Angular correlations between unidentified charged trigger ($t$) and associated ($a$) particles are measured by the ALICE experiment in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV for transverse momenta $0.25 < p_{T}^{t,\, a} < 15$ GeV/$c$, where $p_{T}^t > p_{T}^a$. The shapes of the pair correlation distributions are studied in a variety of collision centrality classes between 0 and 50% of the total hadronic cross section for particles in the pseudorapidity interval $|\eta| < 1.0$. Distributions in relative azimuth $\Delta\phi \equiv \phi^t - \phi^a$ are analyzed for $|\Delta\eta| \equiv |\eta^t - \eta^a| > 0.8$, and are referred to as "long-range correlations". Fourier components $V_{n\Delta} \equiv \langle \cos(n\Delta\phi)\rangle$ are extracted from the long-range azimuthal correlation functions. If particle pairs are correlated to one another through their individual correlation to a common symmetry plane, then the pair anisotropy $V_{n\Delta}(p_{T}^t, p_{T}^a)$ is fully described in terms of single-particle anisotropies $v_n (p_{T})$ as $V_{n\Delta}(p_{T}^t, p_{T}^a) = v_n(p_{T}^t) \, v_n(p_{T}^a)$. This expectation is tested for $1 \leq n \leq 5$ by applying a global fit of all $V_{n\Delta} (p_{T}^t, p_{T}^a)$ to obtain the best values $v_{n}\{GF\} (p_{T})$. It is found that for $2 \leq n \leq 5$, the fit agrees well with data up to $p_T^a \sim 3$-4 GeV/$c$, with a trend of increasing deviation as $p_{T}^t$ and $p_{T}^a$ are increased or as collisions become more peripheral. This suggests that no pair correlation harmonic can be described over the full $0.25 < p_{T} < 15$ GeV/$c$ range using a single $v_n(p_T)$ curve; such a description is however approximately possible for $2 \leq n \leq 5$ when $p_T^a < 4$ GeV/$c$. For the $n=1$ harmonic, however, a single $v_1(p_T$ curve is not obtained even within the reduced range $p_T^a < 4$ GeV/$c$.
Amplitudes of the VnDelta harmonics versus n for events with trigger particles having transverse momenta in the range 2-2.5 GeV and associated particles in the range 1.5-2.0 GeV for two centrality classes 0-2% and 2-10%. Note that in the paper the data are plotted multiplied by 100.
Amplitudes of the VnDelta harmonics versus n for events with trigger particles having transverse momenta in the range 2-2.5 GeV and associated particles in the range 1.5-2.0 GeV for three centrality classes 10-20%, 20-30% and 40-50%. Note that in the paper the data are plotted multiplied by 100.
Amplitudes of the VnDelta harmonics versus n for events with trigger particles having transverse momenta in the range 8-15 GeV and associated particles in the range 6-8 GeV for two centrality classes 40-50% and 0-20%. Note that in the paper the data are plotted multiplied by 100.
We present two-dimensional (2D) two-particle angular correlations on relative pseudorapidity $\eta$ and azimuth $\phi$ for charged particles from Au-Au collisions at $\sqrt{s_{\rm NN}} = 62$ and 200 GeV with transverse momentum $p_t \geq 0.15$ GeV/$c$, $|\eta| \leq 1$ and $2\pi$ azimuth. Observed correlations include a {same-side} (relative azimuth $< \pi/2$) 2D peak, a closely-related away-side azimuth dipole, and an azimuth quadrupole conventionally associated with elliptic flow. The same-side 2D peak and away-side dipole are explained by semihard parton scattering and fragmentation (minijets) in proton-proton and peripheral nucleus-nucleus collisions. Those structures follow N-N binary-collision scaling in Au-Au collisions until mid-centrality where a transition to a qualitatively different centrality trend occurs within a small centrality interval. Above the transition point the number of same-side and away-side correlated pairs increases rapidly {relative to} binary-collision scaling, the $\eta$ width of the same-side 2D peak also increases rapidly ($\eta$ elongation) and the $\phi$ width actually decreases significantly. Those centrality trends are more remarkable when contrasted with expectations of jet quenching in a dense medium. Observed centrality trends are compared to {\sc hijing} predictions and to the expected trends for semihard parton scattering and fragmentation in a thermalized opaque medium. We are unable to reconcile a semihard parton scattering and fragmentation origin for the observed correlation structure and centrality trends with heavy ion collision scenarios which invoke rapid parton thermalization. On the other hand, if the collision system is effectively opaque to few-GeV partons the observations reported here would be inconsistent with a minijet picture.
