Tag Archives: Hadron Structure

Generalized PDFs Imply a Gravitomagnetic Moment!?!?!?

Today I’m writing conference proceedings, which are boring me to write, so they will probably be inhumanely boring to read, and lethally boring to publish. I may try to write them so the first letters spell out a hidden message, just to stay focused.

Part of the way I’m constructively procrastinating is skimming a review paper on Generalized Parton Distributions. They’re a pretty cool idea. So QCD can’t be perturbatively calculated at arbitrarily soft scales, so nobody knows how to directly calculate from first principles whats happening inside of hadrons. The lattice folk are making progress here, but that technique takes a lot of power, so those calculations can’t easily get incorporated into general calculations.   You can parametrize what’s happening in a hadron, measure it, and the factorization theorem tells you your resulting functions are universal, modulo an evolution of the factorization scale. So we can measure parton distributions functions here at HERA, and then you can roll them up to the LHC/TeVatron scales or down to a fixed target, and everyone agrees on what these functions are and do. If you are operating at first order, the vanilla type of PDFs naively tell you what the probability of finding a quark or gluon of a certain type and certain longitudinal momentum is. At higher orders the interpretation isn’t so clear, but they still return a real scalar. There’s no interference, no helicity, no transverse momentum. You can tack on spin or other stuff, but its always a bit of a blunt object.  How the proton gets its spin out of the quark-gluon shimmy is still a big mystery, so theorists have been experimenting with difference ways to combine PDFs and form factors, to include interference terms, and understand all components of nulceon spin. The situation is stabilizing a bit, and this paper seems to imply that the parameterization they describe is widely used.

I got a bit shocked by the following couple of lines:

…according to an extension of the equivalence principle of general relativity to describe the interaction of the nucleon with the external gravitational field one arrives to the interpretation of B(0) as an anomalous gravitomagnetic moment being the analog of the anomalous magnetic moment [47]. There is also evidence supporting the conjecture that the equivalence principle is valid separately for quarks and gluons resulting in exact equipartition of momenta and angular momenta in the nucleon. The most precise numerical support comes from lattice calculations [48].

AH!  What!!?!?!  Who said anything about gravity!?!?!  But it’s not really what it looked like at first glance.  B(0) is zero, btw, so whatever you want to call it is moot, but the cool thing is that [47] paper, where the author sees a relationship similar to the equivalence principle, and this cancels out that B(0) thing at all orders.  I can’t do GR, so I can’t comment on the validity of the approach, but its a cool idea…..