Pion femtoscopy in $p$ $+$ $p$ collisions at $\sqrt{s}=200$ GeV

The STAR Collaboration at the BNL Relativistic Heavy Ion Collider has measured two-pion correlation functions from $p+p$ collisions at $\sqrt{s}=200$ GeV. Spatial scales are extracted via a femtoscopic analysis of the correlations, though this analysis is complicated by the presence of strong nonfemtoscopic effects. Our results are put into the context of the world data set of femtoscopy in hadron-hadron collisions. We present the first direct comparison of femtoscopy in $p+p$ and heavy ion collisions, under identical analysis and detector conditions.

Figure 1

Cartesian projections of the 3D correlation function from $p+p$ collisions at $=200$ GeV for $k_T=[0.35,0.45]$ $\mathrm{GeV}/c$ (blue triangles). Femtoscopic effects are parametrized with the form in Eq. (11); different curves represent various parametrizations of nonfemtoscopic correlations used in the fit and described in detail in Sec. 2b.

Figure 2

First three nonvanishing moments of the spherical harmonic decomposition of the correlation function from $p+p$ collisions at $\sqrt{s}=200$ GeV, for $k_T=[0.15,0.25]$ $\mathrm{GeV}/c$. Femtoscopic effects are parametrized with the form in Eq. (11); different curves represent various parametrizations of nonfemtoscopic correlations used in the fit and described in detail in Sec. 2b. The superscript RE in $A_{l,m}^{\mathrm{RE}}$ stands for the real part of $A_{l,m}$.

Figure 3

As for Fig. 2, but for $k_T=[0.25,0.35]$ $\mathrm{GeV}/c$.

Figure 4

As for Fig. 2, but for $k_T=[0.35,0.45]$ $\mathrm{GeV}/c$.

Figure 5

As for Fig. 2, but for $k_T=[0.45,0.60]$ $\mathrm{GeV}/c$.

Figure 6

$m_T$ dependence of the 3D femtoscopic radii in $p+p$ collisions at $\sqrt{s}=200$ GeV for different parametrizations of the nonfemtoscopic correlations. See text for more details. Data have been shifted slightly in the abscissa for clarity.

Figure 7

Correlation functions for oppositely signed pion pairs from minimum-bias $p+p$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV as measured by the STAR Collaboration (filled red circles) and as simulated with the pythia event generator (open circles). See text for details.

Figure 8

Same as Fig. 7, but for like-sign pions.

Figure 9

$m_T$ dependence of $R_{\mathrm{inv}}$ from $p+p$ collisions at $\sqrt{s}=200$ GeV for different parametrizations of the nonfemtoscopic correlations used in the fit procedure.

Figure 10

Multiplicity dependence of $R_{\mathrm{inv}}$ from $p+p$ collisions at $\sqrt{s}=200$ GeV for different parametrizations of the nonfemtoscopic correlations. Pions within the range of $k_T=[0.15,0.60]$ $\mathrm{GeV}/c$ were used in the analysis.

Figure 11

Multiplicity dependence of the HBT radii from $p+p$, $\mathrm{Cu}+\mathrm{Cu}$ [56], and $\mathrm{Au}+\mathrm{Au}$ [55, 56] collisions from STAR compared with results from other experiments [11]. Left and right panels show radii measured with $\langle k_T\rangle \approx 0.2$ and 0.39 $\mathrm{GeV}/c$, respectively. Radii from $p+p$ collisions are shown by blue (standard fit) and red (EMCIC fit) stars.

Figure 12

Ratio of the HBT radii from $\mathrm{Au}+\mathrm{Au}$ collisions [55] to results from $p+p$ collisions plotted vs the transverse mass.

Figure 13

Multiplicity dependence of the 1D femtoscopic radius $R_{\mathrm{inv}}$ from hadronic collisions measured by STAR, E735 [38], and ABCDHW [70] collaborations.

Figure 14

Multiplicity dependence of radius and time-scale parameters to two-dimensional correlation functions measured by STAR, E735 [38], UA1 [71], AFS [72], and NA5 [73]. The legend on the right indicates that the first seven sets of data points come from fits to Eq. (7), in which case the parameter $R_B/2$ is plotted in the upper panel; the last five sets of data points come from fits to Eq. (8), for which $R_G$ is plotted. As discussed in Sec. 2a and confirmed by STAR and UA1, $R_G\approx R_B/2$. The UA1 Collaboration set $\tau \equiv 0$ in their fits.

Figure 15

One-dimensional femtoscopic radii from $p+p$ collisions at RHIC and $p+\mathrm{p̄}$ collisions at the Tevatron [38] are plotted vs the transverse momentum $k_T\equiv ({\mathrm{p⃗}}_{1,T}+{\mathrm{p⃗}}_{2,T})/2$ [see Eq. (2)].

Figure 16

Transverse momentum dependence of fit parameters to two-dimensional correlation functions. STAR results from fit to Eq. (8), compared to measurements by E735 [38], NA27 [45], and NA22 [74]. The SPS experiments NA22 and NA27 set $\tau \equiv 0$ in their fits. STAR and E735 data are plotted vs $k_T\equiv ({\mathrm{p⃗}}_{1,T}+{\mathrm{p⃗}}_{2,T})/2$ [cf. Eq. (2)]. NA27 reported results in terms of $\left|\mathrm{P⃗}\right|$ and NA22 in terms of $2\left|\mathrm{P⃗}\right|$. For purposes of plotting here, $k_T\approx \sqrt{(}2/3)|\mathrm{P⃗}|$ was assumed.

Figure 17

T ransverse mass dependence of 3D femtoscopic radii from particle collisions. Data from NA22 [32], NA49 preliminary [78], OPAL [33], L3 [44], and DELPHI [79].