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 finalstate 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.
Leading order Feynman diagrams for $\Lambda ^0_ b \rightarrow { J \mskip 3mu/\mskip 2mu\psi } \Lambda(\Sigma^0)$ and $\Xi_b^0\rightarrow { J \mskip 3mu/\mskip 2mu\psi } \Xi^0(\Lambda)$ decays. 
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feynJXi.pdf [103 KiB] HiDef png [131 KiB] Thumbnail [190 KiB] *.C file 

Distribution of the $ { J \mskip 3mu/\mskip 2mu\psi } \Lambda$ mass for Run 2 data. Error bars without data points indicate empty bins. Also shown is the projection of the joint fit to the data. The thick (blue) solid curve shows the total fit. For illustrative purposes, the $\Lambda ^0_ b \rightarrow { J \mskip 3mu/\mskip 2mu\psi } \Sigma^0$ signal component is artificially scaled to its measured upper limit. The shapes are identified in the legend. 
LOG_RU[..].pdf [91 KiB] HiDef png [610 KiB] Thumbnail [273 KiB] *.C file 

Result of the hypothesis tests conducted using the CLs method by varying ${\cal{R}}$ is shown. The observed CLs distribution is shown by the round (black) points. The expected CLs distribution (based on the background only hypothesis) is shown by the dashed line (black), with 1 and 2$\sigma$ uncertainty bands depicted in dark shaded (green) and light shaded (yellow) bands. The observed and expected upper limits are obtained by seeing where the bands cross the pvalue of 0.05 shown as the horizontal (red) line. 
CLs_new.pdf [14 KiB] HiDef png [157 KiB] Thumbnail [126 KiB] *.C file 

Distribution of $ { J \mskip 3mu/\mskip 2mu\psi } \Lambda$ mass for Run 1 data. Error bars without data points indicate empty bins. Also shown is the projection of the joint fit to the data. The thick (blue) solid curve shows the total fit. The $\Lambda ^0_ b \rightarrow { J \mskip 3mu/\mskip 2mu\psi } \Sigma^0$ signal component is artificially scaled to its measured upper limit. The rest of the shapes are identified in the legend. 
LOG_RU[..].pdf [96 KiB] HiDef png [567 KiB] Thumbnail [257 KiB] *.C file 

Distributions of $ { J \mskip 3mu/\mskip 2mu\psi } \Xi^$ mass shown as points with error bars for (left) Run 1 and (right) Run 2 data. The total fit to data is shown as a solid (blue) curve. The $\Xi_b^\rightarrow { J \mskip 3mu/\mskip 2mu\psi } \Xi^$ signal is fit with the sum of two Crystal Ball functions with the same mean and width, but different tail parameters, shown as the dashed (blue) curve. The combinatorial background shape is fit with an exponential function, shown as a dashed (red) curve. 
Fit_Jp[..].pdf [25 KiB] HiDef png [262 KiB] Thumbnail [213 KiB] *.C file 

Fit_Jp[..].pdf [25 KiB] HiDef png [256 KiB] Thumbnail [211 KiB] *.C file 

Animated gif made out of all figures. 
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Results from the fit to the $ { J \mskip 3mu/\mskip 2mu\psi } \Lambda$ mass distribution. The fitted yields are indicated by $N$. Note $N_{\Xi_b \rightarrow { J \mskip 3mu/\mskip 2mu\psi } \Xi}$ indicates the sum of $\Xi_b^$ and $\Xi_b^0$ decays. 
Table_1.pdf [66 KiB] HiDef png [52 KiB] Thumbnail [27 KiB] tex code 
Created on 04 April 2020.