Index: rapgap.tex =================================================================== --- rapgap.tex (revision 186351) +++ rapgap.tex (working copy) @@ -1,17 +1,18 @@ -%\clearpage \section{Rapidity gap cross section} Since it is not possible to measure the whole mass of the diffractively dissociated system due to the limited coverage in the forward region of the detector, one can alternatively measure the size of the corresponding pseudorapidity gap~\cite{Nurse:2011vt}. -The forward and backward gaps are reconstructed in $\eta$ starting from $|\eta|\pm4.7$ and the larger of those gaps is defined as the -largest forward rapidity gap, $\Delta\eta^{F}$. -The uncorrected distribution of the forward rapidity gap size is given in Fig.~\ref{fig:raw} with the comparisons of different MC models. +In each reconstructed event, the size of the gap between each edge of the detector at $\eta=+4.7$ and $\eta=-4.7$ and +the position in $\eta$ of the first particle found in moving away from the edge is designated as the largest forward rapidity gap, $\Delta\eta^F$. +The uncorrected distribution of the forward rapidity gap size is shown in Fig.~\ref{fig:raw} with the predictions of various MC models. +%The forward and backward gaps are reconstructed in $\eta$ starting from $|\eta|\pm4.7$ and the larger of those gaps is defined as the +%largest forward rapidity gap, $\Delta\eta^{F}$. -\begin{figure}[t] +\begin{figure}[h] \begin{center} -\includegraphics[width=0.6\textwidth]{figrapgap/Fig12a.pdf} +\includegraphics[width=0.57\textwidth]{figrapgap/Fig12a.pdf} \end{center} -\caption{Comparison of uncorrected forward rapidity gap size ($\Delta\eta^{F}$) distribution (black points) with the different MC models (colored lines).} +\caption{Comparison of measured uncorrected forward-gap-size distribution, $\Delta\eta^{F}$ (black points), with various MC model predictions.} \label{fig:raw} \end{figure} @@ -24,100 +25,107 @@ %\label{fig:gapalgo} %\end{figure} %Diffractive events at CMS can be typically characterized by a region of the detector, in pseudorapidity space devoid of any particle production, known as a pseudorapidity gap.The size of the pseudorapidity gap ($\Delta\eta$) is related with the mass of the diffractively dissociated system ($M_{X}$) and with the fractional momentum loss of the proton ($\xi$) by $\Delta\eta\sim$ -ln$\xi$ where $\xi=M_{X}^2 / s$. Since it is not possible to measure the whole mass of the diffractively dissociated system due to the limited coverage in the forward region of the detector, one can alternatively measure the size of the corresponding pseudorapidity gap~\cite{Nurse:2011vt}. - %In this analysis, the forward and backward gaps are calculated by taking the absolute difference of the edge of the detector ($|\eta|\pm4.7$) with the $\eta$ of the particle closest to the edge. Later, the larger of the forward and backward gaps is defined as the largest forward rapidity gap, $\Delta\eta^{F}$. An illustration of the forward rapidity gap algorithm is given in Fig.~\ref{fig:gapalgo} where the red filled areas represent the $\eta$ segments hit by the particles in an event. - \subsection{Corrections for experimental effects}\label{sec:expcorrections} -The differential cross section of forward rapidity gaps is determined with the following formula, +The differential cross section of forward rapidity gaps is determined in bins of $\Delta\eta^F$ with the formula \begin{equation} - \frac{\mathrm{d}\sigma(\Delta\eta^{F})}{\mathrm{d}\Delta\eta^{F}} = \frac{A(\Delta\eta^{F})}{\Delta\eta_{binwidth}}\frac{N(\Delta\eta^{F})-N_{BG}(\Delta\eta^{F})}{\epsilon(\Delta\eta^{F})\times \mathcal{L}} + \frac{\mathrm{d}\sigma(\Delta\eta^{F})}{\mathrm{d}\Delta\eta^{F}} = \frac{A(\Delta\eta^{F})}{\Delta\eta_{\rm bin}}\frac{N(\Delta\eta^{F})-N_{BG}(\Delta\eta^{F})}{\epsilon(\Delta\eta^{F})\times \mathcal{L}}, \end{equation} -where $A(\Delta\eta^{F})$ is the correction factor for the migration between bins, $\Delta\eta_{binwidth}$ is the bin width of the each bin measurement, $N(\Delta\eta^{F})$ is the number of minimum bias events and $N_{BG}(\Delta\eta^{F})$ is number of background events obtained from circulating beams. The $\epsilon(\Delta\eta^{F})$ is the trigger efficiency of single side BSC trigger with at least two offline hits and the $\mathcal{L}$ is total integrated luminosity. The data used for the nominal results correspond to an integrated luminosity of $20.3$ $\mu b^{-1}$ with an average pile-up of $0.0066$. +where $A(\Delta\eta^{F})$ is the correction factor for the migration between bins, $\Delta\eta_{\rm bin}$ is the bin width, +$N(\Delta\eta^{F})$ is the number of minimum bias events, and $N_{BG}(\Delta\eta^{F})$ is the number of background events obtained +from circulating beams. The $\epsilon(\Delta\eta^{F})$ is the trigger efficiency of a single-side BSC trigger with at least two offline +hits, and $\mathcal{L}$ is the total integrated luminosity. The data used for the signal extraction correspond to an integrated +luminosity of $20.3$ $\mu b^{-1}$ with an average pile-up of $0.0066$. %\subsubsection{Uncorrected results and beam background}\label{sec:background} %\subsubsection{Trigger Efficiency}\label{sec:trigger} -%\begin{figure}[t] -%\begin{center} -%%\subfigure[]{\includegraphics[width=0.5\textwidth]{figrapgap/Fig12a.pdf}} -%\includegraphics[width=0.6\textwidth]{figrapgap/Fig12b.pdf} -%\end{center} -%\caption{Beam background from unpaired bunches.} -%\label{fig:rawbg} -%\end{figure} +The background from circulating beams, given in Fig.~\ref{fig:rawbg}, is estimated from unpaired bunches using zero-bias dataset, and scaled by 0.5 considering the number of satellite bunches, which is twice larger than the number of collision bunches. The background is numerically subtracted from each measured $\Delta\eta^{F}$ bin. The overall background is found to be $\approx0.7\%$. %$\sim$0.7\%. +\begin{figure}[h] +\begin{center} +%\subfigure[]{\includegraphics[width=0.5\textwidth]{figrapgap/Fig12a.pdf}} +\includegraphics[width=0.57\textwidth]{figrapgap/Fig12b.pdf} +\end{center} +\caption{Beam background from unpaired bunches.} +\label{fig:rawbg} +\end{figure} %The uncorrected distribution of the forward rapidity gap size is given in Fig.~\ref{fig:raw} with the comparisons of different MC models. Also the beam background is presented. -The background from circulating beams, given in Fig.~\ref{fig:rawbg}, is estimated from unpaired bunches using zero bias dataset and scaled by 0.5 considering the number of satellite bunches which is twice larger than the number of collision bunches. The background is numerically subtracted from each measured $\Delta\eta^{F}$ bin and the overall background is found as $\sim$0.7\%. - %\subsubsection{Trigger efficiency}\label{sec:trigger} -The single side BSC trigger efficiency obtained from zero bias data for at least two offline hits in either side of the BSC is given in Fig.~\ref{fig:bscsys}. The trigger efficiency correction factors are obtained from a fit to the data. The discrepancy between the fit and the data points has a small effect on the results and is covered by the systematics. +The single-side BSC trigger efficiency, obtained from zero-bias data for at least two offline hits in either side of the BSC, is shown in Fig.~\ref{fig:bscsys}. The trigger efficiency correction factors are obtained from a fit to the data. The discrepancy between the fit and the data-points has a small effect on the results and is covered by the systematics. +The migration matrix between the truth and reconstructed $\Delta\eta^{F}$ according to {\sc pythia8-mbr ($\epsilon=0.08$)} is given in Fig.