| 1 |
anastass |
1.1 |
\section{Azimuthal symmetry}
|
| 2 |
|
|
|
| 3 |
|
|
The first step of the HCAL calibration with collisions data is to equalize the response in
|
| 4 |
|
|
$\phi$ for each $\eta$ ring. The procedure takes advantage of the azimuthal
|
| 5 |
|
|
symmetry of the detector and the corresponding $\phi$-symmetric energy
|
| 6 |
|
|
deposition from minimum bias (MinBias) events.
|
| 7 |
|
|
The intercalibration is
|
| 8 |
|
|
performed by comparing the average energy deposit in a calorimeter cell
|
| 9 |
|
|
to the mean of the average energy distributions in the entire $\eta$-ring
|
| 10 |
|
|
(cells with $i\eta$=const).
|
| 11 |
|
|
One of the main challenges is the large channel to channel noise fluctuations
|
| 12 |
|
|
(200-300 MeV) and relatively small signal in HB and HE
|
| 13 |
|
|
(a few~MeV in HB at $i\eta$=1, a few~tens~MeV in HE at $i\eta$=21).
|
| 14 |
|
|
The conditions are more favorable in HF where the noise is
|
| 15 |
|
|
comparable or even lower then the signal (about a hundred~MeV in HF at $i\eta$=30, and a few hundreds~MeV
|
| 16 |
|
|
at $i\eta$=40).
|
| 17 |
|
|
|
| 18 |
|
|
\subsection{General description}
|
| 19 |
|
|
|
| 20 |
|
|
%Correction of the azimuthal symmetry is the relative correction, which set
|
| 21 |
|
|
%gains such, that energy deposition from the signal from the uniform event
|
| 22 |
|
|
%is the same over eta-ring.
|
| 23 |
|
|
%The main problem to provide this kind of corrections
|
| 24 |
|
|
%in HB comes from the large fluctuation of noise from channel to channel in
|
| 25 |
|
|
%comparison with the value of the signal from pp minbias
|
| 26 |
|
|
%event.
|
| 27 |
|
|
|
| 28 |
|
|
|
| 29 |
|
|
There are two possible approaches to obtain correction coefficients using MinBias events and the azimuthal symmetry of HCAL:
|
| 30 |
|
|
\begin{enumerate}
|
| 31 |
|
|
\item {Direct comparison of the mean deposited energy in the cells after noise subtraction}
|
| 32 |
|
|
\item {Analysis of the variances of the signal and noise samples}
|
| 33 |
|
|
\end{enumerate}
|
| 34 |
|
|
% correction using the mean values
|
| 35 |
|
|
In the first approach the correction for each cell is given by
|
| 36 |
|
|
|
| 37 |
|
|
\begin{equation}
|
| 38 |
|
|
Corr_{i\eta,i\phi} = <E_{i\eta,i\phi}>/(1/N_{i\phi} \times \sum_{N_{\phi}} <E_{i\eta,i\phi}> )
|
| 39 |
|
|
\end{equation}
|
| 40 |
|
|
where $N_{\phi}$ is the number of HCAL cells in an i$\eta$ ring, and
|
| 41 |
|
|
$<E_{i\eta,i\phi}> = <E_{i\eta,i\phi}^{signal}>+<E_{i\eta,i\phi}^{noise}>$ is the
|
| 42 |
|
|
mean energy deposition in the HCAL cell. After pedestal subtraction
|
| 43 |
|
|
and assuming
|
| 44 |
|
|
$<E_{i\eta,i\phi}^{noise}>=0$, we have $<E_{i\eta,i\phi}> = <E_{i\eta,i\phi}^{signal}>$.
|
| 45 |
|
|
The uncertainty on the estimation of the coefficients
|
| 46 |
|
|
$\sqrt{\Delta^2 (<E_{i\eta,i\phi}^{signal}>) + \Delta^2 (<E_{i\eta,i\phi}^{noise}>)}$,
|
| 47 |
|
|
is dominated by the uncertainty on the noise estimation. If we want to achieve a precision
|
| 48 |
|
|
of better than 2\% in the middle of HB (i$\eta$=1) we need to collect a few tens million events.
