Charged pion production in $2A$ to $8A\phantom{\rule{0.3em}{0ex}}\text{GeV}$ central $\text{Au}+\text{Au}$ Collisions

Charged pion production in $2 A$ to $8 A GeV$ central $Au + Au$ Collisions

J. L. Klay et al. (E895 Collaboration)

Phys. Rev. C 68, 054905 – Published 26 November 2003

Abstract

Momentum spectra of charged pions over nearly full rapidity coverage from target to beam rapidity have been extracted from $0 - 5 %$ most central $Au + Au$ collisions in the beam energy range from $2 A$ to $8 A GeV$ by the E895 experiment. Using a thermal parametrization to fit the transverse mass spectra, rapidity density distributions are extracted. The observed spectra are compared with predictions from the RQMD version 2.3 cascade model and also to a thermal model including longitudinal flow. The total $4 π$ yields of the charged pions are used to infer an initial-state entropy produced in the collisions.

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Received 1 July 2003

DOI:https://doi.org/10.1103/PhysRevC.68.054905

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Vol. 68, Iss. 5 — November 2003

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Figure 1
$⟨ d E ∕ d x ⟩$ as a function of rigidity at $6 A GeV$ . A parametrized Bethe-Bloch prediction is used to fix the mean energy loss for each particle species as a function of rigidity. The narrow slices illustrate the location of the $⟨ d E ∕ d x ⟩$ projections shown in Fig. 2.
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Figure 2
Projections of the positive and negative (inset) particles $⟨ d E ∕ d x ⟩$ at midrapidity and $0.125 < m_{t} - m_{0} < 0.150 {GeV ∕ c}^{2}$ , in the rigidity ranges indicated on Fig. 1. The $(m_{t} - m_{0}, y)$ ranges were calculated assuming the pion mass. The function used to fit the data is the two-Gaussian model (described in the text) of the single-particle $⟨ d E ∕ d x ⟩$ distributions, one for each particle type. The integrals under the pion peaks are the total yield for the fitted $(m_{t} - m_{0}, y)$ bin and the contributions from all other particles are discarded.
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Figure 3
EOS TPC total “efficiency” ( $\equiv 1 ∕ correction$ , including effects of acceptance, tracking efficiency, and momentum resolution) for pions produced in $2 A$ , $4 A$ , $6 A$ , and $8 A GeV$ $0 - 5 %$ central $Au + Au$ collisions. The efficiencies are obtained from GEANT simulations of the detector response to Monte Carlo tracks embedded into real data events and propagated through the reconstruction chain. The contours, shown in steps of $\sim 15 %$ , include the effects of geometric acceptance, tracking efficiency, and momentum resolution.
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Figure 4
Invariant yield per event as a function of $m_{t} - m_{0}$ for $π^{-}$ at $2 A$ , $4 A$ , $6 A$ , and $8 A GeV$ . Midrapidity is shown unscaled, while the 0.1 unit forward∕backward rapidity slices are scaled down by successive factors of 10. The functions plotted with the data are two-slope Boltzmann parametrizations described in the text.
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Figure 5
Invariant yield per event as a function of $m_{t} - m_{0}$ for $π^{+}$ at $2 A$ , $4 A$ , $6 A$ , and $8 A GeV$ . Midrapidity is shown uscaled, while the 0.1 unit forward∕backward rapidity slices are scaled down by successive factors of 10. The functions plotted with the data are two-slope Boltzmann parametrizations described in the text.
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Figure 6
Pion transverse mass spectra at midrapidity for $2 A$ , $4 A$ , $6 A$ , and $8 A GeV$ (uppermost curves on Figs. 4 and 5). Two-slope thermal fits are shown superposed on the data along with the contributions to the total from the two separate inverse slope terms in Eq. (3).
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Figure 7
Rapidity dependence of the fit parameters from $2 A GeV π^{-} m_{t} - m_{0}$ spectra fits with a two-slope model. The leftmost panels show the inverse slope parameters. $T_{1}$ (indicated by closed triangles) dominates the low- $(m_{t} - m_{0})$ range of the spectra, whereas $T_{2}$ (indicated by closed squares) dominates the high- $(m_{t} - m_{0})$ end of the spectra. The middle panels show the two $d N ∕ d y$ fit parameters ( $d N ∕ {d y}_{1}$ in open triangles and $d N ∕ {d y}_{2}$ in open squares) and the rightmost panels show the total $d N ∕ d y$ , which is the sum of $d N ∕ {d y}_{1}$ and $d N ∕ {d y}_{2}$ . The top row reports the fit results when all four parameters are allowed to be independent in the fit. The bottom row shows the results for the remaining three parameters when the high- $(m_{t} - m_{0})$ inverse slope is fixed to the Gaussian estimation. Note that the total $d N ∕ d y$ is fairly insensitive to the interplay among the parameters.
