Photon beams at the ROKK-1M facility

Extensive tests of a prototype of the Belle ECL calorimeter were carried out using photon beams produced at the ROKK-1M facility of BINP in the photon energy range from 20 MeV to 5.4 GeV. Fig. shows the layout of the ROKK-1M facility. The beam of backward scattered photons was used in the photon energy range below 850 MeV. The photon energy was determined by measuring the scattered electron energy by the tagging system, the energy resolution of which was $\sigma_E/E \sim 10^{-3}$. The second harmonic of a (Nd:YAG) pulse laser corresponds to the photon energy of 2.34 eV. The Compton photon (CP) energy spectrum is roughly uniform with a sharp edge at the maximum CP energy, $E_C = 4\gamma^2 \omega_0/(1 + 4 \gamma \omega_0/m_e)$, where $\omega_0$ is the energy of the laser photon and $m_e$ is the electron mass. The photon energy resolution was kept less than 1 % for a wide range of photon energies by optimizing the electron beam energies. The main background process for Compton photons is the beam electron bremsstrahlung at the residual gas nuclei. As will be described later, bremsstrahlung photons were used to obtain the energy resolution for high energy photons.

Figure: Layout of the VEPP-4M experimental region with the KEDR tagging system. $Q_1$ and $Q_2$ are quadrupoles, and $M_1$ and $M_2$ are bending magnets.

The experimental setup is shown in Fig. The prototype consists of a 6 $\times$ 6 matrix of the CsI($Tl$) counters with the same characteristics as those of the Belle ECL counters. The support frame of the counters allowed to move the prototype within $\pm$ 10 cm in the vertical and horizontal directions as well as to adjust the angle of the prototype to the photon beam within $\pm$ 0.2 rad. The layout of the readout system used in the tests is shown in Fig. . The trigger signal was produced by coincidence of the laser pulse, a signal from the tagging system, and the beam crossing phase in the absence of the signal from the veto counter.

Figure: Experimental layout. CsI(Tl) crystals are represented by 1, drift-tube hodoscopes by 2, plastic scintillation counters for cosmic trigger by 3, a lead collimator by 4, a veto counter by 5, and a movable platform for the position adjustment by 6.

Figure: Schematic diagram of the beam test experiment.

The energy deposition in a crystal is calculated as $E_i = \alpha_i A_i$, where $E_i$ is the energy deposition in the $i$th crystal, $A_i$ is the corresponding ADC channel, and $\alpha_i$ is the calibration coefficient. One of the simple ways of calibration is to use cosmic rays, as described in the section of the calibration by cosmic rays. The average energy deposition in the crystal is proportional to the track length within the crystal volume which depends both on the particle angle and coordinate along the crystal. For a minimum ionizing particle the average energy deposition per unit length in CsI is 5.67 MeV/cm that provides about 30-40 MeV energy deposition in each counter.
The tracks of cosmic muons were reconstructed by the hodoscopes of the muon streamer tubes. The hodoscope position resolution of 15 mm is sufficient to measure the track length inside the crystal with an accuracy better than 1.5 % when a particle crosses two opposite side surfaces. The calibration by cosmic rays was performed regularly between beam-test runs. Fig. shows the longitudinal nonuniformity of light collection of a typical counter. The mean nonuniformity in the longitudinal direction for all the crystals used in the tests was about 7 %.

Figure: Longitudinal non-uniformity of light collection of the crystal.

As the electronics noise is the crucial point for the calorimeter resolution at low energies, this characteristic was carefully studied. The noise value was estimated by a pedestal distribution width both for a single channel and for the sum of a few channels. By fitting the pedestal distributions, the noise contributions from a single channel ($\sigma_{i,0}$) and the sum of $n$ channels ($\sigma_n$) were determined. The coherent and incoherent noise components are separated using the following equations:

$$\sigma^2_{i,0} = \sigma^2_{i,inc} + \sigma^2_{i,coh}$$ (7)

$$\sigma^2_n = \sum^n_{i = 1} \sigma^2_{i,inc} + \left(\sum^n_{i = 1} \sigma^i_{i,coh}\right)^2$$ (8)

