Two-particle azimuthal correlations in $e^+e^-$ collisions at 91--209 GeV with archived ALEPH data at LEP-2

We present the first measurement of two-particle angular correlations of charged particles produced in $e^+e^-$ annihilation up to $\sqrt{s}=$ 209 GeV. This analysis utilized the archived hadronic $e^+e^-$ data at center-of-mass energy between 91 and 209 GeV collected with the ALEPH detector at LEP between 1992 and 2000. The angular correlation functions are measured over a broad range of pseudorapidity and full azimuth as a function of charged particle multiplicity for the first time with LEP-2 data. At 91 GeV, no significant long-range correlation is observed in either the beam coordinate analysis or the thrust coordinate analysis, where the latter is sensitive to a medium expanding transverse to the color string between the outgoing $q\bar{q}$ pair from the Z boson decays. Results with $e^+e^-$ data at higher collision energy than 91 GeV, providing higher event multiplicity reach up to around 50, are presented for the first time. The thrust axis analysis shows a long-range near-side excess in the two-particle correlation function. We performed Fourier series decomposition of the two-particle correlation functions. In high multiplicity events with more than 50 particles, the extracted Fourier coefficients $v_2$ and $v_3$ magnitudes in data are larger than the MC reference.