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Figure 8
Rapidity dependence of the fit parameters from $4 A GeV π^{-} m_{t} - m_{0}$ spectra fits with a two-slope model. See caption of Fig. 7 for details.
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Figure 9
Rapidity dependence of the fit parameters from $6 A GeV π^{-} m_{t} - m_{0}$ spectra fits with a two-slope model. See caption of Fig. 7 for details.
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Figure 10
Rapidity dependence of the fit parameters from $8 A GeV π^{-} m_{t} - m_{0}$ spectra fits with a two-slope model. See caption of Fig. 7 for details.
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Figure 11
Rapidity dependence of the fit parameters for each beam energy from the $π^{+}$ $m_{t} - m_{0}$ spectra fits with a two-slope model. (See caption of Fig. 7 for more details.) The high- $(m_{t} - m_{0})$ inverse slope parameters have been fixed to the $π^{-}$ parametrized values.
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Figure 12
Yield per event of $π^{-}$ (left-hand panel) and $π^{+}$ (right-hand panel) in $0 - 5 %$ central $Au + Au$ collisions at $2 A$ , $4 A$ , $6 A$ , and $8 A GeV$ integrated over $m_{t} - m_{0}$ as a function of rapidity. A Gaussian parametrization is applied to extract the $4 π$ yields. Reported uncertainties are statistical plus systematic.
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Figure 13
RQMD nature of pion last collision, “lastcl,” before freeze-out at $2 A GeV$ for impact parameter, $b ⩽ 3 fm$ .
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Figure 14
RQMD nature of pion last collision, “lastcl,” before freeze-out at $8 A GeV$ for impact parameter, $b ⩽ 3 fm$ .
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Figure 15
RQMD charged pion spectra at midrapidity for collisions with impact parameter, $b ⩽ 3 fm$ . The contribution to the spectra from pions whose last interaction was a $Δ$ decay and the sum of all other processes are shown separately.
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Figure 16
Ratios of pion yield for different production mechanisms to the total yield as a function of $m_{t} - m_{0}$ at midrapidity from RQMD collisions with impact parameter, $b ⩽ 3 fm$ . The contribution to the spectra from pions whose last interaction was a $Δ$ decay and from the sum of all other processes are shown separately.
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Figure 17
Rapidity density of charged pions from RQMD calculations for collisions with impact parameter, $b ⩽ 3 fm$ . The contribution from $Δ$ resonance decay pions and the sum of all other processes are also plotted separately to show the relative contribution to the pion yields from $Δ$ decays. For comparison, the data from Figs. 7, 8, 9, 10, 11 are also shown.
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Figure 18
$π^{-}$ , $π^{+}$ , and proton rapidity density distributions at $2 A$ , $4 A$ , $6 A$ , and $8 A GeV$ . The expectation for isotropic emission from a stationary thermal source is indicated with dashed lines, whereas the solid curves represent the form including longitudinal flow from the proton $η_{\max}$ values given in Ref. [23]. In all cases the thermal model is too narrow. The proton data and the longitudinal expansion velocity come from Ref. [23].
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Figure 19
Mean pion multiplicity per participant vs $F$ , the Fermi energy variable. The solid symbols represent data from heavy ion collisions, whereas the open symbols come from $p + p$ interactions. The E895 data points are indicated by stars. The third-order polynomial fit to the heavy ion data shows that a smooth trend with $F$ is possible, although the low energy and high energy data (including RHIC results) can be well described by separate linear parametrizations whose slopes differ by a factor of $\approx 1.3$ [24].
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Physical Review C

covering nuclear physics

Charged pion production in $2 A$ to $8 A GeV$ central $Au + Au$ Collisions

J. L. Klay et al. (E895 Collaboration)

Phys. Rev. C 68, 054905 – Published 26 November 2003

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Physical Review C

covering nuclear physics

Charged pion production in 2A to 8AGeV central Au+Au Collisions

J. L. Klay et al. (E895 Collaboration)

Phys. Rev. C 68, 054905 – Published 26 November 2003

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Charged pion production in $2 A$ to $8 A GeV$ central $Au + Au$ Collisions