Detector (draft in 2014. 8-2014. 10)

The High Intensity Electron-Positron Accelerator Facility (HIEPAF) will work at the c.m.s. energy of 2-7GeV and reach the luminosity of L=1035cm-2s-1. The requirements of the detector system on it must match the event characteristics, with emphasis on those demands crucial to achieve the most important physics objectives.

2. 
   Physics Requirements (assigned to Haiping)
   

2. 
   General Considerations
   

1. 
   (nearly) 4π detector solid angle coverage for both charged and neutral particles, and uniform response for all particles;
   
2. 
   high resolution of momentum and angular for charged particles; and high resolution of energy and position for photons ;
   
3. 
   superior PID ability (e///K/p/g) and high detection efficiency for low momenta particles;
   
4. 
   precision luminosity measurement;
   
5. 
   work under high luminosity environment.
   

The expected key features of the HIEPAF detector system are listed below.

1. 
   Vertexing performance and low-momenta tracking eff.
   
2. 
   Tracking system: p_T resolution 0.5~0.7% @1GeV/c and dE/dx resolution <7%, low material budget ().
   
3. 
   PID π/K (and K/p) 3-4 separation up to 2GeV/c with modest material budget (<0.5X₀)
   
4. 
   EMC stochastic term <2%/√E and constant term <0.75%, angular resolution?
   
5. 
   MUC / suppression power >10, down to p=0.5GeV/c.
   

The Inner Silicon Detector (ISD) is a silicon detector utilizing advanced active pixel sensors and/or silicon strip technology. Its inner layers closest to the beam pipe provide additional precise hits that connect the particle track reconstructed in the Main Drift Chamber (MDC) and the collision point. The conceptual design of ISD aims to improve the track momentum resolution and to improve the tracking efficiency, in particular for low transverse momentum (p_T < 500 MeV) particles. Therefore, minimizing the multiple scatterings requires very low material budget. Although there is no requirement to reconstruct secondary vertices for the heavy-flavor particles, the sufficient spatial resolution is still needed to achieve high momentum resolution. In addition, the ISD should response fast to survive in high luminosity environment (~10³⁵ cm^-2s^-1). The following sections will introduce options of the existing vertex detectors in high energy experiments, the conceptual design of the ISD and its performance estimated via simulation and theoretical calculations.

Introduced in this section are two successful designed and tested vertex detectors recently used in high energy experiments, with low material and high resolutions, the Heavy Flavor Tracker (HFT) in STAR experiment and the Vertexing Detector (VXD) in Belle-II. They both show expected performance during the beam-on operations.

The STAR HFT consists of 4 layers of silicon detectors grouped into three sub-systems with different technologies, guaranteeing increasing (better) resolution when tracking from the Time Projection Chamber (TPC) towards the vertex of the collision. The Silicon Strip Detector (SSD) uses an existing detector in double-sided strip technology. It forms the outermost layer of the HFT. The Intermediate Silicon Tracker (IST), consisting of a layer of single-sided strip-pixel detectors, is located inside the SSD. Two layers of silicon pixel detector (PXL) are inside the IST. The pixel detectors have the resolution necessary for a precision measurement of the displaced vertices of open heavy-flavor hadron decays. The table below lists the key parameters of the HFT design

The PXL detector is designed with 10 sectors with 4 ladders (1 inner ladder and 3 outer ladders) in each sector, supported by carbon fiber frame. For each ladder 10 pixel pitches with 20.720.7 mm² size each are attached on top of the cupper or aluminum cable, resulting in 0.52%X₀ or 0.37%X₀, respectively. Signals are readout directly by the cable and collected at the end of the ladder with RDO (?) buffers and drivers.

Figure 1: PXL ladder and sensor pitches.
The PXL detector used an advanced commercial CMOS technology, Monolithic Active Pixel Sensors (MAPS). The sensor and signal processing are integrated in the same silicon wafer with digital output. The sensor is thinned to 50 m. Signal is created in the low-doped epitaxial layer (typically ~10-15 m). MIP signal is limited to <1000 electrons. Charge collection is mainly through thermal diffusion (~100 ns), reflective boundaries at p-well and substrata. The power dissipation is ~170mW/cm², which is similar to sun light.
Figure 2: MAPS operation algorithm.
The table below lists the performance parameters of PXL detector.

The read out time per sensor is limited by the frame integration time of 100-200 ms. The operation mode is column parallel readout with integrated serial data sparsification. Figure 3 and 4 shows some performance examples of the HFT detector.

Figure 3: Left: Number of hits per sensor during the data taking in 2014 run. Right: TPC tracks and PXL hits association.

Figure 4: Impact parameter (DCA) resolution as a function of momentum. Data show good agreement with MC simulation.

Compared with STAR HFT, the vertexing detectors in the Belle-II experiment, consisting of 4 layers of Silicon Vertex Detector (SVD) and 2 layers of Pixel Detector (PXD), is with a bit worse resolution but faster readout.

Belle-II operates in the similar low energy environment of KEKB (10.58 GeV) as HIEPAF (2-7 GeV) and with higher luminosity (~810³⁵ cm^-2s^-1). This requires very low mass and fast detector. The two layers of PXD are 1.4 cm and 2.2 cm in radius, consisting of 8 and 12 modules for the innermost layer and the second, respectively. In the active pixel matrix region, the thickness is ~75 m. Note the innermost layer is very close to beam pipe. This provides precise constrains on the track projecting to the collision point but is also technically challenging due to high radiation environment.

