Evidence for transverse-momentum- and pseudorapidity-dependent event-plane fluctuations in PbPb and $p\mathrm{Pb}$ collisions

A systematic study of the factorization of long-range azimuthal two-particle correlations into a product of single-particle anisotropies is presented as a function of $p_{\mathrm{T}}$ and $\eta$ of both particles and as a function of the particle multiplicity in PbPb and $p\mathrm{Pb}$ collisions. The data were taken with the CMS detector for PbPb collisions at $\sqrt{s_{{}_{\mathrm{NN}}}}=2.76$ TeV and $p\mathrm{Pb}$ collisions at $\sqrt{s_{{}_{\mathrm{NN}}}}=5.02$ TeV, covering a very wide range of multiplicity. Factorization is observed to be broken as a function of both particle $p_{\mathrm{T}}$ and $\eta$. When measured with particles of different $p_{\mathrm{T}}$, the magnitude of the factorization breakdown for the second Fourier harmonic reaches 20% for very central PbPb collisions but decreases rapidly as the multiplicity decreases. The data are consistent with viscous hydrodynamic predictions, which suggest that the effect of factorization breaking is mainly sensitive to the initial-state conditions rather than to the transport properties (e.g., shear viscosity) of the medium. The factorization breakdown is also computed with particles of different $\eta$. The effect is found to be weakest for mid-central PbPb events but becomes larger for more central or peripheral PbPb collisions, and also for very-high-multiplicity $p\mathrm{Pb}$ collisions. The $\eta$-dependent factorization data provide new insights to the longitudinal evolution of the medium formed in heavy ion collisions.

Figure 1

The $p_{\mathrm{T}}$-dependent factorization ratio, $r_2$, as a function of $p_{\mathrm{T}}^a-p_{\mathrm{T}}^b$ in bins of $p_{\mathrm{T}}^a$ for different centrality ranges of PbPb collisions at $\sqrt{s_{{}_{\mathrm{NN}}}}=2.76$ TeV. The curves show the calculations from a viscous hydrodynamic model [24] using MC-Glauber and MC-KLN initial-condition models, and an $\eta /s$ value of 0.12. Each row represents a different centrality range, while each column corresponds to a different $p_{\mathrm{T}}^a$ range. The horizontal solid lines denote the $r_2$ value of unity. The error bars correspond to statistical uncertainties, while systematic uncertainties are negligible for the $r_n$ results and thus are not shown.

Figure 2

Similar distributions as shown in Fig. 1, but for the factorization ratio $r_3$.

Figure 3

Factorization ratio, $r_2$, as a function of $p_{\mathrm{T}}^a-p_{\mathrm{T}}^b$ in bins of $p_{\mathrm{T}}^a$ for 0%–0.2% centrality PbPb data at $\sqrt{s_{{}_{\mathrm{NN}}}}=2.76$ TeV compared to viscous hydrodynamic calculations [24] using MC-Glauber and MC-KLN initial-condition models, and three different values of $\eta /s$. The horizontal solid lines denote the $r_2$ value of unity. The error bars correspond to statistical uncertainties, while systematic uncertainties are negligible for the $r_n$ results and thus are not shown.

Figure 4

The $p_{\mathrm{T}}$-dependent factorization ratio $r_2$ as a function of $p_{\mathrm{T}}^a-p_{\mathrm{T}}^b$ in bins of $p_{\mathrm{T}}^a$ for four $N_{\text{trk}}^{\text{offline}}$ ranges in 5.02 TeV $p\mathrm{Pb}$ collisions. The curves show the predictions from hydrodynamic calculations for $p\mathrm{Pb}$ collisions of Ref. [25]. The horizontal solid lines denote the $r_2$ value of unity. The error bars correspond to statistical uncertainties, while systematic uncertainties are negligible for the $r_n$ results and thus are not shown.

Figure 5

Similar distributions as shown in Fig. 4, but for the factorization ratio $r_3$.

Figure 6

The $p_{\mathrm{T}}$-dependent factorization ratio $r_2$ as a function of $p_{\mathrm{T}}^a-p_{\mathrm{T}}^b$ in bins of $p_{\mathrm{T}}^a$ for two $N_{\text{trk}}^{\text{offline}}$ ranges of 5.02 TeV $p\mathrm{Pb}$ and 2.76 TeV PbPb collisions. The horizontal solid lines denote the $r_2$ value of unity. The error bars correspond to statistical uncertainties, while systematic uncertainties are negligible for the $r_n$ results and thus are not shown.

Figure 7

The $p_{\mathrm{T}}$-dependent factorization ratios $r_2$ and $r_3$ as a function of event multiplicity in $p\mathrm{Pb}$ and PbPb collisions. The curves show the calculations for PbPb collisions from viscous hydrodynamics in Ref. [24] with MC-Glauber and MC-KLN initial-condition models and $\eta /s=0.12$, and also from hydrodynamic predictions for PbPb and $p\mathrm{Pb}$ data in Ref. [25]. The horizontal solid lines denote the $r_2$ (top) and $r_3$ (bottom) value of unity. The error bars correspond to statistical uncertainties, while systematic uncertainties are negligible for the $r_n$ results and thus are not shown.

Figure 8

A schematic illustration of the acceptance coverage of the CMS tracker and HF calorimeters, and the procedure for deriving the $\eta$-dependent factorization ratio $r_n({\eta }^a,{\eta }^b)$.

Figure 9

The $\eta$-dependent factorization ratio $r_2$ as a function of ${\eta }^a$ for $3.0<{\eta }^b<4.0$ and $4.4<{\eta }^b<5.0$, averaged over $0.3<p_{\mathrm{T}}^a<3.0$ GeV/$c$, in eight centrality classes of PbPb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV. The curves correspond to fits to the data for $4.4<{\eta }^b<5.0$ given by Eq. (12). The horizontal solid lines denote the $r_2$ value of unity. The error bars correspond to statistical uncertainties, while systematic uncertainties are negligible for the $r_n$ results and thus are not shown.

Figure 10

Similar distributions as shown in Fig. 9, but for the factorization ratio $r_3$.

Figure 11

Similar distributions as shown in Fig. 9, but for the factorization ratio $r_4$ in fewer centrality ranges.

Figure 12

The square root of the product of factorization ratios, $\sqrt{r_2({\eta }^a,{\eta }^b)r_2(-{\eta }^a,-{\eta }^b)}$, as a function of ${\eta }^a$ for $3.0<{\eta }^b<4.0$ and $4.4<{\eta }^b<5.0$, averaged over $0.3<p_{\mathrm{T}}^a<3.0$ GeV/$c$, in four multiplicity classes of $p\mathrm{Pb}$ collisions at $\sqrt{s_{{}_{\mathrm{NN}}}}=5.02$ TeV. The curves correspond to fits to the data for $4.4<{\eta }^b<5.0$ using Eq. (12). The horizontal solid lines denote the $r_2$ value of unity. The error bars correspond to statistical uncertainties, while systematic uncertainties are negligible for the $r_2$ results and thus are not shown.

Figure 13

The $F_n^{\eta }$ parameter as defined in Eq. (12) as a function of event multiplicity in PbPb collisions at $\sqrt{s_{{}_{\mathrm{NN}}}}=2.76$ TeV for $n=2$ to 4 and $p\mathrm{Pb}$ collisions at $\sqrt{s_{{}_{\mathrm{NN}}}}=5.02$ TeV for $n=2$. The error bars correspond to statistical uncertainties, while systematic uncertainties are negligible for the $r_n$ results and thus are not shown.