| Summary: | Abstract The rare hyperon decay Σ+ → pℓ + ℓ − is a flavour-changing neutral current process mediated by an s → d transition that occurs only at loop level within the Standard Model. Consequently, this decay is highly suppressed, making it a promising avenue for probing potential new physics. While phenomenological calculations have made important progress in predicting the decay amplitude, there remains a four-fold ambiguity in the relevant transition form factors that prevents a unique prediction for the branching fraction and angular observables. Fully resolving this ambiguity requires a first-principles Standard-Model calculation, and the recent observation of this process using LHCb Run 2 data reinforces the timeliness of such a calculation. In this work, we present the first lattice-QCD calculation of this decay, performed using a 2+1-flavour domain-wall fermion ensemble with a pion mass of 340 Mev. At a small baryon source-sink separation, we observe the emergence of a signal in the relevant baryonic four-point functions. This allows us to determine the positive-parity form factors for the rare hyperon decays from first-principles, albeit with large statistical and systematic uncertainties.
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