Soft probes of the QGP: Pb-Pb and p-Pb CMS results

The CMS collaboration measured second-order single-particle anisotropy, v 2 , using 2-, 4-, 6- and 8-particle correlations as well as the Lee-Yang Zero method in pPb and PbPb collisions. This result shows that the correlations found in the small and highly asymmetric pPb collision system are long-range and have a many-particle origin. Deeper insight into the nature of these correlations is achieved by studying the factorization breaking e ﬀ ect which appears trough a p T -dependent event plane angle, caused by the initial-state ﬂuctuations. The e ﬀ ect is largest for the most-central PbPb collisions (up to 20%), while it is on the level of few percent for peripheral PbPb and high-multiplicity pPb events. Hydrodynamics models which include a p T -dependent event plane angle semi-quantitatively describe the data and suggest that the e ﬀ ect is mainly determined by the initial-state conditions. e ﬀ ect of r 2 factorization breaking, up to about 20%, is found in the case of ultra-central PbPb collisions. For peripheral PbPb collisions, as well as for high-multiplicity pPb collisions, the size of the e ﬀ ect is on the level of few percent. The data are semi-quantitatively described by hydrodynamic models, with p T -dependent event plane angle ﬂuctuations induced by initial-state ﬂuctuations. These results can be used to constrain the transverse ﬂuctuations in the initial nucleus-nucleus overlap region.


Introduction
The Quark-Gluon Plasma (QGP), formed in the relativistic heavy-ion collisions, undergoes a collective expansion which is called flow. In such collisions, colliding nuclei intersect in such as way as to form a spatially anisotropic overlap region, which due to the interactions between the constituents of the formed system, converts into a momentum anisotropy. As a consequence, particles are preferentially emitted in the plane with the biggest pressure gradient. This plane is called the event plane (EP) and it is characterized via its azimuthal angle Ψ n . The final azimuthal angle particle distribution can be Fourier decomposed as A most significant part of the composite signal comes from the second Fourier component, v 2 , called 'elliptic flow'. Due to the initial-state fluctuations, the overlap region is not perfectly lenticular which as a consequence have appearance of higher orders Fourier coefficients. The third Fourier component, the triangular flow, v 3 , appears to be a significant source of the overall signal too, especially in the central collisions.
If particles are correlated with the event plane, then they are also mutually correlated. This enables the use of the two-and multi-particle correlations as a promising tool to study collective phenomena in relativistic protons and nuclei collisions. Two dimensional (2D) particle correlations in Δφ and Δη, which are differences in azimuthal angle φ and in pseudorapidity η between particles in a pair, have a rich structure. Especially, it showed existence of the ridge, long-range structure in |Δη| in vicinity of Δφ=0, in both PbPb (1) and pPb (2) collisions. A similar correlation has been found even in the smallest pp system (3) with very high multiplicity. In order to avoid short-range correlations arising from jet fragmentation for example, a cut on |Δη| could be applied 1 . Then, performing a projection of the constructed 2D particle correlations onto the Δφ axis, we obtain azimuthal correlations of particle pairs which could also be characterized by a Fourier decomposition The results in this contribution are, in fact, obtained by the direct calculations of Fourier coefficients V nΔ as where ... means averaging over many pairs and over many events of interest. The indices S and B stand for signal and background. The background distribution is calculated in the same way as the signal one with the only difference that particles forming a pair are taken from different events with similar multiplicities and within 2 cm wide range of vertex position in the z direction. The subtraction of the background takes into account the effects of detector non-uniformity. The direct calculation of V nΔ has an advantage that it is not affected by the finite bin widths of the Δφ − Δη histogram, which is especially relevant for higher-order Fourier harmonics. Beside the two-particle correlations, there are methods which use many-particle correlations in order to extract the magnitudes of the Fourier coefficients. In this contribution, the corresponding cumulants, c n {2k}, k = 2, 3, 4 are calculated according to the prescription described in detail in (4,5).
The hydrodynamics is usually used to explain seen phenomena in large nucleus-nucleus collision system, while different theoretical models are trying to explain it for the small systems formed in pp or pPb collisions. Usual assumption that EP angle Ψ n does not depend on p T leads to factorization of two-particle Fourier coefficients, V nΔ , from Eq.(2) in a product of single-particle Fourier coefficients from Eq.(1).
Recently, it was shown in (6) and (7) that not only v n but also the EP angle Ψ n could depends on p T . Due to the initial-state fluctuations, even if the only source of the correlations is hydrodynamic motion, the Ψ n is not any more a plane common for the whole event and its value becomes p T dependent. In that case, Eq.(4) becomes inequality and factorization is broken. A newly proposed variable is used to measure directly the magnitude of the factorization breaking effect. As single-particle anisotropy coefficients are mainly canceled, the r n is approximately equal to cos[n(Ψ n (p T 1 )−Ψ n (p T 2 ))]. In the case where the effect is entirely driven by the collective flow, the r n achieved value smaller (equal) than one when factorization breaks (holds). The r n value greater than one means that there are unremoved non-flow effects.

