Background subtraction methods for precision measurements of di-hadron and jet-hadron correlations in heavy ion collisions

Di-hadron correlationsand jet-hadron correlations are frequently used to study interactions of the quark gluon plasma with the hard partons that form jets. The existing background subtraction methods for these studies depend on several assumptions and independent measurements of the Fourier coefficients of the combinatorial background. In this paper, we present a method for determining the background using a fit to the reaction plane dependence of the background-dominated region of the near side to extract the background. We also fit the of the background-dominated region of the near side without the reaction plane dependence. To test the accuracy of these methods, a simple model is used to simulate di-hadron and jet-hadron correlations with a combinatorial background similar to that observed in the data. The true signal is compared to the extracted signal. The results are compared to results from two variants of the zero-yield-at-minimum (ZYAM) method. We test these methods for midperipheral and central collisions and for di-hadron and jet-hadron correlations. These methods are more precise than the ZYAM method with fewer assumptions about the shape and level of the combinatorial background, even in central collisions where the experimental resolution on the measurement of the reaction plane dependence is poor. These methods will allow more accurate studies of modifications of the away-side jet and will be particularly useful for studies of jet-hadron correlations, where the combinatorial background is poorly constrained from previous studies.

Figure 1

Di-hadron correlations for trigger momenta 8 $<p_T^{\mathrm{t}}<$ 10 GeV/$c$ within pseudorapidities $\left|\eta \right|<$ 0.5 and associated particles within $\left|\eta \right|<$ 0.9 with momenta 1.0 $<p_T^{\mathrm{a}}<$ 2.0 GeV/$c$ in $p+p$ collisions at $\sqrt{s}=2.76$ TeV in pythia [11]. The signal is normalized by the number of equivalent Pb+Pb collisions in our simulations and corrected for the acceptance using the mixed event correction described in the text.

Figure 2

Di-hadron correlation signal for trigger momenta 8 $<p_T^{\mathrm{t}}<$ 10 GeV/$c$ within pseudorapidities $\left|\eta \right|<$ 0.5 and associated particles within $\left|\eta \right|<$ 0.9 with momenta 1.0 $<p_T^{\mathrm{a}}<2.0$ GeV/$c$ in 30–40% Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ TeV. The signal is normalized by the number of Pb+Pb collisions. The signal is from Fig. 1 and the generation of the background is discussed in the method section.

Figure 3

Acceptance correction for a trigger with a flat distribution within $\left|\eta \right|<0.5$ and an associated particle with a flat distribution within $\left|\eta \right|<0.9$.

Figure 4

Top: Signal + background for di-hadron correlations in 30–40% Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV in the region 1.0 $<|\mathrm{\Delta }\eta |<$ 1.4. This is compared to the true background, the background from the modified ZYA1 method, and the background from the NSF method. (See text for details.) The fit for the NSF method is to Eq. (3) to order $n=4$ from $\left|\mathrm{\Delta }\varphi \right|< \pi$/2 and has ${\chi }^2$/NDF = 63.6/45. Bottom: Ratios of the background from the NSF and ZYA1 methods to the true background.

Figure 5

Top: The true signal for di-hadron correlations in 30–40% Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV. This is compared to the signal extracted using the background from the ZYA1 method, the modified ZYA1 method, and the background extracted from the NSF method for $\left|\mathrm{\Delta }\varphi \right|< \pi$/2 using the fit shown in Fig. 4. (See text for details.) Bottom: Differences between the true signal and the signal extracted using the background from the ZYA1 method, modified ZYA1 method, and the background from the RPF method.

Figure 6

Top: The true signal for di-hadron correlations in 0–10% Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV. This is compared to the signal extracted using the background from the ZYA1 method, the modified ZYA1 method, and the background extracted from the NSF method for $\left|\mathrm{\Delta }\varphi \right|< \pi$/2. Bottom: Differences between the true signal and the signal extracted using the background from the ZYA1 method, modified ZYA1 method, and the background from the RPF method.

Figure 7

Top: The true signal for jet-hadron correlations in 30–40% Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV. This is compared to the signal extracted using the background from the ZYA1 method, the modified ZYA1 method, and the background extracted from the NSF method for $\left|\mathrm{\Delta }\varphi \right|< \pi$/2. Bottom: Differences between the true signal and the signal extracted using the background from the ZYA1 method, modified ZYA1 method, and the background from the RPF method.

Figure 8

Top: Signal+background for di-hadron correlations in 30–40% Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV in the region 1.0 $<|\mathrm{\Delta }\eta |<$ 1.4. This is compared to the true background, the background from the modified ZYA1 method, and the background from the NSF method. (See text for details.) The fit for the NSF method is to Eq. (3) to order $n=4$ from $\left|\mathrm{\Delta }\varphi \right|<$ 1.25 and has ${\chi }^2$/NDF = 50.8/35. Bottom: Ratios of the background from the NSF and ZYA1 methods to the true background.

Figure 9

Schematic diagram showing the reaction plane angles used in the analysis.

