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arxiv: 2601.19141 · v3 · submitted 2026-01-27 · ✦ hep-ph · hep-th· nucl-th

Origin of the nucleon gravitational form factor B_N(t): Exposition in light-front holographic QCD

Xianghui Cao , Bheemsehan Gurjar , Chandan Mondal , Chen Chen , Yang Li This is my paper

Pith reviewed 2026-05-16 11:18 UTC · model grok-4.3

classification ✦ hep-ph hep-thnucl-th
keywords nucleon gravitational form factorB_N(t)light-front holographic QCDform factor suppressionS-wave nucleonlongitudinal dynamics
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0 comments X

The pith

The nucleon's gravitational form factor B_N(t) stays small at finite t due to a cancellation from an antisymmetric factor in its light-front wave functions.

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

This paper establishes that the observed smallness of B_N(t) in the nucleon stems from a basic cancellation inside its wave functions modeled in light-front holographic QCD. An antisymmetric piece in the longitudinal momentum sharing makes the relevant integral for the form factor disappear completely when the wave functions are symmetric between quarks. With the realistic, S-wave dominated nucleon structure, the cancellation is not perfect but still strong enough to keep B_N(t) suppressed over a range of momentum transfers. The result offers a dynamical explanation for why this form factor can often be ignored in calculations such as near-threshold charmonium production, on top of its vanishing at zero momentum transfer.

Core claim

Using light-front holographic QCD, the gravitational form factor B_N(t) is shown to be controlled by an antisymmetric factor arising from the longitudinal dynamics of the nucleon's light-front wave functions; this factor forces B_N(t) to vanish exactly in the symmetric limit and produces substantial suppression for the physical, S-wave dominated nucleon.

What carries the argument

Antisymmetric factor in the longitudinal dynamics of the light-front holographic QCD wave functions, which produces the cancellation in the expression for B_N(t).

If this is right

  • B_N(t) vanishes exactly when the nucleon's longitudinal wave functions are symmetric.
  • The small value of B_N(t) signals the dominance of S-wave components in the nucleon.
  • This cancellation justifies setting B_N(t) to zero in many phenomenological applications such as near-threshold J/ψ production.

Where Pith is reading between the lines

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

  • If the same longitudinal antisymmetry appears in other holographic models, similar suppressions should appear for other hadrons.
  • Relaxing the S-wave assumption while keeping the holographic framework could quantify how higher partial waves lift the suppression.
  • Direct lattice calculations at moderate t could test whether the predicted suppression matches the wave-function origin proposed here.

Load-bearing premise

The light-front holographic QCD wave functions correctly capture the dominant S-wave character and longitudinal momentum sharing inside the physical nucleon.

What would settle it

A direct computation of B_N(t) from lattice QCD or a different model that yields a large value despite using symmetric or S-wave dominated wave functions would contradict the cancellation mechanism.

Figures

Figures reproduced from arXiv: 2601.19141 by Bheemsehan Gurjar, Chandan Mondal, Chen Chen, Xianghui Cao, Yang Li.

Figure 1
Figure 1. Figure 1: FIG. 1. The gravitational form factor [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The longitudinal wave function [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Different partial waves of the longitudinal wave func [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Gravitational form factor [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

Recent lattice QCD simulations and phenomenological models indicate that the nucleon's gravitational form factor $B_N(t)$ remains remarkably small at finite momentum transfer $t$. While $B_N(0) = 0$ is a known consequence of the equivalence principle, the physical origin of its suppression at finite $t$ has not been fully elucidated. In this work, we demonstrate that the smallness of $B_N(t)$ arises from a fundamental cancellation within the nucleon's wave functions. Using light-front holographic QCD, we show that $B_N(t)$ is governed by an antisymmetric factor in the longitudinal dynamics that leads to the exact vanishing of the form factor in the symmetric limit and significant suppression for realistic nucleon structures. Our results suggest that the smallness of $B_N(t)$ is a signature of the nucleon's dominant S-wave character, providing a formal justification for its frequent omission in practical applications like near-threshold $J/\psi$ production.

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 / 1 minor

Summary. The manuscript claims that the smallness of the nucleon gravitational form factor B_N(t) at finite momentum transfer arises from a cancellation within the nucleon's light-front wave functions in light-front holographic QCD. An antisymmetric factor in the longitudinal momentum fraction x enforces exact vanishing of B_N(t) in the symmetric limit and strong suppression for realistic structures, which the authors interpret as a direct signature of the nucleon's dominant S-wave character and a justification for omitting B_N(t) in applications such as near-threshold J/ψ production.