The CMS experiment and data used
The CMS detector consists out of several subdetectors (8) and it is placed within a super-conducting solenoid which produces 3.8 T magnetic field enabling precise measurements of particle momenta. The analysis, presented in this paper, is performed using data collected by CMS experiment at the LHC energies of √ s NN = 2.76 TeV and 5.02 TeV in PbPb and pPb with integrated luminosities of 160 μb −1 and 35 nb −1 , respectively. 1 In this analysis, thanks to a large CMS coverage in η, a wide |Δη| >2.0 cut has been applied.
The data used in this analysis comes mainly from the silicon tracker. The silicon tracker measures charged particles with pseudorapidities from the range |η| < 2.5 and transverse momenta above 0.3 GeV/c. The detailed information on cuts used for the online triggers, offline event selections, track reconstruction and selections are listed in (9)

Results
CMS measured the second-order single-particle anisotropy, v 2 , using the two-and higher order (4-th, 6-th and 8-th) particle correlations as well as the Lee-Yang Zero method both in PbPb and in pPb collisions over a wide multiplicity interval (9). These results, obtained by averaging over 0.3 < p T < 3.0 GeV/c and within |η| <2.4, are shown in Fig. 1 and v 2 {LYZ} are in a very good mutual agreement. Also, they are consistently below the corresponding v 2 {2} values. This result shows that correlations found in the small and highly asymmetric pPb collision system are long-range and have a many-particle origin. All applied methods show that v 2 increases with increase of multiplicity in PbPb collisions. In pPb collisions, the v 2 {2} has a modest increase, while v 2 from higher order particle correlations stays nearly constant with multiplicity. Such different behavior could be explained by the presence of lenticular shape of the overlapping region in PbPb collisions, while in the case of pPb collisions the shape of the overlapping region is determined by the initial-state fluctuations.   The very first experimental measurement of the factorization breaking has been performed for PbPb collisions at √ s NN =2.76 TeV in (11). In this contribution, the analysis is expanded to a much wider centrality range. Also, the effect is studied for high multiplicity pPb collisions at √ s NN =5.02 TeV. A systematic comparison between the experimental data and two hydrodynamic models (7,12) is also included. To quantify the effect of the factorization breaking, the r n observable is plotted vs the transverse momentum difference, p trig T − p assoc T , between the particles forming pairs of interest. By construction, r n = 1 when trigger and associated particle belongs to the same p T interval. Also, the calculations are performed only for p trig T ≥ p assoc T . The p T -dependent results on factorization ratio r 2 and r 3 can be found in Fig. 4 and Fig. 5 respectively in (10) 2 . The shown error bars correspond to statistical uncertainties only, as the systematic uncertainties are negligible with respect to the statistical ones. In the case of r 2 , the size of the effect increases with an increase of the difference between p trig T and p assoc T , with p trig T and going to more central collisions. The maximal effect of ≈20% is achieved in ultra-central 0-0.2% collisions. For centralities below 5%, the size of the effect is at the level of few %. In the case 2 Due to the limited space these figures are not shown in this contribution of third-order harmonic the factorization holds better then in the case of the second-order harmonic. The r 3 shows a very weak centrality dependence with the biggest value of about 5% at large values of p trig T − p assoc T . In order to get better insights on the origin of long-range correlations observed in high-multiplicity pPb collisions, the r 2 and the r 3 measurements are also performed for high-multiplicity pPb collisions. The results for the r 2 in function of p trig T − p assoc T are shown in Fig. 2. Four rows correspond to four analyzed multiplicity intervals, while four columns correspond to four different trigger's p T . The r 2 shows factorization breaking of the similar size