Probing lepton flavour universality with $$\Lambda _b$$ decays to $$\tau ^+\tau ^-$$ final states

Abstract We present a study of the rare baryonic decay $$\Lambda _b \rightarrow \Lambda \tau ^+ \tau ^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:mi>Λ</mml:mi> <mml:msup> <mml:mi>τ</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>τ</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math> as a probe of new physics (NP) coupled preferentially to third-generation fermions. Within the Standard Model, we evaluate the branching ratio and the lepton-flavour-universality (LFU) ratio $$R_{\Lambda }^{\tau /\mu },$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>R</mml:mi> <mml:mrow> <mml:mi>Λ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>τ</mml:mi> <mml:mo>/</mml:mo> <mml:mi>μ</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> including both perturbative and long-distance charm contributions. We show that the LFU ratio can be predicted with an uncertainty below 10%. Possible NP effects arising from lepton non-universal dynamics are analysed within an effective field theory framework motivated by the current anomalies in $$b \rightarrow c\tau \nu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>b</mml:mi> <mml:mo>→</mml:mo> <mml:mi>c</mml:mi> <mml:mi>τ</mml:mi> <mml:mi>ν</mml:mi> </mml:mrow> </mml:math> and $$b \rightarrow s\mu ^+\mu ^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>b</mml:mi> <mml:mo>→</mml:mo> <mml:mi>s</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:mrow> </mml:math> transitions. In this context, $$R_{\Lambda }^{\tau /\mu }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>R</mml:mi> <mml:mrow> <mml:mi>Λ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>τ</mml:mi> <mml:mo>/</mml:mo> <mml:mi>μ</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> can be enhanced by several orders of magnitude, offering a clear target for upcoming searches. The implications for the related mode $$\Lambda _b \rightarrow pK\tau ^+\tau ^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:mi>p</mml:mi> <mml:mi>K</mml:mi> <mml:msup> <mml:mi>τ</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>τ</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math> are also briefly discussed.