Photon-photon gravitational scattering Since photons carry energy, general relativity tells us that they should interact gravitationally. Photons are massless so they shouldn't couple to gravitons. But gravitons do couple to massive electrons.
So, in a quantum theory of gravity, would the lowest-order gravitational interaction of photons look something like this?

If not, why? (If yes, I'd also like some further elaboration.)
 A: I seriously don't know what I was thinking when I asked the question. Here's what I figured out in the meantime...
I wrote down the Lagrangian with the Maxwell field coupled to gravity (Einstein-Hilbert action):
$$\mathcal{L} = - \frac{\sqrt{g}}{4} g^{\alpha \beta}g^{\mu \nu} F_{\alpha \beta} F_{\mu \nu}$$
Expanding out the Lagrangian in the de Donder and Lorenz gauges, i.e.
$$\partial_\mu h^{\mu \nu} =\frac{1}{2} \partial^{\nu} h$$
$$ \partial_\mu A^\mu = 0 \, ,$$
I get this:
$$\mathcal{L} = -\frac{1}{4} (F_{\mu \nu})^2 - \frac{\kappa}{2} h^{\mu \nu} \left( -F_{\alpha \mu} F^{\alpha}_{\nu} + \frac{1}{4} \eta_{\mu \nu} (F^{\sigma \lambda})^2 \right) + \frac{\kappa^2}{4} \left[ \frac{1}{2} \left( h^2 - 2(h^{\mu \nu})^2 \right) \left(-\frac{1}{4} (F_{\sigma \lambda})^2 + F_{\alpha \beta} F_{\mu \nu}(h h^{\alpha \mu} \eta^{\beta \nu} - 2h^{\alpha \lambda} h^{\mu}_{\lambda} \eta^{\beta \nu} - h^{\alpha \mu} h^{\beta \nu} \right) \right] + \mathcal{O}(\kappa^3) $$
From this, I conclude that there is a tree level process in which photons exchange a graviton. The photon-photon-graviton vertex should therefore be:
$$V^{\alpha \beta \mu \nu} (p', p)= \frac{i \kappa}{2} \left[ ( \eta^{\alpha \beta} \eta^{\mu \nu} -  \eta^{\alpha \mu}\eta^{\beta \nu} - \eta^{\alpha \nu}\eta^{\beta \mu} ) p' \cdot p - \eta^{ \alpha \beta } p'^{ \mu} p^{ \nu} +\eta^{ \mu \beta } p'^{ \alpha} p^{ \nu} - \eta^{\mu \nu  } p'^{\alpha } p^{\beta } + \eta^{  \alpha \nu} p'^{ \mu} p^{\beta } + \eta^{\beta \nu  } p'^{ \mu} p^{\alpha }- \eta^{  \mu \nu} p'^{\beta } p^{\alpha }+\eta^{  \alpha \mu} p'^{\beta } p^{ \nu} \right] $$

I think this should be it... correct me if I'm wrong.
A: Photons carry energy, they couple to gravitons. Any energy couples to gravitons. Part of the reason why not renormalizable.
Thus the lowest diagram is probably the 2 photons to 2 gravitons diagram, or for two photons scattered (in and out) probably just the 1 virtual graviton in betWeen. Not clear to me that those would not be allowed. 
