A study of φ-meson spin alignment with the AMPT model Shaowei Lan 1 Zi-Wei Lin 1,2, Shusu Shi 1, Xu Sun 1 1 Central China Normal University 2 East Carolina University
Outline Introduction Modified AMPT model Analysis method and results extraction of φ-meson spin alignment parameter ρ 00 Hadron cascade effect Acceptance effect: pseudorapidity coverage effect transverse momentum dependence Summary 2017/07/21 QPT2017 2
Introduction STAR Phys. Rev. C 77, 061902(R)(2008) Mike Lisa. https://drupal.star.bnl.gov/star/system/files/uclavorticityworkshopfeb2016v3.pdf Non-central heavy ion collisions have large initial angular momentum. Due to spin-orbit coupling, this orbital angular momentum may result in net polarization of produced particles along the direction of the initial angular momentum (L) perpendicular to the reaction plane. 2017/07/21 QPT2017 3
φ-meson spin alignment Why φ meson spin alignment φ-mesons, which have small hadronic scattering cross sections, are expected to originate predominantly from primordial production. Z. Liang and X. Wang, Phys. Lett. B 629,20-26(2005) The 00-conponent of ϕ-meson spin density matrix (ρ 00 ) can be measured by angular distribution of decay daughter ϕ K + +K - using: dn dcosθ ~ (1-ρ 00) +(3ρ 00-1) cos 2 θ A deviation of ρ 00 from 1/3 indicates a spin alignment of φ-meson. θ* is the angle between the polarization direction and the momentum direction of K in the rest frame of φ-meson. P STAR: QM2017 Xu Sun 2017/07/21 QPT2017 4
A MultiPhase Transport Model Four Main Parts: The initial condition. Partonic scattering. Hadronization. Hadronic scattering. Zi-Wei Lin, Ko, Li, Zhang and Pal, Phys. Rev. C 72, 064901 (2005) Modified part : Added input ρ 00 parameter to specify the degree of spin alignment of φ-mesons at decay. Angular momentum direction is calculated event-by-event. Au+Au at s NN = 200GeV with String Melting, partonic scattering cross section = 3 mb. 2017/07/21 QPT2017 5
ρ 00 extraction Input ρ 00 = 0.2 Background : Event Mixing technique. Invariant mass distributions for 7 different cosθ bins. Fit cosθ distribution with: dn dcosθ = N 0 [(1-ρ 00 ) +(3ρ 00-1) cos 2 θ ] 2017/07/21 QPT2017 6
Direction of angular momentum Physical: the initial angular momentum of the overlap volume can be directly calculated in AMPT model. Observed: experimentally the direction of angular momentum can be estimated by the normal of the reconstructed event plane. Event plane method: Q n,x = w i cos (nφ i ) Q n,y = w i sin (nφ i ) ψ n = 1 n tan 1 Q n,y Q n,x Poskanzer and Voloshin Phys. Rev. C 58.1671(1998) 2017/07/21 QPT2017 7
Hadronic scattering effect Input ρ 00 = 0.2 Input ρ 00 = 1/3 ρ phy 00 : calculated with direction of angular momentum. Hadronic scatterings (HS) after φ-meson decays are irrelevant for φmeson ρ phy 00. 2017/07/21 QPT2017 8
Use ρ obs phy 00 to extract ρ 00 ρ obs 00 calculated with reconstructed event plane. ρ phy 00 : calculated with direction of angular momentum. obs ρ 00 and ρ phy 00 are found to be linearly correlated. obs In experiment only ρ 00 can be measured. obs However, ρ 00 needs to be corrected to extracted ρ 00 phy. 2017/07/21 QPT2017 9
Effect of finite η coverage Input ρ 00 = 0.2 Input ρ 00 = 1/3 The extracted ρ 00 depends on the η cut of kaons. When the cut is below η <1, a narrower η acceptance gives a significantly larger ρ phy 00 value than the input ρ 00. A narrow η cut on kaons tends to exclude kaons along beam directions, therefore exclude kaons from φ decays around θ ~ 90 degrees. 2017/07/21 QPT2017 10
Effect of finite p T φ coverage Input ρ 00 = 0.2 Input ρ 00 = 1/3 With the η coverage of η <1, the extracted ρ phy 00 depends on transverse momentum. Larger deviation from the input ρ 00 value is observed in low p T range. Without η cut, p T cut does not affect the extracted ρ phy 00 value (same as input ρ 00 ). 2017/07/21 QPT2017 11
Summary AMPT extended with an input ρ 00 parameter specifies the degree of φmeson spin alignment versus the direction of angular momentum when φ mesons decay. Hadron scatterings after φ-meson decays are found to have no effect on the extraction of the φ-meson ρ 00 parameter. A narrow η coverage strongly affects the extracted φ-meson ρ 00 value. This η-cut effect mainly comes from low-p T φ mesons. 2017/07/21 QPT2017 12
Thank you! 2017/07/21 QPT2017 13
Back up 2017/07/21 QPT2017 14
Observe In Experiment STAR preliminary STAR: QM2017 Xu Sun 2017/07/21 QPT2017 15
Effect of finite η coverage 2017/07/21 QPT2017 16