Weak decays Ξ Q → Λ Q π

The weak decays Ξ b → Λ b π and Ξ c → Λ c π, in which the heavy quark is not destroyed, are discussed. The branching fractions for these decays, corresponding to an absolute rate of order 0.01 ps −1 , should be at a one percent level for the b hyperons and at a (few) per mill level for Ξ c , possibly making feasible their experimental study in future. It is shown, through an application of the heavy quark limit, the flavor SU(3) symmetry, and PCAC, that the ∆I = 1/2 rule should hold very well in these decays, and also that the Ξ b decays are purely S wave in the symmetry limit, while the difference between the S wave amplitudes of the Ξ c decays and those for the Ξ b is related, in terms of the heavy quark expansion, to the difference of the total decay rates within the (Ξ c , Λ c) triplet of charmed hyperons. We also comment on the amplitudes of the semileptonic transitions Ξ Q → Λ Q ℓ ν and on the weak radiative decays Ξ Q → Λ Q γ.