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Markov Chain Monte Carlo analysis to probe trilinear $R$-parity violating SUSY scenarios and possible LHC signatures

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Pith's one-line read A Bayesian MCMC fit to neutrino, Higgs, and flavor data constrains the trilinear R-parity-violating couplings λ_i33 and λ'_i33 to at most ~10^-4, with tanβ below 15, in bino- and stop-LSP supersymmetric scenarios.

arxiv 2411.08112 v2 pith:5N345WNH submitted 2024-11-12 hep-ph

Arghya Choudhury , Sourav Mitra , Arpita Mondal , Subhadeep Mondal This is my paper · ORCID
classification hep-ph
keywords susytrilinearobservablesparameterregionsscenariosviolatingcarlo
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Supersymmetry is an extension of the Standard Model that predicts a partner particle for every known particle. In the simplest version, a symmetry called R-parity protects protons from decaying. The version studied here allows R-parity to be violated, and the resulting trilinear couplings can generate tiny masses for neutrinos at one loop. The authors take a model with five such couplings, λ133, λ233 and λ'133, λ'233, λ'333, which give neutrinos their masses and mixings, and combine it with a fixed supersymmetric spectrum of heavier particles.

They then run a Markov Chain Monte Carlo, a statistical sampling algorithm, to find which values of these couplings fit sixteen observables: neutrino mass splittings and mixing angles, the 125 GeV Higgs boson mass and its couplings, and three B-meson decay rates. The fit returns posterior distributions, meaning the probability of each coupling value given the data. In both the normal and inverted neutrino mass hierarchies, the trilinear couplings are confined to about 10^-4 or below, and tanβ, the ratio of the two Higgs vacuum values, is below 15 at 99% confidence. A model with only the λ' couplings fails to fit the solar neutrino splitting and is discarded.

The authors also translate the allowed regions into LHC signatures. For a bino LSP, the decays produce tau-rich final states, and the inverted hierarchy would give about 30% more signal events than the normal hierarchy at the HL-LHC. For a stop LSP, ATLAS limits exclude part of the allowed region, especially near the best-fit point, and only heavier stops with large bτ branching ratios survive.

Extended reading notes

Core claim

The paper's central claim, from the abstract and Section 8, is: 'Our results indicate that the lepton number violating trilinear couplings λi33 (i=1,2) and λ′j33 (j=1,2,3) can be at most of the order of 10−4 or even smaller while tan β is restricted to below 15 even when 3σ allowed regions are considered.' If correct, the one-loop neutrino mass mechanism in this class of RPV MSSM models is viable only in a narrow, tau-rich corner of parameter space, and the posterior distributions provide a statistical map of that corner.

Load-bearing premise

The constraints assume that neutrino masses are generated solely by the five diagonal couplings λ_i33 (i=1,2) and λ'_i33 (j=1,2,3) at one loop, with all other RPV operators (bilinear and off-diagonal trilinear) set exactly to zero (Sec. 1) and with degenerate sfermion masses at a fixed scale m̃ ≈ 2 TeV (Eqs. 2.6-2.8, Table 3). If additional RPV couplings were present, or if the sfermion mass scale were higher, the same neutrino oscillation data could be fit with different, generally less restrictive, individual coupling bounds. This truncation is the structural premise that turns the fit into sharp upper limits.

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Editorial analysis

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

Assumptions & free parameters 12 free parameters · 7 assumptions · 0 invented entities

The central constraints rest on the one-loop RPV neutrino mass formulas, the restriction to five diagonal couplings, the fixed sparticle spectrum, and the seven fitted SUSY parameters; the derived upper limits are conditional on these choices.

