Weak decays ΞQ→ΛQπ

The weak decays Ξb→Λb π and Ξc→Λc 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 Ξc, 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 ΔI=1/2 rule should hold very well in these decays, and also that the Ξb decays are purely S wave in the symmetry limit, while the difference between the S wave amplitudes of the Ξc decays and those for the Ξb is related, in terms of the heavy quark expansion, to the difference of the total decay rates within the (Ξc, Λc) triplet of charmed hyperons. We also comment on the amplitudes of the semileptonic transitions ΞQ→ΛQ ℓ ν and on the weak radiative decays ΞQ→ΛQ γ.