# Pressure in the proton, from gravitational form factors?

A paper in Nature is getting some press, for having calculated "the pressure distribution inside the proton".

But the theory behind the calculation seems a little odd. Apparently the data pertains to the scattering of an electron from a quark via the exchange of two photons. But each photon has spin 1, so that adds up to spin 2 like a graviton... and then there's talk about gravitational form factors, as if there are sufficient formal similarities with the two-photon electromagnetic form factors (?) that gravitational calculations can be transposed to the electromagnetic context.

I'm not at all saying this is impossible, but I am a little skeptical. Does anyone have an informed opinion on the validity of this work, and its methods?

• BvU

## Answers and Replies

TeethWhitener
Science Advisor
Gold Member
So I’m not an expert by any means here, but the paper interested me as well. The theory seems to have been established pretty firmly in the literature. Here’s a short review:
https://link.springer.com/content/pdf/10.1007/s11467-016-0573-6.pdf

My rough understanding of it: The gravitational form factors are matrix elements of the energy momentum tensor. Their Fourier transform gives the spatial distribution of mass (or energy) in the proton—cf. electric form factor, whose Fourier transform gives the spatial charge distribution. For reasons beyond my ken, in the proton, this seems to apply only to the quarks and not the gluons (thus pressure distribution instead of energy distribution). I don’t really get this part and am probably misinterpreting what I am reading.

Anywho, direct measurement of the gravitational form factor requires measuring the graviton-proton interaction, which obviously isn’t experimentally feasible currently. But since gravitational mass and inertial mass are equivalent (according to the equivalence principle), you can indirectly get at the inertial mass distribution via the generalized Parton distribution. Which is what the Nature paper does. They gather information about he GPD using a scattering regime called “deeply virtual inelastic scattering.”

Edit: the GPD gets access to the off-diagonal elements of the gravitational form factor— these are momentum correlations among the quarks. The diagonal elements are related in some simple way to the mass of the quarks.

• Craftek_Ana