Muon identification and B physics studies at the Tevatron Collider Experiment DO

This dissertation describes muon particle identification and studies of final states, including the di-muon resonance J/ψ at the DØ experiment at the Fermilab Tevatron Collider.; Time-to-distance relation studies for the muon proportional drift tubes have led to a parametrization allowing the determination of the muon trajectory to an accuracy of 400 microns.; I present three early results based on the di-muon data collected in the running period 2001–2002: the first measurement of the inclusive J/ψ production cross section over an extended rapidity range (0.0–1.8) at $s$ = 1.96 TeV, a preliminary measurement of the $B0s$ meson lifetime by using the decay mode $B0s$ → J/ψ&phis;, and a preliminary measurement of the $B0d$ meson lifetime via the decay mode $B0d$ → J/ψK*.