4.3. Probes of new physics beyond the electroweak scale

It is intriguing - and at the same time suggestive - that the observed flux of CRs beyond the GZK-energy is well matched by the flux predicted for cosmogenic neutrinos [511, 512]. Of course, this is not a simple coincidence: any proton flux beyond E_pCMB^th is degraded in energy by photoproducing ⁰ and ^±, with the latter in turn decaying to produce cosmogenic neutrinos. The number of neutrinos produced in the GZK chain reaction compensates for their lesser energy, with the result that the cosmogenic flux matches well the observed CR flux beyond 10²⁰ eV. Recently, the prospect of an enhanced neutrino cross section has been explored in the context of theories with large compact dimensions. ⁽⁴⁹⁾ In these theories, the extra spatial dimensions are responsible for the extraordinary weakness of the gravitational force, or, in other words, the extreme size of the Planck mass [514, 515]. For example, if spacetime is taken as a direct product of a non-compact 4-dimensional manifold and a flat spatial n-torus Tⁿ (of common linear size 2r_c), one obtains a definite representation of this picture in which the effective 4-dimensional Planck scale, M_Pl ~ 10¹⁹ GeV, is related to the fundamental scale of gravity, M_D, according to M²_Pl = 8 M_D²⁺ⁿ r_cⁿ. Within this framework, virtual graviton exchange would disturb high energy neutrino interactions, and in principle, could increase the neutrino interaction cross section in the atmosphere by orders of magnitude beyond the SM value; namely ~ [E / (10¹⁰ GeV] mb [516, 517, 518]. However, it is important to stress that a cross section of ~ 100 mb would be necessary to obtain consistency with observed showers which start within the first 50 g / cm² of the atmosphere. This is because Kaluza-Klein modes couple to neutral currents and the scattered neutrino carries away 90% of the incident energy per interaction [519]. Moreover, models which postulate strong neutrino interactions at super-GZK energies also predict that moderately penetrating showers should be produced at lower energies, where the neutrino-nucleon cross section reaches a sub-hadronic size. Within TeV scale gravity is likely to be sub-hadronic near the energy at which the cosmogenic neutrino flux peaks, and so moderately penetrating showers should be copiously produced [520]. Certainly, the absence of moderately penetrating showers in the CR data sample should be understood as a serious objection to the hypothesis of neutrino progenitors of the super-GZK events.

Large extra dimensions still may lead to significant increases in the neutrino cross section. If this scenario is true, we might hope to observe black hole (BH) production (somewhat more masive than M_D) in elementary particle collisions with center-of-mass energies TeV [521, 522, 523]. In particular, BHs occurring very deep in the atmosphere (revealed as intermediate states of ultrahigh energy neutrino interactions) could trigger quasi-horizontal showers and be detected by cosmic ray observatories [524, 525, 526, 527, 528]. Additionally, neutrinos that traverse the atmosphere unscathed may produce BHs through interactions in the ice or water and be detected by neutrino telescopes [529, 530]. Interestingly, _{N BH} M_D^{(-4+2n) / (1+n)}. Therefore, the non-observation of the almost guaranteed flux of cosmogenic neutrinos can be translated into bounds on the fundamental Planck scale. For n 5 extra spatial dimensions compactified on Tⁿ, recent null results from CR detectors lead to M_D > 1.0 - 1.4 TeV [531, 532]. These bounds are among the most stringent and conservative to date. In the near future, PAO will provide more sensitive probes of TeV-scale gravity and extra dimensions [533]. Certainly, the lack of observed deeply-penetrating showers can be used to place more general, model-independent, bounds on _N [492, 534, 535, 536].

Up to now we have only discussed how to set bounds on physics beyond the SM. An actual discovery of new physics in cosmic rays is a tall order because of large uncertainties associated with the depth of the first interaction in the atmosphere, and the experimental challenges of reconstructing cosmic air showers from partial information. However, a similar technique to that employed in discriminating between photon and hadron showers can be applied to search for signatures of extra-dimensions. Specifically, if an anomalously large quasi-horizontal deep shower rate is found, it may be ascribed to either an enhancement of the incoming neutrino flux, or an enhancement in the neutrino-nucleon cross section. However, these two possibilities may be distinguished by separately binning events which arrive at very small angles to the horizontal, the so-called "Earth-skimming" events [537, 538]. An enhanced flux will increase both quasi-horizontal and Earth-skimming event rates, whereas a large BH cross section suppresses the latter, because the hadronic decay products of BH evaporation do not escape the Earth's crust [539]. For a more detailed discussion of neutrino interactions in the Earth atmosphere within TeV scale gravity scenarios see e.g. [1].

⁴⁹ A point worth noting at this juncture: the neutrino-nucleon cross section can also be significantly enhanced at center-of-mass energies 100 TeV (within the SM) via electroweak instanton-induced processes [513]. Back.