~\ref{fig:matrix}. A better correlation is observed with a $p_{T} > 200$ MeV cut at truth level. The corresponding hadron-level definition of the analysis considers all stable final-state particles with $p_{T} >200$ MeV in $|\eta|<4.7$. The Bayesian unfolding method was used to correct the data for the migration between bins. + % Fig 13 -\begin{figure}[t] +\begin{figure}[h] \begin{center} -\includegraphics[width=0.6\textwidth]{figrapgap/Fig13.pdf} +\includegraphics[width=0.57\textwidth]{figrapgap/Fig13.pdf} \end{center} -\caption{Single side BSC trigger efficiency for at least two hits (offline) in either side of the BSC. The trigger efficiency correction factors are obtained from a fit to the data. The discrepancy between the fit and the data points has a small effect on the results and is covered by the systematics.} +\caption{The single-side BSC trigger efficiency for at least two hits (offline) in either side of the BSC. The trigger efficiency correction factors are obtained from a fit to the data. The discrepancy between the fit and the data-points has a small effect on the results and is covered by the systematics.} \label{fig:bscsys} \end{figure} %\subsubsection{Unfolding}\label{sec:unfolding} -The migration matrix between the truth and reconstructed $\Delta\eta^{F}$ according to {\sc pythia8-mbr ($\epsilon=0.08$)} is given in Fig.~\ref{fig:matrix}. A better correlation is observed with a $p_{T} > 200$ MeV cut at truth level. The corresponding hadron level definition of the analysis considers all stable final state particles with $p_{T} >200$ MeV in $|\eta|<4.7$. The Bayesian unfolding method is used to correct the data for the migration between bins. - % Fig 14 -\begin{figure}[t] +\begin{figure}[!t] \begin{center} -\includegraphics[width=0.6\textwidth]{figrapgap/Fig14.pdf} \\ +\includegraphics[width=0.60\textwidth]{figrapgap/Fig14.pdf} \\ \end{center} -\caption{Migration matrix between the truth and reconstructed $\Delta\eta^{F}$ according to {\sc pythia8-mbr} ($\epsilon = 0.08$) for stable final state particles with $p_{T} > 200$~MeV in $|\eta|<4.7$. The plot is normalized to the unity in columns.} +\caption{Migration matrix between the truth and reconstructed $\Delta\eta^{F}$ according to {\sc pythia8-mbr} ($\epsilon = 0.08$) for stable final-state particles with $p_{T} > 200$~MeV in $|\eta|<4.7$. The plot is normalized to the unity in each column.} \label{fig:matrix} \end{figure} \subsection{Systematic uncertainties}\label{sec:uncertainties} -The following uncertainties taken into account and sum in quadrature to estimate the final systematic error on the measurement. +The following uncertainties were taken into account and summed in quadrature to estimate the final systematic error on the measurement. \begin{itemize} - \item HF energy scale uncertainty, - \item PF particle thresholds uncertainty, + \item HF energy-scale uncertainty, + \item PF energy thresholds uncertainty, \item Modeling uncertainty, - \item Unfolding technique uncertainty, + \item Unfolding-technique uncertainty, \item Luminosity uncertainty. \end{itemize} -HF Energy scale uncertainty is estimated by varying the energy of PF HF objects in MC by $\pm$10\% up and down. The noise thresholds of PF objects are raised by 10\% to determine the systematic uncertainty of the PF object thresholds. The model dependence of the hadronization is carried out using {\sc pythia8} and {\sc pythia6} where both models are evolved separately and the average of the differences with the default unfolded data are taken as the uncertainty. It is the dominant source of the uncertainty particularly in the $1 < \Delta\eta^F < 3$ region. The different parametrization of the diffraction modeling is taken into account using a {\sc pythia8-mbr} sample generated with $\epsilon=0.104$. -The systematic uncertainty on the unfolding technique is studied by switching between the default Bayesian method and bin-by-bin method. In addition, a $\pm4$\% normalization uncertainty is added due to the uncertainty on the integrated