in all four multiplicity intervals. As in the case of PbPb collisions, the size of the effect increases with an increase of p trig T − p assoc T and with p trig T . The maximal magnitude of the effect reaches only a few percent and it is much smaller than the one seen in ultra-central PbPb collisions, but it is comparable with the r 2 values found in those PbPb collisions which have multiplicities similar to high-multiplicity pPb events. The results of r 3 , shown in Fig. 3, are presented in the same format as those for the r 2 ratio. Within currently available statistics, there is no significant factorization breaking in very high multiplicity pPb events (185< No f f line trk <260). For lower multiplicity pPb events, particularly for 120< N o f f line trk <150, the r 3 value exceeds one. This is a direct indication that there is a significant contributions of back-to-back jet correlations in the signal distributions used to extract the V nΔ coefficients as the event multiplicity decreases, because the r n ratios predicted by hydrodynamic models with a p T -dependent event plane angle fluctuations would always be equal or less than one, according to Eq. 6.
Beside the experimental data points, in Fig. 2 and 3 are also shown predictions from Kozlov et al. hydrodynamic model (12). This model semi-quantitatively describes the experimental results. In Kozlov et al. model, a modified MC-Glauber initial-state model is used. The contributing entropy density in the transverse plane is distributed according to a 2D Gaussian distribution whose width can vary and which represents the transverse granularity of fluctuations. The experimentally found r n ratios are found to be most sensitive just to that width. The r 2 data values are better described with a width parameter of 0.4 fm, while the width of 0.8 fm gives a r n ratio practically equal to unity and thus underestimates the effect observed in the data. For both cases, the calculations are found to be nearly insensitive to different η/s values. This finding is consistent with the hydrodynamic calculations (7) Fig. 4. Additionally, at the top of the figure the centrality axis is shown which is applicable only for PbPb collisions. The r 2 factorization breaking effect in PbPb events increases dramatically as the collisions become more central than 0 − 5%. Going from central to peripheral PbPb collisions, the size of the r 2 effect quickly decreases to only few percent. The effect in r 3 remains at 2 − 3% level and it is nearly independent of centrality. The hydrodynamic model predictions for PbPb collisions (7) with MC Glauber and MC-KLN initial conditions and η/s =0.12 are also shown in dashed lines as a function of centrality. Neither of the two used intial-state conditions can describe the data quantitatively, although the multiplicity dependence is qualitatively reproduced. In the case of pPb collisions, the r 2 ratios show little multiplicity dependence and they are consistent with predictions of Kozlov et al. hydrodynamic model (12). The r 3 ratios in pPb go significantly above 1 at lower multiplicities, due to the onset of non-flow correlations.

Summary
Using the CMS detector, the azimuthal dihadron correlations are studied as a function of transverse momentum in PbPb collisions at √ s NN =2.76 TeV and pPb collisions at √ s NN = 5.02 TeV. In this contribution the factorization of Fourier coefficients, V nΔ , into a product of single-particle azimuthal anisotropies, v n , has been studied. A strong effect of r 2 factorization breaking, up to about 20%, is found in the case of ultra-central PbPb collisions. For peripheral PbPb collisions, as well as for high-multiplicity pPb collisions, the size of the effect is on the level of few percent. The data are semi-quantitatively described by hydrodynamic models, with p T -dependent event plane angle fluctuations induced by initial-state fluctuations. These results can be used to constrain the transverse fluctuations in the initial nucleus-nucleus overlap region.  7) with MC-Glauber and MC-KLN initial condition models and η/s = 0.12, and also hydrodynamics predictions for pPb collisions with η/s = 0.08 (12).