|
| 49 |
|
|
Therefore, the simplicity and transparency of this approach is offset by the need of large data samples.
|
| 50 |
|
|
|
| 51 |
|
|
% use subtraction via variances
|
| 52 |
|
|
The second approach relies on noise removal through subtracting the variance of noise from the variance in the measured energy.
|
| 53 |
|
|
The correction factor in this case is given by:
|
| 54 |
|
|
\begin{equation}
|
| 55 |
|
|
Corr_{i\eta,i\phi} = \sqrt{<\Delta^2 R_{i\eta,i\phi}>/(1/N(i\eta) \times \sum_{N_{\phi}} <\Delta^2 R_{i\eta,i\phi}> )}
|
| 56 |
|
|
\end{equation}
|
| 57 |
|
|
where $$\Delta^2 R_{i\eta,i\phi} = <\Delta^2 (E_{i\eta,i\phi}^{signal}) + \Delta^2 (E_{i\eta,i\phi}^{noise})> - <\Delta^2 (E_{i\eta,i\phi}^{noise})>$$
|
| 58 |
|
|
Assuming no correlations between noise and signal deposition in the calorimeter we get $$\Delta^2 R_{i\eta,i\phi} = <\Delta^2 (E_{i\eta,i\phi}^{signal})>.$$
|
| 59 |
|
|
|
| 60 |
|
|
The minimum sample for achieving 2\% uncertainty on the signal
|
| 61 |
|
|
variance (due to the residual noise contribution) is of the order of a few millions
|
| 62 |
|
|
of events.
|
| 63 |
|
|
|
| 64 |
|
|
This method requires substantially smaller samples but it is still sensitive to
|
| 65 |
|
|
the noise level in a channel. For noisier channels we need larger statistics.
|
| 66 |
|
|
|
| 67 |
|
|
The phi inter-calibration with MinBias events requires knowledge of the electronics noise in a channel. We use the same data sample for estimating both the signal and the noise. For HB and HE calibration, the first four time slices (0-3) in a digi are used to estimate the noise $<\Delta^2 (E_{i\eta,i\phi}^{noise})>$ while time slices 4-8 contain both signal and noise and give us $<\Delta^2 (E_{i\eta,i\phi}^{signal}) + \Delta^2 (E_{i\eta,i\phi}^{noise})>$. In HF, windows of three time slices are going to be
|
| 68 |
|
|
used for noise and signal.
|
| 69 |
|
|
|
| 70 |
|
|
%\begin{itemize}
|
| 71 |
|
|
%\item For each run we calculate
|
| 72 |
|
|
%$<\Delta^2 (E_{i\eta,i\phi}^{noise})>$
|
| 73 |
|
|
%(0-3 time slices) and
|
| 74 |
|
|
%$<\Delta^2 (E_{i\eta,i\phi}^{signal}) + \Delta^2 (E_{i\eta,i\phi}^{noise})>$
|
| 75 |
|
|
%(4-7 time slices) and perform noise variance subtraction
|
| 76 |
|
|
%($\Delta^2 R_{i\eta,i\phi}$).
|
| 77 |
|
|
%
|
| 78 |
|
|
%\item For each $i\eta$-ring we calculate the mean variance over 72 or 36 or 18
|
| 79 |
|
|
%readouts depending on the ring:
|
| 80 |
|
|
%$$\Delta^2 R_{mean j} = 1/Nphi x \sum_{i\phi} {\Delta^2 R_{i\eta,i\phi}}$$
|
| 81 |
|
|
%
|
| 82 |
|
|
%\item Correction coefficient:
|
| 83 |
|
|
% $$K(i,j) = \sqrt(\Delta^2 R_{mean j}/\Delta^2 R_{i\eta,i\phi}$$
|
| 84 |
|
|
%\end{itemize}
|
| 85 |
|
|
|
| 86 |
|
|
|
| 87 |
|
|
|
| 88 |
|
|
\subsection{Workflow}
|
| 89 |
|
|
|
| 90 |
|
|
|
| 91 |
|
|
Due to the small expected signal and the requirement of no correlation between signal and noise,
|
| 92 |
|
|
the calibration data has to be collected with no zero suppression (NZS) of the HCAL readouts.
