Flavor physics with $\Lambda_b$ baryons

At the LHC, bottom baryons are being produced in unprecedented quantities, which opens up a new field for flavor physics. For example, the decay $\Lambda_b \to p \mu^- \bar{\nu}$ can be used to obtain a novel determination of the CKM matrix element $|V_{ub}|$, and the decay $\Lambda_b \to \Lambda \mu^+ \mu^-$ probes the weak interactions at the loop level. The first lattice calculations of the relevant $\Lambda_b \to p$ and $\Lambda_b \to \Lambda$ form factors have recently been performed using domain-wall light quarks and static $b$ quarks. To further reduce the theoretical uncertainty, one has to go beyond the static approximation. Here I present new calculations of $\Lambda_b \to p$, $\Lambda_b \to \Lambda$, and $\Lambda_b \to \Lambda_c$ form factors using a relativistic heavy-quark action.