Yes, they do experience gravity, for example, gravitational lensing. Einstien's relativity considers mass and energy as equivalent things, which plays a key role in this process.
All interactions are energy-momentum exchange processes, independent of whether they have mass or not. Massless particles are energy-momentum fields, and gravitational fields are also energy-momentum fields. When they are superimposed, this energy-momentum exchange process is equivalent to a massless particle experiencing gravity.
Even the interference between a photon and a photon can be considered as an energy-momentum exchange process.
“…All interactions are energy-momentum exchange processes, independent of whether they have mass or not….”
- that looks as a rather vague claim, while that
“….. Massless particles are energy-momentum fields, and gravitational fields are also energy-momentum fields. When they are superimposed, this energy-momentum exchange process is equivalent to a massless particle experiencing gravity.…”
- is simply incorrect. All particles, including “massless” ones [though note, that the term “massless” is fundamentally wrong, all particles have both – the inertial, in full consistence with the first Newton law, mass, and the gravitational mass] aren’t some fields, if we say not about some “mathematical” fields, as, say a “field of velocities”, of “stresses”, etc.,
- but about just physical fields, i.e. that correspond to at least four fundamental Nature Gravity, Electric, Strong, and Weak forces,
- really particles fundamentally aren’t some “excitations” of the fields – though yeah, that is a tenet in mainstream QFT,
- really the fields are created by just particles; more concretely by corresponding the Forces charges the particles are charged by which;
- as the Forces’ mediators, by which the particles correspondingly gravitationally, EM, strongly, etc., exchange and so interact.
The Gravity Force is fundamentally utmost universal Force, and all particles, including “massless ones”, have the Gravity charges “gravitational masses”.
At that the Forces’ mediators, just which [mediators] compose the Forces’ “classical” fields don’t have energy [including there cannot be fundamentally some the fields’ “energy densities”, etc.], and just so, say, stable particles are stably billions of years despite that always constantly radiate something.
Etc., more see the Shevchenko-Tokarevsky’s 2007 initial model of Gravity and Electric Forces in
https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces , and
We must first understand that there is gravity. Mass as the geometry of space is laid out here by me. The mass with its volume pushes the surrounding 3-dimensional space in the 4th dimension. If there is another body with mass on the slope of the gravitational funnel, then they will attract. If a massless photon moves near a massive body, then its path will lengthen, since the movement along the slope is longer than a straight line. That is why the speed of light in matter is less than in vacuum. Massless particles do not experience gravity in the sense that they are not attracted to mass. But the speed of movement of such a particle is affected by gravity.