|
| 93 |
|
|
A special HcalNZS stream was set up to collect MinBias events for our calibration needs.
|
| 94 |
|
|
Once per 4096 events the full HCAL is read without application of hardware zero suppression.
|
| 95 |
|
|
The data in this stream is processed by a dedicated Producer at Tier0 which creates a
|
| 96 |
|
|
compact AlCaReco output data format. The event content is essentially the
|
| 97 |
|
|
estimated energy in each channel in both the signal and noise time windows, along with
|
| 98 |
|
|
event trigger information.
|
| 99 |
|
|
For azimuthal symmetry we select all triggers except the zero-bias one.
|
| 100 |
|
|
The AlCaReco data are directed to the CERN analysis Facility (CAF) where further analysis and extraction of correction coefficients are performed.
|
| 101 |
|
|
The workflow was tested during several exercises starting from 2006 year.
|
| 102 |
|
|
|
| 103 |
|
|
|
| 104 |
|
|
\subsection{Systematics sources}
|
| 105 |
|
|
|
| 106 |
|
|
The performance of the discussed techniques and the corresponding systematics were studied with
|
| 107 |
|
|
Monte Carlo samples generated for $pp$ collisions center of mass energies of 10 TeV and 900 GeV.
|
| 108 |
|
|
|
| 109 |
|
|
Details on the data samples and the used triggers are presented in table~\ref{table_stat}.
|
| 110 |
|
|
|
| 111 |
|
|
\begin{table}[!Hhtb]
|
| 112 |
|
|
\caption{Data samples selected by the different L1 trigger bits: EG1+EG2+DEG1 means selection of events with
|
| 113 |
|
|
one cluster in ECAL with energy more than 1 GeV or one cluster in ECAL with energy more than 2 GeV or two
|
| 114 |
|
|
clusters with energy more than 1 GeV each. ZB - no selections are applied.
|
| 115 |
|
|
EG2 is selection of events with at least one cluster with energy more than 2 GeV.
|
| 116 |
|
|
HFRing24 means the selection of events with sum of energy deposition in rins 2 to 4.
|
| 117 |
|
|
L1 trigger selection efficiency shows the fraction of events selected by the
|
| 118 |
|
|
indicated L1 trigger bit.}
|
| 119 |
|
|
\label{table_stat}
|
| 120 |
|
|
\begin{center}
|
| 121 |
|
|
\begin{tabular}{|c||c|c|c|c|} \hline
|
| 122 |
|
|
CMSSW version & Collision energy&L1 Trigger bit &L1 trigger efficiency& Number of events after trigger selection\\ \hline
|
| 123 |
|
|
219 &10 TeV &EG1+EG2+DEG1 &0.2& 8.9 mln\\ \hline
|
| 124 |
|
|
31X &10 TeV &ZB &1& 10 mln\\ \hline
|
| 125 |
|
|
31X &10 TeV &EG1+EG2+DEG1 &0.34& 10 mln\\ \hline
|
| 126 |
|
|
31X &10 TeV &EG2 &0.1& 3 mln\\ \hline
|
| 127 |
|
|
31X &10 TeV &HFRing24 &0.12& 3.4 mln\\ \hline
|
| 128 |
|
|
31X &0.9 TeV &EG2 &0.019& 0.19 mln\\ \hline
|
| 129 |
|
|
\end{tabular}
|
| 130 |
|
|
\end{center}
|
| 131 |
|
|
\end{table}
|
| 132 |
|
|
|
| 133 |
|
|
Different trigger bit selections leads to the different mean
|
| 134 |
|
|
energy deposition per tower as shown in Figs~\ref{fig_hb_sim_en}-\ref{fig_hf_sim_en}
|
| 135 |
|
|
for HB and HF correspondingly.
