[Paper Review] Resolving LSND anomaly by neutrino diffraction

Kenzo Ishikawa, Yutaka Tobita|arXiv (Cornell University)|Sep 14, 2011

Neutrino Physics Research2 references3 citations

TL;DR

This paper proposes that the LSND anomaly—excess electron neutrino events at short baselines—arises from a novel diffraction effect in neutrino wave packets, not new physics. By analyzing finite-time S-matrix evolution, the authors show that neutrino detection probabilities exhibit a T-dependent diffraction term sensitive to average neutrino mass squared, resolving the LSND excess without flavor oscillation, while charged leptons show no such effect due to their larger mass and helicity suppression.

ABSTRACT

In the charged pion decay, a neutrino is produced in pair with a charged lepton and they have the same production rate. In this paper we show that neutrinos have their own space-time correlations in a wide area and are detected in a different manner from charged leptons, owing to extremely small mass. The neutrino flux reveals a unique interference effect in the form of diffraction of non-stationary waves. The diffraction component of the flux shows a slow position-dependence and leads to an electron neutrino at short base-line regions. The electron neutrino flux at short distances is attributed to the neutrino diffraction and the one at long distances is to the normal flavor oscillation. The former depends upon the average mass-squared $\bar m^2_ν$ and the latter depends upon the mass-squared difference $δm^2_ν$. The LSND and the two neutrino experiment (TWN) measure $\bar m^2_ν$ and the other experiments measure $δm^2_ν$. Hence they are consistent with each other. The neutrino diffraction would supply valuable information on the absolute neutrino mass.

Motivation & Objective

• To resolve the long-standing LSND anomaly, where electron neutrino events exceed expectations at short baselines.
• To explain the discrepancy between LSND/TWN experiments (measuring average neutrino mass squared) and long-baseline experiments (measuring mass-squared differences).
• To demonstrate that finite-time S-matrix evolution reveals a diffraction component in neutrino fluxes, absent in standard asymptotic S-matrix treatments.
• To show that this diffraction effect is observable only in neutrinos due to their small mass and relativistic invariance, not in charged leptons.
• To provide a consistent framework that preserves unitarity and lepton number conservation while explaining the anomalous electron neutrino flux.

Proposed method

• Uses a finite-time S-matrix $ S[T] = \Omega_-^\dagger(T)\Omega_+(T) $, defined via Møller operators at finite time T, to describe pion decay dynamics.
• Applies wave packet formalism to model time-dependent neutrino and charged lepton detection probabilities, incorporating retarded and interference effects.
• Derives the diffraction term $ P_{\text{diff}}^{(\nu)}(T) = C T \sum_i \tilde{g}(T, \omega_{\nu_i}) |U_{i,e}|^2 $, where $ \tilde{g}(T, \omega) $ is a time- and mass-dependent interference function.
• Computes $ \tilde{g}(T, \omega) $ via $ T g(T, \omega) = -i \int_0^T dt_1 dt_2 \frac{\epsilon(\delta t)}{|\delta t|} e^{i\omega \delta t} $, showing it remains finite for neutrinos but vanishes for charged leptons at macroscopic T.
• Compares theoretical diffraction flux with LSND and TWN experimental data, finding excellent agreement for $ \bar{m}^2_\nu \approx 0.25-1.0 \, \text{eV}^2/c^4 $.
• Demonstrates that the diffraction component violates helicity suppression, allowing electron neutrinos to be produced at 10–20% of muon neutrino flux at maximum.

Experimental results

Research questions

• RQ1 Why do LSND and TWN experiments observe an excess of electron neutrinos at short baselines, while other experiments do not?
• RQ2 Can the observed electron neutrino excess be explained without invoking sterile neutrinos or new physics?
• RQ3 How does finite-time evolution of the S-matrix alter neutrino detection probabilities compared to the standard asymptotic S-matrix?
• RQ4 Why is the diffraction effect significant for neutrinos but negligible for charged leptons?
• RQ5 Does the diffraction mechanism preserve unitarity and lepton number conservation despite apparent non-conservation in detection rates?

Key findings

• The diffraction component of the neutrino flux, $ P_{\text{diff}}^{(\nu)}(T) $, is finite and T-dependent, arising from energy-nonconserving final states in the finite-time S-matrix.
• The diffraction term depends on the average neutrino mass-squared $ \bar{m}^2_\nu $, while the normal term depends on the mass-squared difference $ \delta m^2_\nu $, explaining why LSND and TWN measure $ \bar{m}^2_\nu $ and other experiments measure $ \delta m^2_\nu $.
• The diffraction flux for electron neutrinos is enhanced at short distances due to the breakdown of helicity suppression, reaching up to 10–20% of the muon neutrino flux.
• The diffraction component vanishes for charged leptons because $ \tilde{g}(T, \omega_l) \to 0 $ at macroscopic T due to their larger mass, consistent with experimental observations.
• The theory reproduces LSND and TWN data with excellent agreement for $ \bar{m}^2_\nu \approx 0.25-1.0 \, \text{eV}^2/c^4 $, resolving the anomaly without new particles.
• Unitarity and lepton number conservation are preserved because the apparent decrease in detection probability with T is due to retarded and interference effects, not actual particle loss.