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Proton Decay in Product Group Unification

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Jason L. Evans, Masahiro Ibe, Tsutomu T. Yanagida

High Energy Physics - Phenomenology · Submitted 24 Sep 2020 · 58 references

Pith's verdict: The minimal-model exclusion is solid and worth knowing; the extended-model lifetime claim is a target, not a proof, because dimension-5 decay from the admitted triplet mixing is never computed.

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arXiv ID2009.11448 (version 1)
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CitationJason L. Evans, Masahiro Ibe, Tsutomu T. Yanagida. "Proton Decay in Product Group Unification." arXiv:2009.11448 (2020). https://pith.science/paper/VF2SG2HX
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The paper

The paper claims

Minimal SU(5)×U(2)_H product-group unification is already excluded by dimension-6 proton decay; an axion-linked extension reaches observable lifetimes.

The reading

This paper asks whether the simplest product-group unification model, SU(5)×U(2)_H, can survive proton decay bounds. It argues that the minimal version is already excluded: the gauge-coupling matching conditions force the SU(5) X bosons to be light, and dimension-6 proton decay then shortens the proton lifetime below current experimental limits unless the hidden U(1)_H coupling is non-perturbatively large. The paper then shows that adding a 5 and 5-bar pair whose color triplets remain light, with their mass set by Peccei-Quinn breaking at $10^{10}$–$10^{12}$ GeV, shifts the matching conditions so the X bosons become heavy enough. In that extended model the proton lifetime reaches roughly $10^{34}$–$10^{35}$ years, which would be visible to the next generation of proton decay searches, and the dark matter can be a mixture of a Wino-like neutralino and the axion.

What carries the argument

The load-bearing object is the gauge-coupling matching condition at the unification scale, Eq. (8), which ties the heavy SU(5) X-boson mass to $g_{1H}^2(M_G)$, the hidden U(1)_H gauge coupling. Because the standard-model hypercharge is a diagonal subgroup of SU(5) and U(1)_H, a small hidden coupling drags $M_X$ down exponentially through $M_X = M_G \exp(\cdots)$, shortening the proton lifetime. The extension works through Eq. (32), a second matching relation: a light $5+\bar 5$ pair with triplet mass $\mu_5$ deflects the running and raises $M_X$ by the factor $(M_{G0}/\mu_5)^{2/15}$, with the doublet partners made heavy by pairing with $2+\bar 2$ fields. The mechanism that makes $\mu_5$ naturally small is the Peccei-Quinn symmetry, whose breaking scale $10^{10}$–$10^{12}$ GeV produces both the axion and the triplet mass $\lambda_P \langle P\rangle$.

Extended reading notes

Core claim

The paper's central claim is that the minimal SU(5)×U(2)_H product-group unification model is excluded by dimension-6 proton decay, and that a modest extension—one extra $5+\bar 5$ pair with a companion $2+\bar 2$ pair—restores viability. The decisive relation is Eq. (8), which expresses the X-boson mass $M_X$ in terms of the hidden gauge coupling $g_{1H}^2$ at the GUT scale; requiring perturbativity up to the cutoff caps $g_{1H}^2$ at about 3.68, and at that value $M_X$ is too small. Fig. 1 shows the proton lifetime then falls below current bounds unless $g_{1H}^2 \gtrsim 6$. In the extended model, Eq. (32) gives $M_X \simeq (M_{G0}/\mu_5)^{2/15} M_{X0}$, so color-triplet masses $\mu_5 \lesssim 10^{12}$ GeV raise $M_X$ enough to bring the lifetime to $10^{34}$–$10^{35}$ years. The paper identifies $\mu_5$ with the Peccei-Quinn breaking scale, making the axion a natural dark-matter component alongside the Wino LSP.

Load-bearing premise

The numerical lifetimes assume the new light color-triplet fields mix only weakly with the ordinary matter and Higgs fields of the supersymmetric standard model, so X-boson exchange remains the dominant proton decay channel; the paper notes that sizable mixing would alter the lifetime and branching fractions but does not compute that effect.

Editorial extensions

If this is right

  • The minimal SU(5)×U(2)_H model, without extra incomplete multiplets, cannot satisfy both perturbativity ($g_{1H}^2 \le 3.68$) and proton decay bounds (need $g_{1H}^2 \gtrsim 6$).
  • Adding one $5+\bar 5$ pair with light color triplets raises the X-boson mass and lifts the proton lifetime into the $10^{34}$–$10^{35}$ year range.
  • If $\mu_5$ is tied to Peccei-Quinn breaking, the axion naturally accompanies the Wino LSP as dark matter, and the axion-photon coupling is enhanced by a factor of three relative to a GUT-complete $5+\bar 5$ axion multiplet.
  • Because dimension-6 decay dominates, the model predicts clean two-body channels $p\to\pi^0 e^+$ and $p\to\pi^0 \mu^+$ as the primary signatures.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same light-incomplete-multiplet rescue could be attempted in SU(5)×U(3)_H product unification, but the paper notes there is no equally motivated intermediate mass scale; the Peccei-Quinn connection is specific to the U(2)_H case.
  • If triplet–Higgs mixing is not negligible, dimension-5 operators could shorten the lifetime below the quoted range, so the $10^{34}$–$10^{35}$ year window is conditional on that mixing being small.
  • The correlation between proton lifetime and axion abundance means combined null results from proton decay, Wino dark matter searches, and axion searches can jointly constrain the model's parameter space.
Original abstract

