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.
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.
We report on the measurement of two-pion correlation functions from pp collisions at $\sqrt{s}=900$ GeV performed by the ALICE experiment at the Large Hadron Collider. Our analysis shows an increase of the HBT radius with increasing event multiplicity, in line with other measurements done in particle- and nuclear collisions. Conversely, the strong decrease of the radius with increasing transverse momentum, as observed at RHIC and at Tevatron, is not manifest in our data.
Two-particle correlation functions for like-sign and unlike sign pion pairs.
Two-particle correlation functions for like-sign and unlike sign pion pairs.
Two-particle correlation functions for like-sign and unlike sign pion pairs.
An updated analysis using about 1.5 million events recorded at $\sqrt{s} = M_Z$ with the DELPHI detector in 1994 is presented. Eighteen infrared and collinear safe event shape observables are measured as a function of the polar angle of the thrust axis. The data are compared to theoretical calculations in ${\cal O} (\alpha_s^2)$ including the event orientation. A combined fit of $\alpha_s$ and of the renormalization scale $x_{\mu}$ in $\cal O(\alpha_s^2$) yields an excellent description of the high statistics data. The weighted average from 18 observables including quark mass effects and correlations is $\alpha_s(M_Z^2) = 0.1174 \pm 0.0026$. The final result, derived from the jet cone energy fraction, the observable with the smallest theoretical and experimental uncertainty, is $\alpha_s(M_Z^2) = 0.1180 \pm 0.0006 (exp.) \pm 0.0013 (hadr.) \pm 0.0008 (scale) \pm 0.0007 (mass)$. Further studies include an $\alpha_s$ determination using theoretical predictions in the next-to-leading log approximation (NLLA), matched NLLA and $\cal O(\alpha_s^2$) predictions as well as theoretically motivated optimized scale setting methods. The influence of higher order contributions was also investigated by using the method of Pad\'{e} approximants. Average $\alpha_s$ values derived from the different approaches are in good agreement.
The weighted value of ALPHA-S from all the measured observables using experimentally optimized renormalization scale values and corrected for the b-mass toleading order.
The value of ALPHA-S derived from the JCEF and corrected for heavy quark mass effects. The quoted errors are respectively due to experimental error, hadronization, renormalization scale and heavy quark mass correction uncertainties.
Energy Energy Correlation EEC.
We have studied the energy-energy correlation in e+e− annihilation into hadrons at √s =29 GeV using the Mark II detector at the SLAC storage ring PEP. We find to O(αs2) that αs=0.158±0.003±0.008 if hadronization is described by string fragmentation. Independent fragmentation schemes give αs=0.10–0.14, and give poor agreement with the data. A leading-log shower fragmentation model is found to describe the data well.
Correlation data from the original PEP-5 detector.
Correlation Asymmetry data from the original PEP-5 detector.
Correlation data from the upgraded detector.
Energy correlations have been measured with the MARK II detector at the PEP storage ring (Stanford Linear Accelerator Center) at c.m. energy of 29 GeV and are compared to first-order QCD predictions. Fragmentation processes are significant and limit the precision with which the first-order strong-coupling constant can be determined.
CORRELATION IS THE ENERGY WEIGHTED CROSS SECTION FOR OBSERVING THE ENERGY E1 IN THE SOLID ANGLE DOMEGA1 AND THE ANGLE E2 IN THE SOLID ANGLE DOMEGA2.SUMMED OVER ALL PAIRS OF PARTICLES IN DOMEGA1 AND DOMEGA2 AND ALL EVENTS.
MEASUREMENT OF THE STRONG COUPLING CONSTANT.
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