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arxiv: 2606.09166 · v1 · pith:RTJNWUMWnew · submitted 2026-06-08 · ✦ hep-ph

The Muon and Tau Electric Dipole Moments in the B-L Supersymmetric Standard Model

Wen-Hui Zhang , Jin-Lei Yang , Zhao-Feng Ge , Yu-Li Yan , Yin-Jie Zhang This is my paper

Pith reviewed 2026-06-27 16:25 UTC · model grok-4.3

classification ✦ hep-ph
keywords B-LSSMelectric dipole momentsmuon EDMtau EDMCP violationsupersymmetrytwo-loop contributions
0
0 comments X

The pith

The B-L supersymmetric standard model generates muon EDMs within Phase II experimental sensitivity and tau EDMs up to 10^{-21} e cm.

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

The paper examines how CP-violating effects in the B-L supersymmetric standard model contribute to the electric dipole moments of the muon and tau. It derives general analytical expressions for these contributions, incorporating two-loop diagrams. Numerical analysis reveals that the conventional mu-term dominates the EDMs, but parameters unique to the B-LSSM also play a notable role. In a large portion of the model's parameter space, the muon EDM is expected to be measurable in the next phase of proposed experiments, and the tau EDM can reach magnitudes around 10^{-21} e cm. Such predictions are relevant because upcoming precision measurements could test this supersymmetric extension.

Core claim

After considering corrections from some two-loop diagrams, the contributions in the B-LSSM to the EDMs of charged leptons are presented analytically in general forms. The numerical results show that the traditional μ-term in most SUSY models makes dominant contributions to d_μ and d_τ, while the B-LSSM specific CPV parameters also induce significant effects. It is found that across a substantial region of the B-LSSM parameter space, d_μ falls well within the projected sensitivity at Phase II of the proposed experiment, and |d_τ| can reach about 10^{-21} e·cm.

What carries the argument

The CP-violating phases associated with the B-LSSM soft terms and the μ parameter, which enter the one- and two-loop Feynman diagrams contributing to lepton EDMs.

If this is right

  • The muon EDM lies within the projected sensitivity of Phase II experiments over substantial parameter space.
  • The magnitude of the tau EDM can reach approximately 10^{-21} e cm.
  • The B-LSSM-specific CP-violating parameters contribute significantly to the EDMs in addition to the standard mu-term.
  • These values are achieved while satisfying existing experimental bounds on the model parameters.

Where Pith is reading between the lines

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

  • If the EDMs are measured at the predicted levels, it would favor B-LSSM over minimal supersymmetric models.
  • Full consistency with dark matter and flavor constraints may restrict the viable parameter space further.
  • Similar calculations could be extended to other leptonic observables or to the electron EDM for comparison.
  • Observation of non-zero tau EDM would point to new sources of CP violation beyond the standard model.

Load-bearing premise

The CP-violating phases and soft-breaking parameters in the B-LSSM can be chosen independently while satisfying constraints from flavor-changing neutral currents and dark matter relic density.

What would settle it

If Phase II experiments measure a muon EDM significantly below the lower bound of the predicted values in the B-LSSM scans, or if the tau EDM is found to be much smaller than 10^{-21} e cm, the claim of substantial viable parameter space would be falsified.

Figures

Figures reproduced from arXiv: 2606.09166 by Jin-Lei Yang, Wen-Hui Zhang, Yin-Jie Zhang, Yu-Li Yan, Zhao-Feng Ge.

Figure 1
Figure 1. Figure 1: FIG. 1. The one-loop level diagrams contributing to the charged lepton EDMs. [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The considered two-loop level diagrams contributing to the charged lepton EDMs, where [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The numerical results of [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Effects of B-LSSM specific CPV parameters on [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Scatter plots of [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
read the original abstract

Recently proposed experiments are expected to significantly improve the measurement sensitivities of the electric dipole moments (EDMs) of muon ($d_\mu$) and tau ($d_\tau$). Given that theoretical predictions for $d_\mu$ and $d_\tau$ typically surpass those for the electron EDM, this work focuses on studying the contributions from the CP-violating (CPV) effects in the B-L supersymmetric (SUSY) standard model (B-LSSM) to $d_\mu$ and $d_\tau$. After considering the corrections from some two-loop diagrams, the contributions in the B-LSSM to the EDMs of charged leptons are presented analytically in general forms. The numerical results show that the traditional $\mu$-term in most SUSY models makes dominant contributions to $d_\mu$ and $d_\tau$, while the B-LSSM specific CPV parameters also induce significant effects. It is found that across a substantial region of the B-LSSM parameter space, $d_\mu$ falls well within the projected sensitivity at Phase II of the proposed experiment, and $|d_\tau|$ can reach about $10^{-21}e\cdot\text{cm}$.