$$\textless \sigma^2_{i,coh} \textgreater = \frac{\sigma^2_n - \sum^n_{i = 1} \sigma^2_{i,0}}{n^2 -n}$$ (9)

$$\textless \sigma^2_{i,inc} \textgreater = \frac {\left( \sum^n_{i = 1} \sigma_{i,coh}\right)^2 - \sigma ^2_n}{n^2 - n}$$ (10)

where $\sigma_{i,inc}$ and $\sigma_{i,coh}$ stand for the incoherent and coherent noise components of the $i$th channel, respectively. The total incoherent and coherent noise components were determined to be 189-250 keV and 17-50 keV, respectively. It was found that the dominant part of the coherent noise came from the ADC itself. The latest measurement of the coherent noise of 17 keV gives a substantially improved noise level. These results are very satisfactory.
For reconstruction of the photon energy the energy deposition in the 3 $\times$ 3 ($E_9$) and the 5 $\times$ 5 ($E_{25}$) matrix around the crystal with the maximum energy was used. Using the energy measured by the tagging system $E_{TS}$ as a photon energy $E_{\gamma}$, the energy resolution dependence on the photon energy was studied for each beam energy from the low limit determined by the tagging system acceptance up to the Compton edge. Distributions of the ratio $E_9/E_{\gamma}$ or $E_{25}/E_{\gamma}$ have an asymmetric shape which was fitted by the normal logarithmic function written as

where is the deposited energy, is the energy corresponding to the peak position, is a parameter describing the asymmetry of the distribution, and N is the normalization factor. The energy resolution is defined by the full width at half maximum of the distribution as

(12)

(13)

and is expressed via

(14)

The energy resolution of the CsI was obtained by the relation

(15)

Since the tagging system resolution is better than 1 % for 100 MeV, the effect of the subtraction is small. Another possibility to measure the CsI energy resolution is the analysis of the edge of the Compton photon spectrum detected by the CsI matrix. This method does not use information from the tagging system and provides an independent check of the results. The CsI energy distribution is fitted by the convolution of the function of Eq.() and Compton distribution approximated by

(16)

where is the Compton spectrum edge. Examples of the fit are shown in Fig. .

Figure: Typical Compton-edge distributions at (a) 109.8 MeV and (b) 508.3 MeV. The solid curves are the fitted results.

In the latest measurement [64] the bremsstrahlung edge was also used to determine the energy resolution at higher energies. The same procedure was used as for the Compton edge analysis. A typical distribution is shown in Fig. .

Figure: (a) Typical bremsstrahlung energy distribution for a 4036 MeV electron beam and (b) an expanded view of the edge region with the fitted curve.

The energy resolution was obtained for the 3 $\times$ 3 and 5 $\times$ 5 CsI matrices in two ways: the total energy sum was used in the first method and the energy sum from the counters above a certain threshold energy in each matrix was used in the second method. Fig. shows the results of the analysis. Figures (c) and (d) correspond to the energy resolution for the threshold energy of 0.5 MeV. The energy resolution without threshold for the 5 $\times$ 5 matrix is substantially better at higher energies, above 100 MeV, than that for the 3 $\times$ 3 matrix because of better energy containment, while it is appreciably poorer at lower energies, below 30 MeV, due to large contribution of summed electronics noise. This situation in the low energy region has been improved by applying an optimum threshold energy. Fig. shows the energy resolution as a function of threshold energy at various photon energies. At photon energies below 100 MeV the threshold energy above 2 MeV degrades the energy resolution. On the other hand, the energy resolution is very insensitive to the threshold energy at photon energies above 300 MeV. In the photon energy range of interest the threshold energy of 0.5 MeV seems to be optimum. The resolutions obtained by the three methods are consistent over the energy range from 20 MeV to 5.4 GeV.

Figure: Energy resolution as a function of incident photon energy for the (a) 3 $\times$ 3 and (b) 5 $\times$ 5 matrices with the total energy sum, and for the (c) 3 $\times$ 3 and (d) 5 $\times$ 5 matrices with a 0.5 MeV threshold. The error bars are the rms values of four measurements taken with the crystals (3, 3), (3, 4), (4, 3) and (4,4) into the photon beam.

