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arxiv: 2606.26676 · v1 · pith:KTDWHYTSnew · submitted 2026-06-25 · ✦ hep-ph · gr-qc

Torsional four-fermion interaction for Majorana neutrinos

Indrajit Ghose , Amitabha Lahiri This is my paper

Pith reviewed 2026-06-26 04:39 UTC · model grok-4.3

classification ✦ hep-ph gr-qc
keywords Majorana neutrinosspacetime torsionfour-fermion interactionType I see-sawsterile neutrinosneutrino oscillationsT violationmatter effects
0
0 comments X

The pith

Torsion generated by fermions produces a four-fermion interaction that supplies an extra effective mass to Majorana neutrinos traveling through matter.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that eliminating the torsion field sourced by fermions leaves an effective four-fermion contact interaction. For Majorana neutrinos that obtain their masses through the Type I see-saw, this interaction supplies an additional matter potential beyond the standard electroweak term and permits sterile neutrinos to couple to ordinary matter through the same channel. New mixing angles between the torsion-induced fields and the mass eigenstates are introduced, and the resulting shifts in the neutrino mass matrix are computed analytically for one-sterile plus one-active and one-sterile plus two-active cases, both when the torsion term is diagonal and when it is not. Time-reversal violation is then examined in the two-active-plus-one-sterile scenario under specific choices of those mixing angles. A reader would care because these corrections alter the predicted oscillation probabilities of neutrinos inside dense matter and open a possible window onto gravitational effects at laboratory energies.

Core claim

When neutrinos are Majorana fermions and become massive via the Type I SeeSaw mechanism, the torsional four-fermion interaction contributes an effective mass for neutrinos propagating through matter, similar to the Wolfenstein term, while also allowing sterile neutrinos to interact with all fermions via the torsion-induced term and introducing new mixing parameters between the torsion fields and the mass eigenstates. Analytic expressions for the modified masses and mixings are obtained in the one-sterile plus one or two active neutrino scenarios, both for diagonal and non-diagonal torsional interactions in the mass basis. Time-reversal violation is analyzed in the 2+1 scenario for particular

What carries the argument

The effective four-fermion interaction obtained after eliminating the torsion field generated by fermions.

If this is right

  • The torsional term acts as an extra contribution to the Wolfenstein matter potential felt by neutrinos.
  • Sterile neutrinos acquire direct interactions with all fermions through the torsion channel.
  • New mixing parameters between torsion and mass eigenstates modify the effective mass matrix and therefore the oscillation probabilities.
  • In the 2+1 scenario, certain choices of the torsion-mass mixing produce observable T violation.
  • The size of the corrections depends on whether the torsional interaction is taken diagonal or non-diagonal in the mass basis.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the effect is present, it would link neutrino propagation inside neutron stars or the early universe to an underlying gravitational degree of freedom.
  • Existing global fits to oscillation data could already place bounds on the new torsion-induced mixing angles.
  • The same four-fermion structure might generate analogous matter potentials for charged leptons or quarks if the torsion coupling is universal.
  • Matching the effective operator to a ultraviolet-complete torsion theory would be needed to predict the numerical size of the new parameters.

Load-bearing premise

The torsional four-fermion interaction can be treated as an effective operator that is either diagonal or non-diagonal in the neutrino mass basis, with new mixing parameters between torsion and mass eigenstates introduced without further dynamical justification from the underlying torsion theory.

What would settle it

A precision measurement of neutrino oscillation probabilities in ordinary matter that matches standard electroweak predictions with no additional matter-induced mass shift or T-violating signal in a 2+1 sterile-active model.

read the original abstract

Fermions generate spacetime torsion, which can be eliminated, leaving behind an effective four-fermion interaction. This term will contribute an effective mass for neutrinos propagating through matter, similar to the Wolfenstein term coming from electroweak interactions. When the neutrinos are Majorana fermions and become massive via the Type I SeeSaw mechanism, there can be additional effects due to sterile neutrinos interacting with all fermions via the torsion-induced term, as well as due to the presence of new mixing parameters. We consider different scenarios with one sterile and one or two active neutrinos -- when the torsional interaction is diagonal in the mass basis and when it is not -- and analytically find these modifications. The T violation in the 2+1 scenario is discussed for some specific mixing between the torsion fields and the mass fields.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that eliminating torsion from the Einstein-Cartan action yields an effective four-fermion interaction that contributes an additional matter-induced mass term for Majorana neutrinos realized via the Type-I seesaw. It further asserts that sterile neutrinos and new mixing parameters between torsion and mass eigenstates produce additional modifications to neutrino propagation, with explicit analytic results given for 1+1 and 2+1 scenarios (both diagonal and non-diagonal torsional couplings) and a discussion of T violation in the 2+1 case for selected values of the new mixing angles.

Significance. If the new mixing parameters can be shown to arise dynamically rather than being inserted by hand, the work would identify a torsion-induced contribution to neutrino oscillations that is distinct from the standard Wolfenstein term and could affect T-violating observables in the presence of steriles. The analytic treatment of multiple mixing scenarios is a positive feature, but the absence of a derivation tying the mixing parameters to the underlying torsion theory or seesaw Lagrangian reduces the result to a parameterization study rather than a robust prediction.

major comments (2)
  1. [Abstract and non-diagonal torsional interaction discussion] Abstract and the paragraph introducing the non-diagonal case: the claim that 'new mixing parameters' appear when the torsional interaction is non-diagonal in the mass basis is not accompanied by any derivation showing how these parameters emerge from the Einstein-Cartan action or the Type-I seesaw Lagrangian. The parameters are introduced as free inputs whose values control the reported modifications to propagation and T violation; this renders the central claim dependent on an ad-hoc extension rather than a consequence of the torsion theory.
  2. [2+1 scenario T-violation discussion] Discussion of the 2+1 scenario: the T-violation results are presented only for 'some specific mixing between the torsion fields and the mass fields.' Because these mixing angles are unconstrained by the underlying action, the reported T-violating effects are not generic predictions but depend on the arbitrary choice of the mixing parameters; a concrete mapping from the axial-current coupling of torsion to the mass-basis mixing matrix is required to establish that the effects survive.
minor comments (2)
  1. The explicit form of the torsional four-fermion Lagrangian after integrating out the torsion field is not displayed; including it (with the standard axial-current coupling) would clarify the starting point for both the diagonal and non-diagonal cases.
  2. Consistency checks against the known limit of vanishing torsion coupling or recovery of the standard Wolfenstein term when steriles decouple are not shown; adding these would strengthen the presentation.

