Fundamental role of the retarded potential in the electrodynamics of superluminal sources: reply to comment

Neither Eq. (6.52) of Jackson [Classical Electrodynamics, 3rd ed. (Wiley, 1999)], or Hannay's derivation of that dquation in the preceding Comment [J. Opt. Soc. Am. A, ... (2009)], are applicable to a source whose distribution pattern moves faster than light in vacuo with nonzero acceleration. It is assumed in Hannay's derivation that the retarded distribution of the density of any moving source would be smooth and differentiable if its rest-frame distribution is. By working out an explicit example of a rotating superluminal source with a bounded and smooth density profile, we show that this assumption is erroneous. The retarded distribution of a rotating source with a moderate superluminal speed is, in general, spread over three disjoint volumes (differing in shape from each other and from the volume occupied by the source in its rest frame) whose boundaries depend on the spacetime position of the observer. Hannay overlooks the fact that the limits of integration in his expression for the retarded potential (which delineate the boundaries of the retarded distribution of the source) are not differentiable functions of the coordinates of the observer at those points on the source boundary that approach the observer, along the radiation direction, with the speed of light at the retarded time. In the superluminal regime, derivatives of the integral representing the retarded potential are well defined only as generalized functions

Long-range angular correlations on the near and away side in p-Pb collisions at root S-NN=5.02 TeV

Angular correlations between charged trigger and associated particles are measured by the ALICE detector in p-Pb collisions at a nucleon-nucleon centre-of-mass energy of 5.02 TeV for transverse momentum ranges within 0.5 < P-T,P-assoc < P-T,P-trig < 4 GeV/c. The correlations are measured over two units of pseudorapidity and full azimuthal angle in different intervals of event multiplicity, and expressed as associated yield per trigger particle. Two long-range ridge-like structures, one on the near side and one on the away side, are observed when the per-trigger yield obtained in low-multiplicity events is subtracted from the one in high-multiplicity events. The excess on the near-side is qualitatively similar to that recently reported by the CMS Collaboration, while the excess on the away-side is reported for the first time. The two-ridge structure projected onto azimuthal angle is quantified with the second and third Fourier coefficients as well as by near-side and away-side yields and widths. The yields on the near side and on the away side are equal within the uncertainties for all studied event multiplicity and p(T) bins, and the widths show no significant evolution with event multiplicity or p(T). These findings suggest that the near-side ridge is accompanied by an essentially identical away-side ridge. (c) 2013 CERN. Published by Elsevier B.V. All rights reserved

Underlying Event measurements in pp collisions at root s=0.9 and 7 TeV with the ALICE experiment at the LHC

We present measurements of Underlying Event observables in pp collisions at root s = 0 : 9 and 7 TeV. The analysis is performed as a function of the highest charged-particle transverse momentum p(T),L-T in the event. Different regions are defined with respect to the azimuthal direction of the leading (highest transverse momentum) track: Toward, Transverse and Away. The Toward and Away regions collect the fragmentation products of the hardest partonic interaction. The Transverse region is expected to be most sensitive to the Underlying Event activity. The study is performed with charged particles above three different p(T) thresholds: 0.15, 0.5 and 1.0 GeV/c. In the Transverse region we observe an increase in the multiplicity of a factor 2-3 between the lower and higher collision energies, depending on the track p(T) threshold considered. Data are compared to PYTHIA 6.4, PYTHIA 8.1 and PHOJET. On average, all models considered underestimate the multiplicity and summed p(T) in the Transverse region by about 10-30%

Direct observation of the dead-cone effect in quantum chromodynamics

The direct measurement of the QCD dead cone in charm quark fragmentation is reported, using iterative declustering of jets tagged with a fully reconstructed charmed hadron

Neutral pion and η meson production in proton–proton collisions at √s=0.9 TeV and s=√7 TeV

he first measurements of the invariant differential cross sections of inclusive π0 and η meson production at mid-rapidity in proton–proton collisions at s=0.9 TeV and s=7 TeV are reported. The π0 measurement covers the ranges 0.4<pT<7 GeV/c and 0.3<pT<25 GeV/c for these two energies, respectively. The production of η mesons was measured at s=√7 TeV in the range 0.4<pT<15 GeV/c. Next-to-Leading Order perturbative QCD calculations, which are consistent with the π0 spectrum at s=0.9 TeV, overestimate those of π0 and η mesons at s=√7 TeV, but agree with the measured η/π0 ratio at s=√7 TeV