Effect of centrality bin width corrections on two-particle number and transverse momentum differential correlation functions

Two-particle number and transverse momentum differential correlation functions are powerful tools for unveiling the detailed dynamics and particle production mechanisms involved in relativistic heavy-ion collisions. Measurements of transverse momentum correlators $P_2$ and $G_2$, in particular, provide added information not readily accessible with better known number correlation functions $R_2$. However, it is found that the $R_2$ and $G_2$ correlators are somewhat sensitive to the details of the experimental procedure used to measure them. They exhibit, in particular, a dependence on the collision centrality bin width, which may have a rather detrimental impact on their physical interpretation. A technique to correct these correlators for collision centrality bin-width averaging is presented. The technique is based on the hypothesis that the shape of single- and pair-probability densities vary slower with collision centrality than the corresponding integrated yields. The technique is tested with Pb-Pb simulations based on the HIJING and ultrarelativistic quantum molecular dynamics models and shown to enable a precision better than 1% for particles in the kinematic range $0.2\le p_{\mathrm{T}}\le 2.0$ GeV/$c$.

Figure 1

Longitudinal projection of the two-particle normalized cumulants $R_2^{\mathrm{CI}}$ (left) and $R_2^{\mathrm{CD}}$ (right) for the most central Pb-Pb collisions produced with the HIJING event generator. Top panels show uncorrected results for the 0–5 % centrality bin together with those from the 0–1 %, 2–3 %, and 4–5 % centrality bins, middle panels show corrected 0–5 % centrality bin results compared with the weighted average of those from the 0–1 %, 1–2 %, 2–3 %, 3–4 %, and 4–5 % centrality bins, while bottom panels show their ratio.

Figure 2

Longitudinal projection of the two-particle normalized cumulants $R_2^{\mathrm{CI}}$ (left) and $R_2^{\mathrm{CD}}$ (right) for 5% most central Pb-Pb collisions produced with the UrQMD event generator. Top panels show uncorrected results for the 0–5 % centrality bin together with those from the 0–1 %, 2–3 %, and 4–5 % centrality bins, middle panels show corrected 0–5 % centrality bin results compared with the weighted average of those from the 0–1 %, 1–2 %, 2–3 %, 3–4 %, and 4–5 % centrality bins, while bottom panels show their ratio.

Figure 3

Longitudinal projection of the two-particle transverse momentum correlations $G_2^{\mathrm{CI}}$ for default transverse momentum range particles (left) and for the reduced (see text) transverse momentum range particles (center) and $G_2^{\mathrm{CD}}$ for the default transverse momentum range particles (right) for the 5% most central Pb-Pb collisions produced with the HIJING event generator. Top panels show uncorrected results for the 0–5 % centrality bin together with those from the 0–1 %, 2–3 %, and 4–5 % centrality bins, middle panels show corrected 0–5 % centrality bin results compared with the weighted average of those from the 0–1 %, 1–2 %, 2–3 %, 3–4 %, and 4–5 % centrality bins, while bottom panels show their ratio.

Figure 4

Longitudinal projection of the two-particle transverse momentum correlations $G_2^{\mathrm{CI}}$ (left) and $G_2^{\mathrm{CD}}$ (right) for the 5% most central Pb-Pb collisions produced with the UrQMD event generator. Top panels show uncorrected results for the 0–5 % centrality bin together with those from the 0–1 %, 2–3 %, and 4–5 % centrality bins, middle panels show corrected 0–5 % centrality bin results compared with the weighted average of those from the 0–1 %, 1–2 %, 2–3 %, 3–4 %, and 4–5 % centrality bins, while bottom panels show their ratio.

Figure 5

Azimuthal projections of the two-particle transverse momentum correlations $R_2^{\mathrm{CI}}$ for the whole $p_{\mathrm{T}}$ range (left) and $G_2^{\mathrm{CI}}$ for the reduced $p_{\mathrm{T}}$ range (right) for the 5% most central Pb-Pb collisions produced with the HIJING event generator. Top panels show uncorrected results for the 0–5 % centrality bin together with those from the 0–1 %, 2–3 %, and 4–5 % centrality bins, middle panels show corrected 0–5 % centrality bin results compared with the weighted average of those from the 0–1 %, 1–2 %, 2–3 %, 3–4 % and 4–5 % centrality bins, while bottom panels show their ratio.

Figure 6

Longitudinal projection of the two-particle transverse momentum correlation $P_2^{\mathrm{CI}}$ for the 5% most central Pb-Pb collisions produced with the HIJING event generator (left) and the UrQMD event generator (right). Top panels show uncorrected results for the 0–5 % centrality bin together with those from the 0–1 %, 2–3 %, and 4–5 % centrality bins, middle panels show corrected 0–5 % centrality bin results compared with the weighted average of those from the 0–1 %, 1–2 %, 2–3 %, 3–4 %, and 4–5 % centrality bins, while bottom panels show their ratio.