Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A self-consistent calculation of non-spherical Bose-Einstein correlation functions with Coulomb final-state interaction

Márton I. Nagy, Dániel Kincses, Máté Csanád

TL;DR

The paper tackles the challenge of accurately modeling Bose-Einstein correlations with Coulomb final-state interactions for non-spherical, Lévy-stable sources in heavy-ion collisions. It develops a self-consistent 3D framework by reformulating the Coulomb integral in Fourier space, deriving semi-analytic expressions for the Coulomb-corrected correlator via functionals $\mathcal{A}_1$ and $\mathcal{A}_2$, and providing a public software package for fully 3D computations. The authors apply the method to elliptically contoured Lévy sources and compare full 3D results with traditional spherical approximations, illustrating when the latter are adequate and when the full treatment is necessary, with emphasis on frame transformations between PCMS and LCMS. This work enables more precise femtoscopy analyses for high-statistics heavy-ion data and offers practical guidance for systematic uncertainties in experimental analyses.

Abstract

Particle correlations and femtoscopy are a rich subfield of high-energy physics. As the experimental data become more precise, there is an increasing need for the theoretical calculations to provide better and more general descriptions of the measurements. One of the important new directions is the investigation of the precise shape of the Bose-Einstein correlation functions utilizing Lévy-stable distributions. This work is a direct follow-up to our previous study, in which we developed a novel method for calculating Bose-Einstein correlation functions including the Coulomb final-state interaction. In this paper, we present a self-consistent generalization of the previous approach to non-spherical source functions and investigate the validity of the previously applied approximations assuming spherical symmetry. We present a software package that includes the calculation of a fully three-dimensional correlation function including the Coulomb interaction.

A self-consistent calculation of non-spherical Bose-Einstein correlation functions with Coulomb final-state interaction

TL;DR

The paper tackles the challenge of accurately modeling Bose-Einstein correlations with Coulomb final-state interactions for non-spherical, Lévy-stable sources in heavy-ion collisions. It develops a self-consistent 3D framework by reformulating the Coulomb integral in Fourier space, deriving semi-analytic expressions for the Coulomb-corrected correlator via functionals and , and providing a public software package for fully 3D computations. The authors apply the method to elliptically contoured Lévy sources and compare full 3D results with traditional spherical approximations, illustrating when the latter are adequate and when the full treatment is necessary, with emphasis on frame transformations between PCMS and LCMS. This work enables more precise femtoscopy analyses for high-statistics heavy-ion data and offers practical guidance for systematic uncertainties in experimental analyses.

Abstract

Particle correlations and femtoscopy are a rich subfield of high-energy physics. As the experimental data become more precise, there is an increasing need for the theoretical calculations to provide better and more general descriptions of the measurements. One of the important new directions is the investigation of the precise shape of the Bose-Einstein correlation functions utilizing Lévy-stable distributions. This work is a direct follow-up to our previous study, in which we developed a novel method for calculating Bose-Einstein correlation functions including the Coulomb final-state interaction. In this paper, we present a self-consistent generalization of the previous approach to non-spherical source functions and investigate the validity of the previously applied approximations assuming spherical symmetry. We present a software package that includes the calculation of a fully three-dimensional correlation function including the Coulomb interaction.
Paper Structure (7 sections, 123 equations, 8 figures)

This paper contains 7 sections, 123 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Bose-Einstein correlations and the Coulomb effect
  3. Coulomb integral in Fourier space
  4. Results and discussion
  5. Summary and outlook
  6. Calculation of $\mathcal{D}_{1\lambda}$ and $\mathcal{D}_{2\lambda}$
  7. The $\lambda{\to}0$ limit of $\mathcal{D}_{1\lambda}$ and $\mathcal{D}_{2\lambda}$

Figures (8)

  • Figure 1: The $a$--$\beta$--$\varphi$ coordinate system, suited for the calculation of $\mathcal{A}_1$ as in Eq. (\ref{['e:A1final']}).
  • Figure 2: The $b$--$y$--$\varphi$ coordinate system, suited for the calculation of $\mathcal{A}_2$ as in Eq. (\ref{['e:A2Pfinal']}).
  • Figure 3: An example plot showing the 3D correlation function of Eq. \ref{['e:C2Coulomblambda']}, with a given set of parameters, in 1D slices along the three axes of the Bertsch-Pratt coordinate system.
  • Figure 4: Comparison of the full (blue markers and line) and the approximative (orange line) 3D calculation of Eqs. \ref{['e:C2Coulomblambda']} and \ref{['e:C2Coulombapprox']}, taking the LCMS-PCMS difference into account, with a given set of parameters and $\beta_T$, in 1D slices along the three axes of the Bertsch-Pratt coordinate system.
  • Figure 5: Averaged relative difference of the full and approximative 3D calculations of Fig. \ref{['f:coulcorrcompare']}, as a function of $\beta_T$. The average was taken over momentum differences with all coordinates smaller than 150 MeV/$c$.
  • ...and 3 more figures