Measurement of event background fluctuations for charged particle jet reconstruction in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV

The effect of event background fluctuations on charged particle jet reconstruction in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV has been measured with the ALICE experiment. The main sources of non-statistical fluctuations are characterized based purely on experimental data with an unbiased method, as well as by using single high $p_{\rm T}$ particles and simulated jets embedded into real Pb-Pb events and reconstructed with the anti-$k_{\rm T}$ jet finder. The influence of a low transverse momentum cut-off on particles used in the jet reconstruction is quantified by varying the minimum track $p_{\rm T}$ between 0.15 GeV/$c$ and 2 GeV/$c$. For embedded jets reconstructed from charged particles with $p_{\rm T} > 0.15$ GeV/$c$, the uncertainty in the reconstructed jet transverse momentum due to the heavy-ion background is measured to be 11.3 GeV/$c$ (standard deviation) for the 10% most central Pb-Pb collisions, slightly larger than the value of 11.0 GeV/$c$ measured using the unbiased method. For a higher particle transverse momentum threshold of 2 GeV/$c$, which will generate a stronger bias towards hard fragmentation in the jet finding process, the standard deviation of the fluctuations in the reconstructed jet transverse momentum is reduced to 4.8-5.0 GeV/$c$ for the 10% most central events. A non-Gaussian tail of the momentum uncertainty is observed and its impact on the reconstructed jet spectrum is evaluated for varying particle momentum thresholds, by folding the measured fluctuations with steeply falling spectra.

Figures

Figure 1

Dependence of charged particle background $p_{\rm t}$ density $\rho$ on uncorrected multiplicity of tracks used for jet finding ($|\eta| < 0.9$). The dotted line is a linear fit to the centroids in each multiplicity bin. The insets show the projected distributions of $\rho$ and raw multiplicity for the 10% most central events
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Figure 2

$\delta$${\pt}$ of random cones in the 10% most central Pb--Pb events for the three types of random cone probes with
${p_{\rm t}^{\rm min}} = 0.15$\,GeV/$c$. A Gaussian fit to the left-hand-side and its extrapolation to positive $\delta\pt$ are shown for measured Pb--Pb events and for randomized Pb--Pb events ($\mu^{\rm LHS}$ and $\sigma^{\rm LHS}$ in GeV/$c$). The solid line is a fit to the $\delta\pt$ distribution for the randomized events with a $\Gamma$ distribution shifted to zero (Eq. 2) as approximation for the shape in case of independent particle emission.
\begin{align*} (2)   f^{\Gamma}(\delta\pt) = A \cdot a_{b} /\Gamma(a_{p}) \cdot (a_b \delta\pt+a_p)^{a_p-1} \cdot e^{-(a_b \delta\pt + a_p)} \end{align*}
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Figure 3

$\delta\pt$ distribution for random cones, averaged over the full azimuth and separated for three bins of random cone azimuthal orientations with respect to the measured event plane. In the bottom panel the distributions have been shifted to zero using the mean of the left-hand-side Gaussian fit ($\mu^{\rm LHS}$)
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Figure 4

Dependence of the standard deviation of the $\delta\pt$ distributions on uncorrected charged particle multiplicity, compared to the limit derived from the measured track $\pt$ spectrum (Eq. 3) and from additional elliptic and triangular flow contributions (Eq. 4) $R = 0.4$, ${p_{\rm t}^{\rm min}}$ = 0.15 GeV/c
\begin{align*} (3)   $\sigma(\delta{\pt}) = \sqrt{N_{\rm A} \cdot \sigma^2(\pt) + N_{\rm A} \cdot \langle \pt \rangle^2}$
   (4)    $\sigma(\delta{\pt}) = \sqrt{N_{\rm A} \cdot \sigma^2(\pt) + \left(N_{\rm A} + \sigma^2_{\rm NP}{(N_{\rm A})}\right) \cdot \langle \pt \rangle ^2} \end{align*}
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Figure 5

$\delta{\pt}$ distribution of charged particles for jet reconstruction with the three methods in the 10% most central Pb-Pb events for ${p_{\rm t}^{\rm min}}$= 0.15GeV/c, 1GeV/c, and 2GeV/c
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