Figure: Energy threshold dependence of the energy resolution at various photon energies.

The energy resolution obtained with the threshold energy of 0.5 MeV (Figs. (c) and (d)) can be fitted by the quadratic sum () of three terms as follows:

(17)

for the 3 $\times$ 3 matrix sum, and

(18)

for the 5 $\times$ 5 matrix sum, E in GeV. Since details of the fitted results are not completely identical, we quote the latest results.
The linearity of the energy response was studied in the energy range from 20 MeV to 5.4 GeV by fitting the edge of the Compton and bresstrahlung spectra. The correlation between obtained by fitting the data and the theoretical edge value () calculated from the electron beam energy is plotted in Fig. (a). The value of was obtained from the energy sum of the 5 $\times$ 5 matrix with a threshold energy of 0.5 MeV. The linearity defined as is plotted in Fig. (b). For all energy ranges, is smaller than because of shower leakage from the central 5 $\times$ 5 counters. At higher energies the leakage from the rear end of the crystal becomes dominant. The major part of the error bars comes from the rms deviation of the four measurements, for which the photon beam was injected at different crystals.The total uncertainty including the electronics nonlinearity was estimated to be approximately $\pm$ 1 %. We conclude that the energy deposit in the 5 $\times$ 5 matrix with a 0.5 MeV threshold reproduced the absolute photon beam energy within $-$3 $\pm$ 2 % in a broad energy range from 20 MeV to 5.4 GeV. A GEANT simulation could reproduce the experimental data well within $\pm$ 1 %, except for a small systematic shift of $-$2 % below 100 MeV.

Figure: (a) The incident photon energy versus the measured energy in CsI from data, and (b) the energy linearity obtained from the data.

A narrow photon beam of rectangular shape (4 mm $\times$ 4 mm) was used to study the position dependence of energy deposition and energy resolution. Figs. and show the measured position dependence of the energy deposit and energy resolution as a function of lateral horizontal position. The Compton photon beam in the energy range of MeV was used. Small decreases in energy and degradations in energy resolution were measured at the air gap and the aluminum fin (0.5 mm thick). The GEANT Monte Carlo simulation reproduced the behavior of the data quite well.

Figure: Position dependence of the energy deposit. The solid triangles and circles are the results obtained by a GEANT Monte Carlo simulation.

Figure: Position dependence of the energy resolution. The open triangles and circles are the results obtained by a GEANT Monte Carlo simulation.

The position resolution was measured by moving the prototype in the transverse direction along the horizontal plane. First the shower center of gravity () was calculated using the relation

(19)

where is the $x$(or $y$)-coordinate of the center of the $i$th counter and $E_i$ is its energy deposit. A scatter plot of the average versus the photon impact coordinate () is shown in Fig. (a). The position is smeared uniformly within the aperture of the collimator. The center of gravity gives the correct position at the center of the crystal and at the gap between two crystals, but shows systematic shifts at the other positions. In order to correct the systematic effect an empirical function was used to get the correlation between and and to calculate the corrected position . Fig. (b) shows a scatter plot of versus . The systematic shift seen in Fig. (a) is almost removed. The residual distribution ( ) corresponds to the average resolution of the corrected beam-impact position.

Figure: Scatter plots of and (a) before and (b) after a correction. The gap between the crystals is shown by the thick vertical lines. The solid curve in (a) is the fit to an empirical formula.

Figure shows the position dependence of the spatial resolution for 470 MeV photons. The solid and open circles correspond to the experimental data and Monte Carlo results, respectively. The energy dependence of the average position resolution is shown in Fig. as a function of photon energy. The points above 1 GeV are Monte Carlo data. The solid curve is fitted by the relation

where is measured in units of GeV.
The present results of the energy and spatial resolutions measured by the photon beams for the Belle ECL prototype counters are in reasonable agreement with those measured using the electron beam at KEK in the energy range above 1 GeV [59].

Figure: Position dependence of the spatial resolution for 470 MeV photons.

Figure: Energy dependence of the average position resolution. The solid curve is a fit to Eq. .