Product group unification is an attractive alternative to simple grand unification. It solves the infamous doublet-triplet splitting problem and the dimension-5 proton decay problems without introducing any fine-tuning. Furthermore, the matter multiplets are still embedded into unified SU(5) representations. In this paper, we discuss proton decay of the simplest product group unification model based on SU(5)XU(2)_H . We find that the minimal setup of the model has already been excluded by dimension-6 proton decay. We also show that a simple extension of the model, with naturally generated SU(5) incomplete multiplets, can rectify this problem. We find that the proton lifetime will be in reach of coming experiments like DUNE and Hyper-K, when the mass of the incomplete multiplet is associated with the Peccei-Quinn symmetry breaking. In this case, the dark matter may be an admixture of the Wino LSP and the axion.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,136 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.86 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.45 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Product group unification is an attractive alternative to simple grand unification. It solves the infamous doublet-triplet splitting problem and the dimension-5 proton decay problems without introducing any fine-tuning. Furthermore, the matter multiplets are still embedded into unified SU(5) representations. In this paper, we discuss proton decay of the simplest product group unification model based on SU(5)XU(2)_H . We find that the minimal setup of the model has already been excluded by dimension-6 proton decay. We also show that a simple extension of the model, with naturally generated SU(5) incomplete multiplets, can rectify this problem. We find that the proton lifetime will be in reach of coming experiments like DUNE and Hyper-K, when the mass of the incomplete multiplet is associated with the Peccei-Quinn symmetry breaking. In this case, the dark matter may be an admixture of the Wino LSP and the axion.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Product group unification is an attractive alternative to simple grand unification. background 1.00 0.06 0.02 asserted 0.97
s1 It solves the infamous doublet-triplet splitting problem and the dimension-5 proton decay problems without introducing any fine-tuning. background 0.93 0.14 0.07 asserted 1.00
s2 Furthermore, the matter multiplets are still embedded into unified SU(5) representations. background 0.96 0.12 0.03 asserted 1.00
s3 In this paper, we discuss proton decay of the simplest product group unification model based on SU(5)XU(2)_H . contribution 0.98 0.53 0.04 asserted 0.81
s4 We find that the minimal setup of the model has already been excluded by dimension-6 proton decay. result 0.99 0.94 0.21 asserted 1.00
s5 We also show that a simple extension of the model, with naturally generated SU(5) incomplete multiplets, can rectify this problem. result 0.49 0.93 0.20 asserted 0.99
s6 We find that the proton lifetime will be in reach of coming experiments like DUNE and Hyper-K, when the mass of the incomplete multiplet is associated with the Peccei-Quinn symmetry breaking. result 0.98 0.92 0.43 asserted 0.97
s7 In this case, the dark matter may be an admixture of the Wino LSP and the axion. interpretation 0.78 0.62 0.07 hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.95.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Left) The proton lifetime as a function of
Figure 2. µ5 dependence of proton lifetime, p → π 0 + e + in PGM for given value of g 2 1H at the GUT scale. Since it is very possible that the soft masses of PGM are non-universal, we will look at more generic mass spectra. Since the dimension-6 proton decay is quite insensitive to the sfermion masses, we will consider the case where only the Higgs soft masses are non-universal. This will relax the tension on the proton lifetime coming from the Higgs mass measurement and allow us to more fully explore the parameter space consistent with product group unification. We begin our study of…
Figure 3. The lightest Higgs boson mass, mh, the LSP abundance, and the proton lifetime for the universal PGM as a function of tan β. The effects discussed above can be see in
Figure 4. The tan β (top) and the m3/2 (bottom) dependence of mh (left) and of the proton lifetime (right). Here, we take m2 Hu = m2 3/2 and m2 Hd = 0 as an example of the non-universal Higgs mass. For the bottom two figures in
Figure 5. The tan β and m3/2 dependence of the lightest Higgs boson mass in units of GeV (red lines) and the proton lifetime in units of 1035 years (green dotted lines). Here, we take m2 Hu = 0 and m2 Hd = m2 3/2 as an example of the non-universal Higgs mass. The blue dashed line is where the Wino masses give the correct thermal relic density for dark matter. The pink shaded region is excluded by the non-perturbative Yukawa coupling. dependence of the proton lifetime on m3/2 in
Figure 6. The m2 Hu and m2 Hd dependence of the lightest Higgs boson mass in units of GeV (red lines) and the proton lifetime in units of 1035 years (green dotted lines). The blue dashed line is where the Wino masses give the correct thermal relic density for dark matter. The yellow dashed line is where cW = 0. The pink shaded region is excluded by the failure of the EWSB. The last set of figures,

Figures reproduced from arXiv:2009.11448 by the authors.

References
How the literature uses it

3 arXiv papers cite this in 3 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 2 sentences without a confident label

Cites it as background 1 paper

What it cites · 37 sentences without a confident label

Uses data or values from 3 papers
Cites as background 9 papers

Discussion

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