Steve Giddings on Black Hole production

The pascos 2007 conference ended in London today, but I have been in the mountains for the last three days already, enjoying the nice weather and pleasant hikes. However, I haven’t forgotten one last duty: I wanted to report on a talk I heard last Tuesday. So here are my notes from the talk by Steve Giddings, who discussed “Black Holes in High Energy Collisions”.

He started by saying that black hole production could be the most spectacular physics at future colliders, and perhaps they will be accessible at the LHC. But even f that is not the case, black hole production raises some very important theoretical issues that we need to address.

In general, at collision energies E>M(Planck) we can form a black hole. That energy regime appears far away from the capabilities of any conceivable accelerator, let alone the LHC. But we have a proposed scenario where gravity becomes strong at a scale of one TeV or in the thereabouts, and consequently the scale of M(Planck) could be that small too.

Models with TeV-scale gravity scenarios include two classes: one is the large extra dimensions (LED) scenario. The other, being more explored these days, is the one involving a large warping of space. LEDs allow gravity field lines to spread out into them, so that in our 4-dimensional world we experience a weak gravity. With a warped volume you can still have the same effect. If we construct a theory with large extra dimensions, we run in trouble with gauge theory unless we have a way to make the gauge world 4-dimensional. Brane worlds have this function, and many such scenarios are being investigated.

After introducing the topic from a general standpoing, Steve focused on model-independent features of black hole production – a good idea, which allowed me to follow better his discussion in the talk without having to fiddle with theoretical details. At high energy there is a “natural” small expansion parameter, which is the ratio between Planck mass and collision energy, M(Planck)/E. There are of course model dependent effects, ones in particular appearing at energy of the order of M(Planck). But one can avoid focusing on what happens for a scattering right at threshold, and indeed Giddings decided to rather discuss the behavior at the high energy limit, which is much more model-independent.

The basic phenomenological scenario is simple: in a brane the two colliding particles will create a black hole, within a trapped surface – a region of density so high no radiation can escape. We have to understand how the black hole decays by describing what happens as a sequence of phases: balding, spindown, Schwarzschild, Planck. Giddings said he would summarize these phases, indicating recent improvements in their understanding, building on original results.

Formation of a black hole comes first. Working in a 1/E expansion, it is basically a classical process: the collision of two high-energy strings of particles is described as shock waves of Aichelburg-Sexl shocks. The things getting close together form a trapped surface even before they collide.

By knowing that there is a trapped surface (something that can be demontrated), even without knowing its exact structure one can compute its size, and from that a cross section and a lower limit on the mass. Recent improvements in computing the size have focused on computing the cross section estimate at parton level, from dimensional grounds and parton distribution functions of the projectiles.

The size of the trapped surface has implications for the mass. The first decay stage is the balding stage. A black hole has no hair: it quickly balds, shedding its multipole moments by emitting gravitational and electromagnetic radiation. That increases its spin. The mass is at least 60% of the available center-of-mass energy at the end, in a dimension 10 scenario.

The next phase after balding is the spindown. The black hole is spinning, and it begins to emit Hawking radiation. Preferentially it sheds angular momentum, on the time scale of t = E^(D-1/D-3). One must thus calculate higher-D Hawking emission rates, which is a hard problem. Some extrapolations were made from 4-dimensions. There is much ongoing work on this. One of the surprises is that spindown and its signatures may be even more prominent than previously estimated. 80% of the mass loss occurs in spindown effects as opposed to 25% estimated in four dimensions. This suggests looking for experimental signatures of that effect, like characteristic dipole patterns.

The third stage occurs once the black hole has shed its angular momentum: it continues to Hawking radiate, which is now the subdominant feature of the decay (20%). One can compute the power spectrum and relative emission rates. This is the better understood Schwarzschild regime. Predictions include approximately thermal multiplicities and a suppression of low-energy gauge bosons. However, what we need is a full study of the evolution through spindown and Schwarzschild phases, to determine the energy spectrum of the produced bodies, the relative multiplicities, and the event shapes, such as angular distributions and other observables.

Then there is a fourth phase: the black hole reaches the Planck scale. Hic sunt leones: here known physics breaks down. We expect a few particles coming out, with energy of that order of magnitude, but we do not really know the details of what we should expect.

Now, what are the experimental expectations at the LHC ? The first question is what energy we need to produce black holes, of course. The threshold is still M(Planck)>=1 TeV. If that is the scale, a rule of thumb is that the mass of the black hole is greater or equal to 5 TeV. The rate for producing such things could optimistically approach 1Hz, though unknown inelasticity could suppress the cross section somewhat. One Hertz is a huge rate of course, given a signature that would be hard to miss.

Signatures of course require event generators. However they at present simulate the decay with just a Schwarzschild phase, without spindown. Assuming spindown dominance is confirmed, that suggests more work is needed for detailed quantitative predictions of the phenomenology one would observe. Nonetheless, striking qualitative signatures can still be inferred.

The signatures include a potentially large cross section (increasing of course with energy), a relatively high sphericity of the event shape, a high multiplicity of primaries, many hard transverse leptons and jets, and a thermally determined ratio of species. Also, angular distributions characterizing spindown are to be expected. Finally, as you make black holes at high rate, you suppress hard jets production rates.

Steve then discussed briefly the possibility of black hole formation in cosmic rays. The center-of-mass energy reached by the highest energy cosmic rays can be up to 100 TeV. In principle their signature could be seen by Auger, Ice cube, Amanda. So a meaningful question for these experiments is, can they rule out the production of black holes at LHC by non observing a signal ? It appears that a non-observation of black hole signatures by Auger for 5 years can push the limit to Mp=2 TeV, but there are uncertainties and theoretical issues that make this a rather vague prediction.

In conclusion, if we are very lucky we will be able to see some hints of black hole production from Auger, otherwise we will have to wait to see what the LHC brings. On the theory side, building detailed Tev-scale gravity models has been very challenging, but much progress is being made. Whether or not black hole production is accessible in the near future, its possibility raises prodfound theoretical questions that can guide the next revolution in quantum gravity.