Simulated Author's Rebuttal

2 responses · 2 unresolved

We appreciate the referee's thorough review and constructive feedback on our manuscript. We address each major comment below. Our analysis is primarily phenomenological in exploring the effects of possible non-diagonal torsional couplings.

read point-by-point responses

  1. Referee: Abstract and the paragraph introducing the non-diagonal case: the claim that 'new mixing parameters' appear when the torsional interaction is non-diagonal in the mass basis is not accompanied by any derivation showing how these parameters emerge from the Einstein-Cartan action or the Type-I seesaw Lagrangian. The parameters are introduced as free inputs whose values control the reported modifications to propagation and T violation; this renders the central claim dependent on an ad-hoc extension rather than a consequence of the torsion theory.

    Authors: We agree that no derivation is provided for how the mixing parameters between the torsional interaction and the mass eigenstates arise from the Einstein-Cartan action or the Type-I seesaw. These parameters are introduced to parameterize the possibility of non-diagonal couplings in the effective four-fermion interaction when expressed in the mass basis. The manuscript explores the resulting modifications to neutrino propagation and T violation under this assumption. We will update the abstract and introduction to make this parameterization explicit and avoid implying a derivation from the fundamental theory. revision: partial

  2. Referee: Discussion of the 2+1 scenario: the T-violation results are presented only for 'some specific mixing between the torsion fields and the mass fields.' Because these mixing angles are unconstrained by the underlying action, the reported T-violating effects are not generic predictions but depend on the arbitrary choice of the mixing parameters; a concrete mapping from the axial-current coupling of torsion to the mass-basis mixing matrix is required to establish that the effects survive.

    Authors: The T-violation discussion is limited to specific mixing angles to illustrate that T-violating effects can occur in the 2+1 scenario with non-diagonal torsional couplings. We concur that without a mapping from the axial-current coupling in the torsion interaction to the mixing matrix in the mass basis, these effects are not shown to be generic. The paper does not derive such a mapping, focusing instead on the analytic expressions for the propagation. This is a genuine limitation of the present work. revision: no

standing simulated objections not resolved
  • Derivation of the mixing parameters from the Einstein-Cartan action or Type-I seesaw Lagrangian
  • Concrete mapping from the axial-current coupling of torsion to the mass-basis mixing matrix for the T-violation effects

Circularity Check

1 steps flagged

New mixing parameters between torsion fields and mass eigenstates introduced by hand; T-violation effects computed from these free inputs

specific steps
  1. fitted input called prediction [Abstract]
    "When the neutrinos are Majorana fermions and become massive via the Type I SeeSaw mechanism, there can be additional effects due to sterile neutrinos interacting with all fermions via the torsion-induced term, as well as due to the presence of new mixing parameters. We consider different scenarios with one sterile and one or two active neutrinos -- when the torsional interaction is diagonal in the mass basis and when it is not -- and analytically find these modifications. The T violation in the 2+1 scenario is discussed for some specific mixing between the torsion fields and the mass fields."

    The modifications and T-violation results are obtained by assuming the interaction can be non-diagonal and then inserting new mixing parameters between torsion and mass eigenstates. These parameters function as free inputs whose specific values directly determine the computed effects; no equation or derivation in the paper shows they emerge from the underlying torsion theory, making the 'predictions' equivalent to calculations with chosen inputs.

full rationale

The paper's central results on modifications to neutrino propagation and T violation rely on introducing additional free mixing parameters when the torsional four-fermion interaction is taken to be non-diagonal in the mass basis. These parameters are not derived from the Einstein-Cartan action, the SeeSaw mechanism, or any dynamical principle stated in the paper; instead, specific values are chosen and the effects are then calculated analytically. This makes the reported T violation a direct consequence of the chosen inputs rather than an independent prediction. The diagonal case avoids this issue, but the non-diagonal scenarios that generate the new claims reduce to the inserted parameters. No self-citation chain or renaming is involved, but the load-bearing step qualifies as a fitted-input-called-prediction pattern.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The work rests on the standard assumption that torsion can be integrated out to a local four-fermion operator, the Type I SeeSaw for Majorana masses, and the introduction of new mixing parameters between torsion and mass bases; no new particles or forces are postulated beyond the sterile neutrinos already required by SeeSaw.

free parameters (1)
  • mixing parameters between torsion and mass fields
    Introduced to parameterize the coupling of the torsional interaction to the mass eigenstates in the 2+1 scenarios.
axioms (2)
  • domain assumption Fermions generate spacetime torsion which can be eliminated leaving an effective four-fermion interaction
    Foundational step stated in the first sentence of the abstract.
  • domain assumption Neutrinos are Majorana fermions acquiring mass via the Type I SeeSaw mechanism
    Required for the additional effects from sterile neutrinos to appear.

pith-pipeline@v0.9.1-grok · 5660 in / 1381 out tokens · 39854 ms · 2026-06-26T04:39:15.936071+00:00 · methodology

discussion (0)

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