section on jet pt shift systematic

ch4-07-pt-shift.tex

@@ -1,29 +1,84 @@
 \subsection{Jet Transverse Momentum Shift}
 
-The asymmetries calculated using the 2006 RHIC data are plotted against the ratio of the charged pion \(p_{T}\) and the ``true'' \(p_{T}\) of the away-side jet, which incorporates a number of corrections to the actual measured value.  Various factors bias the measured jet momentum:
-%
-\begin{itemize}
-  \item pileup TPC tracks in the jet cone radius
-  \item finite energy resolution convoluted with a steeply failing \(p_T\) spectrum
-  \item fragmentating hadrons falling outside the cone radius
-  \item underlying event interactions depositing energy in the cone radius
-\end{itemize}
-%
-The first two items are detector effects which can be corrected, while the latter two involve an interaction between the reconstruction algorithm and the physics that is best accounted for using a systematic uncertainty.
+The asymmetries calculated using the 2006 RHIC data are plotted against the
+ratio of the charged pion \(p_{T}\) and the ``true'' \(p_{T}\) of the away-side
+jet, which incorporates a number of corrections to the actual measured jet
+\(p_T\). Various factors bias this measured quantity, including pileup tracks in
+the TPC, finite resolution effects, possible detector miscalibrations,
+out-of-cone hadronization of fragmenting partons, and in-cone underlying event
+effects. The pileup and finite energy resolution are detector effects which can
+be corrected in the analysis, while the remaining sources of bias are best
+accounted for using a systematic uncertainty.
+
+\subsubsection{Jet $p_T$ Scale Corrections}
+
+TPC pileup has a relatively small effect on the jet momentum in the 2006 run. An
+event-mixing analysis using zerobias data concluded that pileup adds an average
+of 50 MeV to each jet. The bin migration caused by the $\sim$ 25\% jet energy
+resolution results in a much larger \(p_T\) bias. This effect is investigated by
+running the jet reconstruction algorithm on final-state particles in the Pythia
+record to generate a ``particle'' jet and comparing the \(p_{T}\) of that jet
+with the \(p_{T}\) of the ``detector'' jet formed from the tracks and towers of
+the full detector simulation. The comparison is repeated for a broad envelope of
+calibration parameters, tracking efficiencies, and detector states in order to
+account for a possible detector miscalibration.
+
+The hadronization and underlying event biases are not accounted for in the above
+analysis. Out-of-cone hadronization is subprocess-dependent, since quark jets
+typically have a harder fragmentation profile than gluon jets, while the
+underlying event effect is isotropic in \(\eta \times \phi\) space and largely
+independent of jet \(p_T\). The two effects are closely connected in the Pythia
+Monte Carlo simulations. The combined effect from these two sources of bias was
+estimated by comparing jets at the ``fragmented parton'' level with the particle
+jets described above. In simulations of fragmented parton jets the underlying
+event and hadronization processes are turned off.
 
-TPC pileup turns out to have a relatively small effect on the jet momentum in the 2006 run.  An event-mixing analysis using zerobias data concluded that pileup adds an average of 50 MeV to each jet.  The bin migration caused by the $\sim$ 25\% energy resolution results in a much larger \(p_T\) bias.  This effect is investigated by running the jet reconstruction algorithm on final-state particles in the Pythia record to generate a ``particle'' jet and comparing the \(p_{T}\) of that jet with the \(p_{T}\) of the ``detector'' jet formed from the tracks and tower of the full detector simulation.  The size of the average shift from measured jet \(p_T\) to particle jet \(p_T\) s a function of measured \(p_T\) shown in Figure~\ref{} and can be parameterized as
+Figure~\ref{fig:jet-pt-shift} plots the size of the shift from detector jet
+\(p_T\) to particle jet \(p_T\) in bins of detector \(p_T\). The error bars
+represent statistical uncertainties on the size of the shift, while the square
+brackets denote combined systematic uncertainties from the detector
+miscalibration envelope and the hadronization and underlying event effects. The
+solid line is a polynomial fit to the data points:
 %
 \begin{equation}
-  p_{T,true} = 1.538 + 0.8439*p_{T,meas} - 0.001691*p_{T,meas}^2.
+  \Delta p_T = 1.538 - 0.1561*p_T - 0.001691*p_T^2.
 \end{equation}
+%
+This shift is applied to each accepted jet before calculating the fragmentation
+variable ``z'' used in the 2006 asymmetry analysis.
 
-Finally, out-of-cone hadronization and underlying event interactions bias the measured jet energy in different ways.  The hadronization effect is expected to be subprocess-dependent, since quark jets typically have a harder fragmentation profile than gluon jets, while the underlying event effect is isotropic in \(\eta \times \phi\) space and largely independent of jet \(p_T\).
+\begin{figure}
+  \centering
+  \includegraphics[width=0.7\textwidth]{figures/jet-pt-shift}
+  \caption{Correction to measured jet $p_T$.  The data points represent the size of the shift in each measured jet $p_T$ bin, with statistical uncertainties attached.  The solid line is a polynomial fit to those data points, and the outer error bars represent systematic uncertainties due to detector miscalibration, out-of-cone hadronization, and underlying event effects summed in quadrature.}
+  \label{fig:jet-pt-shift}
+\end{figure}
 
+\subsubsection{Effect on $A_{LL}$}
 
-The uncertainty on the magnitude of the shift is shown in Figure~\ref{fig:jet-pt-shift-uncertainty}.  This uncertainty arises from limited statistics in the Monte Carlo sample, from uncertainties in the jet energy scale due to possible inaccuracies in the calibration of the TPC and EMCs, and from 
-\begin{figure}
+The bias on \(A_{LL}\) introduced by a systematic error in the jet \(p_T\) scale
+corrections is estimated by a maximum extent uncertainty. We evaluate \(A_{LL}\)
+using new \(p_T\) shift parameterizations generated from fits to the 1 $\sigma$
+total uncertainty bands on the nominal \(p_T\) shift. The average magnitude of
+the change in \(A_{LL}\) obtained using these alternative \(p_T\) shifts gives
+us the size of the systematic uncertainty. The final values for this uncertainty
+are given in Table~\ref{tab:syst-pt-shift}.
+
+\begin{table}
   \centering
-  \includegraphics[width=0.7\textwidth]{figures/jet-pt-shift-uncertainty}
-  \caption{$1 \sigma$ uncertainty band on the size of the correction from measured jet $p_T$ to particle jet $p_T$.}
-  \label{fig:jet-pt-shift-uncertainty}
-\end{figure}
+  \begin{tabular}{|c||c|c||c|c|}
+    \hline
+    $z$ & $\pi^-~\delta A_{LL}$ & $\pi^+~\delta A_{LL}$ \\
+    % \multirow{2}{*}{$z$} & \multicolumn{2}{c}{$\delta A_{LL}$ ($10^{-2}$)} \\
+    % \cline{2-3}
+    % & $\pi^-$ & $\pi^+$ \\
+    \hline
+    0.20 - 0.30 & 0.003 &  0.004 \\
+    0.30 - 0.45 & 0.005 &  0.007 \\
+    0.45 - 0.65 & 0.016 &  0.016 \\
+    0.65 - 1.00 & 0.010 &  0.016 \\
+    \hline
+  \end{tabular}
+  \caption{Systematic uncertainty on $A_{LL}$ due to possible errors in the correction from detector jet $p_T$ to true jet $p_T$.}
+  \label{tab:syst-pt-shift}
+\end{table}