arxiv: 2604.24335 · v1 · submitted 2026-04-27 · ✦ hep-ph · hep-ex

Recognition: unknown

CP violation in Sigma^+to pell^+ell^- within the standard model and beyond

Xiao-Gang He , Jusak Tandean , German Valencia

Authors on Pith no claims yet

Pith reviewed 2026-05-08 03:05 UTC · model grok-4.3

classification ✦ hep-ph hep-ex

keywords CP violationhyperon decaysrare decaysstandard modelnew physicsLHCbabsorptive phasesdecay asymmetry

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The pith

New physics can produce CP-violating rate asymmetries up to tens of percent in the rare decay of the sigma-plus hyperon to a proton and lepton pair.

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 violation can appear in the rare decay Sigma-plus to proton plus lepton pair, both in the muon and electron channels. Long-distance effects within the standard model generate large absorptive phases in the decay amplitude. These phases can interfere with new-physics amplitudes to create a sizable difference between the decay rates of the hyperon and its antiparticle. A reader would care because LHCb has already observed the muon mode and can soon measure both particle and antiparticle channels with enough precision to test this effect.

Core claim

Within the standard model the dominant long-distance contributions to Sigma-plus to proton lepton-pair decays supply large absorptive phases. When these phases interfere with new-physics amplitudes the resulting CP-violating asymmetry between the hyperon and antihyperon decay rates can reach several tens of percent. The same mechanism applies to the dielectron channel and, with suitable adjustments, to the radiative decay Sigma-plus to proton photon. LHCb can therefore probe the asymmetry by comparing the two charge-conjugate modes in the near future.

What carries the argument

Interference between long-distance standard-model amplitudes that carry large absorptive phases and possible new-physics amplitudes in the transition.

Load-bearing premise

The long-distance standard-model pieces must generate sufficiently large imaginary parts in the amplitudes to allow strong constructive interference with new physics without being ruled out by other data.

What would settle it

An LHCb measurement finding the decay-rate asymmetry below a few percent in the muon channel for both hyperon and antihyperon would rule out the large new-physics contribution scenario.

read the original abstract

The LHCb collaboration has recently observed the rare hyperon decay $\Sigma^+\to p\mu^+\mu^-$. It can also measure the corresponding antihyperon channel with comparable precision and is thus in a position to extract information on $CP$ violation in this mode. Interestingly, the long-distance contributions that dominate it within the standard model provide large absorptive phases that could drive substantial $CP$ violation through interference with potential new-physics contributions. Here we explore this possibility, finding that the decay rate asymmetry is currently allowed to be as high as tens of percent, which can be probed by LHCb in the near future. We additionally consider the same with regard to the dielectron mode $\Sigma^+\to pe^+e^-$ as well as the related radiative one $\Sigma^+\to p\gamma$.

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.

Desk Editor's Note private letter to a colleague

The paper shows the CP asymmetry in the new Σ⁺→pℓ⁺ℓ⁻ mode can reach tens of percent with new physics thanks to SM long-distance phases, but the bound likely overstates the range once the measured rate is enforced.

read the letter

The paper's central result is that the rate asymmetry in this hyperon decay can be as large as tens of percent in the presence of new physics, because the standard model long-distance pieces supply big absorptive phases that can interfere. This is new for this specific mode, which LHCb just observed. What the paper does well is to work out the kinematics and the interference terms using effective theory, and to give numerical estimates for both the muon and electron channels plus the radiative one. It connects theory directly to what LHCb can measure soon. The soft spot is the handling of the long-distance contributions. The stress-test concern is valid: to get the maximum asymmetry you need the phase difference near 90 degrees and similar sizes for the amplitudes, but that same variation affects the total rate, which has to stay within the experimental limits. If the long-distance magnitude and phase are not completely free but tied to the same hadronic physics that determines the branching ratio, then the allowed new-physics range could be narrower. The paper treats them as somewhat independent, which may inflate the upper bound. The math looks standard for this area, with no obvious errors in the setup. Citations are to relevant prior work on hyperon form factors. This paper is aimed at flavor physicists who want to think about CP violation in baryon decays rather than just mesons. A reader who cares about near-term LHCb results on rare hyperons will find it useful as a guide to what to look for. It deserves a serious referee because the idea is timely and the calculation is accessible, even if the assumptions on the phases need scrutiny. I recommend sending it to peer review.

Referee Report

2 major / 3 minor

Summary. The paper examines CP violation in the rare hyperon decay Σ⁺ → p ℓ⁺ ℓ⁻ (ℓ = μ, e) and the related radiative mode Σ⁺ → p γ. It argues that dominant long-distance Standard Model contributions generate large absorptive phases that can interfere with new-physics amplitudes to produce CP rate asymmetries as large as tens of percent, potentially accessible to LHCb measurements of both hyperon and antihyperon channels.