|
| 136 |
|
|
|
| 137 |
|
|
\begin{figure}[!Hhtb]
|
| 138 |
|
|
\begin{center}
|
| 139 |
|
|
\includegraphics*[width=10cm]{figs/signal_neg_sim_mom1_hb.eps}
|
| 140 |
|
|
\caption{Mean simulated energy per tower versus the number of ring in HB for different trigger selections as indicated in Table 1.}
|
| 141 |
|
|
\label{fig_hb_sim_en}
|
| 142 |
|
|
\end{center}
|
| 143 |
|
|
\end{figure}
|
| 144 |
|
|
|
| 145 |
|
|
\begin{figure}[!Hhtb]
|
| 146 |
|
|
\begin{center}
|
| 147 |
|
|
\includegraphics*[width=10cm]{figs/signal_neg_sim_mom1_hf.eps}
|
| 148 |
|
|
\caption{Mean simulated energy per tower as a fintion of $i\eta$ index in HB
|
| 149 |
|
|
for different trigger selections as indicated in Table 1.}
|
| 150 |
|
|
\label{fig_hf_sim_en}
|
| 151 |
|
|
\end{center}
|
| 152 |
|
|
\end{figure}
|
| 153 |
|
|
|
| 154 |
|
|
Dead and anomalous channels are excluded from the procedure.
|
| 155 |
|
|
|
| 156 |
|
|
The main sources of systematic biases and systematic uncertainties in the determination of the correction factors are:
|
| 157 |
|
|
\begin{itemize}
|
| 158 |
|
|
\item Residual noise contamination after subtraction. This source can be reduced by increasing the sample size.
|
| 159 |
|
|
\item Geometrical structures of HCAL.\\
|
| 160 |
|
|
At the interaction point we have some energy distribution for the flow of particles in the
|
| 161 |
|
|
direction of the each calorimeter tower. We assume that when averaged over a large number of events the deposited energy is the same for all towers in a ring of constant $i\eta$.
|
| 162 |
|
|
|
| 163 |
|
|
The distribution of particles actually reaching each particular tower can be different
|
| 164 |
|
|
from that at the vertex due to the magnetic field and the amount of dead material in
|
| 165 |
|
|
front of the tower.
|
| 166 |
|
|
The solenoidal magnetic field prevents charged particles $p_T$ less than 0.9-1 GeV from reaching the HCAL surface but it should not disturb the azymuthal symmetry of the particle flow.
|
| 167 |
|
|
However, due to the inhomogenius material structure of the
|
| 168 |
|
|
detector the distributions of energy deposited in tower is not the same any more for
|
| 169 |
|
|
all towers in an $i\eta$ ring.
|
| 170 |
|
|
%It can be considered as different cuts applied for energy in towers.
|
| 171 |
|
|
|
| 172 |
|
|
If we ignore the material effects, the noise, and the magnetic field, the first and second moments of the energy distribution from particles reaching the HCAL towers are given by
|
| 173 |
|
|
$$<x_j>= \int_0^E{xf(x)dx}$$
|
| 174 |
|
|
$$<x_j^2> = \int_0^E{x^2f(x)dx}$$
|
| 175 |
|
|
In the presence of magnetic field, these moments change to
|
| 176 |
|
|
$$<x_j> = \int_{a_j}^E{xf(x)dx}$$
|
| 177 |
|
|
$$<x_j^2> = \int_{a_j}^E{x^2f(x)dx},$$
|
| 178 |
|
|
where $a_j$ are the same for all towers.
|
| 179 |
|
|
If different amounts of material are placed in front of different towers $a_j$ are no longer the same for all the towers in the $i\eta$ ring.
|
| 180 |
|
|
|
| 181 |
|
|
We studied the effects of the geometry structure in front of HCAL using simulated energy deposits with zero noise and assuming no channel-to-channel miscalibration.
|
| 182 |
|
|
We apply the calibration procedure and examine the structure of the derived correction factors.
|
| 183 |
|
|
In case of no geometry effects we should get identical coefficients for all cells in the $i\eta$ ring.
|
| 184 |
|
|
The correction coefficients calculated using the mean simulated energy deposited per tower are shown in Figs.~\ref{fig_eta1}-~\ref{fig_eta32} for representative $i\eta$ rings in HB, HE, HF (HB: $\eta=1$; HE: $\eta=21$, HF: $\eta=32$).
|
| 185 |
|
|
The variances and the mean values are affected differently by these cuts.
