Performance of ALICE AD modules in the CERN PS test beam

Two modules of the AD detector have been studied with the test beam at the T10 facility at CERN. The AD detector is made of scintillator pads read out by wave-length shifters (WLS)coupled to clean fibres that carry the produced light to photo-multiplier tubes (PMTs). In ALICE the AD is used to trigger and study the physics of diffractive and ultra-peripheral collisions as well as for a variety of technical tasks like beam-gas background monitoring or as a luminometer. The position dependence of the modules' efficiency has been measured and the effect of hits on the WLS or PMTs has been evaluated. The charge deposited by pions and protons has been measured at different momenta of the test beam. The time resolution is determined as a function of the deposited charge. These results are important ingredients to better understand the AD detector, to benchmark the corresponding simulations, and very importantly they served as a baseline for a similar device, the Forward Diffractive Detector (FDD), being currently built and that will be in operation in ALICE during the LHC Runs 3 and 4.

LHC in Run 3 and 4. In order to exploit the increased luminosity and interaction rate in this period, ALICE is now implementing a significant upgrade of its detectors and systems [6].
Among the detectors being upgraded is the ALICE Diffractive (AD) detector [7], whose new implementation is known as the Forward Diffraction Detector (FDD). Both detectors are composed of two arrays installed at each side of the nominal interaction point in ALICE. Each array is made of 4 sectors, which are made of two layers of identical modules. Each module is made of a plastic scintillator pad, wave-length shifters (WLS), optical fibres and photo-multiplier tubes (PMTs). Both detectors have the exact same geometry, but the materials of the FDD are faster. Here, the main contribution comes from the WLS bar re-emission time that will be reduced from 8.5 ns to 0.9 ns. At the same time, the news PMTs have 19 dynodes (instead 16 as the AD PMTs) which will reduce after-pulses and also have a more extensive dynamic range. Both the AD and the FDD cover the same pseudorapidity (η) ranges of −6.9 < η < −4.9 and 4.7 < η < 6.3. Furthermore, the FDD will be also equipped with the possibility of having continuous read-out [8] in addition to the standard trigger mode. The main tasks carried out by the AD and to be taken over by the FDD are to participate at the level zero of the trigger system of ALICE, to provide physics information for the analysis of diffractive and ultra-peripheral collisions and to contribute technical measurements like beam-background monitoring, act as a luminometer, measure the centrality in collisions of heavy nuclei and others.
This article reports the analysis of several test-beam measurements which were carried out with two AD modules to determine their characteristics and performance. The data was collected in 2015 at the T10 PS beam at CERN to study the efficiency, time resolution and charge measurement of these modules. These results are not only needed to understand better the response of the AD detector-used in many ongoing analyses of ALICE data from Run 2-, but also to learn about the potential of the new FDD. The rest of this article is organised as follows: in Sec. 2 the trigger configuration and the placement of the AD detectors in the experimental set-up are described. Sec. 3 reports the results of the analysis of the efficiency, time response and charge measurement obtained with the different components of the detector, and when relevant as a function of the beam energy and and the type of particles-pions and protons-delivered by the beam. Finally in Sec. 4, the conclusions of these studies are summarised.

Experimental set-up
Two modules, denoted as ADA and ADC, were tested. They are shown in Fig. 1. The ADA and ADC modules are identical to the modules used in ALICE at positive and negative pseudorapidities, respectively.
These modules are made of Bicron BC-404 plastic scintillator, with WLS bars Eljen EJ-208 in two of the sides.
The bars are coupled to clear fibres leading the light to Hamamatsu R5946 PMTs. The lengths of the optical fibres were shorter in the test beam, where 47 cm-long fibers were used for both modules instead of 100 cm and 54 cm for ADA-type modules, and 250 cm for ADC-type modules. The different lengths are due to the available space and the placement requirements in the ALICE cavern and LHC tunnel, where the detectors are placed, but which were not present during the studies with the test beam. During the test the PMTs were operated at 1500 and 1650 V for ADA and ADC, respectively. The read-out was also identical to the one installed in ALICE [9]; in particular, the signal from the AD modules was split into two signals, one to measure the deposited charge and the other, amplified by ten, to determine the arrival time of the particles.
The T10 beam at the Proton Synchrotron (PS) machine [10] was used as a source. The beam consisted  The drawing is not to scale. mainly of pions (π + ) and protons (p + ). The following beam momenta were chosen: 1.0, 1.5, 2.0 and 6 GeV/c. The relative momentum resolution was 1.3%.
The set-up for the data taking in the test beam is shown in Fig. 2. In addition to the AD modules, one can also see two other scintillator modules labelled black-start and black-end, as well as two Cherenkov radiators denoted as T0-start and T0-end [11]. These devices were used to provide triggers and reference timing for the measurements presented below. The specific configurations for these tasks depended on the measurement being carried out and are described in the corresponding sections.
The final device involved in the measurements was a silicon pixel sensor positioned at the edge of the scintillator pad, as shown in Fig. 3. This detector has an ALPIDE chip as those used for the upgrade of the Inner Tracking System [12] and for the new Muon Forward Tracker [13] of ALICE. The chip is based on the CMOS MAPS technology; it has an array of 512 × 1024 pixels with a size of 26.88 × 29.24 µm 2 and a sensitive area of 1.376 × 3.0 cm 2 . Figure 3: Location of the scintillator, the WLS bars, the fibres, the PMT, and the pixel detector, as well as the definition of the coordinate system whose origin lies at the centre of the plastic scintillator.

