arxiv: 2605.06362 · v1 · submitted 2026-05-07 · ✦ hep-ph

Recognition: unknown

Towards Precision Neutrino Fits in GUTs: Relevance of One-Loop Finite Corrections

Chee Sheng Fong , Shaikh Saad

Authors on Pith no claims yet

Pith reviewed 2026-05-08 08:27 UTC · model grok-4.3

classification ✦ hep-ph

keywords SO(10) GUTneutrino mass matrixone-loop correctionsfermion mass fitsradiative effectsmixing anglesgrand unification

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The pith

One-loop finite corrections shift neutrino masses and mixings by 30-40% in minimal SO(10) GUTs.

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

The paper performs a dedicated analysis of fermion mass fits in the minimal SO(10) grand unified theory by incorporating one-loop finite corrections to the neutrino mass matrix. It shows that parameter regions reproducing all fermion masses and mixings at tree level produce significant deviations once these corrections are included. Because the same Yukawa parameters govern quarks, charged leptons, and neutrinos, the effects propagate across sectors in a correlated manner. The work argues that these changes reach 30-40% and cannot be neglected given current and future neutrino oscillation precision.

Core claim

In the minimal SO(10) GUT the same set of Yukawa parameters simultaneously governs quark masses, charged lepton masses, and neutrino properties. Incorporating one-loop finite corrections to the neutrino mass matrix causes regions that successfully fit data at tree level to yield deviations of order 30-40% in neutrino masses and leptonic mixing parameters. These radiative corrections propagate across all fermion sectors and reshape the viable parameter space in a highly non-trivial way.

What carries the argument

One-loop finite corrections to the neutrino mass matrix, computed from the Yukawa interactions of the minimal SO(10) model and applied to tree-level successful fits.

If this is right

Tree-level fitting procedures alone are insufficient for precision neutrino data and can misidentify viable regions.
Radiative corrections must be included to obtain reliable predictions for neutrino observables in SO(10) models.
The correlated propagation of corrections across quark and lepton sectors imposes tighter constraints on the shared Yukawa parameters.
Ongoing and future neutrino experiments will be sensitive to these loop-induced deviations at the reported size.

Where Pith is reading between the lines

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

Similar loop corrections should be examined in non-minimal SO(10) variants or other GUTs to check if the 30-40% scale persists.
Threshold effects at the GUT scale could combine with these finite corrections to alter the overall shift pattern.
Cross-checks using precise quark and charged-lepton mass data might independently constrain the size of the neutrino-sector corrections.

Load-bearing premise

The computed one-loop finite corrections accurately capture the dominant radiative effects, and higher-order or threshold corrections do not substantially reduce the reported 30-40% deviations.

What would settle it

A full two-loop calculation showing that higher-order terms largely cancel the one-loop shifts, or a precision neutrino experiment finding mixing angles and mass-squared differences that match tree-level predictions to within 10% accuracy.

Figures

Figures reproduced from arXiv: 2605.06362 by Chee Sheng Fong, Shaikh Saad.

**Figure 1.** Figure 1: Xii defined in eq. (2.9) as a function of Mi . The black horizontal dashed line indicates unity while the vertical dashed lines show three representative values: Mi = {104 , 1012 , 1014} GeV with their respective Xii values in percentage. 2.1 One-loop finite corrections to the neutrino masses In the right-handed neutrino Ni mass diagonal basis, the one-loop corrected neutrino mass matrix takes the followin… view at source ↗

**Figure 2.** Figure 2: The evolution of neutrino masses and mixing angles under RGE from the GUT scale down to the MZ scale where the dashed (solid) lines correspond to BM I (BM II). Importance of One-Loop Corrections Observable tree-level One-loop Relative change (%) m1 (meV) 4.15 × 10−5 2.83 × 10−5 −31.8 m2 (meV) 8.65 × 10−3 7.22 × 10−3 −16.5 m3 (meV) 5.04 × 10−2 3.49 × 10−2 −30.6 θ12 (deg) 33.57 32.68 −2.64 θ23 (deg) 48.34 50… view at source ↗

read the original abstract

In this work, we perform a dedicated analysis of fermion mass fits in the minimal $SO(10)$ grand unified theory (GUT), going beyond the tree-level approximation by incorporating one-loop finite corrections to the neutrino mass matrix. We show that parameter regions that successfully reproduce all fermion masses and mixings at tree level can lead to significant deviations in neutrino masses and leptonic mixing parameters once the radiative corrections are included. These results expose a limitation of conventional tree-level fitting procedures and highlight the sensitivity of neutrino observables to loop effects. Since in the minimal $SO(10)$ GUT the same set of Yukawa parameters simultaneously governs quark masses, charged lepton masses, and neutrino properties, these radiative corrections propagate across all fermion sectors, reshaping the viable parameter space in a highly non-trivial and correlated manner. We find that the largest corrections to the masses and mixing angles are of order $\mathcal{O}(30\%)$-$\mathcal{O}(40\%)$, therefore, cannot be neglected. In light of the current precision of neutrino oscillation measurements, and the expected improvements from ongoing and future experiments, we demonstrate that the inclusion of one-loop effects is essential for a consistent and reliable exploration of the parameter space, with important implications for the predictivity of $SO(10)$ GUTs.

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.

