Lisa Randall: Black holes out of reach of LHC

This week I am spending a few days at CERN to get back on track with CMS activities after my long vacations. I was planning to follow the talks of the Physics Days this afternoon, but as I learned that Lisa Randall was about to give a seminar on “Black Holes and Quantum Gravity at the LHC”  I could not resist and changed my plans to accommodate it.

If you allow a slip to inappropriate comments, Lisa Randall is notoriously not only an esteemed and well-known theorist, but also a quite attractive woman – a powerful mix, capable of turning to jello the knees of most men. Today she wore a nice black and white dress which left her shoulders and arms exposed, a necklace of mother-of-pearl, and a wide-band silver bracelet with colored stones. Her hair was collected in a pony tail. She looked nice and fit – for some reason it made me think she probably works out on a regular basis.Lisa talked in front of a large audience – I could count about 150 heads – which packed the auditorium. She was introduced by the convener by what must have been the shortest introduction in the history of theoretical seminars ever, something like:

 “Hre’s Lisa, she’ll tlk ’bout bloles quagity”.

I’m serious. Hilarious, but an odd note if combined with the fact that, despite my attempt at an initial applause, the audience stood quite still. She balked not, and started to talk with no further ado.

So let me do the same and try to put together some notes from her seminar. As always when I discuss things above my head, be compassionate with my ignorance, and grateful for my effort. In other words, don’t shoot the pianist.

The talk focused on models with higher dimensions of quantum gravity in the context of a low quantum gravity scale. How low ? Well, as low as one can hope for – about 1 TeV or so. Naturally, at the LHC one would expect quite dramatic signatures. Should LHC be looking at black hole production or elsewhere ? It turns out that the best way is to look for compositeness scales. But let’s not jump to the conclusions yet.

The questions experimentalists have to ask themselves at the start of a project like the LHC, which will explore unknown new energy scale and domains, are like “Are we optimizing existing searches for the signatures we might have access to ?”, “Are we sure we are not missing possible searches ?”, “Will this get me a salary increase ?”. The latter is my own contribution to the list. One interesting question, connected to the scope of Lisa’s talk, is: “If there is new physics, but it lies at a higher energy scale than the one directly accessible by the machine, how do we maximize our chances to see it ?”

Historically, the reason that black holes appear so promising as compared with other possible signatures is the predicted huge cross section for their production if there is a low quantum gravity scale. Lisa ventured to compute that if quantum gravity turns on at a scale of a TeV, one gets 100 pb cross sections at the LHC for producing black holes, naively. There is no suppression from gauge couplings, so it is indeed a large signal. Also, the signature is spectacular, since these objects are predicted to decay into large multiplicity final state, with highly spherical distributions. Very distinctive, unmistakable new physics.

But the problem is that the idyllic picture is not very realistic. The onset of a non-perturbative regime where black holes are produced and decay with those signatures is much above the QG scale, and this appears to be above the reach of even our brand new pupil, the LHC. The poor sucker has not emitted the first burp yet, and it is already criticized for being a midget. In any case, at threshold one would not see the striking signatures, but maybe something can be saved. How much could we learn from that ?

Randall was very clear in stating that LHC is unlikely to make classical BH states decaying with Hawking radiation. She appeared to be interested in assessing the damage: and the answer is that, if you have a low quantum gravity scale and you cross it, you will have a change in the two-particle final states. Things are not calculable, but there appear to still be distincitve experimental signatures that are capable of distinguishing among different models.

Lisa did not discuss much what brought the optimism down in the last few years. She just stated that you have to go well above M, the energy scale of quantum gravity, to be sure to hit the striking signatures publicized in the past. The parton distribution functions of the proton drop rapidly with the fraction of parton momentum, and since we are by necessity near threshold, the value of the latter is very important in determining what the rate of the new process is going to be. To make matters worse, M is convention-dependent. Factors of fly around easily, and although one knows these are only conventions and what one cares for is just the actual threshold, there is a big difference between 1 TeV and 2 TeV for the LHC. So the picture is fuzzy.

