[Paper Review] Constraining Neutrino Velocities and Lorentz Invariance Violation in the Neutrino Sector using the IceCube PeV Neutrino Events

F. W. Stecker|arXiv (Cornell University)|Jun 25, 2013

Noncommutative and Quantum Gravity Theories1 citations

TL;DR

This paper constrains Lorentz invariance violation (LIV) in the neutrino sector using IceCube's PeV neutrino events and Crab Nebula flare data. By analyzing time-of-flight differences and vacuum Cherenkov radiation constraints, it derives a stringent upper limit of δν ≤ 5.6×10⁻¹⁹ on superluminal neutrino velocity, significantly improving upon SN1987A limits.

ABSTRACT

The observation of two PeV-scale neutrino events reported by Ice Cube can, in principle, allows one to place constraints on Lorentz invariance violation (LIV) in the neutrino sector. After first arguing that at least one of the IceCube events was of extragalactic origin, I derive an upper limit for {\it the difference} between putative superluminal neutrino and electron velocities of $\le \sim 5.6 imes 10^{-19}$ in units where $c = 1$, confirming that the observed PeV neutrinos could have reached Earth from extragalactic sources. I further derive a new constraint on the superluminal electron velocity, obtained from the observation of synchrotron radiation in the Crab Nebula flare of September, 2010. The inference that the $>$ 1 GeV $\gamma$-rays from synchrotron emission in the flare were produced by electrons of energy up to $\sim 5.1$ PeV indicates the non-occurrence of vacuum Cerenkov radiation by these electrons. This implies a new, strong constraint on superluminal electron velocities $\delta_e \le \sim 5 imes 10^{-21}$. It immediately follows that one then obtains an upper limit on the superluminal neutrino velocity {\it alone} of $\delta_{ u} \le \sim 5.6 imes 10^{-19}$, many orders of magnitude better than the time-of-flight constraint from the SN1987A neutrino burst. However, if the electrons are {\it subluminal} the constraint on $|\delta_e| \le \sim 8 imes 10^{-17}$, obtained from the Crab Nebula $\gamma$-ray spectrum, places a weaker constraint on superluminal neutrino velocity of $\delta_{ u} \le \sim 8 imes 10^{-17}$.

Motivation & Objective

• To test Lorentz invariance violation (LIV) in the neutrino sector using high-energy astrophysical neutrino events.
• To determine whether the observed PeV neutrinos could have originated from extragalactic sources under LIV scenarios.
• To derive improved constraints on superluminal neutrino velocities by combining IceCube data with synchrotron radiation observations from the Crab Nebula.
• To assess the impact of electron velocity constraints on the resulting bounds for neutrino superluminal velocities.

Proposed method

• Analyzes the time-of-flight difference between PeV neutrinos and photons from extragalactic sources, assuming LIV in the neutrino sector.
• Uses the observed PeV neutrino events from IceCube to infer that at least one is of extragalactic origin, enabling LIV constraints.
• Applies the absence of vacuum Cherenkov radiation in the Crab Nebula flare to constrain electron velocities, assuming electrons up to 5.1 PeV emit synchrotron γ-rays.
• Derives a bound on superluminal electron velocity δe ≤ 5×10⁻²¹ from the non-observation of vacuum Cherenkov radiation in the Crab flare.
• Transfers the electron velocity constraint to a bound on neutrino velocity via the relation δν ≤ δe + δν, assuming neutrinos are superluminal.
• Considers the alternative scenario where electrons are subluminal, deriving a weaker bound on δν based on the Crab spectrum.

Experimental results

Research questions

• RQ1 Can the IceCube PeV neutrino events be used to constrain Lorentz invariance violation in the neutrino sector?
• RQ2 What is the maximum allowed superluminal velocity difference between neutrinos and electrons, given the observed PeV neutrino events?
• RQ3 How do observations of synchrotron γ-rays from the Crab Nebula flare constrain electron velocities and, by extension, neutrino velocities?
• RQ4 What is the resulting upper limit on superluminal neutrino velocity when electron velocity constraints are applied?
• RQ5 How do the derived bounds compare to existing constraints from SN1987A neutrino observations?

Key findings

• The analysis confirms that at least one of the IceCube PeV neutrino events is of extragalactic origin, enabling LIV constraints.
• A stringent upper limit of δν ≤ 5.6×10⁻¹⁹ is derived for the superluminal neutrino velocity difference, assuming neutrinos are superluminal.
• The absence of vacuum Cherenkov radiation in the Crab Nebula flare implies a strong constraint on electron superluminal velocity: δe ≤ 5×10⁻²¹.
• This electron constraint directly implies δν ≤ 5.6×10⁻¹⁹, which is many orders of magnitude tighter than the SN1987A time-of-flight limit.
• If electrons are subluminal, the constraint on δν weakens to δν ≤ 8×10⁻¹⁷, based on the Crab spectrum.
• The results represent a significant improvement over previous LIV bounds in the neutrino sector, particularly when electron velocity constraints are leveraged.