Using a protonproton collision data sample corresponding to an integrated luminosity of 3 fb$^{1}$ collected by LHCb at centerofmass energies of 7 and 8 TeV, about 3800 $\Xi_b^0\to\Xi_c^+\pi^$, $\Xi_c^+\to pK^\pi^+$ signal decays are reconstructed. From this sample, the first measurement of the $\Xi_b^0$ baryon lifetime is made, relative to that of the $\Lambda_b^0$ baryon. The mass differences $M(\Xi_b^0)M(\Lambda_b^0)$ and $M(\Xi_c^+)M(\Lambda_c^+)$ are also measured with precision more than four times better than the current world averages. The resulting values are $\frac{\tau_{\Xi_b^0}}{\tau_{\Lambda_b^0}} = 1.006\pm0.018\pm0.010$, $M(\Xi_b^0)  M(\Lambda_b^0) = 172.44\pm0.39\pm0.17 MeV/c^2$, $M(\Xi_c^+)  M(\Lambda_c^+) = 181.51\pm0.14\pm0.10 MeV/c^2$, where the first uncertainty is statistical and the second is systematic. The relative rate of $\Xi_b^0$ to $\Lambda_b^0$ baryon production is measured to be $\frac{f_{\Xi_b^0}}{f_{\Lambda_b^0}}\frac{{\cal{B}}(\Xi_b^0\to\Xi_c^+\pi^)}{{\cal{B}}(\Lambda_b^0\to\Lambda_c^+\pi^)}\frac{{\cal{B}}(\Xi_c^+\to pK^\pi^+)}{{\cal{B}}(\Lambda_c^+\to pK^\pi^+)} = (1.88\pm0.04\pm0.03)\times10^{2}$, where the first factor is the ratio of fragmentation fractions, $b\to\Xi_b^0$ relative to $b\to\Lambda_b^0$. Relative production rates as functions of transverse momentum and pseudorapidity are also presented.
Invariant mass spectrum for (left) $\Lambda ^0_ b \rightarrow \Lambda ^+_ c \pi ^ $ and (right) $\Xi ^0_ b \rightarrow \Xi^+_ c \pi ^ $ candidates along with the projections of the fit. 
Lb2LcP[..].pdf [22 KiB] HiDef png [322 KiB] Thumbnail [238 KiB] *.C file 

Xib2Xi[..].pdf [30 KiB] HiDef png [320 KiB] Thumbnail [226 KiB] *.C file 

Efficiencycorrected yield ratio of $\Xi ^0_ b \rightarrow \Xi^+_ c \pi ^ $ relative to $\Lambda ^0_ b \rightarrow \Lambda ^+_ c \pi ^ $ decays in bins of decay time. A fit using an exponential function is shown. The uncertainties are statistical only. 
CorrYi[..].pdf [14 KiB] HiDef png [61 KiB] Thumbnail [45 KiB] *.C file 

Efficiencycorrected yield ratio of $\Xi ^0_ b \rightarrow \Xi^+_ c \pi ^ $ relative to $\Lambda ^0_ b \rightarrow \Lambda ^+_ c \pi ^ $ decays as functions of (left) $p_{\rm T}$ and (right) pseudorapidity, $\eta$. The points are positioned along the horizontal axis at the weighted average value within each bin. The uncertainties are statistical only. 
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Xb_eta[..].pdf [13 KiB] HiDef png [76 KiB] Thumbnail [69 KiB] *.C file 

Distributions of the $p K ^ \pi ^+ $ invariant mass for (left) $\Lambda ^+_ c $ and (right) $\Xi^+_ c $ candidates along with the projections of the fit. 
Lb2LcP[..].pdf [29 KiB] HiDef png [218 KiB] Thumbnail [168 KiB] *.C file 

Xib2Xi[..].pdf [30 KiB] HiDef png [308 KiB] Thumbnail [219 KiB] *.C file 

Animated gif made out of all figures. 
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Summary of systematic uncertainties on the reported measurements. Below, PR represents the relative uncertainty on the production ratio measurement. 
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Supplementary material full pdf 
supple[..].pdf [85 KiB] 

These 3 figures compare recent masses and lifetimes to those measured in this paper. 
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Fig6.pdf [12 KiB] HiDef png [82 KiB] Thumbnail [70 KiB] *C file 

Fig7.pdf [13 KiB] HiDef png [62 KiB] Thumbnail [52 KiB] *C file 
Created on 18 October 2019.