1 Introduction

The theory of strong interactions, Quantum Chromodynamics (QCD), predicts that at sufficiently high energy density nuclear matter transforms into a deconfined state of quarks and gluons known as Quark–Gluon Plasma (QGP) [1, 2]. One of the possible signatures of a transition between the hadronic and partonic phases is the enhancement of fluctuations of the number of produced particles in the hadronic final state of relativistic heavy-ion collisions [3,4,5]. Event-by-event fluctuations and correlations may show critical behaviour near the phase boundary, including the crossover region where there is no thermal singularity, in a strict sense, associated with the transition from a QGP phase to a hadron-gas phase. A correlation analysis of event-by-event abundances of pions, kaons and protons produced in \(\text{ Pb--Pb }\) collisions at LHC energies may provide a connection to fluctuations of globally conserved quantities such as electric charge, strangeness and baryon number, and therefore shed light on the phase structure of strongly interacting matter [6].

In view of the predicted criticality signals at crossover for vanishing net-baryon densities [7], event-by-event fluctuations of relative particle yields are studied using the fluctuation measure \(\nu _\mathrm{dyn}[A,B]\) [8] defined in terms of moments of particle multiplicity distributions as

$$\begin{aligned} \nu _\mathrm{dyn}[A,B]= & {} \dfrac{\langle N_{A}(N_{A}-1) \rangle }{{\langle N_{A} \rangle }^{2}} + \dfrac{\langle N_{B}(N_{B}-1) \rangle }{{\langle N_{B} \rangle }^{2}} \nonumber \\&- 2\dfrac{\langle N_{A}N_{B} \rangle }{\langle N_{A} \rangle \langle N_{B} \rangle }, \end{aligned}$$

where \(N_{A}\) and \(N_{B}\) are the multiplicities of particles A and B measured event-by-event in a given kinematic range. The \(\nu _\mathrm{dyn}[A,B]\)Footnote 1 fluctuation measure contrasts the relative strength of fluctuations of species A and B to the relative strength of correlations between these two species. It vanishes when the particles A and B are produced in a statistically independent way [8, 9].

This study at LHC energies is of particular importance for establishing the energy and system size dependence of \(\nu _{\mathrm{dyn}}\) in order to understand the trend observed at lower collision energies from the RHIC Beam Energy Scan (BES) results reported by the STAR collaboration [10]. Furthermore, the advantage of this fluctuation measurement is its robustness against non-dynamical contributions such as those stemming from participant nucleon fluctuations and finite particle detection efficiencies [8, 11]. Measurements of the \(\nu _{\mathrm{dyn}}\) observable for net-charge fluctuations were already published by ALICE [12]. Moreover, for identified particles, it was measured at the Super Proton Synchrotron (SPS) [13] and at the Relativistic Heavy-Ion Collider (RHIC) [