[Paper Review] How large is the fraction of superluminal neutrinos at OPERA

Walter Winter|arXiv (Cornell University)|Oct 3, 2011

Particle physics theoretical and experimental studies7 citations

TL;DR

This paper investigates the fraction of superluminal neutrinos in the OPERA experiment's data, assuming only a subset—such as sterile neutrinos—travel faster than light. Using the nonlinear structure of the proton waveform as a constraint, it finds a minimal superluminal fraction of 17% at 3 sigma, challenging purely sterile neutrino models and limiting systematic errors that smear the signal.

ABSTRACT

Various approaches aim to describe the recent analysis by the OPERA experiment, which indicates that neutrinos travel faster than the speed of light. We demonstrate that any such theoretical or experimental explanation must not destroy the complicated (nonlinear) structure of the proton waveform recovered in the neutrino signal. As one example, consider that only a fraction of the neutrinos travel faster than the speed of light, such as sterile neutrinos. We fit the OPERA data including this fraction as a free variable, assuming that the OPERA result is correct. In our analysis, the best-fit values are 50% of the neutrinos being superluminal and (v-c)/c = 4.5 10^{-5}, where the neutrino velocity increases as the fraction of superluminal neutrinos decreases. The minimal fraction of superluminal neutrinos is found to be 17% (3 sigma), which is constrained by the non-linearity of the proton waveform. This minimal fraction challenges the hypothesis that only sterile neutrinos travel faster than the speed of light. In addition, we demonstrate that an experimental effect introducing a smearing between the proton waveform and neutrino signal, as expected for some systematical errors, is also limited by the shape of the waveform. Finally, we illustrate that even stronger constraints may be obtained from the recent analysis with a short-bunch beam, in spite of the low statistics.

Motivation & Objective

• To determine the minimum fraction of superluminal neutrinos consistent with the OPERA experiment's anomalous faster-than-light signal.
• To assess whether a purely sterile neutrino explanation for superluminal behavior is viable under waveform constraints.
• To evaluate how systematic errors affecting signal smearing are limited by the nonlinear shape of the proton waveform.
• To explore whether future short-bunch beam data could yield stronger constraints despite low statistics.

Proposed method

• Fits the OPERA neutrino signal data using a model where a free fraction of neutrinos are superluminal, with velocity excess (v−c)/c as a variable.
• Imposes the constraint that the reconstructed proton waveform must retain its complex nonlinear structure, rejecting models that distort it.
• Uses the observed nonlinearity of the proton waveform as a physical bound on possible systematic effects or signal smearing.
• Applies statistical analysis to derive confidence intervals on the superluminal fraction, particularly at the 3 sigma level.
• Considers the implications of short-bunch beam data for tightening constraints, even with limited statistics.
• Analyzes the interplay between the fraction of superluminal neutrinos and the velocity excess, showing an inverse relationship.

Experimental results

Research questions

• RQ1 What is the minimum fraction of superluminal neutrinos allowed by the nonlinear structure of the proton waveform in the OPERA data?
• RQ2 Can a model in which only sterile neutrinos are superluminal be consistent with the observed waveform constraints?
• RQ3 How do systematic errors that smear the neutrino signal relative to the proton waveform affect the interpretation of the OPERA result?
• RQ4 To what extent can future short-bunch beam data improve constraints on superluminal neutrino fractions?
• RQ5 How does the velocity excess (v−c)/c depend on the fraction of superluminal neutrinos in the fitted model?

Key findings

• The best-fit fraction of superluminal neutrinos is 50%, with a velocity excess of (v−c)/c = 4.5 × 10⁻⁵.
• The minimal fraction of superluminal neutrinos is constrained to 17% at the 3 sigma confidence level, due to the nonlinearity of the proton waveform.
• This minimal fraction challenges the hypothesis that only sterile neutrinos are superluminal, as such a model would require a fraction below the observed lower bound.
• Systematic effects causing smearing between the proton waveform and neutrino signal are limited by the same nonlinear waveform structure.
• Even with low statistics, the short-bunch beam analysis offers potential for stronger constraints on superluminal neutrino fractions.
• The velocity excess (v−c)/c increases as the fraction of superluminal neutrinos decreases, indicating a trade-off in the model.