First quantized approaches to neutrino oscillations and second quantization

Abstract

Neutrino oscillations are treated from the point of view of relativistic first quantized theories and compared to second quantized treatments. Within first quantized theories, general oscillation probabilities can be found for Dirac fermions and charged spin 0 bosons. A clear modification in the oscillation formulas can be obtained and its origin is elucidated and confirmed to be inevitable from completeness and causality requirements. The left-handed nature of created and detected neutrinos can also be implemented in the first quantized Dirac theory in the presence of mixing; the probability loss due to the changing of initially left-handed neutrinos to the undetected right-handed neutrinos can be obtained in analytic form. Concerning second quantized approaches, it is shown in a calculation using virtual neutrino propagation that both neutrinos and antineutrinos may also contribute as intermediate particles. The sign of the contributing neutrino energy may have to be chosen explicitly without being automatic in the formalism. At last, a simple second quantized description of the flavor oscillation phenomenon is devised. In this description there is no interference terms between positive and negative components, but it still gives simple normalized oscillation probabilities. A new effect appearing in this context is an inevitable but tiny violation of the initial flavor of neutrinos. The probability loss due to the conversion of lefthanded neutrinos to right-handed neutrinos is also presented.

Intrinsic flavor violation for massive neutrinos

“…28 is based on a formalism that uses a unitarily inequivalent vacuum that guarantees initial neutrino flavor conservation [28] but also implies slightly different oscillation formulas [31]. Instead, [32] or fermionic [33,34] wave packets but its magnitude could not be determined without the full consideration of the interaction responsible for neutrino creation. The further inclusion of radiative corrections to the formalism developed in Sec.…”

Flavor neutrino states for pedestrians

“…which is unacceptable because it tells us that flavor is undefined even at t = 0 [29,30]. A similar paradox was also pointed out in Ref.…”

“…We can evaluate the oscillation formula as the expectation value of the flavor charge on a reference neutrino state [27,28,29]:…”

“…The notation here is slightly different respect to Refs. [29,37], in order to get in touch with the next section. For plane waves, ϕ σ (p z − p 0 ) = δ(p z − p 0 ).…”

Neutrino mixing and oscillations in quantum field theory: a comprehensive introduction

“…where Ψ T f = (ν e , ν µ , ν τ ) , Ψ T m = (ν 1 , ν 2 , ν 3 ) and and M is the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix [49]: The notation here is slightly different with respect to Refs. [143][144][145], in order to get in touch with previous sections. For plane waves, ϕ σ (p z − p 0 ) = δ(p z − p 0 ).…”