Significance. If the numerical bounds hold after accounting for rate constraints, the work identifies a promising near-term probe of CP violation in hyperon decays that exploits the interplay between SM long-distance phases and possible NP Wilson coefficients. It supplies a concrete framework for interpreting future LHCb data on multiple modes and gives credit to existing form-factor literature while extending it to CP-odd observables.

major comments (2)

[§4] §4 (numerical results): the statement that the asymmetry 'is currently allowed to be as high as tens of percent' is obtained by maximizing the CP-odd interference while holding the branching ratio inside the experimental window. However, the total rate Γ ∝ |A_LD_SM + A_NP|^2 couples the real and imaginary parts; varying the NP amplitude to maximize the phase difference necessarily shifts the CP-even rate, so the quoted upper bound may be an overestimate unless the LD uncertainty band is explicitly shown to absorb the shift.
[§3.2] §3.2 (NP contributions): the allowed ranges for the asymmetry are expressed in terms of free NP Wilson coefficients and external LD form factors/phases taken from prior literature. No combined marginalization or error propagation over the LD parameters (consistent with the measured rate) is presented, which makes the 'tens of percent' figure dependent on those external inputs rather than derived internally.

minor comments (3)

[Abstract] The abstract and introduction would benefit from a brief statement of the current experimental upper limit on the branching ratio to set the scale for the allowed NP contributions.
[Figure 2] Figure 2 (or equivalent) showing the asymmetry versus NP coefficient should include the SM-only point and the experimental rate constraint as a shaded region for clarity.
[§2] A short table summarizing the input values for LD phases and form factors (with references) would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and indicate the revisions we will make.

read point-by-point responses

Referee: [§4] §4 (numerical results): the statement that the asymmetry 'is currently allowed to be as high as tens of percent' is obtained by maximizing the CP-odd interference while holding the branching ratio inside the experimental window. However, the total rate Γ ∝ |A_LD_SM + A_NP|^2 couples the real and imaginary parts; varying the NP amplitude to maximize the phase difference necessarily shifts the CP-even rate, so the quoted upper bound may be an overestimate unless the LD uncertainty band is explicitly shown to absorb the shift.

Authors: We thank the referee for this important clarification. In our scan we do enforce that the total branching ratio remains inside the experimental window for every choice of NP Wilson coefficients; the quoted maximum asymmetry is therefore already conditional on that constraint. Nevertheless, to make the role of LD uncertainties fully transparent we will add a new figure and accompanying text in §4 that shows the allowed asymmetry range for several representative values of the LD form factors and phases (within their literature uncertainties) while keeping the rate fixed. This will demonstrate explicitly that the shifts induced by NP can be absorbed by the LD band without violating the experimental bound. revision: partial
Referee: [§3.2] §3.2 (NP contributions): the allowed ranges for the asymmetry are expressed in terms of free NP Wilson coefficients and external LD form factors/phases taken from prior literature. No combined marginalization or error propagation over the LD parameters (consistent with the measured rate) is presented, which makes the 'tens of percent' figure dependent on those external inputs rather than derived internally.

Authors: The referee correctly notes that we have not performed a statistical marginalization over the LD parameters. Our approach treats the LD contributions as external inputs taken from the literature and restricts the NP parameter space so that the predicted rate lies inside the measured window. In the revised manuscript we will add a short subsection (or appendix) that propagates the quoted LD uncertainties through the asymmetry formula, presenting the resulting range for both central LD values and their extremes while always enforcing the rate constraint. A full Bayesian marginalization over LD and NP parameters simultaneously would constitute a separate, more computationally intensive study; we will acknowledge this limitation and supply the sensitivity analysis requested. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central results rely on external inputs and constraints.

full rationale

The paper computes the CP asymmetry in terms of Wilson coefficients (from SM or NP) and hadronic form factors taken from prior literature or treated as free parameters subject to measured branching ratios and other observables. No step reduces a claimed prediction to a fitted input by construction, nor does any load-bearing premise rest solely on self-citation chains. The allowed range of tens of percent is an upper bound obtained by scanning parameters consistent with existing data, which is standard phenomenological practice and does not constitute circularity under the defined criteria.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The claim relies on standard-model effective operators for ΔS=1 transitions, phenomenological parametrization of long-distance contributions, and the assumption that new-physics amplitudes can be added without additional constraints from other processes.

free parameters (2)

new-physics Wilson coefficients
Left free to vary within bounds that reproduce the observed branching fraction while maximizing the asymmetry.
long-distance form factors and phases
Taken from external calculations or fitted to data; their precise values determine the size of the absorptive part.

axioms (2)

domain assumption Long-distance contributions dominate the decay amplitude and generate large imaginary phases.
Invoked to explain why SM CP violation can be sizable even though short-distance SM contributions are small.
domain assumption New-physics contributions can be treated as additive amplitudes in an effective theory without violating other constraints.
Allows the interference term to reach the quoted size.

pith-pipeline@v0.9.0 · 5445 in / 1400 out tokens · 51304 ms · 2026-05-08T03:05:58.164421+00:00 · methodology

discussion (0)

Reference graph

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