Measurements of particle production and particle correlations in proton-proton and proton-ion collisions with LHCb

In this thesis, measurements of particle production and particle correlations using proton-proton ($pp$) and proton-ion ($p\text{Pb}$) collisions recorded with the $\mbox{LHCb}$ experiment at the Large Hadron Collider are presented. The charged particle multiplicity and the differential charged particle density are studied in $pp$ collisions at a centre-of-mass energy of $\sqrt{s}=7\mathrm{\,Te\kern -0.1em V}$. The measurement is performed for events with at least one charged particle in the kinematic range of ${p>2{\mathrm{\,Ge\kern -0.1em V\!/}c}}$, $p_{\rm T}>0.2{\mathrm{\,Ge\kern -0.1em V\!/}c}$ and $2.0<\eta<4.8$. The mean particle multiplicity, $\mu$, and the corresponding root-mean-square deviation, $\sigma$, are measured to be ${\mu=11.30\pm0.01\pm0.09}$ and ${\sigma=9.50\pm0.01\pm0.02}$, where the uncertainties are statistical and systematic, respectively. Results for particle multiplicities and particle densities are presented as functions of $\eta$ and $p_{\rm T}$ of the particles, and are compared to predictions from different Monte Carlo event generators. Furthermore, a measurement of two-particle angular correlations is performed by using charged particles produced in $p\text{Pb}$ collisions at a nucleon-nucleon centre-of-mass energy of $\sqrt{s_{\scriptscriptstyle N\!N}}=5.02\mathrm{\,Te\kern -0.1em V}$. Data with two different beam configurations are analysed, in which either the proton or the nucleus remnant is traversing the $\mbox{LHCb}$ detector. The particle correlations are measured using the azimuthal angle separation, $\Delta\phi$, and pseudorapidity separation, $\Delta\eta$. The emergence of a correlation structure on the near side ($\Delta\phi=0$), elongated over a long range in $\Delta\eta$ is observed for particles in a $p_{\rm T}$-range of $1-3{\mathrm{\,Ge\kern -0.1em V\!/}c}$ in events exhibiting a high particle multiplicity. This measurement is the first observation of the $\textit{near-side ridge}$ in $p\text{Pb}$ collisions in the forward region and complements similar observations in $pp$ and $p\text{Pb}$ collisions in the central rapidity region.