Lambda_b -> Lambda l+ l- form factors and differential branching fraction from lattice QCD

We present the first lattice QCD determination of the ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }$ transition form factors that govern the rare baryonic decays $\Lambda_b \to \Lambda l^+ l^-$ 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 $\Lambda_b \to \Lambda l^+ l^-$with$l=e,\mu,\tau$ within the standard model. We find agreement with a recent CDF measurement of the ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\mu }^{+}{\mu }^{-}$ differential branching fraction.