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arxiv: 2506.04370 · v2 · submitted 2025-06-04 · ✦ hep-ph · gr-qc· hep-ex

Dark Matter Induced Proton Decays

Ranjeet Kumar , Rahul Srivastava This is my paper

Pith reviewed 2026-05-19 10:36 UTC · model grok-4.3

classification ✦ hep-ph gr-qchep-ex
keywords proton decaydark matterZ4 symmetryB+L symmetryleptoquarksone-loop processesdark sector mediators
0
0 comments X p. Extension

The pith

Proton decay occurs at one loop mediated by dark matter particles through a residual Z4 symmetry

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

The paper proposes that proton decay and dark matter stability arise from the same spontaneous breaking of a global U(1)B+L symmetry. This breaking leaves behind a Z4 symmetry that keeps dark matter stable while blocking proton decay at tree level. Proton decay therefore appears only at one loop, with dark sector particles as mediators. The proton lifetime scales directly with the dark matter mass, so that heavier dark matter makes the proton more stable. Mediator masses around the TeV scale remain allowed by present lifetime limits and could appear in collider searches as leptoquarks carrying exotic B+L charges.

Core claim

Spontaneous breaking of the global U(1)B+L symmetry yields a residual Z4 symmetry. This Z4 symmetry guarantees dark matter stability and forbids proton decay at tree level, so decay occurs only at one loop through dark-sector particles. The proton lifetime is thereby linked to the dark matter mass, with larger dark matter masses corresponding to longer proton lifetimes. Mediator masses of order TeV remain consistent with current experimental bounds on proton decay.

What carries the argument

Residual Z4 symmetry produced by spontaneous breaking of global U(1)B+L, which stabilizes dark matter while restricting proton decay to one-loop mediation by dark sector particles

Load-bearing premise

The spontaneous breaking of the global U(1)B+L symmetry produces a residual Z4 symmetry that simultaneously ensures dark matter stability and forbids proton decay at tree level.

What would settle it

A measured proton lifetime that fails to increase with increasing dark matter mass, or the absence of the predicted exotic-B+L leptoquark signals at TeV energies in collider data

Figures

Figures reproduced from arXiv: 2506.04370 by Rahul Srivastava, Ranjeet Kumar.

Figure 1
Figure 1. Figure 1: FIG. 1: The diagrams depict the stability of the DM candidate under residual [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Proton decay at one-loop level mediated by new dark sector particles, where [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Correlation between the proton lifetime [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Representative Feynman diagrams illustrating loop-level (a, conserved [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The relic density as a function of DM mass [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: The variation of the spin-independent WIMP–nucleon cross section with respect to [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Feynman diagrams depicting the pair production of leptoquark [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Production cross section of leptoquark [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Three-body and two-body decay modes of the leptoquark [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Three-body decay width of [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Two-body decay width of [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Branching ratios of [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Leading-order Feynman diagrams for the pair production of the heavy charged [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Production cross section of the heavy charged lepton [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: Four-body and two-body decay modes of the heavy charged lepton [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: Decay width of [PITH_FULL_IMAGE:figures/full_fig_p017_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17: One-loop Feynman diagram for proton decay via new dark sector particles in the [PITH_FULL_IMAGE:figures/full_fig_p019_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18: One-loop calculation of proton decay, where [PITH_FULL_IMAGE:figures/full_fig_p020_18.png] view at source ↗
read the original abstract

We propose a novel theoretical framework in which proton decay is induced by the dark matter. While proton decay requires violation of the $B+L$ symmetry, dark matter stability often relies on the presence of an unbroken symmetry. These seemingly distinct phenomena are unified through the global $U(1)_{B+L}$ symmetry inherent in the Standard Model. Its spontaneous breaking leads to a residual $Z_4$ symmetry, which ensures dark matter stability and forbids proton decay at tree level. Consequently, proton decay occurs at the one-loop level, mediated by dark sector particles. The proton lifetime is linked with the dark matter, the heavier dark matter mass enhancing proton stability, and vice versa. The $\mathcal{O}$(TeV) masses of the mediators remain consistent with current proton lifetime limits, making them accessible to experimental searches. In particular, the leptoquark mediating proton decay, carrying exotic $B+L$ charges, leads to a distinctive signature in collider searches. By intertwining proton decay, dark matter stability, and collider phenomenology, this framework offers distinctive signatures that can be probed in current and future experiments.

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 proposes a novel theoretical framework in which proton decay is induced by dark matter. Spontaneous breaking of the global U(1)_{B+L} symmetry leaves a residual Z_4 symmetry that stabilizes the dark matter candidate while forbidding proton decay at tree level, allowing it only at one-loop level mediated by dark-sector particles. The proton lifetime is linked to the dark matter mass such that heavier dark matter enhances stability, with O(TeV) mediator masses remaining consistent with current limits; the exotic-B+L leptoquark yields distinctive collider signatures.