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

1 major / 1 minor

Summary. The manuscript derives general analytic expressions for the electric dipole moments of the muon and tau in the B-L supersymmetric standard model (B-LSSM), including contributions from two-loop diagrams. It identifies the conventional μ-term as the dominant source while noting significant additional effects from B-LSSM-specific CP-violating phases and soft-breaking parameters. Numerical scans are presented to show that d_μ lies within the projected sensitivity of Phase II experiments over a substantial region of parameter space and that |d_τ| can reach ~10^{-21} e cm.

Significance. If the numerical results remain valid once all phenomenological constraints are imposed, the work would establish that the B-LSSM can produce observable muon and tau EDMs, furnishing testable predictions for forthcoming experiments and illustrating the phenomenological impact of the model's extra CP-violating phases. The provision of analytic forms that incorporate two-loop corrections is a positive feature that facilitates reproducibility and extension to related models.

major comments (1)
  1. [Numerical results section] Numerical results section (and abstract claim): The headline statement that d_μ falls within projected Phase-II sensitivity 'across a substantial region of the B-LSSM parameter space' is load-bearing. The text does not demonstrate that the scanned values of the B-LSSM CP-violating phases (e.g., those entering the μ-term and B-L gaugino sectors) simultaneously satisfy constraints from FCNC processes such as μ→eγ and b→sγ or from neutralino relic density. Without explicit verification that a non-empty viable region survives these bounds, the quoted numerical reach cannot be regarded as a robust prediction.
minor comments (1)
  1. [Abstract] The abstract refers to 'some two-loop diagrams' without naming them; a short parenthetical list or reference to the relevant subsection would improve clarity for readers scanning the abstract.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the thorough review and for highlighting the need to ensure our numerical claims are robust under additional phenomenological constraints. We address the major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Numerical results section] Numerical results section (and abstract claim): The headline statement that d_μ falls within projected Phase-II sensitivity 'across a substantial region of the B-LSSM parameter space' is load-bearing. The text does not demonstrate that the scanned values of the B-LSSM CP-violating phases (e.g., those entering the μ-term and B-L gaugino sectors) simultaneously satisfy constraints from FCNC processes such as μ→eγ and b→sγ or from neutralino relic density. Without explicit verification that a non-empty viable region survives these bounds, the quoted numerical reach cannot be regarded as a robust prediction.

    Authors: We agree that the current numerical scans, while illustrative of the EDM contributions from the μ-term and B-LSSM-specific CPV phases, do not explicitly impose the full set of constraints from μ→eγ, b→sγ, and neutralino relic density. The parameter choices were guided by basic consistency with SUSY mass bounds and electroweak symmetry breaking, but a dedicated scan incorporating these observables is required to confirm a viable region. In the revised version we will add an updated numerical section that performs a constrained scan: we will require BR(μ→eγ) < 4.2×10^{-13}, BR(b→sγ) within 3σ of the experimental value, and Ωh² ≈ 0.12, while retaining the two-loop EDM expressions. We will then demonstrate that a non-empty subset of the B-LSSM parameter space still yields d_μ within the projected Phase-II reach. The abstract claim will be qualified to reflect this constrained viable region. revision: yes

Circularity Check

0 steps flagged

Analytic expressions and parameter scans are independent of inputs

full rationale

The paper first derives general analytic forms for the charged-lepton EDMs from the B-LSSM Lagrangian after including specified two-loop diagrams; these expressions are presented as functions of the model parameters and CP-violating phases. Numerical results are then obtained by scanning the parameter space. No equation reduces a claimed prediction to a fitted input by construction, no load-bearing uniqueness theorem is imported from self-citation, and no ansatz is smuggled via prior work. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the B-LSSM framework itself, whose additional CP-violating phases and soft terms are treated as free inputs whose values are scanned numerically; no independent evidence for those phases is supplied.

free parameters (1)
  • B-LSSM CP-violating phases and soft-breaking parameters
    The abstract states that these parameters induce significant effects and that substantial regions of their space yield detectable EDMs; they are therefore scanned or chosen by hand.
axioms (1)
  • domain assumption Standard supersymmetric model assumptions including R-parity and the existence of the B-L gauge symmetry
    The entire calculation presupposes the B-LSSM particle content and Lagrangian structure.

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discussion (0)

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