The pseudorapidity distributions of charged hadrons in proton-lead collisions at nucleon-nucleon center-of-mass energies $\sqrt{s_{_\mathrm{NN}}} =$ 5.02 and 8.16 TeV are presented. The measurements are based on data samples collected by the CMS experiment at the LHC. The number of primary charged hadrons produced in non-single-diffractive proton-lead collisions is determined in the pseudorapidity range $|\eta_\mathrm{lab}| <$ 2.4. The charged-hadron multiplicity distributions are compared to the predictions from theoretical calculations and Monte Carlo event generators. In the center-of-mass pseudorapidity range $|\eta_\mathrm{cm}| < 0.5$, the average charged-hadron multiplicity densities $<\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta_{\mathrm{cm}}>$$\vert_{|\eta_{\mathrm{cm}}| < 0.5}$ are 17.31 $\pm$ 0.01 (stat) $\pm$ 0.59 (syst) and 20.10 $\pm$ 0.01 (stat) $\pm$ 0.85 (syst) at $\sqrt{s_{_\mathrm{NN}}} =$ 5.02 and 8.16 TeV, respectively. The particle densities per participant nucleon are compared to similar measurements in proton-proton, proton-nucleus, and nucleus-nucleus collisions.
The azimuthal anisotropy Fourier coefficients ($v_n$) in 8.16 TeV pPb data are extracted via long-range two-particle correlations as a function of event multiplicity and compared to corresponding results in pp and PbPb collisions. Using a four-particle cumulant technique, $v_n$ correlations are measured for the first time in pp and pPb collisions. The $v_2$ and $v_4$ coefficients are found to be positively correlated in all collision systems. For high multiplicity pPb collisions an anticorrelation of $v_2$ and $v_3$ is observed, with a similar correlation strength as in PbPb data at the same multiplicity. The new correlation results strengthen the case for a common origin of the collectivity seen in pPb and PbPb collisions in the measured multiplicity range.
The collective behavior of K$^0_\mathrm{S}$ and $\Lambda/\bar{\Lambda}$ strange hadrons is studied by measuring the elliptic azimuthal anisotropy ($v_2$) using the scalar-product and multiparticle correlation methods. Proton-lead (pPb) collisions at a nucleon-nucleon center-of-mass energy $\sqrt{s_\mathrm{NN}}$ = 8.16 TeV and lead-lead (PbPb) collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV collected by the CMS experiment at the LHC are investigated. Nonflow effects in the pPb collisions are studied by using a subevent cumulant analysis and by excluding events where a jet with transverse momentum greater than 20\GeV is present. The strange hadron $v_2$ values extracted in \pPb collisions via the four- and six-particle correlation method are found to be nearly identical, suggesting the collective behavior. Comparisons of the pPb and PbPb results for both strange hadrons and charged particles illustrate how event-by-event flow fluctuations depend on the system size.
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