This thesis reports the branching fraction measurement of the rare Cabibbo-suppressed
decay Λ0 b → pπ −μ+ μ− . The decay is observed for the first time with a 5.5σ deviation from
the background-only hypothesis. This is the first observation of a b→ d quark transition
in the baryon sector. The dataset used for the measurement corresponds to 3 fb−1 of pp
collisions collected at the LHCb experiment at CERN. The branching fraction is measured
using Λ0 b →J/ψ (→μ+ μ−)pπ − as a normalisation channel and is measured as
B(Λ0 b → pπ−μ+ μ−) = (6.9 ± 1.9 ± 1.1+1.3
−1.0 ) × 10−8 ,
where the first error is the statistical uncertainty, the second is the systematic uncertainty
and the third is the uncertainty on B(Λ0 b → J/ψ pπ−). The measurement of B(Λ0 b →
pπ −μ+ μ− ) can be combined with the branching fraction measurement for Λ0 b → pK − μ+μ−
to give constraints on the ratio of CKM matrix elements |Vtd/Vts|. Such a determination of |Vtd/Vts| requires a theory prediction for the ratio of the relevant form factors.
This thesis also reports the ratio of tracking efficiencies, [epsilon_{rel}] , between data and simulation
for Ks 0 → π +π− decays occurring within the LHCb detector acceptance. As Ks 0 particles
are long-lived, their associated tracking efficiencies are less precisely determined compared
to those of shorter-lived particles. The average value of [epsilon_{rel}] for Ks 0 → π+ π − decays, where
the Ks 0 has a flight distance of > 1 m, is found to be
∼[ epsilon_{rel}] = 0.70 ± 0.02.
To perform this calibration measurement a novel technique was developed which has
the potential to be used in measuring the value of [epsilon_{rel}] for other decays involving long-lived
particles.