<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>R</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>J</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>ψ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">→</mml:mo><mml:mi>J</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>ψ</mml:mi><mml:msup><mml:mrow><mml:mo>ℓ</mml:mo></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup><mml:msub><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:mrow><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> Lepton Flavor Universality Violating Observables from Lattice QCD
Judd Harrison, C. T. H. Davies, Andrew Lytle
Abstract
We use our lattice QCD computation of the ${B}_{c}\ensuremath{\rightarrow}J/\ensuremath{\psi}$ form factors to determine the differential decay rate for the semitauonic decay channel and construct the ratio of branching fractions $R(J/\ensuremath{\psi})=\phantom{\rule{0ex}{0ex}}\mathcal{B}({B}_{c}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\tau}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}})/\mathcal{B}({B}_{c}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}})$. We find $R(J/\ensuremath{\psi})=0.2582(38)$ and give an error budget. We also extend the relevant angular observables, which were recently suggested for the study of lepton flavor universality violating effects in $B\ensuremath{\rightarrow}{D}^{*}\ensuremath{\ell}\ensuremath{\nu}$, to ${B}_{c}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\ell}\ensuremath{\nu}$ and make predictions for their values under different new physics scenarios.