Study of the hadronisation process from single hadron and hadron-pair production in SIDIS at COMPASS

Hadron production in hard scattering reactions is described by the hadronization mechanism which combines quarks into final-state hadrons. Within the theoretical framework of leading-twist collinear QCD, the cross section for hadron production in semi-inclusive deep-inelastic scattering can be factorized into a hard scattering cross section describing the hard interaction at the quark level calculable in perturbative QED, and non-perturbative universal functions: parton distribution functions which reflect the quark structure of initial-state hadrons and collinear fragmentation functions which encode details on the hadronization process. In the last decades, a major effort has been achieved on theoretical and experimental levels and allowed to constraint, with very high precision, parton distribution functions except strange quark distribution, which still carries large uncertainties. Fragmentation functions, however, remain at a very preliminary stage of study with a growing interest in a more accurate and precise knowledge. Nowadays, while pion fragmentation functions are known with a limited precision and kaon fragmentation functions are poorly known, the situation for dihadron fragmentation functions turns out to be behind the schedule and no studies or measurements have been yet performed.Measuring both single hadron and hadron pair multiplicities in semi-inclusive deep inelastic scattering at COMPASS represent a fundamental contribution towards a better understanding of the hadronization process and a first measurement for hadron pair multiplicities in SIDIS. These measurements will be presented and discussed.