A closer look at isodoublet vector leptoquark solution to the $$ {R}_{D^{\left(\ast \right)}} $$ anomaly

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>We discuss a model with a SU(2)<jats:sub><jats:italic>L</jats:italic></jats:sub> doublet vector leptoquark (LQ), motivated by the recent experimental results relating to the lepton universality of <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \overline{B} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math></jats:alternatives></jats:inline-formula> → <jats:italic>D</jats:italic><jats:sup>(*)</jats:sup><jats:inline-formula><jats:alternatives><jats:tex-math>$$ \tau {\overline{\nu}}_{\tau } $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>τ</mml:mi> <mml:msub> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>τ</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>. We find that scalar operators predicted by the LQ are favored to explain the deviations, taking into account the recent LHCb result. We investigate the extensive phenomenology of the model and conclude that <jats:italic>B</jats:italic><jats:sub><jats:italic>s</jats:italic></jats:sub> → <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \tau \overline{\tau} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>τ</mml:mi> <mml:mover> <mml:mi>τ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math></jats:alternatives></jats:inline-formula>, <jats:italic>B</jats:italic> → <jats:inline-formula><jats:alternatives><jats:tex-math>$$ K\tau \overline{\tau} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Kτ</mml:mi> <mml:mover> <mml:mi>τ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math></jats:alternatives></jats:inline-formula>, <jats:italic>B</jats:italic><jats:sub><jats:italic>u</jats:italic></jats:sub> → <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \tau {\overline{\nu}}_{\tau } $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>τ</mml:mi> <mml:msub> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>τ</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> and high-<jats:italic>p</jats:italic><jats:sub><jats:italic>T</jats:italic></jats:sub> di-<jats:italic>τ</jats:italic> lepton signatures at the LHC will probe the interesting parameter region in the near future.</jats:p>