luminosity measurement~\cite{lumi1, lumi2}. Each source of the uncertainties sum in quadrature and the total uncertainty in each $\Delta\eta^F$ interval is applied symmetrically as upward and downward. Finally, the region ($\Delta\eta^F > 8.4$) is removed due to the very large uncertainty and the trigger inefficiency in that region. +The HF energy-scale uncertainty is estimated by varying the energy of PF HF objects in MC by $\pm$10\%. The noise thresholds of PF objects were raised by 10\% to determine the systematic uncertainty of the PF-object thresholds. The model dependence of the hadronization is carried out using {\sc pythia8} and {\sc pythia6}, where both models are evolved separately and the average of the differences with the default unfolded data is taken as the uncertainty. It is the dominant source of the uncertainty particularly in the $1 < \Delta\eta^F < 3$ region. The different parametrization of the diffraction modeling is taken into account using a {\sc pythia8-mbr} sample generated with $\epsilon=0.104$. +The systematic uncertainty on the unfolding technique is studied by switching between the default Bayesian method and the bin-by-bin method. In addition, a $\pm4$\% normalization uncertainty is added due to the uncertainty on the integrated luminosity measurement~\cite{lumi1, lumi2}. +All above uncertainties are summed in quadrature, and the total uncertainty is applied symmetrically upwards and downwards. Finally, the region of $\Delta\eta^F > 8.4$ is removed due to the very large uncertainty and the trigger inefficiency in that region. \subsection{Corrected results}\label{sec:correctedresults} -The unfolded and fully corrected differential cross section of the forward rapidity gap size ($\mathrm{d}\sigma / \mathrm{d}\Delta\eta^{F}$) for particles with $p_{T} > 200$ MeV in $|\eta|<4.7$ is given in Fig.~\ref{fig:corrected} with the hadron level predictions of {\sc pythia8-mbr} ($\epsilon = 0.08$ and $0.104$), {\sc pythia8} tune 4C and {\sc pythia6} tune Z2star. Total systematic uncertainty on the measurement which is around 20\% or less is shown with a green band. -The results show that in the limited pseudo-rapidity coverage of the detector,$|\eta|<4.7$, a large fraction of non-diffractive events can be suppressed by $\Delta\eta^{F}>3$ cut. +The unfolded and fully corrected differential cross section of the forward rapidity gap size, $\mathrm{d}\sigma / \mathrm{d}\Delta\eta^{F}$, for particles with $p_{T} > 200$ MeV in $|\eta|<4.7$ is given in Fig.~\ref{fig:corrected}, along with the hadron-level predictions of {\sc pythia8-mbr} ($\epsilon = 0.08$ and $0.104$), {\sc pythia8} tune 4C, and {\sc pythia6} tune Z2star. The total systematic uncertainty on the measurement, which is $<$20\%, is shown with a green band. +The results show that in the limited pseudo-rapidity coverage of the detector,$|\eta|<4.7$, a large fraction of non-diffractive events can be suppressed by a $\Delta\eta^{F}>3$ cut. +ATLAS previously measured the pseudorapidity gap cross section in $|\eta|<4.9$ using all stable final-state particles with $p_{T}>200$~MeV. Although the hadron-level definition is not quite the same (CMS gaps start at $|\eta|=\pm4.7$), a comparison of the CMS result with the ATLAS measurement is given in Fig.~\ref{fig:finalatlas}. The green band represents the total systematic uncertainty of the CMS measurement, +while the ATLAS measurement is incorporated in the error bars of the ATLAS points. The CMS result extends the ATLAS measurement by 0.4 unit of gap size. + +\clearpage + % Fig 15 -\begin{figure}[hb] +\begin{figure}[!t] \begin{center} \subfigure[]{\includegraphics[width=0.5\textwidth]{figrapgap/Fig15a.pdf}} \subfigure[]{\includegraphics[width=0.5\textwidth]{figrapgap/Fig15b.pdf}} \\ \subfigure[]{\includegraphics[width=0.5\textwidth]{figrapgap/Fig15c.pdf}} \subfigure[]{\includegraphics[width=0.5\textwidth]{figrapgap/Fig15d.pdf}} \end{center} -\caption{Unfolded