free parameters (12)
  • lambda_133 = 1.71e-4 (NH best fit)
    Fitted to neutrino mass matrix; enters products with other couplings.
  • lambda_233 = 2.52e-4 (NH best fit)
    Fitted; constrained by mass matrix entry products.
  • lambda_prime_133 = -7.61e-5 (NH best fit)
    Fitted; sign and magnitude set mass matrix texture.
  • lambda_prime_233 = -7.65e-5 (NH best fit)
    Fitted; correlated with lambda_prime_133 via solar splitting.
  • lambda_prime_333 = -1.34e-4 (NH best fit)
    Fitted; dominates the heaviest neutrino mass (Eq. 2.10).
  • mu = 1996 GeV (NH best fit)
    Fitted; enters LR mass insertion and Higgs sector.
  • tan beta = 6.68 (NH best fit)
    Fitted; enters neutrino mass via mu tan beta and Higgs observables.
  • m_q3L (stop model) = 1499 GeV (best fit)
    Fitted only in stop-LSP model; sets stop mass.
  • Common slepton mass m_tilde = 2000 GeV (fixed)
    Fixed by hand; overall scale of the loop-induced neutrino mass, so coupling bounds scale with it.
  • Bino mass M1 / Wino mass M2 = 300 GeV / 1200 GeV (fixed)
    Fixed to evade LHC electroweakino limits; sets LSP/NLSP mass gap and collider signatures.
  • Gluino/squark/MA masses = 3000 GeV each (fixed)
    Fixed heavy; uplifts strong-sector exclusions.
  • At = -5000 GeV (bino), 4500 GeV (stop) (fixed)
    Fixed to keep mh near 125 GeV.
assumptions (7)
  • domain assumption One-loop neutrino mass formulas (Eq. 2.5) with mass insertions for slepton/squark LR mixing.
    Standard RPV result from [16], assumed valid for the numerical SPheno implementation.
  • domain assumption Degenerate sfermion masses and A-terms proportional to Yukawas (Eq. 2.6) leading to the diagonal mass matrix (Eq. 2.8).
    Required to reduce the 40-parameter RPV space to five couplings.
  • domain assumption Only k,l=2,3 (tau/b) loop contributions matter.
    Justified by m_tau^2/m_mu^2 ~ 300 hierarchy, following [51].
  • ad hoc to paper All other RPV couplings, including bilinear and all off-diagonal trilinear, set to zero.
    Crucial truncation; if relaxed, individual coupling bounds can be evaded.
  • domain assumption delta_CP = 0 in the PMNS matrix.
    Cites large CP uncertainty; reduces parameter count.
  • ad hoc to paper Fixed sparticle spectrum as in Table 3 to avoid LHC exclusion.
    The coupling bounds are conditional on this spectrum.
  • domain assumption Higgs mass likelihood uses a flat ±3 GeV window; CMS-only kappa values.
    Standard choice, but the window is wide and weakly constraining.

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Pith. "Pith review of Markov Chain Monte Carlo analysis to probe trilinear $R$-parity violating SUSY scenarios and possible LHC signatures." pith.science (2026). https://pith.science/paper/5N345WNH

@misc{pith2026241108112,
  author       = {Pith},
  title        = {Pith review of: Markov Chain Monte Carlo analysis to probe trilinear $R$-parity violating SUSY scenarios and possible LHC signatures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5N345WNH}},
  note         = {Machine review of arXiv:2411.08112}
}
abstract

In this article, we probe the trilinear $R$-parity violating (RPV) supersymmetric (SUSY) scenarios with specific nonzero interactions in the light of neutrino oscillation, Higgs, and flavor observables. We attempt to fit the set of observables using a state-of-the-art Markov Chain Monte Carlo (MCMC) setup and study its impact on the model parameter space. Our main objective is to constrain the trilinear couplings individually, along with some other SUSY parameters relevant to the observables. We present the constrained parameter regions in the form of marginalized posterior distributions on different two-dimensional parameter planes. We perform our analyses with two different scenarios characterized by our choices for the lightest SUSY particle (LSP), bino, and stop. Our results indicate that the lepton number violating trilinear couplings $\lambda_{i33}$ ($i$=1,2) and $\lambda_{j33}^{\prime}$ ($j$=1,2,3) can be at most of the order of $10^{-4}$ or even smaller while $\tan\beta$ is restricted to below 15 even when $3\sigma$ allowed regions are considered. We further comment on the possible LHC signatures of these LSPs focusing on and around the best-fit regions.

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