonons are also massless. Phonons are collective excitations of the crystal lattice vibration and are massless Goldstone bosons. Even though phonons are massless, they carry momentum by virtue of their wavelength.
Why should a photon have zero momentum. The nonrelativistic formula p=mv does not apply to a relativistic particle and in particular to a photon. For a photon momentum=E/c, where E denotes the energy of the photon.
Girish, there are massless phonons, also known as acoustic phonons, but there are also optical phonons, which follow equations similar to massive particles.
We have almost the same understanding and imagination of large objects (at the level of molecules and larger). But in the case of subatomic particles, there is no clearly defined and visualized concept and there are many uncertainties, especially in the case of photon and graviton. However in this paper we are using the particles without any imagination of them. Photon has a long history in modern physics
Okun, L. B. (2008). Photon: history, mass, charge.
We will focus on energy and momentum of photon. After 1906 Einstein have derived the second postulate of special relativity the constancy of the speed of light by assuming that the light quanta that he proposed in 1905 were massless particles
Field, J. (2014). Einstein and Planck on mass-energy equivalence in 1905-06: a modern perspective. arXiv preprint arXiv:1407.8507.
Please consider that massless of photon is an assumption, only.
Physicists have not stopped on assumption of massless. There are more attempts were made to clarify the photon massless in theoretical and experimental physics. There are good theoretical reasons to believe that the photon mass should be exactly zero, there is no experimental proof of this belief.
Hojman, S. A., & Koch, B. (2013). Closing a window for massive photons. Advances in High Energy Physics, 2013.
These efforts show there is an upper bound on the photon mass, although the amount is very small, but not zero. The tight experimental upper bound of the photon mass restricts the kinematically allowed final states of photon decay to the lightest neutrino and/or particles beyond the Standard Model
Heeck, J. (2013). How stable is the photon? Physical review letters, 111(2), 021801.
Theories and experiments have not limited to photons and graviton will also be included. For gravity there have been vigorous debates about even the concept of graviton rest mass.
Goldhaber, A. S., & Nieto, M. M. (2010). Photon and graviton mass limits. Reviews of Modern Physics, 82(1), 939.
About Rest mass
As we know, some particles such as photons are never seen at rest in any reference frame. So, there are two kinds of particles in physics;
1- Some particles like the photon move only with the speed of light c, in all inertial reference frames. Let’s call these kinds of particles the NR particles or Never at Rest condition particles.
2- Other particles like the electron always move with the speed v
The graviton is a hypothetical elementary particle that mediates the force of gravitation in the framework of quantum field theory. If it exists, the graviton is expected to be massless (because the gravitational force appears to have unlimited range) and must be a spin-2 boson.
Claudia de Rham and her colleagues: "A small graviton mass could also be of a significant physical interest, notably for the cosmological constant problem."
But the biggest problem is knowing the spin and mass of graviton. According to the stress-energy tensor, graviton must be massless and must have a spin of 2. The last motivate a translation of loop quantum gravity into a Feynman sum over histories form: the spin foam formulation.
I would not be too certain about graviton yet.So I would say gluons. because the experimental hypothesis itself is considered as zero-mass.Also, in theory we are able to see this calculations of probability in mass.
For gluons as well as photons being massless exists also a theoretical argument in http://arxiv.org/abs/0912.3892 In the theory presented there exists an exact U(3) gauge symmetry, but no exact SU(2) gauge symmetry, so that the weak force is expected to be massive.