[Paper Review] Constraints from Neutrino Decay on Superluminal Velocities

J. M. Carmona, J. L. Cortés|arXiv (Cornell University)|Oct 3, 2011

Neutrino Physics Research1 references17 citations

TL;DR

This paper investigates neutrino decay via the process $\nu \to \nu\nu\bar{\nu}}$ as a phenomenological constraint on superluminal neutrino velocities, as suggested by the OPERA experiment. It derives the decay width using a modified dispersion relation and shows that a velocity excess of $v-1 \sim 2.5 \times 10^{-5}$ leads to a decay length of about 100 km at 17 GeV, making such superluminal neutrinos inconsistent with long-baseline observations unless the velocity dependence is strongly energy-dependent.

ABSTRACT

The splitting of neutrinos, a viable reaction for superluminal neutrinos, is shown to have phenomenologically relevant consequences if one accepts the recent OPERA results for the velocity of neutrinos. Neutrino splitting can be used to put strong constraints on the energy dependence of the velocity of propagation of neutrinos in a general analysis of modifications of relativistic kinematics and to propose observable effects due to the departures from special relativity in neutrino physics.

Motivation & Objective

• To assess the phenomenological consistency of superluminal neutrinos reported by the OPERA experiment with long-baseline neutrino observations.
• To examine whether neutrino decay via $\nu \to \nu\nu\bar{\nu}}$ can constrain the energy dependence of superluminal neutrino velocities.
• To reconcile the OPERA result with the stringent SN1987A bound on neutrino velocity, which requires $v-1 < 2 \times 10^{-9}$.
• To evaluate the decay length of superluminal neutrinos as a function of their velocity and energy, using a modified dispersion relation.
• To explore the implications of neutrino decay for atmospheric and cosmological neutrino observations.

Proposed method

• Derives the decay width $\Gamma_\nu \sim \frac{3G_F^2}{64\pi^3} E_\nu^5 \left( \frac{E^2 - p^2}{p^2} \right)^4 $ for neutrino splitting under a modified dispersion relation $E^2 = m_\nu^2 + p^2 + \eta p^4 / M_{\text{Pl}}^2$.
• Uses the relation $ \frac{E^2 - p^2}{p^2} \approx 2(\bar{v} - 1) $ to express the decay width in terms of the neutrino velocity $\bar{v}$.
• Applies the decay width to compute the decay length $\ell = 1 / \Gamma_\nu $ for neutrinos with energies around 17 GeV and $v-1 \approx 2.5 \times 10^{-5}$.
• Considers the energy dependence of velocity modifications, assuming $v-1 \sim (p/\Lambda)^{n_<}$, to reconcile OPERA and SN1987A constraints.
• Neglects neutrino mass effects, justified by the threshold $p_{\text{th}} \sim \sqrt{m_\nu \Lambda} \sim \text{MeV}$ being much smaller than the considered energies.
• Assesses the impact of neutrino decay on atmospheric and cosmological neutrino spectra, showing suppression of high-energy tails and impossibility of observing cosmological neutrinos under the model.

Experimental results

Research questions

• RQ1 Can the OPERA result of superluminal neutrinos with $v-1 \approx 2.5 \times 10^{-5}$ be consistent with the SN1987A bound of $v-1 < 2 \times 10^{-9}$?
• RQ2 What is the decay length of superluminal neutrinos with $v-1 \approx 2.5 \times 10^{-5}$, and does it conflict with long-baseline observations?
• RQ3 How does the energy dependence of the velocity modification affect the consistency of neutrino decay with observational constraints?
• RQ4 What are the implications of neutrino decay for the detection of atmospheric and cosmological neutrinos?
• RQ5 How does the validity of the decay width formula depend on the momentum dependence of the neutrino velocity?

Key findings

• The decay length of superluminal neutrinos with $v-1 \approx 2.5 \times 10^{-5}$ at 17 GeV is approximately 100 km, implying they would decay before reaching detectors in long-baseline experiments like OPERA.
• A velocity excess of $v-1 \approx 2.5 \times 10^{-5}$ leads to a decay width of $\Gamma_\nu \sim 10^{-10}$ GeV, resulting in a decay length of about 100 km for 17 GeV neutrinos.
• The OPERA result and the SN1987A bound can be reconciled only if the velocity deviation scales as $v-1 \sim (p/\Lambda)^{n_<}$ with $n_< = 2$, $\Lambda \approx 4$ TeV, and $\Lambda_0 = 20$ GeV.
• The high-energy tail of the atmospheric neutrino spectrum is suppressed due to neutrino splitting, making it a potential observable constraint.
• The observation of cosmological neutrinos becomes impossible under the model, as superluminal neutrinos would decay before reaching Earth.
• The decay width formula used is invalid for momentum-independent velocity, which limits its applicability if the OPERA result reflects a constant velocity at higher energies.