Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2103.13982

Quantum Field Theory of Space-like Neutrino

Jakub Rembieliński·Paweł Caban·Jacek Ciborowski
View original source ↗Read source document ↗Export metadata ↓

Abstract

We performed a Lorentz covariant quantization of the spin-1/2 fermion field assuming the space-like energy-momentum dispersion relation. We a\-chieved the task in the following steps: ($i$) determining the unitary realizations of the inhomogenous Lorentz group in the preferred frame scenario by means of the Wigner-Mackey induction procedure and constructing the Fock space; ($ii$) formulating the theory in a manifestly covariant way by constructing the field amplitudes according to the Weinberg method; ($iii$) obtaining the final constraints on the amplitudes by postulating a Dirac-like free field equation. Our theory allows to predict all chiral properties of the neutrinos, preserving the Standard Model dynamics. We discussed the form of the fundamental observables, energy and helicity, and show that non-observation of the $+\tfrac{1}{2}$ helicity state of the neutrino and the $-\tfrac{1}{2}$ helicity state of the antineutrino could be a direct consequence of the "tachyoneity" of neutrinos at the free level. We found that the free field theory of the space-like neutrino is not invariant under the C and P transformations separately but is CP-invariant. We calculated and analyzed the electron energy spectrum in tritium decay within the framework of our theory and found an excellent agreement with the recent measurement of KATRIN. In our formalism the questions of negative/imaginary energies and the causality problem does not appear.

Explore related subjects

hep-phhep-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jakub Rembieliński, Paweł Caban, Jacek Ciborowski. 2021-03-23. Quantum Field Theory of Space-like Neutrino. https://doi.org/10.1140/epjc%2Fs10052-021-09494-x

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Chiral perturbation theory with vector mesons and the pion electromagnetic form factor

We formulate chiral perturbation theory with vector mesons kept as explicit intermediate degrees of freedom, in the regime where the momentum carried by a vector meson is of order $Q$ while its mass is of order $Λ_χ$. This is the regime relevant to vector-meson exchange in nuclear forces and low-energy nuclear electroweak processes. We use the corresponding power counting and show that it gives a consistent one-loop expansion, with the divergences generated by the leading-order Lagrangian absorbed by next-to-leading-order counterterms. As an application, we calculate the pion electromagnetic form factor. The vector mesons introduce a single new leading-order parameter, $a$. For the KSRF value $a=2$, the nonlocal one-loop contribution to the direct photon--pion vertex vanishes at NLO, while the remaining local term is found to be consistent with zero when fixed from the pion charge radius and $ρ$-meson decay data. Vector-meson dominance therefore emerges as a good numerical approximation at this order. The explicit $ρ$ propagator, kept in its resummed form, also reproduces the observed curvature of the form factor more efficiently than vector-meson-less one-loop ChPT. We also present a phenomenological extension of the form factor into the $ρ$ resonance region, using a resummation of the $ρ$ self-energy. The relation to other formulations with explicit vector mesons is also discussed.

hep-ph↗
arXiv2026

First simultaneous analysis of transverse momentum dependent and collinear parton distributions in the proton

We present the first simultaneous global QCD analysis of unpolarized transverse momentum dependent (TMD) and collinear parton distribution functions (PDFs) in the proton. Our study incorporates data from deep-inelastic scattering, Drell-Yan, inclusive weak boson, $W$+\,charm, and jet production involving PDFs, as well as TMD Drell-Yan and $Z$-boson production data from fixed target and collider experiments sensitive to both TMD and collinear distributions. The analysis is performed at next-to-next-to-leading logarithmic accuracy for QCD resummation in TMD observables and next-to-leading order for observables described in collinear factorization. The combined analysis improves knowledge of both TMD and collinear PDFs, particularly in the sea-quark sector, providing a consistent simultaneous description of the aforementioned observables.

hep-ph↗
arXiv2026

Polarization transfer in $ψ'\toψππ$: a complete spin density matrix analysis framework

A theoretical framework based on the Spin Density Matrix (SDM) formalism is developed to describe polarization transfer in the decay chain $e^+e^- \rightarrow ψ^\prime \rightarrow ψππ$. Explicit relations connecting the SDMs of $ψ^\prime$ and $ψ$ are derived, generalizing Cahn's analysis into a complete SDM treatment. For the dominant $S$-wave $ππ$ emission, the SDM is shown to be perfectly preserved, $ρ_ψ= ρ_{ψ^\prime}$, rendering the $ψ$ an ideal probe of the initial polarization state. Deviations arising from $D$-wave contributions are quantified, and a self-consistency experimental test is proposed that simultaneously validates the framework and constrains partial wave amplitudes. This formalism provides a consistent basis for extracting $ψ$ polarization and for amplitude analyses of subsequent $ψ$ decays in a continuum-background-free environment. The framework extends to other hadronic transitions, including $ψ' \to h_cπ^0$ in charmonium and $Υ(nS) \to Υ(mS)ππ$ in bottomonium, as well as to electroweak processes such as $e^+e^- \to Z^\ast \to ZH$, where the same angular-momentum structure governs polarization transfer -- offering a unified probe of dynamics from charmonium to the Higgs sector.

hep-ph↗