Techniques for multiboson interferometry

The quantum statistics (QS) correlations of identical bosons are well known to be sensitive to the space-time extent and dynamics of the particle emitting source in high-energy collisions. While two-pion correlations are most often experimentally measured, the QS correlations of three pions and higher are rarely explored. A set of techniques to isolate and analyze three- and four-pion QS correlations is presented. In particular, the technique of built correlation functions allows one to more easily study the effects of quantum coherence at finite relative momenta instead of at the unmeasured intercept of correlation functions.

Figure 1

Two-pion symmetrization diagrams. Derived from similar figures in Ref. [19].

Figure 2

Three-pion symmetrization diagrams. Derived from similar figures in Ref. [19].

Figure 3

Four-pion symmetrization diagrams. Derived from similar figures in Ref. [19].

Figure 4

Modification of two-pion QS correlation functions in the presence of partial coherence. The correlation function for a fully chaotic spherically symmetric Gaussian source with $R_{\mathrm{ch}}=8$ fm is shown with a solid black line. Dashed blue and dash-dotted red lines include an additional spherically symmetric coherent component with $R_{\mathrm{coh}}=1$ fm for $G=0.2$ and $G=0.5$, respectively.

Figure 5

Triplet fractions in therminator. Blue triangles (3 interacting pairs), red squares (1 pair), green triangles (2 pairs), and black circles (0 pairs) are shown. The core/halo values (given $f_c^2=0.803$) are shown with blue (3 pairs), red (1 pair), and black (0 pairs) lines.

Figure 6

Quadruplet fractions in therminator. From top to bottom, the markers indicate 6, 3, 1, 5, 4, 2, and 0 interacting pair(s). The core/halo values (given $f_c^2=0.803$) are shown with black (6 interacting pairs), blue (3 pairs), red (1 pair), and green (0 pairs) lines.

Figure 7

$C_2$ versus $q$ calculated in therminator. A Gaussian as well as Edgeworth fit is shown. The fit range is that which is shown in the figure. $0.2<k_{\mathrm{T}}<0.3\text{GeV}/c$.

Figure 8

Three-pion correlations versus $Q_3$ calculated in therminator. A Gaussian as well as Edgeworth fit to the cumulant correlation function is shown. The fits are performed in 3D ($q_{12},q_{23},q_{31}$). The built correlation functions are also shown as block histograms. $0.16<K_{\mathrm{T},3}<0.3\text{GeV}/c$.

Figure 9

Ratio of measured to built three-pion correlation functions.

Figure 10

Four-pion correlations versus $Q_4$ calculated in therminator. The built correlation functions are also shown as a block histogram. $0.16<K_{\mathrm{T},4}<0.3\text{GeV}/c$.

Figure 11

Ratio of measured to built four-pion correlation functions.

Figure 12

$C_2$ versus $q$ calculated in therminator with $G=0.35$ and $t_{ij}=e^{-R_{\mathrm{coh}}^2{q}_{ij}^2/2}$. A Gaussian as well as Edgeworth fit is shown. Further details are the same as in Fig. 7.

Figure 13

Three-pion correlations versus $Q_3$ calculated in therminator with $G=0.35$ and $t_{ij}=e^{-R_{\mathrm{coh}}^2{q}_{ij}^2/2}$. An Edgeworth fit is shown. Further details are the same as in Fig. 8.

Figure 14

Ratio of measured to built three-pion correlation functions with $G=0.35$ and $t_{ij}=e^{-R_{\mathrm{coh}}^2{q}_{ij}^2/2}$.

Figure 15

Four-pion correlations versus $Q_4$ calculated in therminator with $G=0.35$ and $t_{ij}=e^{-R_{\mathrm{coh}}^2{q}_{ij}^2/2}$. Further details are the same as in Fig. 10.

Figure 16

Ratio of measured to built four-pion correlation functions with $G=0.35$ and $t_{ij}=e^{-R_{\mathrm{coh}}^2{q}_{ij}^2/2}$.

Figure 17

$r_3$ calculated in therminator with various types of $T_{ij}$ tabulations/interpolations. The quartic fit is applied to the solid points. Statistical errors are only drawn for the solid points and are the same for the others. The chaotic upper limit is shown with the red dotted line.

Figure 18

$r_4$ calculated in therminator with various types of $T_{ij}$ tabulations/interpolations. The chaotic upper limit is shown with the red dotted line.

Figure 19

$r_3$ calculated in therminator with $G=0.35$ and $t_{ij}=e^{-R_{\mathrm{coh}}^2{q}_{ij}^2/2}$. Bin widths are 5 $\text{MeV}/c$ with cubic interpolation. A quartic fit is shown. Statistical errors are only drawn for the solid points and are the same for the others.

Figure 20

Comparison of same and mixed-charge three-pion FSI correlations. ${\mathrm{\Omega }}_0$ and generalized Riverside (GRS) methods are shown. The calculation was performed in therminator. The bottom panel shows the difference between the two methods, $\mathrm{\Delta }{K}_3=K_3\left({\mathrm{\Omega }}_0\right)-K_3\left(\mathrm{GRS}\right)$, divided by $K_3\left(\mathrm{GRS}\right)-1$.

Figure 21

Multiboson distorted two-pion correlation function compared to the undistorted case. The setting with $n=700$ roughly correspond to $0–5\%$ Pb-Pb collisions at the LHC.

Figure 22

The multiboson distorted three-pion correlation function compared to the undistorted case. Also shown is the built correlation function constructed from the distorted two-pion correlation function in Fig. 21. The setting with $n=700$ roughly correspond to $0–5\%$ Pb-Pb collisions at the LHC.

Figure 23

The multi-boson distorted four-pion correlation function compared to the undistorted case. Also shown is the built correlation function constructed from the distorted two-pion correlation function in Fig. 21. The setting with $n=700$ roughly correspond to $0–5\%$ Pb-Pb collisions at the LHC.