Evidence for the Rare Decay <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:mi>p</mml:mi><mml:msup><mml:mi>μ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>μ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>

A search for the rare decay ${\mathrm{\ensuremath{\Sigma}}}^{+}\ensuremath{\rightarrow}p{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ is performed using $pp$ collision data recorded by the LHCb experiment at center-of-mass energies $\sqrt{s}=7$ and 8 TeV, corresponding to an integrated luminosity of $3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$. An excess of events is observed with respect to the background expectation, with a signal significance of 4.1 standard deviations. No significant structure is observed in the dimuon invariant mass distribution, in contrast with a previous result from the HyperCP experiment. The measured ${\mathrm{\ensuremath{\Sigma}}}^{+}\ensuremath{\rightarrow}p{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ branching fraction is $({2.2}_{\ensuremath{-}1.3}^{+1.8})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$, where statistical and systematic uncertainties are included, which is consistent with the standard model prediction.

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