# Multipion Bose-Einstein correlations in pp, p-Pb, and Pb-Pb collisions at the LHC

Three- and four-pion Bose-Einstein correlations are presented in pp, p-Pb, and Pb-Pb collisions at the LHC. We compare our measured four-pion correlations to the expectation derived from two- and three-pion measurements. Such a comparison provides a method to search for coherent pion emission. We also present mixed-charge correlations in order to demonstrate the effectiveness of several analysis procedures such as Coulomb corrections. Same-charge four-pion correlations in pp and p-Pb appear consistent with the expectations from three-pion measurements. However, the presence of non-negligible background correlations in both systems prevent a conclusive statement. In Pb-Pb collisions, we observe a significant suppression of three- and four-pion Bose-Einstein correlations compared to expectations from two-pion measurements. There appears to be no centrality dependence of the suppression within the 0-50% centrality interval. The origin of the suppression is not clear. However, by postulating either coherent pion emission or large multibody Coulomb effects, the suppression may be explained.

Figures

## Figure 1

 Mixed-charge ($\pm\pm\pm\mp$) four-pion correlations versus $Q_4$ in pp, p--Pb, and Pb--Pb. The full ($C_4^{\rm QS}$), partial cumulant ($a_4^{\rm QS}$), and cumulant ($c_4^{\rm QS}$) correlation functions are shown. The inset figure shows a zoom of $c_4^{\rm QS}$. Systematic uncertainties are shown by the shaded bands. Low and high $K_{\rm T4}$ quadruplets are shown. The average of the charge conjugated correlation functions is shown.

## Figure 2

 Mixed-charge ($\mp\mp\pm\pm$) four-pion correlations versus $Q_4$ in pp, p-Pb, and Pb-Pb. Same details as for Figs. 1(a)-1(f).

## Figure 3

 Same-charge three-pion full and cumulant correlations versus $Q_3$ with Edgeworth fits in pp, p-Pb, and Pb-Pb collisions. Bottom panels show the ratio of the data to the fit. The fits assume $G=0$. The systematic uncertainties for $C_3^{\rm QS}$ are given by the shaded band while those for $c_3^{\rm QS}$ are the same after re-scaling by the ratio of correlation strengths. Only statistical errors are shown for the ratio. The average of the charge conjugated correlation functions is shown.

## Figure 4

 Same-charge four-pion full ($C_4^{\rm QS}$), partial cumulant ($a_4^{\rm QS}$, $b_4^{\rm QS}$), and cumulant ($c_4^{\rm QS}$) correlations versus $Q_4$ in pp (a), p-Pb (b), and Pb-Pb (c) collisions. The solid and dashed block histograms represent $E_4(3)$ and $e_4(3)$ with $G=0$, respectively. Systematic uncertainties shown at the top apply to $C_4^{\rm QS}$. The systematics for the other correlation functions are obtained by scaling down the shaded band by the relative correlation strengths. The systematic uncertainties are similar for the expected and measured correlation functions for which the small difference is shown in the ratio. An additional systematic is drawn for $c_4^{\rm QS}$ and is explained in the systematics section. The bottom panel shows the ratio of measured to expected $C_4^{\rm QS}$. The average of the charge conjugated correlation functions is shown.

## Figure 5

 Three-pion same-charge full ($C_3^{\rm QS}$) and cumulant ($c_3^{\rm QS}$) correlations versus $Q_3$ in Pb-Pb. Expected correlations of the $1^{\rm st}$ type are shown with dashed block histograms with $G=0$. The ratio of measured to expected $C_3^{\rm QS}$ is shown in the bottom panel. The systematic uncertainties are shown by the shaded bands at the top of the figure as explained in Fig. 4(a). The average of the charge conjugated correlation functions is shown.

## Figure 6

 Four-pion same-charge full and cumulant correlations versus $Q_4$ in Pb-Pb. Expected correlations of the $1^{\rm st}$ type are shown with dashed block histograms with $G=0$. The other details are the same as Fig.4(a).

## Figure 7

 Same-charge four-pion full ($C_4^{\rm QS}$) correlations versus $Q_4$. Measured and expected correlations of the $1^{\rm st}$ type are shown. Dashed and solid block histograms show the $G=0$ and $G=32\%$ expected correlations, respectively. Systematic uncertainties are shown at the top. The bottom panel shows the ratio of measured to the expected $C_4^{\rm QS}$. The systematic uncertainties on the ratio are shown with a shaded blue band ($G=0$) and with a thick blue line ($G=32\%$).

## Figure 8

 Same-charge three-pion full ($C_3^{\rm QS}$) correlations versus $Q_3$. Measured and expected correlations of the $1^{\rm st}$ type are shown. Dashed and solid block histograms show the $G=0$ and $G=32\%$ expected correlations, respectively. The other details are the same as in Fig. 7.

## Figure 9

 The extracted coherent fractions ($G$) from same-charge four-pion correlations versus centrality. Systematic uncertainties are given by the shaded band. A linear fit using only the statistical uncertainties is shown by the horizontal red line.

## Figure 1

 The coherent fractions extracted for each $Q_3$ and $Q_4$ bin. Four different extraction procedures are shown. $R_{coh}=R_{ch}$ is assumed.

## Figure 2

 The coherent fractions extracted for each $Q_3$ and $Q_4$ bin for the case when $R_{coh}=0$ is assumed. Four different extraction procedures are shown.

## Figure 3

 Mixed-charge four-pion correlations. The cumulant correlation function, ${\bf c}_4^{\rm QS}$, has been constructed in an alternative way.

## Figure 4

 The mixed-charge three-pion cumulant correlation functions in central Pb-Pb collisions.