Lisa discussed some of the models and the resulting conventions and equations for the schwarzschild radius, the energy scale, and the other main characteristics. I prefer to avoid entering these details in this short writeup, because I am sure I would drop some dimensional factor here or there. Not that many of you would notice, but I’m a perfectionist 🙂

One point which looked important is that in the models considered, the black hole lifetime is bigger than the inverse of the energy scale of quantum gravity. This drives some of the phenomenology of the black hole decay. Another point is that every degree of freedom should carry an insignificant amount of energy with respect to the total; and since we are never going to get far above threshold at the LHC, we will have to be careful to call what we produce a real classical black hole. These things have low entropy close to threshold, and the multiplicity of the decay will be affected.

A critical factor in the computation of the number of particles emitted in the black hole decay is the assumption of the dimensionality of the space: particles emitted in the bulk have more directions in which to oscillate. Furthermore, since the threshold for producing black holes is not M, but a higher energy, even if we did see a black hole, we would not be able to extract M from the total cross section, because of inelasticity effects: not all the energy of the colliding partons goes in the creation of the black hole, due to initial state radiation.

The difficult question to answer is in fact, what fraction of the energy gets trapped inside the horizon? It is of course important since the PDF fall rapidly with energy. What is clear is that the inelasticity effectively increases the threshold. The reduction in cross section due to this effect is enormous, and it is the lack of considering it which has brought some overoptimistic predictions in the past.

So, the upshot is that BH production threshold is higher than originally thought. It means a lower production cross section, a lower reach in black hole mass, and it translates into lower entropy reach as well. The conclusion of Lisa Randall is that we will not produce classical thermal black holes at the LHC. What will we still be able to produce, then ? And what kind of multiplicities should we expect ?

Lisa discussed the calculation of the multiplicity of final state particles. She said that the calculation is totally unreliable. But one thing stays clear: low multiplicity final states will dominate even if we call it black holes. So we have to face the facts, and study 2-body final states: jets and leptons. Can they be distinguished from backgrounds by rate, kinematics, bra size? Yes. For jets, transversality is the key. QCD is dominated by t-channel exchange, i.e., forward scattering. Black hole events are isotropic. So this is really becoming like any other compositeness search: massive states produced at low rapidity.

The most concrete proposal of the talk came now. At the LHC, one should measure the differential cross section for dijet production by determining the angular dependence through  , a variable defined as the ratio of events in a 0 to 0.5 absolute rapidity range by events in other 0.5-wide ranges: is an indicator of strong dynamics.

While describing a scenario where the LHC will have to walk the walk of unclear kinematical analyses rather than being hit in the face by those firework-like signatures that experimentalists have started to dream more and more frequently as of late, Randall was careful to insist that the LHC is indeed a powerful machine, although she fell short of declaring it will make everything clear about quantum gravity. It reminds me of an episode of South Park where chinese conspirators keep american people happy and oblivious by telling them they have larger penises.

After discussing the signature of black holes, Randall really took a walk on the wild side, by delving with the possible signatures of the same kind from alternative models of quantum gravity, such as a weakly coupled string theory. There one apparently expects a resonance behavior, followed by a dramatic drop in transverse cross section, which can be used to distinguish the stringy behavior from the simple production of a new Z’ boson, blah blah.  

In addition to the resonance, you would also see a drop in the quantity . This could also allow to distinguish models: you could decide you are finding a stringy state, and you could even distinguish different stringy models, because the correlation between and the cross section is different for different models.In summary, black holes are not as spectacular as advertised in the past. However, they may still provide lots of information about quantum gravity, through careful studies of processes.

Lisa said she would love to see these studies done by Atlas and CMS: energy-dependent angle studies in dijet production. I bet she will.

After Lisa concluded her talk there were several questions. Some of them were quite critical of the reliance that had been put on the model discussed. I found even some point of acrimony in a couple of questions, but Lisa was not intimidated. She explained she had stated quite clearly the limitations of the results she had been discussing. I was slightly surprised to find a non totally friendly atmosphere. Evidently, times are hard for theorists these days.

In the end, I myself asked a question. I knew from previous blogging on the issue that when one reaches a quantum gravity regime, the QCD cross section of dijet production has to go down, but Lisa had not discussed this feature. She explained that before one reaches the regime when QCD 2-particle cross section gets reduced, the cross section has to go up, in any case. So the dijet cross section reduction that Sabine has first studied happens at a regime that LHC will fail to cover.