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Relativistic Effects in Femtoscopy and Deuteron Formation

Stanislaw Mrowczynski

Abstract

For a long time studies of femtoscopic correlations have provided information about space-time characteristics of particle sources in high-energy collisions. Recently, the correlation functions have been also used to determine interaction parameters of correlated particles which is especially important for short-lived particles, for which scattering experiment are impossible. The abundance of experimental data and their high accuracy require an improved theoretical approach to femtoscopic correlations. We discuss relativistic effects and their role in detail. Since a general relativistic approach is currently unavailable, due to serious theoretical difficulties, the correlation functions must be computed in the center-of-mass frame where the correlated particles are mostly nonrelativistic. This requires transforming the source function to this frame, the consequences of which we discuss. Since the deutron formation has a similar physical origin to femtoscopic correlations, we also discuss relativistic effects in the former process. We illustrate our considerations with calculations of some correlation functions and the deuteron coalescence coefficient to demonstrate a magnitude of relativistic effects. We also argue that a discrepancy between the coalescence coefficient computed with the source radii inferred from the baryon-baryon correlation functions and the experimental data can be removed by taking into account the relativistic elongation of the source radius in the center of mass of correlated particles.

Relativistic Effects in Femtoscopy and Deuteron Formation

Abstract

For a long time studies of femtoscopic correlations have provided information about space-time characteristics of particle sources in high-energy collisions. Recently, the correlation functions have been also used to determine interaction parameters of correlated particles which is especially important for short-lived particles, for which scattering experiment are impossible. The abundance of experimental data and their high accuracy require an improved theoretical approach to femtoscopic correlations. We discuss relativistic effects and their role in detail. Since a general relativistic approach is currently unavailable, due to serious theoretical difficulties, the correlation functions must be computed in the center-of-mass frame where the correlated particles are mostly nonrelativistic. This requires transforming the source function to this frame, the consequences of which we discuss. Since the deutron formation has a similar physical origin to femtoscopic correlations, we also discuss relativistic effects in the former process. We illustrate our considerations with calculations of some correlation functions and the deuteron coalescence coefficient to demonstrate a magnitude of relativistic effects. We also argue that a discrepancy between the coalescence coefficient computed with the source radii inferred from the baryon-baryon correlation functions and the experimental data can be removed by taking into account the relativistic elongation of the source radius in the center of mass of correlated particles.
Paper Structure (13 sections, 58 equations, 4 figures)

This paper contains 13 sections, 58 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Definition of correlation function
  3. Nonrelativistic Koonin Formula
  4. Relativistically covariant source function
  5. Magnitude of relativistic effects
  6. $\Lambda$-$p$ correlations
  7. $p$-$p$ correlations
  8. $\pi$-$\pi$ and $K$-$K$ correlations
  9. Deuteron formation
  10. Non-relativistic formulation
  11. Relativistic formulation
  12. Magnitude of relativistic effects
  13. Summary and conclusions

Figures (4)

  • Figure 1: The $\Lambda$-$p$ correlation function as a function of ${\bf q}=(q,0,0)$ (red) and of ${\bf q}=(0,q,0)$ (blue) computed for $R_s = 1\,$fm and $\gamma = 4$.
  • Figure 2: The $p$-$p$ correlation function as a function of ${\bf q}=(q,0,0)$ (red) and of ${\bf q}=(0,q,0)$ (blue) computed for $R_s = 1\,$fm and $\gamma = 4$.
  • Figure 3: The coalescence coefficient $B$ as a function of $\gamma$.
  • Figure 4: The $\Lambda$-$p$ correlation function as a function of $q =|{\bf q}|$ (green) computed for $R_s = 0.88\,$fm and $\gamma = 1.00$ together with the $\Lambda$-$p$ correlation function as a function of ${\bf q}=(q,0,0)$ (red) and of ${\bf q}=(0,q,0)$ computed for $R_s = 0.64\,$fm and $\gamma = 2.36$.