TWO-PARTICLE CORRELATIONS IN pp COLLISIONS AT 13 TeV MEASURED WITH CMS∗

Results on two-particle angular correlations for charged particles emitted in pp collisions at a center-of-mass energy of 13 TeV are presented as a function of charged-particle multiplicity and transverse momentum (pT). In high-multiplicity events, a long-range (|η| > 2.0), near-side (∆φ = 0) structure emerges in the two-particle ∆η–∆φ correlation functions. The overall correlation strength is similar to that found in earlier pp data at 7 TeV, but is measured up to much higher multiplicity values. A detailed study in pp collisions at 7 TeV of the second-order (v2) azimuthal anisotropy harmonics of charged particles, K S and Λ/Λ̄ particles are extracted from long-range two-particle correlations as a function of particle multiplicity and transverse momentum, and are also compared with values obtained in pPb and PbPb collisions at similar multiplicities.


Introduction
The discovery of long-range two-particle azimuthal correlations at large relative pseudorapidity in high-multiplicity proton-proton [1] and protonlead [2] collisions at CMS has opened up new opportunities of studying novel dynamics of particle production in small but high-density Quantum Chromodynamic (QCD) systems.Similar long-range correlation structures at small relative azimuthal angle ∆φ ≈ 0 were first observed in relativistic nucleus-nucleus (AA) collisions.Such correlations have been extensively studied and it has been suggested that the hydrodynamic collective flow of a strongly interacting and expanding medium is responsible for these long-S.M. Dogra range correlations in large heavy-ion collision systems.A wide range of models have been suggested to explain the emergence of these correlations in pp and pPb collisions, while models based on a hydrodynamic approach can describe many aspects of the observed correlations [3], it has been proposed that initial-state correlations of gluon fields could also lead to similar effects [4].To provide new insights on understanding the long-range correlation phenomenon in high-multiplicity pp collisions, the results of two-particle azimuthal correlations with unidentified charged particles and identified particles of K 0 S and Λ/ Λ are also discussed.The anisotropy harmonics v 2 are extracted at 7 TeV from long-range (|∆η| > 2) two-particle correlations by associating either an unidentified charged particle, or an identified V0 particle (K 0 S , Λ/ Λ ) with another unidentified charged particle and are expressed as a function of particle p T and event multiplicity.

The CMS experiment and two particle correlations
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL, |η| < 3), and a brass and scintillator hadron calorimeter (HCAL, |η| < 3), each composed of a barrel and two endcap sections.Extensive forward calorimetry (HF, 3 < |η| < 5) complements the coverage provided by the barrel and endcap detectors.The silicon tracker measures charged particles within the pseudorapidity range |η| < 2.5.A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in [5].
The distributions in relative azimuthal angle (∆φ = φ trig − φ assoc ) and relative pseudorapidity (∆η = η trig − η assoc ) between trigger and associated particles are constructed to obtain the per-trigger yield, 1 is the same as in [1,2].The dominant correlation peak near (∆η, ∆φ) = (0, 0) due to jet fragmentation, a long-range ridge structure is seen at ∆φ ≈ 0 extending at least 4 units in |∆η|, while such structure is not observed at low multiplicity.On the away side (∆φ ≈ π) of the correlation functions, a long-range structure is also seen and found to exhibit a larger magnitude compared to that on the near side.To quantitatively investigate these long-range nearside correlations, and to provide a direct comparison to pp results at lower collision energy, one-dimensional (1D) distributions in ∆φ are constructed by averaging the signal and background 2D distributions over 2 < |∆η| < 4, as done in [1,2].The correlated portion of the associated yield is estimated by using an implementation of the zero-yield-at-minimum (ZYAM) procedure [6].The details of the analysis are mentioned in [7].
( r a d ia n s ) φ ∆

Results
Figure 2 (a) shows that the associated yield of long-range near-side correlations for events with N offline trk ≥ 105 for 13 TeV, and N offline trk ≥110 for 7 TeV, peaks at the region of 1 < p T < 2 GeV/c for both center-of-mass energies.The yield reaches a maximum around p T ≈ 1 GeV/c and decreases with increasing p T and has no center-of-mass energy dependence.The multiplicity dependence of the associated yield for 1 < p T < 2 GeV/c particle pairs is shown in Fig. 2 (b).For low-multiplicity events, the associated yield determined with the ZYAM procedure is consistent with zero.This indicates that ridge-like correlations are absent or smaller than the negative correlations expected because of, for example, momentum conservation.At higher multiplicity for N offline trk 40, the ridge-like correlation emerges as shown in Fig. 2 (b), with an approximately linear rise of the associated yield and compared with gluon saturation model √ s = 13 TeV [4], which predicts a faster rise than that observed in the data for the very high-multiplicity region.Right plot of Fig. 2 compares the associated yields in pp, pPb, and PbPb collisions for 1 < p T < 2 GeV/c as a function of the N offline trk .In all three systems, the ridge-like correlations become significant at a multiplicity value of about 40, and exhibit a nearly linear increase for higher values.For a given track multiplicity, the associated yield in pp collisions is roughly 10% and 25% of those observed in PbPb and pPb collisions, respectively, which clearly suggests a strong collision system size dependence of the long-range near-side correlations.To investigate more about the origin of long-range correlations, the v 2 measurements for pp collisions at 7 TeV are also studied as a function of p T for inclusive charged particles as well as K 0 S and Λ/ Λ as a function of p T for low-and high-multiplicity event as shown in Fig. 3.The extracted v 2 values mainly reflects back-to-back jet correlations on the away side as there is no evidence of long-range near-side correlation being seen in these lowmultiplicity events.However, for the high-multiplicity events with 110 ≤ N offline trk < 150, a deviation of v 2 between particle species is observed.In the lower p T region of 2.5 GeV/c, the v 2 of K 0 S is bigger than that of Λ/ Λ at a given p T value.Both are consistently below the inclusive charged particle v 2 values.Since most charged particles are pions in this p T range, this indicates that lighter particle species exhibit a stronger azimuthal anisotropy signal similar to the observed in AA collisions [8] and pPb collisions [9].This behavior is found to be qualitatively consistent with hydrodynamic models.

N trig d 2 N
d∆φd∆η .Figure 1 shows the 2D ∆η-∆φ correlation functions, for pairs of a charged trigger particles and a charged associated particle, in low (N offline trk < 35) and high-multiplicity (N offline trk ≥ 105).The definition of N offline trk

Fig. 1 .
Fig.1.The 2D (∆η, ∆φ) two-particle correlation functions in pp collisions at 13 TeV for the pairs of charged particles in the range of 1 < p T < 3 GeV/c.

Fig. 2 .
Fig. 2. Left: Associated yield for the near side of the correlation function for pp data at 7 TeV and 13 TeV, (a) averaged over 2 < ∆η < 4 as a function of p T , (b) for 1 < p T < 2 GeV/c as a function of N offline trk and compared with gluon saturation model [4].Right: Comparison of associated yield in pp collisions at 13 and 7 TeV, with pPb collisions at 5.02 TeV, and PbPb collisions at 2.76 TeV.

Fig. 3 .
Fig. 3.The v 2 results of inclusive charged particles, K 0 S and Λ/ Λ as a function of p T in pp collisions at 7 TeV, for 10 ≤ N offline trk < 20 (left), and 110 ≤ N offline trk < 150 (middle).The v sub 2 results as a function of p T for 110 ≤ N offline trk < 150 is shown in the right panel.The systematic uncertainties are indicated by the shaded areas.