Dalitz decay of $$K^*(892) \rightarrow K \ell ^+\ell ^-$$: a new probe for hadronic structure and dark photon searches

Abstract We present the first comprehensive study of the rare Dalitz decay $$K^*(892) \rightarrow K \ell ^+ \ell ^- (\ell = e, \mu )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>892</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>→</mml:mo> <mml:mi>K</mml:mi> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ℓ</mml:mi> <mml:mo>=</mml:mo> <mml:mi>e</mml:mi> <mml:mo>,</mml:mo> <mml:mi>μ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , providing a prediction for the branching fraction and the dilepton mass spectrum. This decay involves the emission of a virtual photon which converts into a lepton pair, offering a probe of the transition form factor $$F_{K^*K}(q^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>F</mml:mi> <mml:mrow> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mi>K</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> and underlying meson structure. Using a single pole approximation for the form factor, we present the calculation of the branching fraction for this rare decay channel for the first time. Furthermore, we also investigate the potential to search for a light $$A'$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>A</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:math> boson (dark photon) appearing as a narrow resonance in the dilepton spectrum, and discuss the experimental sensitivity and new physics opportunities at the dedicated BESIII experiment. Our results establish $$K^*(892) \rightarrow K \ell ^+ \ell ^- (\ell = e, \mu )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>892</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>→</mml:mo> <mml:mi>K</mml:mi> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ℓ</mml:mi> <mml:mo>=</mml:mo> <mml:mi>e</mml:mi> <mml:mo>,</mml:mo> <mml:mi>μ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> as a new laboratory for hadronic structure and dark-sector searches.