FIG. 1. (Color online) Perspective views of $2 \mathrm{D}$ charge-independent angular correlations $\Delta \rho / \sqrt{\rho_{\mathrm{ref}}}$ on $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ for Au-Au collisions at $\sqrt{s_{N N}}=200$ and $62 \mathrm{GeV}$ (top and bottom rows, respectively). Centrality increases left to right from most peripheral to most central. Corrected total cross-section fractions are (left to right) $84 \%-93 \%, 55 \%-64 \%, 18 \%-28 \%,$ and $0 \%-5 \%$ for the $200-\mathrm{GeV}$ data and $84 \%-95 \%, 56 \%-65 \%$ $18 \%-28 \%,$ and $0 \%-5 \%$ for the $62 \mathrm{GeV}$ data (see Tables III and IV).
FIG. 1. (Color online) Perspective views of $2 \mathrm{D}$ charge-independent angular correlations $\Delta \rho / \sqrt{\rho_{\mathrm{ref}}}$ on $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ for Au-Au collisions at $\sqrt{s_{N N}}=200$ and $62 \mathrm{GeV}$ (top and bottom rows, respectively). Centrality increases left to right from most peripheral to most central. Corrected total cross-section fractions are (left to right) $84 \%-93 \%, 55 \%-64 \%, 18 \%-28 \%,$ and $0 \%-5 \%$ for the $200-\mathrm{GeV}$ data and $84 \%-95 \%, 56 \%-65 \%$ $18 \%-28 \%,$ and $0 \%-5 \%$ for the $62 \mathrm{GeV}$ data (see Tables III and IV).
FIG. 1. (Color online) Perspective views of $2 \mathrm{D}$ charge-independent angular correlations $\Delta \rho / \sqrt{\rho_{\mathrm{ref}}}$ on $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ for Au-Au collisions at $\sqrt{s_{N N}}=200$ and $62 \mathrm{GeV}$ (top and bottom rows, respectively). Centrality increases left to right from most peripheral to most central. Corrected total cross-section fractions are (left to right) $84 \%-93 \%, 55 \%-64 \%, 18 \%-28 \%,$ and $0 \%-5 \%$ for the $200-\mathrm{GeV}$ data and $84 \%-95 \%, 56 \%-65 \%$ $18 \%-28 \%,$ and $0 \%-5 \%$ for the $62 \mathrm{GeV}$ data (see Tables III and IV).
The first measurement of two-pion Bose-Einstein correlations in central Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV at the Large Hadron Collider is presented. We observe a growing trend with energy now not only for the longitudinal and the outward but also for the sideward pion source radius. The pion homogeneity volume and the decoupling time are significantly larger than those measured at RHIC.
Projections of the correlation function C.
Projections of the correlation function C.
Projections of the correlation function C.
Three-particle azimuthal correlation measurements with a high transverse momentum trigger particle are reported for pp, d+Au, and Au+Au collisions at 200 GeV by the STAR experiment. The acoplanarities in pp and d+Au indicate initial state kT broadening. Larger acoplanarity is observed in Au+Au collisions. The central Au+Au data show an additional effect signaling conical emission of correlated charged hadrons.
FIG. 1: (a) Raw two-particle correlation signal $Y_2$ (red), background $aB_{inc}F_2$ (solid histogram), and background systematic uncertainty from a (dashed histograms). (b) Background-subtracted two-particle correlation $\hat{Y}_2$ (red), and systematic uncertainties due to a (dashed histograms) and flow (blue histograms). (c) Raw three-particle correlation $Y_3$. (d) $ba^2Y_{inc}^2$ . (e) Sum of trig-corr-bkgd and trigger flow. Data are from 12% central Au+Au collisions. Statistical errors in (a,b) are smaller than the point size. NOTE: For points with invisible error bars, the point size was considered as an absolute upper limit for the uncertainty.
