[Paper Review] Explanation on Negative Mass-Square of Neutrinos

Tsao Chang, Guang-jiong Ni|ArXiv.org|Sep 25, 2000

Particle physics theoretical and experimental studies8 citations

TL;DR

This paper proposes a new Dirac-type equation for neutrinos as tachyonic fermions—particles with negative mass-squared—to explain the long-standing puzzle of negative neutrino mass-squared values observed in tritium beta decay and pion decay experiments. By introducing a non-hermitian Hamiltonian with a novel matrix $\beta_s = \beta\gamma_5$, the theory maintains CPT invariance and reproduces the two-component Weyl equation in the massless limit, preserving maximal parity violation while allowing superluminal propagation without causality violation via the re-interpretation rule.

ABSTRACT

It has been known for many years that the measured mass-square of neutrino is probably negative. For solving this puzzle, we have further investigated the hypothesis that neutrinos are superluminal fermions. A new Dirac-type equation is proposed and a tachyonic quantum theory is briefly discussed. This equation is equivalent to two Weyl equations coupled together via nonzero mass while respecting the maximum parity violation, and it reduces to one Weyl equation when the neutrino mass becomes zero.

Motivation & Objective

• To resolve the persistent experimental observation of negative neutrino mass-squared values in tritium beta decay and pion decay.
• To investigate whether neutrinos could be tachyons—particles that always travel faster than light—based on negative mass-squared measurements.
• To construct a consistent quantum field theory for tachyonic fermions that respects CPT symmetry and maximal parity violation in weak interactions.
• To replace the conventional Dirac equation with a new formulation that avoids imaginary masses and maintains positive-definite probability density.

Proposed method

• Propose a new Dirac-type equation with a non-hermitian Hamiltonian using a modified $\beta_s$ matrix defined as $\beta_s = \beta\gamma_5$, distinct from the standard Dirac $\beta$ matrix.
• Derive the equation from the energy-momentum relation $E = (c^2p^2 - m_s^2c^4)^{1/2}$, ensuring first-order dependence on momentum operators.
• Express the wave function as a two-component spinor $\Psi = (\varphi, \chi)^T$, leading to a coupled system of two-component equations resembling Weyl equations.
• Demonstrate that in the massless limit ($m_s = 0$), the system reduces to the standard two-component Weyl equation for left-handed neutrinos.
• Establish CPT invariance through space-time inversion symmetry, with $\varphi(-\vec{x},-t) \to \chi(\vec{x},t)$ and $\chi(-\vec{x},-t) \to \varphi(\vec{x},t)$.
• Define probability density $\rho = \Psi^\dagger \gamma_5 \Psi$ and current $\vec{j} = c\Psi^\dagger \gamma_5 \vec{\alpha} \Psi$, ensuring continuity and positive definiteness under specific conditions.

Experimental results

Research questions

• RQ1 Can the observed negative neutrino mass-squared values be consistently explained by a tachyonic fermion model?
• RQ2 Is it possible to construct a quantum field theory for superluminal fermions that avoids causality violations and maintains CPT symmetry?
• RQ3 How does the new Dirac-type equation differ from the standard Dirac equation in structure and physical interpretation?
• RQ4 What is the relationship between the new equation and the two-component Weyl equation in the massless limit?
• RQ5 Does the non-hermitian Hamiltonian in the tachyonic model remain physically viable due to its connection with parity violation?

Key findings

• The proposed tachyonic Dirac equation successfully reproduces the energy-momentum relation $E = (c^2p^2 - m_s^2c^4)^{1/2}$, consistent with negative mass-squared measurements.
• For $m_s(\nu_e) = 1.6$ eV, the model explains the experimental value $m^2(\nu_e) = -2.5 \pm 3.3$ eV$^2$ as arising from a superluminal particle with real proper mass $m_s$.
• The probability density $\rho = \Psi^\dagger \gamma_5 \Psi$ is positive definite when the spinor components are positive, ensuring physical consistency.
• In the massless limit ($m_s = 0$), the system reduces to the standard two-component Weyl equation, preserving maximal parity violation observed in weak interactions.
• The theory maintains CPT invariance under space-time inversion, supporting the consistency of tachyonic fermions in relativistic quantum mechanics.
• The model avoids the use of imaginary masses and provides a framework where superluminal neutrinos do not violate causality due to the re-interpretation rule.