Significance. If the symmetry mechanism and loop-level suppression hold, the work provides a concrete link between dark matter stability and baryon-number violation, yielding falsifiable predictions that tie the proton lifetime directly to the dark matter mass and point to TeV-scale mediators accessible at current colliders. This unified approach offers new search strategies and could guide model building in beyond-Standard-Model physics.

major comments (2)
  1. [§3] §3 (Symmetry Breaking and Residual Z_4): The central claim that the unbroken Z_4 forbids all tree-level B+L-violating operators (e.g., dimension-6 four-fermion terms) while permitting the claimed one-loop diagrams requires explicit verification. The manuscript must list the Z_4 charges of the dark-sector mediators, the exotic-B+L leptoquark, and the DM candidate, then enumerate all relevant operators to confirm none are Z_4-neutral at tree level. Without this, the prohibition of tree-level decay and the resulting lifetime-DM-mass correlation remain unestablished.
  2. [§4] §4 (One-Loop Proton Decay): The statement that the proton lifetime is linked to the dark matter mass, with heavier DM enhancing stability, is presented qualitatively. No explicit one-loop diagrams, Feynman rules, or decay-width formula (e.g., relating Γ_p to mediator masses and DM mass) are shown, nor are numerical lifetime predictions provided to demonstrate consistency with current bounds for O(TeV) mediators. This quantitative link is load-bearing for the main phenomenological claim.
minor comments (1)
  1. [Abstract] The abstract states 'the heavier dark matter mass enhancing proton stability, and vice versa' without specifying the functional dependence; a brief qualifier on the scaling would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and valuable comments on our manuscript. The suggestions help to clarify the key aspects of our proposed framework. We address each major comment below and have made revisions to the manuscript to incorporate the requested details.

read point-by-point responses

  1. Referee: [§3] §3 (Symmetry Breaking and Residual Z_4): The central claim that the unbroken Z_4 forbids all tree-level B+L-violating operators (e.g., dimension-6 four-fermion terms) while permitting the claimed one-loop diagrams requires explicit verification. The manuscript must list the Z_4 charges of the dark-sector mediators, the exotic-B+L leptoquark, and the DM candidate, then enumerate all relevant operators to confirm none are Z_4-neutral at tree level. Without this, the prohibition of tree-level decay and the resulting lifetime-DM-mass correlation remain unestablished.

    Authors: We agree with the referee that an explicit listing of the Z_4 charges and enumeration of operators is necessary to substantiate the claims. In the revised version, we have expanded §3 to include a dedicated table presenting the Z_4 charges assigned to the dark matter candidate, the dark-sector mediators, and the exotic-B+L leptoquark. Following this, we enumerate all dimension-6 B+L violating four-fermion operators and show that none are neutral under the residual Z_4 symmetry, thereby forbidding tree-level proton decay. The one-loop diagrams are permitted because they involve fields whose charge combinations allow effective Z_4 invariance after integrating out the mediators. This addition establishes the symmetry protection rigorously and reinforces the link between the proton lifetime and the dark matter mass. revision: yes

  2. Referee: [§4] §4 (One-Loop Proton Decay): The statement that the proton lifetime is linked to the dark matter mass, with heavier DM enhancing stability, is presented qualitatively. No explicit one-loop diagrams, Feynman rules, or decay-width formula (e.g., relating Γ_p to mediator masses and DM mass) are shown, nor are numerical lifetime predictions provided to demonstrate consistency with current bounds for O(TeV) mediators. This quantitative link is load-bearing for the main phenomenological claim.

    Authors: We recognize that the original manuscript presented the connection between proton lifetime and dark matter mass in a primarily qualitative manner. To provide the necessary quantitative support, the revised manuscript now includes the explicit one-loop Feynman diagrams in §4, along with the derivation of the effective Feynman rules from the model Lagrangian. We derive and present the decay width formula Γ_p, which depends on the masses of the mediators and the dark matter particle through the loop suppression factors. Numerical evaluations are added, demonstrating that for mediator masses around 1-2 TeV, the predicted proton lifetime exceeds the current experimental lower bounds (e.g., >10^34 years) and increases with larger dark matter masses due to the kinematic and coupling structure. These results are summarized in a new figure and table, confirming consistency with observations while highlighting the model's testability. revision: yes

Circularity Check

0 steps flagged

No significant circularity; model construction is self-contained

full rationale

The paper proposes a new particle content and symmetry-breaking pattern (global U(1)_{B+L} broken to residual Z_4) chosen so that DM is stable while proton decay is forbidden at tree level but allowed at one loop. This is a standard model-building construction whose central claims follow directly from the assigned charges and the resulting operator selection rules. No parameter is fitted to data and then relabeled as a prediction, no load-bearing result reduces to a self-citation, and the lifetime–DM-mass relation is an output of the loop calculation rather than an input by definition. The framework is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The framework rests on the assumption that U(1)B+L is a global symmetry whose breaking pattern yields exactly Z4, plus the existence of new dark-sector fields with appropriate charges; no independent evidence for these fields is supplied beyond consistency with lifetime bounds.

free parameters (1)
  • mediator masses
    TeV-scale masses for dark sector particles and leptoquark are chosen to satisfy current proton lifetime limits while remaining experimentally accessible.
axioms (1)
  • domain assumption Global U(1)B+L symmetry exists in the Standard Model and breaks spontaneously to a residual Z4.
    Invoked to unify dark matter stability and tree-level proton decay suppression.
invented entities (1)
  • dark sector mediators with exotic B+L charges no independent evidence
    purpose: Mediate one-loop proton decay while preserving Z4 stability for dark matter.
    New particles introduced to realize the loop-level process; no independent falsifiable prediction beyond mass range is given.

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Reference graph

Works this paper leans on

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