Figure 10

Top: Signal+background for di-hadron correlations in 30–40% Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV in the region 1.0 $<\left|\mathrm{\Delta }\eta \right| <$ 1.4 for in-plane, midplane, and out-of-plane triggers and for all triggers combined. This is compared to the true background, the background from the modified ZYA1 method, and the background from the RPF method. (See text for details.) The data for all angles relative to the reaction plane have been scaled by 1/3 in the top panel in order to fit on the same scale. The fit for the RPF method is to Eq. (8) to order $n=4$ from $\left|\mathrm{\Delta }\varphi \right|< \pi$/2 and has ${\chi }^2$/NDF = 176/138. Bottom: Ratios of the background from the RPF and ZYA1 methods to the true background.

Figure 11

Top: The true signal for di-hadron correlations in 30–40% Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV for in-plane, midplane, and out-of-plane triggers and for all triggers combined. This is compared to the signal extracted using the background from the ZYA1 method, the modified ZYA1 method, and the background extracted from the RPF method for $\left|\mathrm{\Delta }\varphi \right|< \pi$/2 using the fit shown in Fig. 10. (See text for details.) The data for all angles relative to the reaction plane have been scaled by 1/3 in the top panel in order to fit on the same scale. Bottom: Differences between the true signal and the signal extracted using the background from the ZYA1 method, modified ZYA1 method, and the background from the RPF method.

Figure 12

Top: Signal+background for di-hadron correlations in 30–40% Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV in the region 1.0 $<\left|\mathrm{\Delta }\eta \right| <$ 1.4 for in-plane, midplane, and out-of-plane triggers and for all triggers combined. This is compared to the true background, the background from the modified ZYA1 method, and the background from the RPF method. (See text for details.) The data for all angles relative to the reaction plane have been scaled by 1/3 in the top panel in order to fit on the same scale. The fit for the RPF method is to Eq. (8) to order $n=4$ from $\left|\mathrm{\Delta }\varphi \right|<$ 1 and has ${\chi }^2$/NDF = 128/90. Bottom: Ratios of the background from the RPF and ZYA1 methods to the true background.

Figure 13

Top: The true signal for di-hadron correlations in 30–40% Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV for in-plane, midplane, and out-of-plane triggers and for all triggers combined. This is compared to the signal extracted using the background from the ZYA1 method, the modified ZYA1 method, and the background extracted from the RPF method for $\left|\mathrm{\Delta }\varphi \right|<$ 1 using the fit shown in Fig. 12. (See text for details.) The data for all angles relative to the reaction plane have been scaled by 1/3 in the top panel in order to fit on the same scale. Bottom: Differences between the true signal and the signal extracted using the background from the ZYA1 method, modified ZYA1 method, and the background from the RPF method.

Figure 14

Top: Signal+background for di-hadron correlations in 0–10% Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV in the region 1.0 $<|\mathrm{\Delta }\eta |<$ 1.4 for in-plane, midplane, and out-of-plane triggers and for all triggers combined. This is compared to the true background, the background from the modified ZYA1 method, and the background from the RPF method. (See text for details.) The data for all angles relative to the reaction plane have been scaled by 1/3 in the top panel in order to fit on the same scale. The fit for the RPF method is to Eq. (8) to order $n=3$ from $\left|\mathrm{\Delta }\varphi \right|< \pi$/2 and has ${\chi }^2$/NDF = 151/140. Bottom: Ratios of the background from the RPF and ZYA1 methods to the true background.

Figure 15

Top: The true signal for di-hadron correlations in 0–10% Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV for in-plane, midplane, and out-of-plane triggers and for all triggers combined. This is compared to the signal extracted using the background from the ZYA1 method, the modified ZYA1 method, and the background extracted from the RPF method for $\left|\mathrm{\Delta }\varphi \right|< \pi$/2 using the fit shown in Fig. 14. (See text for details.) The data for all angles relative to the reaction plane have been scaled by 1/3 in the top panel in order to fit on the same scale. Bottom: Differences between the true signal and the signal extracted using the background from the ZYA1 method, modified ZYA1 method, and the background from the RPF method.

Figure 16

Top: Signal+background for jet-hadron correlations in 30–40% Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV in the region 1.0 $<\left|\mathrm{\Delta }\eta \right| <$ 1.4 for in-plane, midplane, and out-of-plane triggers and for all triggers combined. This is compared to the true background, the background from the modified ZYA1 method, and the background from the RPF method. (See text for details.) The data for all angles relative to the reaction plane have been scaled by 1/3 in the top panel in order to fit on the same scale. The fit for the RPF method is to Eq. (8) to order $n=4$ from $\left|\mathrm{\Delta }\varphi \right|< \pi$/2 and has ${\chi }^2$/NDF = 193/186. Bottom: Ratios of the background from the RPF and ZYA1 methods to the true background.

Figure 17

Top: The true signal for jet-hadron correlations in 30–40% Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV for in-plane, midplane, and out-of-plane triggers and for all triggers combined. This is compared to the signal extracted using the background from the ZYA1 method, the modified ZYA1 method, and the background extracted from the RPF method for $\left|\mathrm{\Delta }\varphi \right|< \pi$/2 using the fit shown in Fig. 16. (See text for details.) The data for all angles relative to the reaction plane have been scaled by 1/3 in the top panel in order to fit on the same scale. Bottom: Differences between the true signal and the signal extracted using the background from the ZYA1 method, modified ZYA1 method, and the background from the RPF method.