|
| 186 |
|
|
The $\eta$ dependence of the RMS of coefficients obtained with the technique
|
| 187 |
|
|
relying on the ratio of the means is shown in Figs.~\ref{fig_mean_sim_coef}.
|
| 188 |
|
|
The corresponding results when the subtraction via variances technique is applied
|
| 189 |
|
|
are shown in Fig.~\ref{fig_var_sim_coef}.
|
| 190 |
|
|
%4\% of RMS of the coefficients got with mean energies transforms into 2\% of RMS of the coefficients %got with variances.
|
| 191 |
|
|
The spread off coefficients in the latter case is significantly smaller.
|
| 192 |
|
|
This RMS is due to existence of the blocks of material in front of particular channels and unless parts of detectors are removed moments will stay the same for years if no miscalibration of gains appears.
|
| 193 |
|
|
|
| 194 |
|
|
\begin{figure}[!Hhtb]
|
| 195 |
|
|
\begin{center}
|
| 196 |
|
|
\includegraphics*[width=10cm]{figs/coefpl_10T_mom1_30mln_sim_312_EGX_1.eps}
|
| 197 |
|
|
\caption{Correction coefficients calculated using mean simulated energy for the ring with $\eta=1$}
|
| 198 |
|
|
\label{fig_eta1}
|
| 199 |
|
|
\end{center}
|
| 200 |
|
|
\end{figure}
|
| 201 |
|
|
\begin{figure}[!Hhtb]
|
| 202 |
|
|
\begin{center}
|
| 203 |
|
|
\includegraphics*[width=10cm]{figs/coefpl_10T_mom1_30mln_sim_312_EGX_21.eps}
|
| 204 |
|
|
\caption{Correction coefficients calculated using mean simulated energy for the ring with $\eta=21$}
|
| 205 |
|
|
\label{fig_eta21}
|
| 206 |
|
|
\end{center}
|
| 207 |
|
|
\end{figure}
|
| 208 |
|
|
\begin{figure}[!Hhtb]
|
| 209 |
|
|
\begin{center}
|
| 210 |
|
|
\includegraphics*[width=10cm]{figs/coefpl_10T_mom1_30mln_sim_312_EGX_32.eps}
|
| 211 |
|
|
\caption{Correction coefficients calculated using mean simulated energy for the ring with $\eta=32$}
|
| 212 |
|
|
\label{fig_eta32}
|
| 213 |
|
|
\end{center}
|
| 214 |
|
|
\end{figure}
|
| 215 |
|
|
\begin{figure}[!Hhtb]
|
| 216 |
|
|
\begin{center}
|
| 217 |
|
|
\includegraphics*[width=10cm]{figs/Rms_Neg_mom1_sim_all.eps}
|
| 218 |
|
|
\caption{Dependence of the RMS of correction coefficients calculated using mean simulated energy on $\eta$}
|
| 219 |
|
|
\label{fig_mean_sim_coef}
|
| 220 |
|
|
\end{center}
|
| 221 |
|
|
\end{figure}
|
| 222 |
|
|
\begin{figure}[!Hhtb]
|
| 223 |
|
|
\begin{center}
|
| 224 |
|
|
\includegraphics*[width=10cm]{figs/Rms_Neg_mom4_sim_all.eps}
|
| 225 |
|
|
\caption{Dependence of the RMS of correction coefficients calculated using simulated variance on $\eta$}
|
| 226 |
|
|
\label{fig_var_sim_coef}
|
| 227 |
|
|
\end{center}
|
| 228 |
|
|
\end{figure}
|
| 229 |
|
|
|
| 230 |
|
|
|
| 231 |
|
|
The structures are also visible at reconstruction level (Fig.~\ref{fig_eta21_rec})
|
| 232 |
|
|
when digitization and noise are added.
|
| 233 |
|
|
|
| 234 |
|
|
\begin{figure}[!Hhtb]
|
| 235 |
|
|
\begin{center}
|
| 236 |
|
|
\includegraphics*[width=10cm]{figs/coefpl_10T_mom1_30mln_rec_312_EGX_21.eps}
|
| 237 |
|
|
\caption{Correction coefficients calculated using mean reconstructed energy for the ring with $\eta=21$}
|
| 238 |
|
|
\label{fig_eta21_rec}
|
| 239 |
|
|
\end{center}
|
| 240 |
|
|
\end{figure}
|
| 241 |
|
|
|
| 242 |
|
|
|
| 243 |
|
|
We can select blocks of towers with the same amount of material in front and set
|
| 244 |
|
|
azimuthal symmetry corrections separately for towers within the blocks.
