### The AdS/QCD correspondence: delivery failure

Thursday, November 3rd, 2011

As described previously here, there are good theoretical reasons to think that the so called AdS/QCD correspondence should provide a poor description of the collisions of strongly interacting particles like the proton, or their internal quarks and gluons.  The idea for the correspondence was inspired by string theory where is can be shown that special (strongly interacting, supersymmetric, scale invariant)  theories with gluons can be simply described by calculations on a curved 5D space called anti-de Sitter space, and abbreviated as AdS.  While the theory of quantum chromodynamics (QCD) does contain gluons, it is not supersymmetric, not scale invariant, and, it turns out, not strongly interacting enough for the correspondence to work. The problem can be seen fairly easily in collisions.  In QCD collisions of quarks and gluons tend to produce narrow sprays of particles, known as jets, that look something like this:

Jets of particles. The length of the line shows the energy of the particle.

While in AdS theories the produced particle spread out uniformily in all directions like this:

spherical spray of particles

Some theorists have shrugged their shoulders about this problem and tried to apply the AdS/QCD correspondence to heavy ion collision data pointing out that some particular measurements happened to agree with the AdS/QCD prediction.

The BackReaction blog points out that the latest data from the LHC again points to the inadequacies of the AdS/QCD correspondence.

The ratio of the probability of finding a jet in lead-lead collisions to the same probability in proton-proton collisions as a function of the momentum of the jet away from the beam line (aka transverse momemtum P_T). Image from Thorsten Renk, Slide 17 of this presentention

The data most closely follow a model of ordinary QCD jet  production, labelled YaJEM for Yet another Jet Energy-loss Model, rather than the AdS calculation.  For the experts: while the jetty description of QCD continues to work at large number of colors, $N$, the AdS description requires both $N$ and the coupling times the number of colors, $\alpha N$, to be large, and it is the latter condition that fails in the real world.

• Systematics of the charged-hadron $P_T$ spectrum and the nuclear suppression factor in heavy-ion collisions from $\sqrt{s}=200$ GeV to $\sqrt{s} =2.76$ TeV
arxiv.org/abs/1103.5308v2
• Pathlength dependence of energy loss within in-medium showers
arxiv.org/abs/1010.4116
• The AdS/QCD Correspondence: Still Undelivered
arxiv.org/abs/0811.3001

### Varieties of Particle Jets

Friday, September 18th, 2009

A simulation of a string repeatedly breaking looks similar to the jets of particles found in collisions of quarks and gluons.

“Jets” is the name given to sprays of particles, headed in roughly the same direction, that appear when quarks or gluons collide. Jets turn out to be a useful way to relate experimental results on quarks and gluons with the theory of Quantum Chromodynamics (QCD) which describes the interactions of quarks and gluons. Their usefulness arises partly because the jets can be seen to emerge in a simple way.  The primary particles involved in the scattering have a small probability to emit a new gluon which, it turns out, is most likely to head in the direction of the particle that emitted it.  The new gluons have a small probability to emit further gluons, and so on. Iterating this process a few times gives you a jet of quarks and gluons. The gluon emission probability is small because the QCD interaction strength is fairly small in high-energy processes.

It is somewhat surprising that we can also see jets emerge in an entirely different way.  It is known that QCD becomes much simpler if we imagine that the number of “colors” of quarks is a large number, N, rather than the small number, 3, that we find in our Universe.  For large N, the allowed configurations have a flux-tube, or string, connecting every quark to an anti-quark (to make a meson) or have the strings of N quarks meeting at a point (to make a baryon). This “large N approximation” actually does a pretty good job of describing our world, leading to the oft repeated quasi-joke that 3 is a large number.

A baryon, like a proton, consists of three quarks connected by three strings which meet at a junction.

Of course such strings can break.  This occurs when a quark and anti-quark are created at some point along the string.  The energy required to produce the quark and the anti-quark can be offset by the broken string contracting.  In this way we can imagine a heavy meson or baryon with a very long (excited) string decaying into lighter “daughter” mesons and baryons made of shorter strings.

The string in baryon can break to form a new baryon and a new meson.

Imagine producing a quark and an anti-quark in a high energy collision. The quark and the anti-quark would be flying apart in opposite directions with a string stretching between them. Starting with this very excited “meson,”  we could simulate the repeated breaking of the string and see what comes out.  This is a little tricky, the quarks and strings are moving in a complicated way due to all this breaking, but we were able to do it (mainly thanks to Matt Reece’s programming skills).  The result is that the string tends to break into relatively short bits, which therefore have little rest mass (the mass grows like the string length) and thus lots of kinetic energy, since the total energy has to add up to the initial energy. Interestingly the string bits end up mostly going in the directions of the initial quark and anti-quark. This is because in the rest frame of one of the daughter mesons, the subsequent “grand-daughters” are equally likely to go in any direction, but in the rest frame of the lab, the daughter meson was moving rapidly in the direction of the original quark or anti-quark, and the grand-daughters are “thrown” forward in this direction. So we get something that looks very much like a jet.  This is just what is shown in the picture at the top of this page.

This is very different from what happens in theories where the interaction strength and N are both large.  Such theories can be approximately scale invariant in which case they are called conformal field theories (or CFT’s).  CFT’s are thought to be described by almost non-interacting particles moving in a five dimensional anti-de Sitter (AdS) space.  This is the basis of the AdS/CFT correspondence. It is fairly easy to work out what happens in this case, either using CFT methods or direct simulation in AdS.  Each time an excited meson decays into two lighter mesons, most of the initial energy goes into the rest mass of the daughter particles, so they have very little kinetic energy.  This means that there is very little difference between the rest frame of the daughter particle and the rest frame of the lab, so the grand-daughters are equally likely to go in any direction. The result of this type of process is shown below.

When the interaction strength is large enough the jets broaden so much that the events look spherical.

This raises some interesting prospects for the large hadron collider.  First we need fairly precise estimates of standard QCD jets, especially those containing b quarks, so that we can separate out the “old” physics from the new physics, and the stringy picture may be helpful for improving these calculations.  Second, in some scenarios the new physics does look like a CFT, in which case the standard types of analysis will not be helpful in teasing out the underlying information. In that case we will need some new ideas in order uncover the new physics.

(Technical note: in the top and bottom graphic, the length of each lines is proportional to the energy of the particle moving in that direction.)

Monday, June 12th, 2006

Veronica Sanz, photo by Johannes Hirn

Hirn and Sanz have examined models of electroweak symmetry breaking in anti-de Sitter space via boundary conditions. They include additional bulk breaking of electroweak symmetry and find that they can change the spectrum of vector and axial vector resonances so as to make the S parameter negative and thus compatible with precision electroweak tests.