CPH Theory

Here's what didn't happen on Sept. 10th:

The world did not end. Switching on the world's largest and most powerful particle accelerator near Geneva, Switzerland, did not trigger the creation of a microscopic black hole. And that black hole did not start rapidly sucking in surrounding matter faster and faster until it devoured the Earth, as sensationalist news reports had suggested it might.

Of course, because you're alive and reading this article today, you already knew that. Currently the accelerator, an underground ring 5 miles across called the Large Hadron Collider (LHC), has been shut down for repairs. But once the immensely powerful machine starts back up, is there a chance that the doomsday scenario could still occur?

Relax. As Mark Twain might have said, reports of Earth's death have been greatly exaggerated.

"There never really was a danger from the accelerator, but that sure didn't stop people from speculating that there might be!" says Robert Johnson, a physicist at the Santa Cruz Institute for Particle Physics and a member of the science team for NASA's Fermi Gamma-ray Space Telescope, which launched in June to study gamma rays from many phenomena, including possible evaporating black holes.

There are several reasons why the world did not come to an end on Sept. 10th, and why the Large Hadron Collider isn't capable of triggering such a calamity.

First of all, yes, it is true that the LHC might create microscopic black holes. But, for the record, it could not have created one on its first day. That's because the physicists at CERN didn't steer beams of protons into each other to create high-energy collisions. Sept. 10th was just a warmup run. To date, the collider still has not produced any collisions, and it is the extreme energy of those collisions — up to 14 tera-electron volts — that could potentially create a microscopic black hole.

Actually, once the LHC is running again and begins producing collisions, physicists will be ecstatic if it creates a tiny black hole. It would be the first experimental evidence to support an elegant but unproven and controversial "theory of everything" called string theory.

In string theory, electrons, photons, quarks, and all the other fundamental particles are different vibrations of infinitesimal strings in 10 dimensions: 9 space dimensions and one time dimension. (The other 6 space dimensions are hidden by one explanation or another, for example by being "curled up" on an extremely small scale.) Some physicists tout string theory's mathematical elegance and its ability to integrate gravity with the other forces of nature. The widely accepted Standard Model of particle physics does not include gravity, which is one reason why it does not predict that the LHC would create a gravitationally collapsed point — a black hole — while string theory does.

Many physicists have started to doubt whether string theory is true. But assuming for a moment that it is, what would happen when a black hole is born inside the LHC? The surprising answer is "not much." Even if the black hole survives for more than a fraction of a second (which it probably wouldn't), most likely it would be flung out into space. "It would only have the mass of a hundred or so protons, and it would be moving at near the speed of light, so it would easily have escape velocity," Johnson explains. Because the tiny black hole would be less than a thousandth the size of a proton and would have an exceedingly weak gravitational pull, it could easily zip through solid rock without ever touching — or sucking in — any matter. From the perspective of something this tiny, the atoms that make up "solid" rock appear to be almost entirely empty space: the vast space between the atoms' nuclei and their orbiting electrons. So a micro black hole could shoot down through the center of the Earth and out the other side without causing any damage just as easily as it could shoot up through 300 feet of the Swiss countryside. Either way, it would end up out in the near-vacuum of space, where the odds of it touching and sucking in any matter so that it could grow into a menace would be smaller still.

So the first thing a micro-black hole would do is leave the planet safely behind. But there are other, even stronger reasons why scientists believe the LHC poses no threat to Earth. For one, a black hole created in the LHC would almost certainly evaporate before it got very far, most scientists believe. Stephen Hawking, the physicist who wrote A Brief History of Time, predicted that black holes radiate energy, a phenomenon known as Hawking radiation. Because of this steady loss of energy, black holes eventually evaporate. The smaller the black hole, the more intense the Hawking radiation, and the quicker the black hole will vanish. So a black hole a thousand times smaller than a proton should disappear almost instantly in a quick burst of radiation.

Overview schematic
shows the four main experiments and the two ring structure of the LHC

Joining things up
Once in place the magnet have to be connect - a very complicated task.

As explained in the intro about extra dimensions, in the presence of additional large compactified dimensions, it would be possible to produce tiny black holes at future colliders. In this case, we would be able to experimentally test Planck scale physics and the onset of quantum gravity with the Large Hadron Collider (LHC), which is scheduled to start next summer. The formation of black holes is a fairly robust prediction and one of the most general expectations that one can have, even though the details are still subject to research. For me, it is quite amazing to see how this field has evolved during the last decade. Starting from a smiled upon speculation, it has by now become a widely accepted scenario for physics beyond the standard model, which is included in simulations of LHC events.

2. Production of Black Holes

The production of a black hole in a high energy collision is probably the most inelastic process one might think of. Since the black hole is not an ordinary particle of the standard model, and its correct quantum theoretical treatment is unknown, it is commonly treated as a metastable state, which is produced and decays according to the semi-classical formalism of black hole physics. To compute the production details, the cross-section of the black holes can be approximated by the classical geometric cross-section Pi R². A common approach to improve the naive picture of colliding point particles is to treat the creation of the horizon as a collision of two shock fronts in an Aichelburg-Sexl geometry describing the fast moving particles.

Looking at the figure on the left, we also see that, due to conservation laws, the angular momentum of the formed object only vanishes in completely central collisions with zero impact parameter. In the general case, we will have an angular momentum, and the black hole might also carry an electric charge.

