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arxiv: 1907.03557 · v1 · pith:NSF3QTZZnew · submitted 2019-07-01 · ⚛️ physics.gen-ph

Lattice QCD Method To Study Proton Decay

Gouranga C Nayak This is my paper

Pith reviewed 2026-05-25 11:30 UTC · model grok-4.3

classification ⚛️ physics.gen-ph
keywords proton decaylattice QCDnon-perturbative matrix elementpath integralbaryon number violationgrand unified theories
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The pith

A first-principles formula for the proton decay matrix element is derived in QCD so lattice methods can compute it directly.

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

The paper derives an expression for the proton decay matrix element by starting from the QCD path integral and inserting the relevant operator between proton states. This quantity is non-perturbative and therefore inaccessible to ordinary perturbative calculations. The resulting formula is written so that it can be discretized and evaluated numerically on a spacetime lattice. A sympathetic reader would care because an accurate lattice value would let theorists convert experimental lower bounds on proton lifetime into direct constraints on grand-unified models without additional model-dependent assumptions about strong-interaction effects.

Core claim

The proton decay matrix element is expressed as a non-perturbative correlation function obtained by inserting the dimension-six baryon-number-violating operator into the QCD path integral and taking the appropriate matrix element between proton states; the resulting object is presented in a form that can be evaluated by standard lattice QCD techniques.

What carries the argument

The QCD path integral with the proton decay operator inserted between initial and final proton states, discretized on the lattice.

If this is right

  • The matrix element becomes a standard lattice QCD observable that can be computed with existing Monte Carlo methods.
  • Proton lifetime predictions in grand unified theories can incorporate the full non-perturbative QCD contribution.
  • Uncertainties associated with perturbative matching of the decay operator are removed from the calculation.
  • Direct comparison with the experimental lower limit of roughly 10^34 years becomes possible once the lattice number is obtained.

Where Pith is reading between the lines

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

  • The same path-integral construction could be applied to other dimension-six operators that violate baryon or lepton number.
  • Numerical implementation would still require separate control of lattice artifacts, finite-volume corrections, and operator mixing that the paper does not address.
  • If the lattice result differs significantly from older model estimates, it would tighten or loosen the exclusion reach of proton-decay searches for specific grand-unified models.

Load-bearing premise

The proton decay operator can be placed inside the QCD path integral and discretized on the lattice without extra renormalization or effective-field-theory matching steps.

What would settle it

A lattice computation performed with the derived formula that produces a matrix element diverging as the lattice spacing is taken to zero or failing to match any independent non-perturbative estimate would show the formula cannot be used as claimed.

read the original abstract

The proton decay has not been experimentally observed with the lower limit of the proton lifetime being $\gtrsim 10^{34}$ years which is more than the age of the universe. One of the important quantity that appears in the study of the proton decay is the proton decay matrix element which is a non-perturbative quantity in QCD which cannot be calculated by using the perturbative QCD (pQCD) method but it can be calculated by using the lattice QCD method. In this paper we formulate the lattice QCD method to study the proton decay matrix element. We derive the non-perturbative formula of the proton decay matrix element from the first principle in QCD which can be calculated by using the lattice QCD method.

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 to derive a non-perturbative formula for the proton decay matrix element directly from first principles in QCD, asserting that this quantity (inaccessible to perturbative QCD) can be computed using lattice QCD methods. The abstract highlights the experimental lower bound on proton lifetime and positions the work as formulating the lattice approach for this matrix element.

Significance. A complete, first-principles lattice formula for the proton decay matrix element, if it includes all necessary steps for a numerical result, would be significant for constraining GUT models via proton lifetime predictions. The manuscript receives no credit for machine-checked proofs, reproducible code, or falsifiable predictions, as none are present.

major comments (2)
  1. [Abstract] Abstract: the claim of a derivation 'from the first principle in QCD' is unsupported; no explicit formula, lattice action, operator definition, or correlator is provided, so the central claim lacks any visible derivation or data.
  2. [Main text] Main derivation (throughout): the approach assumes the dimension-6 proton decay operator can be directly inserted into the QCD path integral and discretized without EFT matching to the lattice regularization or non-perturbative renormalization (e.g., to RI/MOM), rendering the formula formal rather than a complete calculational method.
minor comments (2)
  1. The manuscript would benefit from explicit comparison to existing lattice QCD literature on four-fermion operators for proton decay.
  2. Consider re-submission to a specialized journal such as Phys. Rev. D or JHEP rather than physics.gen-ph.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed report. We address the major comments point by point below. Our manuscript formulates the lattice QCD approach to the proton decay matrix element by deriving a non-perturbative expression from the QCD path integral; we will revise to make the derivation more explicit and to discuss practical implementation steps.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim of a derivation 'from the first principle in QCD' is unsupported; no explicit formula, lattice action, operator definition, or correlator is provided, so the central claim lacks any visible derivation or data.

    Authors: The main text derives the matrix element by inserting the dimension-6 operator into the QCD path integral and expressing the result as a three-point correlation function between proton interpolators and the decay operator. We acknowledge that the presentation in the submitted version is concise and does not spell out the lattice discretization or the explicit correlator form. We will revise the manuscript to include the explicit continuum formula, the lattice operator definition, and the correlator to be computed numerically. revision: yes

  2. Referee: [Main text] Main derivation (throughout): the approach assumes the dimension-6 proton decay operator can be directly inserted into the QCD path integral and discretized without EFT matching to the lattice regularization or non-perturbative renormalization (e.g., to RI/MOM), rendering the formula formal rather than a complete calculational method.

    Authors: The derivation begins in the continuum and yields a formal expression that is directly amenable to lattice discretization. We agree that a production calculation requires non-perturbative renormalization (e.g., RI/MOM) and matching to the lattice scheme; these steps are standard but lie beyond the scope of the present formulation paper. We will add a dedicated paragraph outlining the required renormalization procedure and the connection to existing lattice techniques for four-fermion operators. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation is a standard path-integral formulation

full rationale

The paper claims to derive a non-perturbative formula for the proton decay matrix element from first principles in QCD for direct lattice evaluation. No equations, self-citations, or steps are present that reduce the claimed result to a fitted parameter, self-definition, or load-bearing prior result by the same authors. The central expression is the conventional QCD path-integral representation of the matrix element, which is independent of the target numerical value and does not rely on renormalization or matching steps being omitted as a definitional trick. This is the most common honest finding for formal lattice-QCD setup papers.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper rests on the standard assumptions of QCD as the theory of strong interactions and on the validity of lattice regularization for non-perturbative quantities; no new free parameters, axioms, or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption QCD is the correct low-energy theory for strong interactions
    Invoked implicitly when stating that the matrix element is a non-perturbative QCD quantity.
  • standard math Lattice discretization provides a valid non-perturbative regularization of QCD
    Required for the claim that the derived formula can be evaluated on the lattice.

pith-pipeline@v0.9.0 · 5634 in / 1268 out tokens · 27366 ms · 2026-05-25T11:30:59.790938+00:00 · methodology

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Reference graph

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