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The Adam optimizer locates Yukawa coupling values in a 33-dimensional space that suppress dimension-five proton decay enough for the lifetime to exceed 5.9 × 10^33 years in an extended supersymmetric SU(5) model.

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2026-06-30 22:56 UTC pith:NRSRLY36

load-bearing objection Adam optimization locates Yukawa points in the 45+45bar SU(5) extension where the p to K+ nu partial lifetime clears the bound, but the single-channel loss leaves other decay modes and unification unchecked. the 3 major comments →

arxiv 2605.09000 v3 pith:NRSRLY36 submitted 2026-05-09 hep-ph

Optimizing Yukawa couplings to suppress Dimension-five Proton Decay in SU(5) GUT

Naoyuki Haba , Junpei Ikemoto , Yasuhiro Shimizu , Toshifumi Yamada This is my paper
classification hep-ph
keywords SU(5) GUTproton decayYukawa couplingssupersymmetrymachine learning optimizationAdam optimizerdimension-five operatorstan beta
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Proton decay mediated by colored Higgsinos through dimension-five operators is a severe problem for the minimal supersymmetric SU(5) grand unified theory. The authors enlarge the Higgs sector with 45 and 45-bar representations and define a loss function from the partial decay width of the process p to K plus anti-nu. They apply the Adam optimizer to search the 33-dimensional space of Yukawa couplings while varying tan beta, checking whether the resulting lifetime can surpass the Super-Kamiokande experimental bound. This addresses the computational intractability of brute-force scans in high-dimensional parameter spaces where traditional methods fail.

Core claim

By minimizing a loss function derived from the partial decay width of p → K⁺ ν-bar with the Adam optimizer, the analysis identifies regions of the 33-dimensional Yukawa coupling parameter space in the SU(5) model with 45 and 45-bar Higgs fields where the proton lifetime surpasses the Super-Kamiokande limit of 5.9 × 10^33 years across a range of tan beta values.

What carries the argument

The Adam optimizer minimizing a loss function based on the p → K⁺ ν-bar partial decay width inside the 33-dimensional Yukawa parameter space of the 45 + 45-bar extended supersymmetric SU(5) GUT.

Load-bearing premise

The loss function based solely on the partial decay width of p to K+ anti-nu is sufficient to capture all relevant constraints on the Yukawa couplings and the 45 plus 45-bar extension does not introduce new decay channels or inconsistencies with unification.

What would settle it

An independent run of the optimizer or a full parameter scan that finds no points where the proton lifetime exceeds 5.9 × 10^33 years would show that no such suppressing regions exist.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The optimized Yukawa couplings reduce the dimension-five proton decay rate below the experimental threshold.
  • Changes in tan beta do not prevent the model from achieving proton lifetimes above the bound.
  • The optimization method enables exploration of GUT parameter spaces that are too large for brute-force techniques.
  • Viable regions satisfying the proton decay constraint are present in the extended model.

Where Pith is reading between the lines

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

  • The same optimizer approach could be applied to additional constraints such as gauge coupling unification or fermion mass hierarchies in the same model.
  • If the optimized couplings also keep other decay modes under control, the model remains phenomenologically viable without further adjustments.
  • Incorporating multiple decay channels into the loss function might produce more robust solutions that survive broader experimental tests.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 1 minor

Summary. The manuscript claims that extending the minimal supersymmetric SU(5) GUT with 45 and ar{45} Higgs representations allows the 33-dimensional Yukawa parameter space to be explored via the Adam optimizer. A loss function based on the partial width of p → K^+ ar ν is minimized, and tan β is varied to determine whether parameter points can be found for which the proton lifetime exceeds the Super-Kamiokande bound of 5.9 × 10^{33} years.

Significance. If validated, the work would illustrate a practical application of gradient-based optimization to a high-dimensional GUT parameter space that is otherwise intractable, potentially providing a template for addressing proton-decay constraints in other supersymmetric models.

major comments (3)
  1. [Abstract] Abstract: the loss function is defined solely on the partial width of p → K^+ ar ν. The total lifetime bound, however, requires that the sum of all decay channels (including p → π^+ ar ν) remains below the experimental limit; no post-optimization verification of other channels or of the total width is described.
  2. [Abstract] Abstract: the 45 + ar{45} extension is introduced to modify Yukawa couplings, yet the text provides no explicit check that this extension neither generates additional dimension-five operators nor shifts the unification scale in a way that would invalidate the chosen optimization target.
  3. [Abstract] Abstract: no numerical results, convergence diagnostics for the Adam optimizer, error estimates on the optimized lifetimes, or cross-checks against other observables (e.g., gauge-coupling unification or fermion masses) are reported, rendering it impossible to assess whether any points actually satisfy the lifetime bound.
minor comments (1)
  1. The abstract states that tan β is varied but does not specify the scanned range or the number of independent optimization runs performed.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and will revise the manuscript to incorporate the suggested improvements.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the loss function is defined solely on the partial width of p → K^+ ar ν. The total lifetime bound, however, requires that the sum of all decay channels (including p → π^+ ar ν) remains below the experimental limit; no post-optimization verification of other channels or of the total width is described.

