1 Introduction

High-energy heavy-ion (A–A) collisions offer a unique possibility to study nuclear matter under extreme temperature and density, in particular the properties of the deconfined quark–gluon plasma (QGP) [1,2,3,4,5,6,7], which was predicted by quantum chromodynamics (QCD) [8,9,10,11,12]. The interpretation of the heavy-ion results depends crucially on the comparison with results from small collision systems such as proton–proton (pp) or proton–nucleus (p–A). Measurements in pp collisions establish a reference for larger systems and are used to test perturbative QCD models. The p–A collisions, which are intermediate between pp and A–A collisions in terms of system size and number of produced particles [13,14,15], are traditionally used to separate initial and final-state effects [16, 17]. However, at the LHC the pseudorapidity density (\(\hbox {d}N_{\mathrm{ch}}/\hbox {d}\eta \)) of final-state charged particles in pp and p–A collisions can reach values comparable to those achieved in semi-peripheral Au–Au [18] and Pb–Pb collisions [19] at the top energies of RHIC and the LHC, respectively. Therefore, there exists a possibility of final-state effects due to the formation of dense matter even in p–A collisions.

During the evolution of the systems formed in A–A or p–A collisions, the yields of short-lived resonances may be influenced by interactions in the late hadronic phase. The re-scattering of the decay products in the medium may prevent the detection of a fraction of the resonances, whereas pseudo-elastic hadron scattering can regenerate them. The strengths of the re-scattering and regeneration effects depend on the scattering cross sections of the decay products, the particle density of the produced medium, the lifetimes of the resonances and the lifetime of the hadronic phase. The latter can be studied by comparing yields of short-lived resonances with different lifetimes to yields of long-lived particles [20,21,22,23]. ALICE has observed that in the most central p–Pb and Pb–Pb collisions [21, 22, 24] the \(\hbox {K}^{*0}/\hbox {K}\) ratio is significantly suppressed with respect to peripheral collisions, pp collisions, and predictions of statistical hadronization models [25, 26]. A similar suppression is also observed for \(\rho ^{0}/\pi \) ratio in central Pb–Pb collisions with respect to peripheral Pb–Pb collisions, pp collisions, and predictions of statistical hadronization models [27]. No suppression is observed for the \({\phi }/\hbox {K}\) ratio, as the \({\phi }\) meson lives ten times longer than the \(\hbox {K}^{*0}\). To provide more insight into the properties of the hadronic phase, other resonances whose lifetimes are in between those of the \(\hbox {K}^{*0}\) (\(\tau _{\mathrm{K}^{*0}} =4.17 \pm 0.04\ \hbox {fm}/c\) [28]) and \(\phi \) (\(\tau _{\phi } = 46.4 \pm 0.14\ \hbox {fm}/c\) [28]) should be studied. The \(\Lambda (1520)\) resonance is a strongly decaying particle having \(\tau _{\Lambda (1520)} = 12.6 \pm 0.8\ \hbox {fm}/c\) [28]. This makes the study of the \(\Lambda (1520)\) resonance important for understanding the evolution of the system. Previously, the STAR experiment at RHIC measured \(\Lambda (1520)\) production in pp, d–Au and Au–Au collisions at a center-of-mass energy per nucleon pair (\(\sqrt{s_{\mathrm{NN}}}\)) of 200 GeV [23, 29] and showed a hint of suppression of the \(\Lambda (1520)/\Lambda \) yield ratio in central Au–Au collisions compared to the values observed in pp and d–Au collisions. A measurement of the \(\Lambda (1520)\) in Pb–Pb collisions at \(\sqrt{s_{\mathrm{NN}}} = 2.76\ \hbox {TeV}\) was reported in [30]. The \(\Lambda (1520)/\Lambda \) yield ratio is found to be suppressed in central (0–20%) Pb–Pb collisions relative to peripheral (50–80%) Pb–Pb collisions. The suppression factor is found to be \(0.54\,\, \pm \,\, 0.08\)(stat)\( \,\,\pm \,\, 0.12\)(sys). The EPOS3 [31,32,33] event generator, which incorporates the UrQMD model [34] to simulate the hadronic phase, predicts a significant suppression of the \(\Lambda (1520)/\Lambda \) yield ratio in central Pb–Pb collisions at \(\sqrt{s_{\mathrm{NN}}} = 2.76\ \hbox {TeV}\) [35]. However, the corresponding Pb–Pb measurements show a stronger suppression than predicted by EPOS3. This motivates the study of the \(\Lambda (1520)\) resonance in different collision systems at the LHC in order to better understand the properties of the hadronic phase. The pp and p–Pb data studied in this paper thus provide important baseline measurements for the corresponding results in Pb–Pb collisions.