FIG. 1: (a) Raw two-particle correlation signal $Y_2$ (red), background $aB_{inc}F_2$ (solid histogram), and background systematic uncertainty from a (dashed histograms). (b) Background-subtracted two-particle correlation $\hat{Y}_2$ (red), and systematic uncertainties due to a (dashed histograms) and flow (blue histograms). (c) Raw three-particle correlation $Y_3$. (d) $ba^2Y_{inc}^2$ . (e) Sum of trig-corr-bkgd and trigger flow. Data are from 12% central Au+Au collisions. Statistical errors in (a,b) are smaller than the point size. NOTE: For points with invisible error bars, the point size was considered as an absolute upper limit for the uncertainty.
FIG. 1: (a) Raw two-particle correlation signal $Y_2$ (red), background $aB_{inc}F_2$ (solid histogram), and background systematic uncertainty from a (dashed histograms). (b) Background-subtracted two-particle correlation $\hat{Y}_2$ (red), and systematic uncertainties due to a (dashed histograms) and flow (blue histograms). (c) Raw three-particle correlation $Y_3$. (d) $ba^2Y_{inc}^2$ . (e) Sum of trig-corr-bkgd and trigger flow. Data are from 12% central Au+Au collisions. Statistical errors in (a,b) are smaller than the point size.
values between 9.9-GeV**2 and 284-GeV**2.
Inclusive γ ∗ γ interactions to hadronic final states where one scattered electron or positron is detected in the electromagnetic calorimeters have been studied in the LEP 1 data taken by ALEPH from 1991 to 1995. The event sample has been used to measure the hadronic structure function of the photon F 2 γ in three bins with 〈 Q 2 〉 of 9.9, 20.7 and 284 GeV 2 .
The measured values of dsig/dx from the ECAL data in the Q**2 bin 35 to 3000 GeV**2 with a mean of 284 +- 49 GeV**2.
The measured values of dsig/dx from the LCAL data in the Q**2 bin 13 to 44 GeV**2 with a mean of 20.67 +- 016 GeV**2.
The measured values of dsig/dx from the LCAL data in the Q**2 bin 6 to 13 GeV**2 with a mean of 9.93 +- 0.04 GeV**2.
We report on an improved measurement of the value of the strong coupling constant σ s at the Z 0 peak, using the asymmetry of the energy-energy correlation function. The analysis, based on second-order perturbation theory and a data sample of about 145000 multihadronic Z 0 decays, yields α s ( M z 0 = 0.118±0.001(stat.)±0.003(exp.syst.) −0.004 +0.0009 (theor. syst.), where the theoretical systematic error accounts for uncertainties due to hadronization, the choice of the renormalization scale and unknown higher-order terms. We adjust the parameters of a second-order matrix element Monte Carlo followed by string hadronization to best describe the energy correlation and other hadronic Z 0 decay data. The α s result obtained from this second-order Monte Carlo is found to be unreliable if values of the renormalization scale smaller than about 0.15 E cm are used in the generator.
Value of LAMBDA(MSBAR) and ALPHA_S.. The first systematic error is experimental, the second is from theory.
The EEC and its asymmetry at the hadron level, unfolded for initial-state radiation and for detector acceptance and resolution. Errors include full statistical and systematic uncertainties.
From an analysis of multi-hadron events from Z 0 decays, values of the strong coupling constant α s ( M 2 Z 0 )=0.131±0.006 (exp)±0.002(theor.) and α s ( M z 0 2 ) = −0.009 +0.007 (exp.) −0.002 +0.006 (theor.) are derived from the energy-energy correlation distribution and its asymmetry, respectively, assuming the QCD renormalization scale μ = M Z 0 . The theoretical error accounts for differences between O ( α 2 s ) calculations. A two parameter fit Λ MS and the renormalization scale μ leads to Λ MS =216±85 MeV and μ 2 s =0.027±0.013 or to α s ( M 2 Z 0 )=0.117 +0.006 −0.008 (exp.) for the energy-energy correlation distribution. The energy-energy correlation asymmetry distribution is insensitive to a scale change: thus the α s value quoted above for this variable includes the theoretical uncertainty associated with the renormalization scale.
Data are at the hadron level, unfolded for initial-state radiation and for detector acceptance and resolution. Note that the systematic errors between bins are correlated.
Alpha-s determined from the EEC measurements. The systematic error is an error in the theory.
Alpha-s determined from the AEEC measurements. The systematic error is an error in the theory.