Efficiency
The efficiency is defined as the fraction of events selected according to Eq. (1): where N AD is the number of events that fulfilled the 3-fold coincidence condition, defined by the logic AND between T0-start, T0-end and the AD module, while N T0 is the total number of events given by the 2-fold coincidence between the T0-start and T0-end. All the triggers are given by the time signal, in particular the ADA and ADC modules are triggered when the time signal is below a −40 mV threshold and inside a 15 ns time window [9]. (This time-window in the electronics is designed to tag beam-beam interaction in the ALICE experiment.) The statistical uncertainty is computed as The first measurement to be presented is the efficiency to detect the incoming particles as a function of the  To quantify the size of the beam and the corresponding shape of the efficiency curves a Gaussian Cumulative This CDF is adjusted to the edges of the efficiency curves. The physical length in the vertical and horizontal axes of both modules are calculated using the differences between the distances of the mean values of the CDF for each case, obtaining a length of X = 22 ± 0.1 cm and Y = 19 ± 0.1 cm for each axis, which are consistent with the physical length of the modules convoluted with the beam size. The value of the σ parameter for the left and right CDF corresponding to each axis are consistent and are averaged to estimate the beam size of each axis to obtain σ Y = 1.13 ± 0.06 cm and σ X = 0.86 ± 0.08 cm.
In order to determine the efficiency at the border of the detector, and to verify that impacts in the WLS bar can be ignored, the silicon pixel sensor is used. The detector is placed so that it covers part of the plastic scintillator and of the WLS bar as shown in Fig. 3. Data taking is triggered by a coincidence in the black-start and black-end scintillators. In this case, the efficiency is defined as: The results are shown in It is worth to mention that for ADC the background shown below 0.55 cm and the small inefficiency for the places above 0.65 cm are attributed to noisy pixels; the same is valid for ADA, but the background is below 0.34 cm and the inefficiencies are above 0.45 cm.
Finally, the efficiency when the beam hits other elements, like the optical connectors, the fibre bundles or the PMT has also been studied. The efficiency to detect a signal for particles hitting the optical connectors (see  rapidly towards zero within some 1.5 cm. The efficiency when the beam hits at X = 55.5 cm, corresponding to the face of the PMT, is 40% and decays rapidly with increasing X, reaching zero at X = 60 cm.

Charge measurement
An example of the charge distribution in the ADA and ADC modules is shown in Fig. 6  This type of distribution is used to extract the MPV as a function of the impact point of the beam spot in Table 1: MPV of the charge measured for pions, protons and the sum of both. For a momentum of 6 GeV/c it is not possible to distinguish the particles using the time-of-flight technique described in the text.

Momentum
Charge (ADC counts) (GeV/c) ADC ADA π + + p + π + p + π + + p + π + p + the detector. This is shown in Fig. 4 with the blue and red markers and the scale in the right-side axes. One observes a slightly different value of the MVP in the ADA and the ADC detectors. This is a geometric effect of the light propagation in the scintillator, because the ADA detector misses a larger semicircle than the ADC module as seen in Fig. 1. The slight dependence on the coordinates of the impact point of the beam spot is also due to the same geometric effect.
The dependences of the MPV on the particle type and on the momentum of the beam have also been studied.
The first is illustrated in Fig. 6, while the latter is shown in Table 1

