# Tag Archives: QCD

## 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…..

## Progress in QCD Pheno for RHIC?

Awesome. I love it when people do good old-fashioned straight-up QCD Pheno. RHIC sees tons of cool effects where the theory just can’t cut the muster, so I get really excited when someone hits QCD head-on, instead of doing something easier, or unfalsifiable.

So I just read this paper this morning, which basically extends DGLAP parton showering to include iteractions with Quark Gluon Plasma. This is pretty cool, as that it seems to qualitatively reproduce some of R_AA supressions. Sad thing is they neglect the reaction of the medium, so I doubt this will describe the mach cone, which is one of my favorite things out of RHIC. Can’t have it all, I guess.

In case you’re wondering, RHIC is a versatile collider on Long Island, which collides combinations of protons, deuterons, copper ions, and gold ions. The goal is to study lots of processes, but most significantly to create really hot, dense conditions where we may be able to observe a phase transition in QCD to something called the quark-gluon plasma. Maybe we already have seen it, but the theory is wicked hard, and no one is certain whether there’s really a phase transition or not. Whatever they are making, the “medium” is hot, dense, and is pretty much in thermal equilibrium as its expanding. They also know that it smears hadronic information, but electromagnetic stuff passes through unscattered. The hadronic smearing I’m talking about seen in the R_AA plots, which are ratios of stuff from gold-gold and proton-proton collisions. The basic idea is, there’s a hard scatter in pp or AuAu which are essentially the same, the energy has to pass through the medium in AuAu, and the distributions are really different. You can read more here from the STAR collaboration. The mach cone thing I mentioned is a hunch that people are seeing something analogous to a sonic boom as partons traverse the medium. This is fantastic, because if you can measure a mach cone, you can measure a speed of “sound.” If you can find a place where the speed of “sound” suddenly changes, thats pretty good evidence for a phase transition, which is the name of the game. Heres some slides of a talk I saw at DIS last year. Its a good introduction and overview to RHIC.

## How low is low?

Whenever there’s talks on low-x stuff here at HERA, a lot of my colleagues skive out. Diffraction is spooky, phenomenological, and in general not well understood. I mean, we’re still using pre-parton model technology (regge stuff) for the predictions. For resolved PHP, the uncertainty on the photon PDFs is tragic, so its not really clear if your testing pQCD or universal factorisation or what. Jets above pseudorapidity of 3.5 or so are usually poorly reconstructed, and people have forgotten why its important. Not a fun place to be in general if you ask me. The reason I mention it here is that there’s some cool stuff out on the arXive today, and LHC physics will be swamped with low-x exchanges. Like it or not, the theory and experimental communities will need to work on this stuff to get a decent signal at LHC.

Problem goes like this: All the stuff below the factorization scale like p-PDFs and structure functions are dependant on the renormalization scale and the Bjorkjen $x$ as well. If you measure, say $F_2^p$ with, HERA, and take this to TeVatron, no problem. QCD tells you explicitly how to evolve these non perturbative functions, but that has to be done with an approximation. The DGLAP evolution equations are re-summed in $log(Q^2)$, and fixed order in $log(1/x_{Bj})$. TeVatron has higher $Q^2$, and their $log(x_{Bj})$ range is twice higher than ours, so if DGLAP rolls here, then it’s cool at TeVatron too, and that’s basically what we observe. Look at page 11 of this this pdf for a plot. On the other hand, the LHC will have a comparable reach in $x$ to HERA ($xapprox 10^{-6}$), but they’ll see alot more low-x schenanigans. While the measureents of pDFS etc are fine, you try to evolve them down to “low” $x_{Bj}$ and you might get nonsense. How low is low? Don’t know.

The forward jets people try to enrich their samples with BFKL ( resummed in $log(1/x_{BJ})$) dynamics, but they usually end up only seeing CCFM (gluan radiation angular ordered) dynamics. This in itself is cool, since we’re talking takeover of new dynamic regimes but it still might not bee good enough at the Major Leagues. Anyhow, some pheno folk just fit some BFKL-Pomeron stuff (I want to see this stuff in DIS, but, oh well) to ZEUS Photoproduction data. They don’t show comparisons to the DGLAP-Pomeron, but these objects are different enough that I’m not complaining. It’s not definite proof of BFKL-dynamics, but its cool. Paper’s here.

In other news relating to useful gauge theories: This paper shows how you can modify an old model developed for $F_2^p$ at low-x from HERA color dipole stuff, and add in BFKL dynamics of the scaling. At high pseudorapidities, where we expect new dynamics, it works significantly better than the old style. In the central region the two models work the same. They even do a back check to HERA at moderate $x_{Bj}$, and it looks ok, except that the plot is cluttered, I’d like to see a re-fit and a ratio plot. I’m no RHIC guy, but it looks cool to me.