<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><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>ℓ</mml:mi><mml:mo mathvariant="bold">+</mml:mo></mml:msup><mml:msup><mml:mi>ℓ</mml:mi><mml:mo mathvariant="bold">−</mml:mo></mml:msup></mml:math>form factors and differential branching fraction from lattice QCD

We present the first lattice QCD determination of the ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}$ transition form factors that govern the rare baryonic decays ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ at leading order in heavy-quark effective theory. Our calculations are performed with $2+1$ flavors of domain-wall fermions, at two lattice spacings and with pion masses down to 227 MeV. Three-point functions with a wide range of source-sink separations are used to extract the ground-state contributions. The form factors are extrapolated to the physical values of the light-quark masses and to the continuum limit. We use our results to calculate the differential branching fractions for ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ with $\ensuremath{\ell}=e$, $\ensuremath{\mu}$, $\ensuremath{\tau}$ within the standard model. We find agreement with a recent CDF measurement of the ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ differential branching fraction.

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