Study of the production of (anti-)deuterons in pp collisions at the LHC with the ALICE experiment

At the LHC an abundant production of light (anti-)nuclei, i.e. with a mass number A $\leq$ 4, is observed. However, although abundantly produced, their production mechanisms are still not completely understood. Indeed, light \mbox{(anti-)nuclei} are characterised by a binding energy of the order of 1 MeV per nucleon and this value is very low if compared with the chemical freeze-out temperature of a Pb--Pb collision ($T_{ch}~\sim$ 150 MeV). Therefore, in principle the observation of such fragile objects is not expected and a comparison of the experimental data with the theoretical predictions can help to shed light on the production mechanism of these loosely bound states. ALICE is the most suitable LHC experiment for the study of light (anti-)nuclei, thanks to its excellent particle identification (PID) capabilities. In particular, the identification of light nuclei is possible via the measurement of the specific energy loss d$E$/d$x$ in the Time Projection Chamber (TPC) and with the time information provided by the Time Of Flight (TOF) detector. Among light (anti-)nuclei, (anti-)deuterons are the lightest and consequently the most abundantly produced. The ALICE Collaboration has measured the production spectra of (anti-)deuterons as a function of charged particle multiplicity $\langle \mathrm{d}N_{ch}/\mathrm{d}\eta\rangle$ in proton-proton (pp) collisions at the energy of $\sqrt{s} = $ 7 TeV, in proton-lead (p--Pb) collisions at $\sqrt{s_{\mathrm{NN}}} = $ 5 TeV and in lead-lead (Pb--Pb) collisions a $\sqrt{s_{\mathrm{NN}}} = $ 2.76 TeV. In this work, the (anti-)deuteron production spectra in pp collisions at $\sqrt{s} = $ 13 TeV as a function of the event charged particle multiplicity and in the Minimum Bias data sample is presented. Thanks to the extremely large data sample collected in 2016 and 2017 by ALICE, consisting of almost 1 billion pp collisions, it has been possible to study the (anti-)deuteron production in very fine multiplicity classes and in particular reaching multiplicities that are similar to those observed in p--Pb collisions. This is a crucial element to have a comparison of different colliding systems and to understand if the production mechanism of light (anti-)nuclei is similar in small and medium-large colliding systems. Relying on the measurement of the (anti-)proton production spectra, the coalescence parameter $B_2$, which is related to the probability to form a deuteron via coalescence, and the ratio between $p_{\mathrm{T}}$-integrated yields of (anti-)deuterons and (anti-)protons d/p are computed. The measurement of $B_2$ and d/p as a function of charged particle multiplicity is a useful tool for shading light on the dependence of the production mechanisms on the system size. The results are also relevant for background studies in the search for dark matter via the measurement of (anti-)nuclei in space and as input for the understanding of the formation of QCD bound states in high energy hadron physics. The results as a function of the charged particle multiplicity are compared with the predictions of the two available classes of phenomenological models, namely the statistical hadronisation model and the coalescence model. This is the first deuteron analysis within the ALICE Collaboration in which such comparison is performed.