    Authors: We agree that the Super-Kamiokande bound applies to the total proton lifetime. While p → K^+ ar ν is the dominant channel in this class of models, we will add explicit post-optimization verification that the summed partial widths of all relevant channels remain below the experimental limit. revision: yes

  2. Referee: [Abstract] Abstract: the 45 + ar{45} extension is introduced to modify Yukawa couplings, yet the text provides no explicit check that this extension neither generates additional dimension-five operators nor shifts the unification scale in a way that would invalidate the chosen optimization target.

    Authors: The 45 + ar{45} extension is included to enlarge the Yukawa texture space while preserving the existing dimension-five operator structure of minimal SUSY SU(5). We will add an explicit verification in the revised manuscript confirming that no new dimension-five operators are generated and that the unification scale remains consistent with the model assumptions used for the optimization target. revision: yes

  3. Referee: [Abstract] Abstract: no numerical results, convergence diagnostics for the Adam optimizer, error estimates on the optimized lifetimes, or cross-checks against other observables (e.g., gauge-coupling unification or fermion masses) are reported, rendering it impossible to assess whether any points actually satisfy the lifetime bound.

    Authors: The manuscript emphasizes the optimization methodology. To permit direct assessment, the revision will include representative numerical results from the Adam runs, convergence diagnostics, error estimates on the resulting lifetimes, and cross-checks confirming gauge-coupling unification and reproduction of fermion masses. revision: yes

Circularity Check

0 steps flagged

No circularity: numerical optimization of explicitly defined loss against external bound

full rationale

The paper defines an explicit loss on the partial width of one decay channel (p → K+ ν-bar), then applies Adam to search the 33D Yukawa space while varying tan β. This is a standard numerical minimization procedure whose output is compared to an independent experimental lower bound (5.9 × 10^33 yr). No derivation chain, self-citation load-bearing step, fitted-input-called-prediction, uniqueness theorem, or ansatz smuggling is present; the target quantity is not recovered by construction from the inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities beyond the standard SUSY SU(5) framework and the added 45 representations.

pith-pipeline@v0.9.1-grok · 5755 in / 1238 out tokens · 20128 ms · 2026-06-30T22:56:13.373969+00:00 · methodology

0 comments
read the original abstract

The minimal supersymmetric $SU(5)$ grand unified theory (GUT) provides a highly compelling framework for physics beyond the Standard Model (SM). However, it suffers from a severe phenomenological challenge: rapid proton decay mediated by colored-Higgsino exchange via dimension-five operators. Resolving this issue often requires adjustments to the Yukawa couplings and the potential sectors, generating a vast and complex parameter space where traditional brute-force numerical scans are rendered computationally intractable due to the curse of dimensionality. In this paper, we overcome this limitation by applying machine learning optimization techniques. We investigate a supersymmetric $SU(5)$ model extended with $\mathbf{45}$ and $\overline{\mathbf{45}}$ Higgs representations, defining a loss function based on the partial decay width of $p \to K^+ \bar{\nu}$. Utilizing the Adam optimizer, we systematically explore the 33-dimensional parameter space to identify regions that suppress proton decay. Furthermore, we vary $\tan \beta$ to thoroughly investigate whether the optimized proton lifetime can consistently exceed the stringent experimental lower bound of $5.9 \times 10^{33}$ years established by the Super-Kamiokande collaboration.

Figures

Figures reproduced from arXiv: 2605.09000 by Junpei Ikemoto, Naoyuki Haba, Toshifumi Yamada, Yasuhiro Shimizu.