and fully corrected differential cross section of the forward rapidity gap size ($\mathrm{d}\sigma / \mathrm{d}\Delta\eta^{F}$) for stable particles with $p_{T} > 200$~MeV in $|\eta|<4.7$ are compared with the hadron level predictions of (a) {\sc pythia8-mbr} ($\epsilon = 0.08$), (b) {\sc pythia8-mbr} ($\epsilon = 0.104$), (c) {\sc pythia8} tune 4C and {\sc pythia6} tune Z2star. The green band represents the total systematic uncertainty on the measurement which is obtained as the quadrature sum of the different uncertainty sources.} +\caption{Unfolded and fully corrected differential cross section of the forward rapidity gap size ($\mathrm{d}\sigma / \mathrm{d}\Delta\eta^{F}$) for stable particles with $p_{T} > 200$~MeV in $|\eta|<4.7$ are compared with the hadron-level predictions of (a) {\sc pythia8-mbr} ($\epsilon = 0.08$), (b) {\sc pythia8-mbr} ($\epsilon = 0.104$), (c) {\sc pythia8} tune 4C and {\sc pythia6} tune Z2star. The green band represents the total systematic uncertainty on the measurement which is obtained as the quadrature sum of the different uncertainty sources.} \label{fig:corrected} \end{figure} -ATLAS previously measured the pseudorapidity gap cross section in $|\eta|<4.9$ using all stable final state particles with $p_{T}>200$~MeV. Although the hadron level definition is not quite the same (CMS gaps start at $|\eta|=\pm4.7$), a comparison of CMS result with ATLAS measurement is given in Fig.~\ref{fig:finalatlas}. The green band represents the total systematic uncertainty of the CMS measurement while the total uncertainty of ATLAS measurement is shown with the error bars on ATLAS points. CMS extends the ATLAS measurement by 0.4 unit of gap size. - \clearpage % Fig 16 -\begin{figure}[t] +\begin{figure}[!t] \begin{center} -\includegraphics[width=0.6\textwidth]{figrapgap/Fig16.pdf} +\includegraphics[width=0.57\textwidth]{figrapgap/Fig16.pdf} \end{center} -\caption{Comparison of CMS measurement (black points) with ATLAS result (blue points). The green band represents the total systematic uncertainty of the CMS measurement and the total uncertainty of ATLAS measurement is shown with the error bars on the ATLAS points. The hadron level definitions of the two measurements are not the same. CMS measures the forward rapidity gap size in $\eta$ starting from $\eta = \pm 4.7$ where the ATLAS limit is $\eta = \pm 4.9$.} +\caption{Comparison of CMS measurement (black points) with ATLAS result (blue points). The green band represents the total systematic uncertainty of the CMS measurement, while the total uncertainty of ATLAS measurement is shown by the error bars on the ATLAS points. The hadron-level definitions of the two measurements are not the same. CMS measures the forward rapidity gap size in $\eta$ starting from $\eta = \pm 4.7$, whereas the ATLAS limit is $\eta = \pm 4.9$.} \label{fig:finalatlas} \end{figure} + +%\clearpage Index: body.tex =================================================================== --- body.tex (revision 186351) +++ body.tex (working copy) @@ -223,7 +223,7 @@ \begin{figure*}[t] \begin{center} -\includegraphics[width=0.65\textwidth]{fig/plot_dySigmaFin08.pdf} +\includegraphics[width=0.62\textwidth]{fig/plot_dySigmaFin08.pdf} \caption{The DD cross sections as a function of $\Delta\eta$ compared to {\sc pythia6}, {\sc pythia8-4c} and {\sc pythia8-mbr} MC predictions. Error bars are dominated by systematic uncertainties, which are discussed in Sec.~\ref{sec:syst}.} \label{fig:7} \end{center} Index: summary.tex =================================================================== --- summary.tex (revision 186351) +++ summary.tex (working copy) @@ -1,4 +1,3 @@ -%\clearpage \section{Summary} Results are reported for the single- and double-diffractive cross sections in pp collisions at $\sqrt{s}=7$ TeV at the LHC using the CMS detector.