Direct Detection of Supersymmetric Particles in Neutrino Telescopes Z. Chacko University of Arizona I. Albuquerque & G. Burdman

Historically cosmic rays have played a very important role in particle physics. Led to the discovery of positron, muon and pion. However there has been very little recent progress in the direct detection of exotic particles. Why is this?

Four reasons jump out! 1. Require centre of mass energy in collision to exceed the mass of any exotic particle being produced. However flux of high energy cosmic rays falls rapidly with energy. 2. Cross-section for heavy particle to be produced falls rapidly with centre of mass energy. Therefore number of events falls very quickly with mass of exotic. Relatively few events!

3. Heavy particles typically have very short lifetimes. A tau is only 20 times heavier than a muon. However, The short lifetime makes it difficult to characterize exotic particles. 4.How does one distinguish an exotic particle from the surrounding debris? These reasons make identification of an exotic very challenging!

An enormous detector can compensate for the reduced number of events, at least partially. This is exactly what large neutrino telescopes offer! These consist of cubic grids of Cerenkov counters placed in ice or water that can detect charged particles passing through. Each side of the grid is of order a kilometer across. Neutrino telescopes offer a new opportunity for the direct detection of charged,quasi-stable exotics produced by cosmic rays.

There remains the problem of identifying exotics. Are there interesting candidate theories that predict quasistable charged particles? Consider supersymmetry! Supersymmetric theories have a discrete symmetry called R-parity, under which all Standard Model particles are + but all supersymmetric particles are --. This means the `Lightest Supersymmetric Particle’, the `LSP’, is stable! What is the LSP? This is generally either the neutralino or the gravitino, depending on the supersymmetry breaking scale. If the LSP is the gravitino, the `Next-to-Lightest Supersymmetric Particle’, the `NLSP’, is typically the superpartner of the right-handed tau, the right-handed stau. In a large class of theories, including gauge mediated models and superWIMP Models, this particle is long-lived and can be directly detected in neutrino telescopes.

How are the staus produced? High energy neutrinos passing through the earth collide with nucleons, resulting in production of a pair of supersymmetric particles, which decay promptly to staus. This is the supersymmetric analogue of the weak processes which give rise to muon events in neutrino telescopes. The signal is a pair of parallel, upward going charged tracks.

What are the dominant diagrams? How large is the corresponding cross-section?

We see that cross-section for stau production is 3-4 orders of magnitude below cross-section to Standard Model particles. Why is this? For a neutrino of energy E to produce a pair of particles whose masses sum to M, the parton it interacts with needs to carry a parton momentum fraction where m is the mass of the nucleon. Since supersymmetric particles are heavier, they require bigger values of x for fixed neutrino energy E. Since parton distribution functions fall with x, the supersymmetric cross-sections are much smaller. Naively, this would imply that any signal of supersymmetry would be swamped. However, this does not happen! The reason is that the smaller cross-section for supersymmetric particles is compensated for by their much larger range.

Why does the range matter? Define P as probability any given neutrino will give rise to an event in the detector. Then, assuming P is much less than one, where P μ is the probability of a muon event, n the number density of nucleons in the earth, σ μ the neutrino-nucleon cross-section to muons and L μ the muon range. Similarly, the probability of a supersymmetric event

Since stau range is larger than muon range as much as three orders of magnitude, this can partially compensate for reduced cross-section. Why is the muon range so much smaller? Consider formula for electromagnetic energy loss, where a(E) and b(E) are slowly varying functions of energy. While a(E) represents energy loss due to ionization, b(E) represents energy loss from radiation. At high energies, radiation losses dominate. Crudely, b(E) scales as the inverse of the mass of the propagating particle. Since the stau is much heavier than the muon, it travels much further. Stau range can be as large as thousands of kilometers. (careful study by Reno, Sarcevic and Su)

Since stau range is very large, the stau tracks will appear nearly parallel. What is their separation in detector? We can estimate the angular separation of the tracks by where E is the energy of the incident neutrino and M is of order the masses of the supersymmetric particles. Then track separation This naïve estimate is justified by a more detailed calculation. The signal is therefore two parallel charged tracks about 100m apart.

What are the possible backgrounds? Parallel tracks arising from independent single muon events are very rare. Instead, the largest background arises from Standard Model processes which result in two muons. The main source of these di-muons is the production of a charmed hadron, which subsequently decays semi-leptonically to a muon. Here H c is a charmed baryon and H x is a strange or non-strange baryon. However we expect most of the di-muon background can be eliminated by making cuts on track separation and angular distribution. Since the muon range is only of order 10 kilometers, much smaller than the stau range, the muon tracks, even if parallel, are only very rarely more than 30m apart. It may also be possible to distinguish individual muon tracks from stau tracks.

How large are the signals? For this we need to know the incident neutrino flux. We will use the Waxman-Bahcall and Mannheim-Protheroe-Rachen bounds as a guide. Results show that first concrete evidence for supersymmetry may emerge from neutrino telescopes. See also analyses of Bi, Wang, Zhang & Zhang, and Ahlers, Kersten & Ringwald.

As explained earlier, the track separations of signal and background tend to be very different.

Conclusions Neutrino telescopes may provide the first concrete evidence for weak scale supersymmetry. More generally, any theory that predicts quasi-stable charged particles at the weak scale which can be pair produced through neutrino-nucleon interactions can be probed in this way.