Another assumption which goes into the production details is the existence of a threshold for the black hole formation. From general relativistic arguments, two point like particles in a head on collision with zero impact parameter (the b in the figure above) will always form a black hole, no matter how large or small their energy. At small energies however, we expect this to be impossible due to the smearing of the wave functions by the uncertainty relation. This then results in a necessary minimal energy to allow for the required close approach. This threshold is of order of the new fundamental scale, though the exact value is unknown since quantum gravity effects should play an important role for the wave functions of the colliding particles. Using the geometrical cross section formula, it is now possible to compute the differential and total cross sections for black hole production. This also allows us to estimate the total number of black holes, that would be created at the LHC per year. Inserting the expected technical details for the collider, one finds a number of approximately 10⁹ created black holes per year! This means, about one black hole per second.

3. Evaporation of Black Holes

1. Balding phase: In this phase the black hole radiates away the multipole moments it has inherited from the initial configuration, and settles down in a hairless state. During this stage, a certain fraction of the initial mass will be lost in gravitational radiation.

2. Evaporation phase: The evaporation phase starts with a spin down phase in which the Hawking radiation carries away the angular momentum, after which it proceeds with emission of thermally distributed quanta until the black hole reaches Planck mass. The radiation spectrum contains all Standard Model particles, which are emitted on our brane, as well as gravitons, which are also emitted into the extra dimensions. It is expected that most of the initial energy is emitted in during this phase in Standard Model particles.

3. Planck phase: Once the black hole has reached a mass close to the Planck mass, it falls into the regime of quantum gravity and predictions become increasingly difficult. It is generally assumed that the black hole will either completely decay in some last few Standard Model particles or a stable remnant will be left, which carries away the remaining energy.

To perform a realistic simulation of the evaporation process, one has to take into account the various particles of the standard model with the corresponding degrees of freedom and spin statistics. In the extra dimensional scenario, standard model particles are bound too our submanifold whereas the gravitons are allowed to enter all dimensions. For a precise calculation one also has to take into account that the presence of the gravitational field will modify the radiation properties for higher angular momenta through backscattering at the potential well. These energy dependent greybody factors can be calculated by analyzing the wave equation in the higher dimensional spacetime and the arising absorption coefficients. A very thorough description of these evaporation characteristics has been given by Kanti in 2004 which confirms the expectation that the bulk/brane evaporation rate is of comparable magnitude but the brane modes dominate.

One of the primary observables in high energetic particle collisions is the transverse momentum of the outgoing particles, p_T(pee-tee), the component of the momentum transverse to the direction of the beam. Two colliding partons with high energy can produce a pair of outgoing particles, moving in opposite directions with high p_T but carrying a color charge, as depicted in the figure to the right.

Due to the quark confinement, the color has to be neutralized. This results in a shower of several bound states, the hadrons, which includes mesons (consisting of a quark and an antiquark, like the pions) as well as baryons (consisting of three quarks, like the neutron or the proton). The number of these produced hadrons and their energy depends on the energy of the initial partons. This process will cause a detector signal with a large number of hadrons inside a small opening angle. Such an event is called a jet.

Due to the high energy captured in the black hole, the decay of such an object is a very spectacular event with a distinct signature. The number of decay products, the multiplicity, is high compared to standard model processes and the thermal properties of the black hole will yield a high sphericity of the event. Furthermore, crossing the threshold for black hole production causes a sharp cut-off for high energetic jets as those jets now end up as black holes instead, and are re-distributed into thermal particles of lower energies. Thus, black holes will give a clear signal. A schematic picture of this process is shown on the left.

It is apparent that the consequences of black hole production are quite disastrous for the future of collider physics! Once the collision energy crosses the threshold for black hole production, no further information about the structure of matter at small scales can be extracted. As it was put by Giddings and Thomas, this would be ''the end of short distance physics''

By now, several experimental groups include black holes into their search for physics beyond the standard model. Ideally, the energy distribution of the decay products allows a determination of the temperature (by fitting the energy spectrum to the predicted shape) as well as of the total mass of the object (by summing up all energies). This then allows to reconstruct the fundamental scale, and the number of extra dimensions. The quality of the determination depends on the uncertainties in the theoretical prediction as well as on the experimental limits e.g. background from standard model processes. Besides the formfactors of black hole production and the greybody factors of the evaporation, the largest theoretical uncertainties turnout to be the final decay and the time variation of the temperature. In case the black hole decays very fast, it can be questioned whether it has time to readjust its temperature at all or whether it essentially decays completely with its initial temperature. Also, the determination of the properties depends on the number of emitted particles. The less particles, the more difficult the analysis

However, in my opinion the most crucial uncertainty are the latest stages of the evaporation. For hadron colliders like the LHC, the last stages with black hole masses close by the production threshold will dominate the signature, since most of the black holes are actually produced out of parton collisions with a total center-of-mass energy close by even this threshold. In hadronic collisions there are thus very little black holes which actually capture the total available energy of 14 TeV, since the proton's energy gets distributed on its constituents. Such a problem would not be present for a lepton collider.

1. Micro Black Holes in Large Extra Dimensions

2. Production of Black Holes

3. Evaporation of Black Holes