Desk Editor's Note private letter to a colleague

One-loop finite corrections can shift neutrino parameters by 30-40% in minimal SO(10) fits, but the paper leaves open whether GUT-scale thresholds dominate or cancel those shifts.

read the letter

The main thing to know is that the authors run numerical fits showing tree-level successful regions in minimal SO(10) produce O(30-40%) changes to neutrino masses and mixings once one-loop finite pieces are added, and they argue this forces a rethink of standard fitting procedures because the same Yukawas feed all fermion sectors. They do a clean job of illustrating the correlated impact across quarks, charged leptons, and neutrinos, which is a useful reminder that tree-level approximations are getting too crude for current neutrino data precision. The numerical demonstration itself is the clearest new element beyond the usual references to tree-level SO(10) work. On the soft spots, the result hinges on treating the computed one-loop finite corrections as the dominant radiative contribution that must be kept. The stress-test concern holds up here: the paper does not appear to demonstrate that threshold corrections from integrating out the heavy 126, 210, and 45 fields are parametrically smaller or have been consistently subtracted in the matching. If those thresholds are O(1), the quoted deviations could shrink or flip sign, weakening the claim that loops are essential. The abstract and visible numerics are also thin on the exact fitting procedure, chosen parameter ranges, and how errors are propagated, so it is difficult to judge how generic the 30-40% figure really is. This paper is for people already doing SO(10) or similar GUT fermion fits who want to see the size of loop effects quantified. A reader in that niche gets value from the concrete example even if they disagree on the thresholds. It deserves a serious referee because the question is legitimate, the method is standard, and the potential impact on model predictivity is real, though revisions on the effective-theory matching will be needed.

Referee Report

1 major / 1 minor

Summary. The manuscript performs a dedicated analysis of fermion mass fits in the minimal SO(10) GUT, incorporating one-loop finite corrections to the neutrino mass matrix beyond the tree-level approximation. It shows that parameter regions reproducing all fermion masses and mixings at tree level can produce O(30-40%) deviations in neutrino masses and leptonic mixing angles once radiative corrections are included, with these effects propagating across sectors due to shared Yukawa parameters. The central claim is that such corrections cannot be neglected and that one-loop effects are essential for consistent and reliable parameter-space exploration given current and future neutrino precision.

Significance. If the reported deviations are robust and the one-loop finite pieces dominate the radiative contributions, the work would demonstrate a clear limitation of conventional tree-level fitting procedures in SO(10) models and strengthen the case for including loops in precision GUT phenomenology. The correlated treatment across quark, charged-lepton, and neutrino sectors is a positive feature.

major comments (1)

[§4] §4 (numerical results and fits): The headline claim that one-loop finite corrections produce O(30-40%) shifts that 'cannot be neglected' and are 'essential' rests on treating these finite pieces as the dominant radiative effect. No quantitative estimate or subtraction is shown demonstrating that GUT-scale threshold corrections (from integrating out the 126, 210, and 45 Higgs representations) are parametrically smaller than the quoted deviations; if thresholds are O(1), the reported shifts could be artifacts of an incomplete effective theory rather than a requirement for precision fits.

minor comments (1)

[Abstract] The abstract states the O(30-40%) figure without referencing the specific parameter point, fitting procedure, or error analysis used to obtain it; a brief pointer to the relevant table or figure would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We provide a point-by-point response to the major comment below.

read point-by-point responses

Referee: [§4] §4 (numerical results and fits): The headline claim that one-loop finite corrections produce O(30-40%) shifts that 'cannot be neglected' and are 'essential' rests on treating these finite pieces as the dominant radiative effect. No quantitative estimate or subtraction is shown demonstrating that GUT-scale threshold corrections (from integrating out the 126, 210, and 45 Higgs representations) are parametrically smaller than the quoted deviations; if thresholds are O(1), the reported shifts could be artifacts of an incomplete effective theory rather than a requirement for precision fits.

Authors: We appreciate the referee highlighting the need to assess GUT-scale threshold corrections from the heavy Higgs representations. Our analysis is restricted to the one-loop finite corrections in the effective theory below the GUT scale, computed from the tree-level Yukawa parameters that fit the fermion masses and mixings. These finite pieces constitute additional, calculable contributions that must be included on top of any tree-level or threshold-corrected result. We do not assert that the finite corrections dominate over thresholds; rather, we show that they induce O(30-40%) shifts in neutrino observables, demonstrating that they cannot be omitted for precision work. A quantitative subtraction of thresholds would require a full specification of the heavy mass spectrum, which is not uniquely fixed in the minimal SO(10) model and lies beyond the present scope. We have added a clarifying paragraph in §4 acknowledging this limitation and noting that both classes of corrections should ultimately be considered together. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation of loop corrections

full rationale

The paper computes one-loop finite corrections to the neutrino mass matrix from the minimal SO(10) GUT Lagrangian and applies them to tree-level fermion mass fits that reproduce quark, charged-lepton, and neutrino data. The reported O(30-40%) shifts in neutrino masses and mixings are direct numerical outcomes of these diagrams evaluated at the fitted points, not quantities fitted or defined in terms of the final observables. No self-definitional steps, fitted inputs relabeled as predictions, or load-bearing self-citations appear in the abstract or central claims. The derivation remains an independent perturbative calculation whose result is falsifiable against external neutrino data.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract provides no explicit list of free parameters or axioms beyond the general minimal SO(10) framework; Yukawa couplings are mentioned as shared across sectors but not enumerated.

free parameters (1)

Yukawa coupling parameters
Shared parameters fitted simultaneously to quark, charged lepton, and neutrino data.

axioms (1)

domain assumption Minimal SO(10) GUT with standard Higgs representations
Assumes the conventional minimal SO(10) setup where all fermions reside in the 16 representation.

pith-pipeline@v0.9.0 · 5527 in / 1210 out tokens · 42151 ms · 2026-05-08T08:27:13.625794+00:00 · methodology

discussion (0)

Reference graph

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