1 Introduction

The study of angular correlations of heavy-flavour (charm and beauty) particles in ultra-relativistic hadronic collisions allows the investigation of fundamental properties of quantum chromodynamics (QCD) in the heavy-flavour domain [1, 2]. In particular, the angular-correlation function between prompt D mesons and charged particles in proton–proton (pp) collisions is sensitive to the mechanisms of charm-quark production, fragmentation, and hadronisation into charm hadrons. The term “prompt” refers to D mesons originating both from direct charm-quark fragmentation and from the strong decay of excited charm resonances, and excludes D mesons produced from beauty-hadron weak decays. The typical structure of the two-dimensional correlation function between “trigger” D mesons and “associated” charged particles, expressed in terms of the pseudorapidity difference (\(\Delta \eta = \eta _{\mathrm{ch}}-\eta _{\mathrm{D}}\)) and azimuthal angle difference (\(\Delta \varphi = \varphi _{\mathrm{ch}}-\varphi _{\mathrm{D}}\)), features a near-side (NS) peak, centred at (\(\Delta \varphi ,\Delta \eta ) = (0,0)\), and an away-side (AS) peak at \(\Delta \varphi = \pi \) that is elongated along \(\Delta \eta \) [3]. Both peaks sit on top of an approximately flat continuum extending over the full (\(\Delta \varphi ,\Delta \eta \)) range. The height and width of the two correlation peaks are sensitive to the charm-quark production mechanisms.

Due to their large mass, the production of charm-quark pairs occurs through hard parton–parton scattering processes with large momentum transfers, and can be described by perturbative QCD (pQCD) calculations. While in leading-order (LO) processes the two quarks are produced back-to-back in azimuth, the next-to-leading-order (NLO) production mechanisms, such as flavour excitation and gluon splitting, can break this topology and alter the shape of the two correlation peaks [4]. Recent studies at the LHC suggest a relevant contribution from gluon splitting to heavy-quark production, possibly underestimated by Monte Carlo (MC) event generators with LO or NLO accuracy [5, 6]. The analysis of the properties of the near-side peak also allows for detailing the fragmentation and hadronisation processes which, starting from a coloured charm quark, lead to the formation of a D meson surrounded by a spray of colourless particles, experimentally identifiable as a charm jet. The production cross section of jets containing D mesons, as well as the jet momentum fraction carried by the D meson along the jet-axis direction, were recently measured by the ALICE and ATLAS Collaborations [7, 8]. In this regard, a systematic and differential analysis of the near-side correlation peak in terms of transverse momenta of trigger D meson (\(p_{\mathrm{T}}^{\mathrm{D}} \)) and other associated fragmenting particles (\(p_{\mathrm{T}}^{\mathrm{assoc}} \)), and of the angular distance of associated particles from the D mesons, can provide additional information with respect to measurements that treat charm jets as a whole entity.

In recent years, the study of high-multiplicity pp collisions has become of particular interest. The ALICE Collaboration has measured a faster-than-linear increase of prompt D-meson self-normalised yields for increasing relative event multiplicity in pp collisions at a centre-of-mass energy of \(\sqrt{s} = 7\) TeV, employing both central- and forward-rapidity multiplicity estimators [