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Corrections to the Smoothness and On-Shell Approximations in Femtoscopy and Coalescence

Isaac G. Smith, Kfir Blum

Abstract

Relativistic heavy-ion collisions produce femtometer-scale sources whose space-time structure can be constrained using two-particle femtoscopic correlations. Standard implementations rely on the smoothness and on-shell approximations, which effectively remove the relative momentum dependence of the particle emission function. We explore the validity of these approximations by deriving model-independent expansions that quantify the leading corrections for femtoscopy and coalescence with arbitrary sources and final-state interactions. The resulting first- and second-order correction terms can be evaluated with essentially the same numerical complexity as the usual Koonin-Pratt expressions; for angle-averaged correlations the first-order contributions vanish by symmetry. We illustrate the framework with explicit calculations in a blast-wave source model. For parameter sets representative of pp and PbPb fits at LHC energies, the corrections are at or below the percent level for pp correlations and deuteron coalescence.

Corrections to the Smoothness and On-Shell Approximations in Femtoscopy and Coalescence

Abstract

Relativistic heavy-ion collisions produce femtometer-scale sources whose space-time structure can be constrained using two-particle femtoscopic correlations. Standard implementations rely on the smoothness and on-shell approximations, which effectively remove the relative momentum dependence of the particle emission function. We explore the validity of these approximations by deriving model-independent expansions that quantify the leading corrections for femtoscopy and coalescence with arbitrary sources and final-state interactions. The resulting first- and second-order correction terms can be evaluated with essentially the same numerical complexity as the usual Koonin-Pratt expressions; for angle-averaged correlations the first-order contributions vanish by symmetry. We illustrate the framework with explicit calculations in a blast-wave source model. For parameter sets representative of pp and PbPb fits at LHC energies, the corrections are at or below the percent level for pp correlations and deuteron coalescence.
Paper Structure (19 sections, 92 equations, 3 figures)

This paper contains 19 sections, 92 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Theoretical Background
  3. The Smoothness Expansion
  4. Angle-Dependent Correlations
  5. Angle-Averaged Correlations
  6. Free Particles
  7. Distinguishable Particles
  8. Identical Particles
  9. Coalescence
  10. The On-Shell Expansion
  11. Explicit Calculations in the Blast Wave Model
  12. The Blast Wave Model
  13. Correlations
  14. Coalescence
  15. Discussion
  16. ...and 4 more sections

Figures (3)

  • Figure 1: Left: $C(q)$ (solid) and $C_\mathrm{smooth}(q)$ (dotted) for various source sizes and transverse momenta. Right: $(C(q)-C_\mathrm{smooth}(q))/C_\mathrm{smooth}(q)$ for the corresponding plots on the left. The green curves in the central row are based on explicit fits to data in alice-data. Fixed parameters are $\Delta\tau=1.5$ fm, $\beta_S=0.5$, $n=2$, and $T=150$ MeV.
  • Figure 2: $(C(q)-C_\mathrm{smooth}(q))/C_\mathrm{smooth}(q)$ for various blast wave parameters and transverse momentum $p_t=0.3$ GeV. Unless indicated otherwise, default parameters are $\Delta\tau=1.5$ fm, $\beta_S=0.5$, $n=2$, $T=150$ MeV.
  • Figure 3: $(\mathcal{B}-\mathcal{B}_\mathrm{smooth})/\mathcal{B}_\mathrm{smooth}$ versus $b$ for coalescence with a Gaussian wavefunction of width $b$. The ratio is plotted for various source sizes, transverse momenta, and temperatures. Fixed parameters are $\Delta\tau=1.5$ fm, $\beta_S=0.5$, and $n=2$. Note that the plots on the right column correspond to the parameters featured in the top and bottom rows of Fig. \ref{['fig:corr-size']}.