|
| 245 |
|
|
The difference between blocks due to material effects has to be set up on top
|
| 246 |
|
|
of these corrections.
|
| 247 |
|
|
|
| 248 |
|
|
\item Digitization
|
| 249 |
|
|
\begin{itemize}
|
| 250 |
|
|
\item Wide digitization bin. Reconstructed mean values are close to the simulated ones while variances are 1.5--2 times wider due to
|
| 251 |
|
|
digitization and conversions.
|
| 252 |
|
|
\item Small range from negative side. For most of channels pedestal is set far enough from 0-bit and noise has a well enough defined gaussian shape. But some of channels may have pedestal too close to zero and, thus, the distribution of reconstructed noise deflects from gaussian for these particular channels. These channels requires the additional treatment.
|
| 253 |
|
|
\end{itemize}
|
| 254 |
|
|
\end{itemize}
|
| 255 |
|
|
|
| 256 |
|
|
RMS of coefficients got with reconstructed energies are presented in Figs.~\ref{fig_rms_mean_rec},~\ref{fig_rms_var_rec}.
|
| 257 |
|
|
|
| 258 |
|
|
\begin{figure}[!Hhtb]
|
| 259 |
|
|
\begin{center}
|
| 260 |
|
|
\includegraphics*[width=10cm]{figs/Rms_Neg_mom1_rec_all.eps}
|
| 261 |
|
|
\caption{RMS of correction coefficients calculated using mean of reconstructed energy distribution in tower.}
|
| 262 |
|
|
\label{fig_rms_mean_rec}
|
| 263 |
|
|
\end{center}
|
| 264 |
|
|
\end{figure}
|
| 265 |
|
|
|
| 266 |
|
|
\begin{figure}[!Hhtb]
|
| 267 |
|
|
\begin{center}
|
| 268 |
|
|
\includegraphics*[width=10cm]{figs/Rms_Neg_mom4_rec_all.eps}
|
| 269 |
|
|
\caption{RMS of correction coefficients calculated using the variances of the
|
| 270 |
|
|
reconstructed energy distribution in tower.}
|
| 271 |
|
|
\label{fig_rms_var_rec}
|
| 272 |
|
|
\end{center}
|
| 273 |
|
|
\end{figure}
|
| 274 |
|
|
|
| 275 |
|
|
\subsection{Summary for Calibrations with MinBias Events}
|
| 276 |
|
|
|
| 277 |
|
|
A set of triggers have been investigated with 10 TeV MinBias sample:
|
| 278 |
|
|
ZB trigger provides too low energy deposition in HB/HE and, thus,
|
| 279 |
|
|
requires much larger statistics
|
| 280 |
|
|
For HB/HE we consider L1EG2 and HF triggers to be the most
|
| 281 |
|
|
perspective. The required number of events depends on whether
|
| 282 |
|
|
we want to count for the geometrical structuresin HB and HE.
|
| 283 |
|
|
4-5 millions of events gives accuracy ~4-5\% for eta<6 and down
|
| 284 |
|
|
to 2\% for eta <28.
|
| 285 |
|
|
HF is found to be not too sensitive to the trigger choice and
|
| 286 |
|
|
requires a few hundreds thousands with EG2 trigger to reach
|
| 287 |
|
|
2\% RMS level.
|
| 288 |
|
|
Geometry structures are well pronounced in HB/HE and HF.
|
| 289 |
|
|
~4\% in HB
|
| 290 |
|
|
~3.5\% in HE
|
| 291 |
|
|
<2\% in HF
|
| 292 |
|
|
The calibration of HF down to 2\% level can be performed with 900 GeV
|
| 293 |
|
|
sample assuming that we get ~200 Kevents with EG2 trigger.
|
| 294 |
|
|
|
