Constraints On Ultra-High Energy New Physics From Cosmic Rays

Deligny cleverly uses ulta-high energy cosmic rays as a natural experiment to discern limits on possible new high energy physics beyond the Standard Model of Particle Physics (BSM) at energies well beyond those that can be explored in existing, and even next generation, particle colliders.

Various phenomena of physics beyond that of the Standard Model could occur at high scale. Ultra-high energy cosmic rays are the only particles available to explore scales above a few dozens of TeV. Although these explorations are much more limited than those carried out with colliders, they provide a series of constraints in several topics such as tests of Lorentz invariance, dark matter, phase transitions in the early universe or sterile neutrinos. Several of these constraints are reviewed in these proceedings of UHECR2024 based on searches for anomalous characteristics in extensive air showers or searches for ultra-high energy gamma rays and neutrinos.

O. Deligny, "Various constraints on BSM physics from extensive air showers and from ultra-high energy gamma-ray and neutrino searches" arXiv:2501.19322 (January 31, 2025).

The body text discusses the following constraints, most of which are rather obscure:

1. Lorentz Violation.

If Lorentz violation (i.e. deviations from special relativity) exists, a certain parameter the suppresses neutral pion decay would be negative, which would also allow individual photons to decay without interacting with other particles. This parameter is observationally constrained by be not smaller than negative 6 parts per 10^21.

In general, the observational constraints on Lorentz violation from this source, as well as from other methodologies, are extremely strict, but can't entirely rule out extremely slight Lorentz violations.

2.  Superheavy dark matter particles

Constraints on superheavy dark matter particles including "inflatons" and spin 3/2 gravitinos can be established:

Other observational astronomy constraints not mentioned also disfavor ultra-heavy dark matter particle candidates, even in the parts of the parameters space where cosmic ray observations alone allow them.

3. Early Universe Phase Transitions

Cosmic strings "are regions of space-time that remain in a symmetry unbroken phase due to boundary conditions that topologically restrict their decay." These would spontaneously decay in the very early universe resulting in a phase transition as the U(1) symmetry and force that holds these strings together completely disappears as the universe cools decaying into still very high energy beyond the Standard Model particles that decay into Standard Model particles.

The energies at which such a phase transition could occur are constrained by ultra-high energy cosmic ray observations.

4. Anomalous Ultra-High Energy Sterile Neutrinos

The body text notes that:

In the SM, the neutrino-nucleon scattering cross-section increases with the energy of the incoming neutrino. Consequently, ultra-high-energy neutrinos may only propagate through the Earth for relatively short distances of the order of O(100) km.

Since the path through Earth to upwards to a neutrino detector is more than 100 km for all but the most grazing angles of approach relative to the surface of the Earth, ultra-high energy neutrinos aren't expected from that direction. But "two “anomalous” radio pulses [have been] observed with the ANITA instrument compatible with EASs developing in the upward direction and inconsistent with SM expectations[.]" 

Efforts have been made to devise SM and BSM explanations for these two outlier data points. An explanation of these anomalies with BSM neutrino physics that could both produce these anomalies, and not produce significantly more anomalies than were observed by ANITA, however, is quite constrained.

One of the less radical BSM neutrino physics possibilities is a sterile neutrino the evades interaction with nucleons in the Earth because it has no weak force interactions until it oscillates into an active high energy neutrino shortly before it reaches the detector. The allowed parameter space of such a sterile neutrino in terms of the oscillation probability U to a sterile neutrino, and the sterile neutrino mass has been established subject to certain assumptions and is shown in the chart below. This mostly limit a sterile neutrino explanation to sterile neutrinos with more than 4 GeV in mass but less than 16 GeV in mass (compared to significantly less than 1 eV for the most massive active neutrino mass, which is ten orders of magnitude smaller), and a probability of transitioning to from sterile neutrino to an active neutrino that is probably in the range of 10^-5 to 10^-6. These parameters are far outside the range that has been suggested by weak anomalies in other searches for sterile neutrinos (which are themselves mutually inconsistent with each other).

Less frequent transition probabilities for a heavy sterile neutrino are discouraged by a lack of close enough sources to produce two ultra-high energy sterile neutrino events, while laboratory based sterile neutrino searches rule out more frequent transition probabilities.

These transition probabilities are four to six orders of magnitude smaller than any of the PMNS matrix neutrino oscillation probabilities, and are two to four orders of magnitude smaller than the smallest CKM matrix probabilities of W boson mediated transitions between first and third generation quark flavors (which differ in mass by five orders of magnitude). Sterile neutrinos of less than 4 GeV masses are also disfavored as an explanation.

This is the only experimental data suggestive of sterile neutrinos with these parameters.