In addition, several measurements [36,37,38] in p–A collisions indicate that these systems cannot be explained as an incoherent superposition of pp collisions, rather suggesting [39, 40] the presence of collective effects. In p–Pb collisions, a significant increase of the average transverse momentum as a function of charged particle density has been observed [41] and this is reminiscent of the effect observed in Pb–Pb collisions, where it is interpreted as a consequence of radial flow. The measurement of the \(p_{\mathrm{T}}\) spectra of the \(\Lambda \)(1520) resonance can further confirm such effects, and thus can be used to better constrain the properties of the collective radial expansion.

Recently, the ALICE Collaboration reported measurements of multi-strange particles in p–Pb collisions [42]. The hyperon-to-pion ratios increase with multiplicity in p–Pb collisions, and range from the values measured in pp to the those in Pb–Pb collisions. The rate of the increase is more pronounced for particles with higher strangeness content. Therefore, it will be interesting to study the production of excited strange hadrons, like \(\Lambda \)(1520), \(\Xi \)(1530), as a function of multiplicity. Doing so in p–Pb collisions would help bridge the gap between the pp and Pb–Pb collision systems.

Throughout this paper, the \(\Lambda \)(1520) resonance will be referred as \(\Lambda ^{*}\). The invariant mass of \(\Lambda ^{*}\) is reconstructed through its hadronic decay channel \(\Lambda ^{*}\rightarrow \hbox {pK}^{-}\), with a branching ratio of \(\hbox {BR} = (22.5 \pm 1)\%\) [28]. The invariant mass distributions of the \(\hbox {pK}^-\) and \(\overline{\mathrm{p}}\hbox {K}^+\) were combined to reduce the statistical uncertainties. Therefore in this paper, unless specified, \(\Lambda ^{*}\) denotes \(\Lambda ^{*}+\overline{\Lambda }^*\). The paper is organized as follows. The experimental setup is briefly presented in Sect. 2. Section 3 describes the data samples and event selection. Section 4 illustrates the analysis procedure as well the determination of the systematic uncertainties. The results are discussed in Sect. 5, and a summary is provided in Sect. 6.

2 Experimental setup

The ALICE [43, 44] detector is specifically designed to study a variety of observables in the high-multiplicity environment achieved in central A–A collisions at LHC energies. The detector is optimized to reconstruct and identify particles produced in the collisions over a wide momentum range.

In this analysis, only the central barrel sub-detectors were used for track reconstruction. These detectors have a common pseudorapidity coverage in the laboratory frame of \(|\eta _{\mathrm{lab}}| < 0.9\), and are placed in a solenoidal 0.5 T magnetic field directed along the beam axis. The Inner Tracking System (ITS) [45] provides high resolution tracking points close to the beam line. The ITS is composed of six cylindrical layers of silicon detectors, located at radial distances between 3.9 and 43 cm from the beam axis. The two innermost layers are Silicon Pixel Detectors (SPD), the two intermediate ones are Silicon Drift Detectors (SDD), and the two outermost ones are Silicon Strip Detectors (SSD). The Time Projection Chamber (TPC) [46] is the main tracking detector of the central barrel. The TPC is a cylindrical drift chamber, and covers the radial distance \(85< r < 247\ \hbox {cm}\). In addition to tracking, the TPC is used for the identification of particles via their specific ionization energy loss \(\hbox {d}E/\hbox {d}x\) as they pass through the active gas region of the TPC. The separation power of particle identification in the TPC defined in terms of standard deviations as a function of particle momentum is discussed in [44]. This analysis uses charged tracks, which are reconstructed using tracking information, both in the ITS and in the TPC. The Time-Of-Flight (TOF) detector [47] is an array of Multi-gap Resistive Plate Chambers (MRPC). The time resolution of TOF is about 85 ps, increasing to about 120 ps due to a worse start-time (collision-time) resolution in the case of low multiplicity events [44]. The TOF is located at a radial distance of \(370< r < 399\ \hbox {cm}\) from the beam axis. The purpose of this detector is to identify particles using the time-of-flight, together with the momentum and path length measured with the ITS and the TPC. The TOF can separate pions from kaons and protons by twice its resolution, for momenta up to 2.5 and \(4\ \hbox {GeV}/c\), respectively.

Forward detectors, such as the V0, T0, and Zero-Degree Calorimeters (ZDC) [48,49,50], are used for triggering and event characterization. The V0 consists of two arrays of 32 scintillator detectors. They cover the full azimuthal angle in the pseudorapidity regions \(2.8< \eta _{\mathrm{lab}}