1 Introduction

The study of hadron production in pp and p–Pb collisions systems can be used as a reference for the interpretation of the heavy-ion results. As resonances are short-lived particles (lifetime \(\approx 10^{-23}\)s), they carry the information regarding the dynamic evolution of particle production in heavy-ion collisions [1]. The measurement of strange hadron production in high-energy hadronic interactions provides a way to study the characteristics of quantum chromodynamics (QCD), the theory of strongly interacting matter. The particle production in asymmetric collision system (e.g. p–Pb) is influenced by nuclear effects in the initial state. Partons from the proton side (backward rapidity) are expected to undergo multiple scattering while traversing the Pb nucleus. Pb-side yields (forward rapidity) are likely to be affected by the properties of the nucleus. Previously, a rapidity-dependent study has been done in d–Au collisions at the Relativistic Heavy-Ion Collider (RHIC) for pions and protons [2]. The rapidity-dependent study of particle production can be carried out by using a ratio called the rapidity asymmetry (\(Y_\mathrm{{asym}}\)), defined as

$$\begin{aligned} Y_\mathrm{{asym}}(p_\mathrm{{T}}) = \frac{Y_\mathrm{{F}}(p_\mathrm{{T}})}{Y_\mathrm{{B}}(p_\mathrm{{T})}}, \end{aligned}$$
(88.1)

where \(Y_\mathrm{{F}}\) and \(Y_\mathrm{{B}}\) are the spectra measured at forward and backward rapidities, respectively.

The study of \(Y_{\textrm{asym}}\) will help to determine the relative contributions of various physics processes to particle production, such as multiple scattering, nuclear shadowing, recombination of thermal partons and parton saturation [2].

We present the measurement of the integrated yields of \({\phi }\) mesons and the integrated-yield ratios of p, K\(^{0}_\mathrm{{s}}\), \({\Lambda , \phi , \Omega }\) and \( {\Xi }\) to pions as a function of charged-particle multiplicity in pp and p–Pb collisions. In addition, the \(Y_\mathrm{{asym}}\) of \({\phi }\) and K*\(^{0}\) in p–Pb collisions at \(\sqrt{s_\mathrm{{NN}}}\) = 5.02 TeV are discussed.

Fig. 88.1
figure 1

[Left Plot] The multiplicity-scaled integrated yield (dN/d\(y / \langle \)d\(N_{\textrm{ch}}\)/d\(\eta \rangle \) for \({\phi }\) as a function of \(\langle \)d\(N_\mathrm{{ch}}/\)d\(\eta \rangle \) in pp collisions at \(\sqrt{s}\) = 7 and 13 TeV and in p–Pb collisions at \(\sqrt{s_\mathrm{{NN}}}\) = 5.02 and 8.16 TeV. [Right plot] The ratio of yield of hadrons (p, K\(^{0}_\mathrm{{s}},{ \Lambda , \phi , \Omega , \Xi } )\) to pions as a function of \(\langle \)d\(N_{\textrm{ch}}\)/d\(\eta \rangle \) in pp, p–Pb, Pb–Pb and Xe–Xe collisions

Fig. 88.2
figure 2

The \(Y_\mathrm{{asym}}\) of \({\phi }\) and K*\(^{0}\) as function of \(p_\mathrm{{T}}\) for various multiplicity classes in p–Pb collisions at \(\sqrt{s_\mathrm{{NN}}}\) = 5.02 TeV at mid-rapidity

2 Results

Figure  88.1 shows multiplicity-scaled integrated yields of the \({\phi }\) as a function of the charged-particle multiplicity in pp collisions at \(\sqrt{s}\) = 7 [3] and 13 TeV and, in p–Pb collisions at \(\sqrt{s_\mathrm{{NN}}}\) = 5.02 [4] and 8.16 TeV. The multiplicity-scaled integrated yield is constant within uncertainty as a function of \(\langle \)d\(N_{\textrm{ch}}\)/d\(\eta \rangle \). The integrated yield is independent of collision systems and energy. The right plot of Fig. 88.1 shows the ratios of the yields of p, K\(^{0}_{s}\), \({\Lambda , \phi , \Xi }\) and \(\Omega \) to pions as a function of charged-particle multiplicity in various collision systems at different energies. The strange to non-strange particle yield ratio shows a significant enhancement with increasing charged-particle multiplicity in pp and p–Pb collisions [5]. No significant energy dependence is observed. Particles having a higher strangeness content show strong enhancement in the yield ratio as a function of the charged-particle multiplicity. The yield ratios show similar behaviour at high multiplicity in pp and p–Pb collisions as the measurements in Pb–Pb collisions.

Fig. 88.3
figure 3

The \(Y_\mathrm{{asym}}\) of \({\phi }\) and K*\(^{0}\) with model (EPOS, HIJING) predictions as a function of \(p_\mathrm{{T}}\) for 0–100 \(\%\) multiplicity in p–Pb collisions at \(\sqrt{s_\mathrm{{NN}}}\) = 5.02 TeV at midrapidity

The rapidity asymmetry ratios (\(Y_\mathrm{{asym}}\)) for \({\phi }\) and K*\(^{0}\) as a function of \(p_\mathrm{{T}}\) for various multiplicity classes based on the V0A detector in p–Pb collisions at \(\sqrt{s_\mathrm{{NN}}}\) = 5.02 TeV are shown in Fig. 88.2. An asymmetry is observed at low \(p_\mathrm{{T}}\), whereas it is consistent with unity within uncertainties at high \(p_\mathrm{{T}}\). The \(Y_\mathrm{{asym}}\) value are large at high multiplicity, and it decreases as going from high to low multiplicity classes. \(Y_\mathrm{{asym}}\) for \({\phi }\) and K*\(^{0}\) shows similar behaviour within uncertainties. Figure  88.3 shows the comparison of \({\phi }\) and K*\(^{0}\) \(Y_\mathrm{{asym}}\) in 0–100\(\%\) multiplicity class with EPOS [6] and HIJING [7] model predictions. Both the models reproduce the data at low \(p_\mathrm{{T}}\), whereas they deviate at high \(p_\mathrm{{T}}\). The HIJING model predictions with and without shadowing parameters show similar behaviour within uncertainties, whereas a large deviation is observed in case of K*\(^{0}\) then \({\phi }\) at high \(p_\mathrm{{T}}\). The EPOS model calculations with UrQMD [8] ON and OFF also show a similar behaviour within uncertainty. The EPOS model shows less deviation for K*\(^{0}\) at high \(p_\mathrm{{T}}\) than the HIJING model.

3 Summary

The multiplicity-scaled integrated yield of \({\phi }\) as a function of the charged-particle multiplicity is independent of collision system and energies. Strangeness enhancement is observed from strange to non-strange hadron yield ratios to pions in pp and p–Pb collisions. The enhancement is larger for particles having larger strangeness content. High multiplicity pp and p–Pb collisions show similar ratios as those measured in Pb–Pb collisions. A rapidity asymmetry is observed at low \(p_\mathrm{{T}}\) in the high multiplicity class. \(Y_\mathrm{{asym}}\) decreases from high to low multiplicity class and it is consistent with unity at high \(p_\mathrm{{T}}\) within uncertainties. EPOS and HIJING models explain the \(Y_\mathrm{{asym}}\) data at low \(p_\mathrm{{T}}\) but show deviation at high \(p_\mathrm{{T}}\). The deviation is more important for HIJING than for EPOS. \(Y_\mathrm{{asym}} \) is also observed to be species independent.