Time resolution
To measure the time resolution one needs two ingredients. First a reference time, and second a correction for the the measured time as a function of the deposited charge, the so-called time slewing. In the set-up shown in Fig. 2 the Cherenkov detectors have the best time resolution, below 50 ps [11], so it is natural to use the T0-end to provide the reference time. Comparing the times of T0-end and the black-start detector it is possible to have a clean separation of the pion and proton components of the beam as demonstrated below, so that the analysis can be done for each particle type separately.
The time measurements are affected by the slewing effect which can be corrected for as follows [15]. The case of pions is used to illustrate the correction, because the effect is the clearest of both cases. The (a) and The effect that this correction has on the time resolution can be seen in Fig. 8 for the case of a beam momentum of 1 GeV/c. The mean time difference for both particle species is obtained from the difference in mean values of the Gaussian distributions fitted to each contribution.
A summary of the time resolutions obtained for the different beam momenta is shown in   resolution is similar for both detectors. It increases with momentum and it is larger for pions than for protons.
For the lower beam momentum, the resolution is below 1 ns and remains well below 1.5 ns even at the largest beam momentum.
Finally, the dependence of the time resolution on the deposited charge for pions at 1 GeV/c is shown in    measurements to validate the model. Once this is done, the model can be used to obtain the energy corresponding to the MPV of the charge distribution.
The first step is to obtain a proper accounting of the time traveled by a given particle while traversing the Table 3: Theoretical and measured time-of-flight differences between pions and protons for the given distances with respect to the T0-end detector for a 1 GeV/c beam momentum after the time-slewing correction.

Detector
Distance ( experimental set-up shown in Fig. 2. The total distance is separated in stages: from black-start to ADC (65.5 cm), then to ADA (3 cm), to T0-start (240.5 cm), to T0-end (62 cm), and finally up to black-end (another 854 cm). The distances are taken from the centre of the AD and black scintillators pads and the centre of the quartz radiator of the T0 detectors, adding 1.5 and 2 cm to the distance with respect to the AD and black scintillators respectively; for T0 detectors, we use the distance at 1 cm from the edge facing the beam.
At each stage the change of momentum due to the energy loss when traversing the detector materials is obtained from a Landau distribution [16] where the most probable energy loss is: Here the detector thickness is x in g·cm −2 , j = 0.2 and δ(βγ) is neglected at low energy; K = 4πN A r 2 e m e c 2 = 0.307075 MeV mol −1 cm 2 , Z and A are the atomic and mass number of the material being crossed, z is the charge number of the incident particle, r e the classical electron radius, m e c 2 the electron mass, N A Avogadro's number, I the mean excitation energy (eV) and δ(βγ) the density effect correction to the ionization energy loss.
The new energy and momentum of the particle is recalculated after each stage using the material budget and E 2 = p 2 c 2 + M 2 c 4 . The material budget comprises the following: for the AD modules 2.5 cm of Bicron 404 [17] each, while the other scintillators are 4 cm thick. The T0 Cherenkov radiators have a more complex composition being made of a 2 cm thick quartz radiator [11] and a PMT. The PMT is modelled by 1 mm of glass (of the vacuum tube), 1 mm of aluminium for the cover at the front and another 1 mm at the back; in addition the 16 dynodes are represented by a 0.1 mm thick layer of iron.
Finally, the time after each stage is computed as where j indicates the particle (i.e. pion or proton) and L the distance traveled. The time-of-flight difference ∆t is calculated subtracting the time of flight of the two different particle species traveling the same distance, Using this model it is possible to compute the expected time differences for the arrival times of a pion and a proton at a given detector. The comparison of the model with the measurement is reported in Table 3 for the case of a 1 GeV/c beam momentum. The agreement is satisfactory for such a simple model of the propagation of the particle beam through the experimental set-up. Once the model has been validated as producing reasonable results for the time-of-flight difference between pions and protons it can be used to estimate a conversion factor between the ADC charge and the deposited energy. The conversion factor is obtained by dividing the estimated energy deposited in the detector over the charge collected for the detector in each measurement (Table 1). This was done for pion and proton beams with momenta of 1, 1.5 and 2 MeV/c. The result is shown in Table 4. The conversion factor is consistent across all cases so it is justified to take the average, which yields ε = 0.832 ± 0.012 MeV/ADC, where the uncertainty is obtained from the standard deviation of the different factors.

Summary and outlook
One ADA and one ADC modules have been studied with test beams. The set-up allows for the measurement of the modules' efficiencies as a function of the beam impact position, and the measurement of the charge deposition as well as the time resolution of the modules. In particular, these two last properties have been studied as a function of the particle species, pion or proton, and the momentum of the test beam. A simple model of the energy deposition on the material of the set-up traversed by the beam particles allows for the conversion of the ADC charge into an energy.
The results show that the modules have a high and uniform efficiency as a function of the impact point and that the hits in other parts of the detector, like the WLS or the PMT, have a lower efficiency which decays steeply outside of a very small range of positions. The set-up allows to separate the pion and proton components of the beam. The charge deposition in both cases has been measured and shown to behave as expected. The time resolution has been measured and shown to be below 1.5 ns for particles depositing little charge in the modules and below 1 ns for particles depositing more charge.
These results allow for a better understanding of the detector and provide key information to benchmark and improve the simulation of the AD detector used during the LHC Run 2 in ALICE. This knowledge can be applied in a straightforward manner to the the FDD being constructed now and that will be in operation in ALICE during the LHC Runs 3 and 4.