  Ratios of isospin amplitudes in hadron decays are a useful probe of the
interplay between weak and strong interactions, and allow searches for physics
beyond the Standard Model. We present the first results on isospin amplitudes
in $b$-baryon decays, using data corresponding to an integrated luminosity of
8.5 fb$^{-1}$, collected with the LHCb detector in $pp$ collisions at center of
mass energies of 7, 8 and 13 TeV. The isospin amplitude ratio
$|A_1(\Lambda_b^0\to J/\psi \Sigma^0)/A_0(\Lambda_b^0\to J/\psi\Lambda)|$,
where the subscript on $A$ indicates the final-state isospin, is measured to be
less than 1/21.8 at 95\% confidence level. The Cabibbo suppressed $\Xi_b^0\to
J/\psi\Lambda$ decay is observed for the first time, allowing for the
measurement $|A_0(\Xi_b^0\to J/\psi\Lambda)/A_{1/2}(\Xi_b^0\to J/\psi\Xi^0)|
=0.37 \pm 0.06\pm 0.02$, where the uncertainties are statistical and
systematic, respectively.