Significance. If the central mechanism holds, the work supplies a structural explanation, rooted in the symmetry properties of holographic wave functions, for the suppression of B_N(t) reported by lattice QCD. This would strengthen the theoretical basis for neglecting the form factor in phenomenological calculations and illustrate how light-front holographic QCD can generate emergent cancellations without additional tuning.

major comments (2)
  1. [§3] The explicit integral or matrix-element derivation demonstrating that the antisymmetric longitudinal factor produces exact cancellation of B_N(t) is not shown; the abstract and main text assert the result follows directly from the wave-function symmetry, yet no intermediate steps, numerical evaluation of the form factor, or comparison to lattice data are provided to verify the suppression beyond internal model consistency.
  2. [§4] The cancellation is demonstrated only within the specific holographic longitudinal ansatz (soft-wall or hard-wall potential plus spin structure). No test is performed under deformations of the longitudinal profile or against non-holographic light-front wave functions, leaving open whether the suppression is a general consequence of S-wave dominance or an artifact of the chosen parametrization.
minor comments (1)
  1. Notation for the longitudinal momentum fraction and the precise definition of the symmetric limit should be stated explicitly at first use to aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major point below and have revised the paper to incorporate explicit derivations and additional discussion as requested.

read point-by-point responses

  1. Referee: [§3] The explicit integral or matrix-element derivation demonstrating that the antisymmetric longitudinal factor produces exact cancellation of B_N(t) is not shown; the abstract and main text assert the result follows directly from the wave-function symmetry, yet no intermediate steps, numerical evaluation of the form factor, or comparison to lattice data are provided to verify the suppression beyond internal model consistency.

    Authors: We agree that the explicit steps were not sufficiently detailed. In the revised manuscript we have added the full integral expression for the gravitational form factor B_N(t) in Section 3, showing how the antisymmetric longitudinal factor (x - 1/2) produces exact cancellation when the transverse wave function is symmetric. We also include numerical evaluations of B_N(t) for the soft-wall and hard-wall holographic wave functions and a direct comparison to existing lattice QCD results, confirming the strong suppression at finite t. revision: yes

  2. Referee: [§4] The cancellation is demonstrated only within the specific holographic longitudinal ansatz (soft-wall or hard-wall potential plus spin structure). No test is performed under deformations of the longitudinal profile or against non-holographic light-front wave functions, leaving open whether the suppression is a general consequence of S-wave dominance or an artifact of the chosen parametrization.

    Authors: The analysis is performed within light-front holographic QCD, where the longitudinal profile is fixed by the holographic potential and the dominant S-wave spin structure naturally generates the required antisymmetry. We have added a clarifying paragraph noting that the cancellation is tied to this S-wave character rather than fine details of the potential; while systematic deformations or comparisons to non-holographic models lie outside the present scope, the result follows directly from the symmetry properties enforced by the holographic framework. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation follows from holographic wave-function symmetry

full rationale

The paper constructs B_N(t) from light-front holographic QCD wave functions whose longitudinal dependence contains an antisymmetric factor by the model's AdS/QCD ansatz. The exact cancellation in the symmetric limit and suppression at finite t follow directly from that structural property applied to the gravitational form-factor overlap integral. No equation reduces to a fitted parameter that was tuned to B_N(t) itself, no self-citation supplies the uniqueness of the antisymmetry, and the wave functions are not redefined in terms of the target observable. The result is therefore a genuine model consequence rather than a tautology.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the light-front holographic QCD framework whose wave functions encode the longitudinal dynamics; these wave functions are constructed from a combination of standard light-front quantization and holographic mapping whose parameters are typically adjusted to nucleon data.

free parameters (1)
  • holographic scale parameter
    Standard parameter in light-front holographic QCD that sets the overall size of the nucleon wave function and is fitted to observables such as the nucleon mass or electromagnetic form factors.
axioms (1)
  • domain assumption Light-front holographic QCD supplies a faithful representation of the nucleon’s dominant S-wave longitudinal dynamics
    Invoked when the paper attributes the suppression directly to the antisymmetric factor present in the model wave functions.

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Forward citations

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