[Paper Review] Limiting velocities as running parameters and superluminal neutrinos

Mohamed M. Anber, John F. Donoghue|arXiv (Cornell University)|Oct 1, 2011

Noncommutative and Quantum Gravity Theories11 references3 citations

TL;DR

This paper proposes a renormalization group (RG) mechanism in which neutrinos exhibit a larger deviation from the speed of light than other particles due to weaker interactions, leading to slower running of their limiting velocity. The model uses a large number of hidden U(1) gauge bosons and Z bosons with power-law running, resulting in a hierarchical suppression of neutrino velocity differences from c, explaining why OPERA-like superluminal neutrino signals could be consistent with constraints on other particles.

ABSTRACT

In the context of theories where particles can have different limiting velocities, we review the running of particle speeds towards a common limiting velocity at low energy. Motivated by the recent OPERA experimental results, we describe a model where the neutrinos would deviate from the common velocity by more than do other particles in the theory, because their running is slower due to weaker interactions.

Motivation & Objective

• To address the puzzle of why neutrinos might have a larger speed deviation from c than other particles, despite stringent experimental bounds on charged leptons.
• To explain how Lorentz symmetry could emerge at low energy through RG running of limiting velocities in a theory with multiple particle species having different fundamental speeds.
• To construct a model where neutrino limiting velocity deviates more from c than charged lepton velocity due to weaker interaction strength and slower running.
• To reconcile the OPERA result with existing constraints by showing that the running of limiting velocities can be tuned via number of fields and interaction strength.

Proposed method

• Uses renormalization group (RG) equations to describe the running of limiting velocities for different particle species, with beta functions dependent on the difference between their respective speeds.
• Introduces a model with a large number of hidden U(1) gauge bosons and Z bosons, with their numbers scaling as a power law with energy scale: $ N_i(\mu) = \Gamma_i (\mu/M_i)^{\alpha_i} $.
• Models the running of the effective coupling constants $ Z_{\ell\nu,Z} $, $ \eta_\ell $, and $ \eta_\nu $, showing that $ \eta_\nu \gg \eta_\ell $ due to weaker interaction strength.
• Performs numerical simulations of the RG flow using power-law running, demonstrating that $ \eta_\ell $ and $ \eta_\nu $ reach very small values rapidly, with $ \eta_\ell \ll \eta_\nu $.
• Considers the validity of perturbative RG treatment, noting that while initial conditions may violate perturbative bounds, non-perturbative evolution could still yield fast running.
• Uses the AdS/CFT correspondence and large extra-dimensions as analogs to justify the power-law scaling of particle species with energy scale.

Experimental results

Research questions

• RQ1 Why do experimental constraints on the speed of light deviation for charged leptons ($ |1 - c_e^2/c_\gamma^2| < 10^{-14} $) appear much tighter than for neutrinos?
• RQ2 Can the RG running of limiting velocities explain why neutrinos might have a larger speed deviation from c than other particles, despite weaker interactions?
• RQ3 How can a model with multiple particle species having different limiting velocities evolve toward a common speed at low energy, and what determines the rate of this approach?
• RQ4 Can a power-law running of effective couplings and species numbers lead to a hierarchical suppression of velocity differences, particularly for neutrinos?
• RQ5 Is it possible to maintain perturbative control in the RG analysis when the number of fields is large and initial couplings are strong?

Key findings

• The RG running of limiting velocities drives different particle species toward a common speed at low energy, with the rate of approach depending on interaction strength.
• Neutrinos, due to weaker interactions, exhibit slower running of their limiting velocity compared to charged leptons, allowing for a larger deviation from c.
• Numerical simulations show that $ \eta_\nu \gg \eta_\ell $, with $ \eta_\ell $ reaching values below the numerical error tolerance, indicating a strong hierarchy.
• The model achieves a final velocity difference for neutrinos from c that is exponentially larger than for charged leptons, due to the power-law running of hidden gauge bosons.
• The effective number of hidden particles is estimated as $ N_\gamma \sim 10^{11} $, $ N_Z \sim 10^4 $, and $ N_\ell \approx 1 $, explaining the hierarchical structure of velocity running.
• The model provides a mechanism for energy-independent neutrino speed in the infrared, consistent with OPERA's energy-independent fit, though it does not resolve the energy-dependent constraints from SN1987a.