Figure 1
Figure 1. Figure 1: Optimization results for the proton decay suppression for tan [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Distributions of the N = 4096 optimized parameters for tan β = 3 (40 bins each). (a) The 9 mixing angles (ϕi , θi , δ, χi) for the unitary matrix Uu. (b) The 9 mixing angles for the unitary matrix Ue. 14 [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 2
Figure 2. Figure 2: (Continued) (c) The 9 mixing angles for the unitary matrix [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of the initial and optimized proton lifetime distributions for tan [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages · cited by 1 Pith paper · 6 internal anchors

  1. [1]

    Unity of All Elementary-Particle Forces,

    H. Georgi and S. L. Glashow, “Unity of All Elementary-Particle Forces,” Phys. Rev. Lett. 32, 438 (1974)

    work page 1974

  2. [2]

    Softly Broken Supersymmetry and SU(5),

    S. Dimopoulos and H. Georgi, “Softly Broken Supersymmetry and SU(5),” Nucl. Phys. B 193, 150-162 (1981)

    work page 1981

  3. [3]

    Naturalness in Supersymmetric GUTS,

    Sakai, N., “Naturalness in Supersymmetric GUTS,” Z. Phys. C11(1981) 153

    work page 1981

  4. [4]

    Proton Decay in Supersymmetric Models,

    N. Sakai and T. Yanagida, “Proton Decay in Supersymmetric Models,” Nucl. Phys. B197, 533-542 (1982)

    work page 1982

  5. [5]

    Supersymmetry at Ordinary Energies. 1. Masses and Conservation Laws,

    S. Weinberg, “Supersymmetry at Ordinary Energies. 1. Masses and Conservation Laws,” Phys. Rev. D26, 287 (1982)

    work page 1982

  6. [6]

    Search for Proton Decay via $p \rightarrow \nu K^{+}$ using 260 kiloton$\cdot$year data of Super-Kamiokande

    K. Abe,et al. [Super-Kamiokande], “Search for proton decay viap→νK + us- ing 260 kiloton·year data of Super-Kamiokande,” Phys. Rev. D 90, 072005, (2014), [arXiv:1408.1195[hep-ex]]. 18

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  7. [7]

    A New Lepton-Quark Mass Relation in a Unified Theory,

    H. Georgi and C. Jarlskog, “A New Lepton-Quark Mass Relation in a Unified Theory,” Phys. Lett. B86, 297-300 (1979)

    work page 1979

  8. [8]

    SU(5) unification revisited,

    A. Giveon, L. J. Hall and U. Sarid, “SU(5) unification revisited,” Phys. Lett. B271, 138-144 (1991)

    work page 1991

  9. [9]

    Branes with Brains: Exploring String Vacua with Deep Reinforcement Learning

    J. Halverson, B. Nelson, and F. Ruehle, “Branes with Brains: Exploring String Vacua with Deep Reinforcement Learning,” JHEP06, 003, arXiv:1903.11616 [hepth]

    work page internal anchor Pith review Pith/arXiv arXiv 1903

  10. [10]

    Exploring the flavor structure of quarks and leptons with reinforcement learning

    S. Nishimura, C. Miyao, and H. Otsuka, “Exploring the flavor structure of quarks and leptons with reinforcement learning,” JHEP23, 021, arXiv:2304.14176 [hep-ph]

    work page Pith review arXiv

  11. [11]

    Truth, beauty, and goodness in grand unification: a machine learning approach

    S. Kawai and N. Okada, “Truth, beauty, and goodness in grand unification: A machine learning approach,” Phys. Lett. B860, 139221 (2025), arXiv:2411.06718 [hep-ph]

    work page Pith review arXiv 2025

  12. [12]

    TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems

    M. Abadi,et al., “TensorFlow: Large-Scale Machine Learning on Heterogeneous Dis- tributed Systems,” (2016), arXiv:1603.04467 [cs.DC]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  13. [13]

    Adam: A Method for Stochastic Optimization

    D. P. Kingma and J. Ba, “Adam: A Method for Stochastic Optimization,” (2014), arXiv:1412.6980 [cs.LG]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  14. [14]

    Improved lattice computation of proton decay matrix elements

    Y. Aoki, T. Izubuchi, E. Shintani and A. Soni, “Improved lattice computation of proton decay matrix elements,” Phys.Rev. D96, no.1, 014506 (2017) [arXiv:1705.01338 [hep-lat]]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  15. [15]

    Unification and Fermion Mass Structure

    G. G. Ross and M. Serna, “Unification and fermion mass structure,” Phys. Lett. B664 (2008) 97, [arXiv:0704.1248 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  16. [16]

    Effect of RRRR dimension five operator on the proton decay in the minimal SU(5) SUGRA GUT model,

    T. Goto and T. Nihei, “Effect of RRRR dimension five operator on the proton decay in the minimal SU(5) SUGRA GUT model,” Phys. Rev. D59(1999) 115009 [arXiv:hep- ph/9808255] 19

    work page arXiv 1999