Table below lists the key parameters of PXD design.

The PXD consists of a fully depleted silicon substrate and is equipped with a p-channel MOSFET structure with an internal gate where the electrons liberated by traversing charged particles are collected. The internal gate modulates the current through the MOSFET at readout time. This kind of DEPFET (DEPleted Field Effect Transistor) pixel sensor is a monolithic structure, with current-digitizing electronics at the ends of the sensor, outside of the acceptance region.

Figure 5: PXD layout and its prototype.

The scheme -pixels followed by strips - has been successfully applied for the detectors at RHIC and LHC. With similar luminosity of KEKB and collision energy, the beam background at small radius of HIEPAF is also similar. This requires ISD to be very light to minimize the multiple scattering. Both STAR PXL and Belle-II PXD are based on thin pixel sensor technology with readout electronics and active cooling outside the acceptance. Both would be ideal options for the ISD consideration. The advantage of DEPFET sensor is the ~10 times faster readout than MAPS.

The ISD will consist of 1 layer of SSD and 2 layers of PXD. The SSD located inside the MDC at a radius of ~10 cm and 2 layers of PXD that are 3 and 6 cm in radius, as shown in the conceptual layout in Fig. 7.

Figure 7: Conceptual layout of the inner tracking system.

Option 1: MDC + HFT-like parameters.

The analytic fast calculation is used to study the performance in tracking with the designed MDC + ISD parameters. The probability to pick up the correct hit can then be described by the following equation:

The probability to pick up the wrong hit is described by the equation:

where σ is the uncertainty in the track extrapolation from the outer detectors to the target layer,  is the background hits density, and ‘a’ (the upper limit of the integral) is the search cone radius. The analytic calculation of the quantity σ includes contributions from the multiple Coulomb scattering (MCS), the detector resolution, and the track position uncertainty due to the quality of track fitting. The quantity  includes contributions from the pile-up events and other tracks in the current event. We have discovered that track fitting errors are the dominant term in the calculation of σ while the detector resolution drops out due to the extremely high resolution of the detectors. So in the simulation study, we have set σ equal to the search radius used by the tracking software at each detector layer.

where σ₁ and σ₂ are the position resolutions on each detector layer, r₁ is the inner layer radius and r₂ is the outer layer radius and θ_mcs is the MCS angle in the first layer of the detector. θ is the angle of entrance into the detector relative to the beam line. The second term, the projection error due to MCS, is the parameter of interest and it is this term that dominates the detector performance at low particle momentum.

The MCS effects are estimated by randomly smearing the scattering angle of the track when projecting to the next layer. The scattering angle is sampled with Gaussian distribution with the rms as:

(4)

where L is the track path length along the incident direction. L/X₀ is the fraction radiation length. In the Kalman filter tracking process, a covariance matrix method is used in the iteration:

Figure 8: Momentum resolution (left) and position resolution (right) from the analytic calculation with Option 1. (change PVD to PXL)

Figure 9: Momentum resolution (left) and position resolution (right) from the analytic calculation with Option 2.
In Fig. 8, the third layer, SSD, helps little in terms of momentum resolution and position resolution, but it helps to connect PXL hits and MDC tracks thus will improve the tracking efficiency. Since efficiency study is more complicated and need further full Geant simulation, here we only use the existing experiment for reference. For example, Figure 10 shows how the STAR SSD helps in the tracking efficiency with full Hijing + Geant simulation.
Figure 10: STAR HFT tracking efficiency.
2.4 Summary

Silicon pixel + strip detectors are now commonly used as inner tracking system in high energy experiment. The concept of these detectors and related technology are mature and under continuous developing. The expected performance of these detectors with low material budget and high resolution is appropriate for the HIEPAF ISD consideration. The inner tracking helps to improve the momentum resolution, position resolution and tracking efficiency, especially for low momentum tracks. However, the man power and knowledge for the silicon detector technology and related electronics in China are far from ready yet.

To fully exploit the physics capability at HIEPAF, it’s essential to have excellent PID performance. From the simulation study in the previous (physics and accelerator) sections, a series of stringent requirements are imposed to the PID detectors. Charged hadrons (, K, p) are to be distinguished up to p=2GeV/c to cover all available kinematics, and need good separation from electrons and muons down to low momentum range. e/h and / rejection power better than 100 and 10 are pursued. Identification of neutral particle (⁰, neutron) and photon is another important aspect of the experiment, as well as the precision measurement of their energies or masses. In this section, we mainly focus on the PID of charged hadrons. The identification of electrons and photons, as well as ⁰ and neutron, are primarily done by the EM calorimeter, which will be discussed in detail in the EMC section. Distinguishing muon from hadrons (especially pion) is briefly introduced in this section, but the majority of the discussion will be left in the MUC section.

According to the basic detector concept, charged particle ID can be obtained by the specific energy loss (dE/dx) measurement at low momentum. With a dE/dx resolution of 6-7%, clean p/K/p ID for p<0.8/1.1 GeV/c is achievable. Further charged particle ID up to p=2GeV/c requires a dedicated PID detector system. At HIEPAF energy, two types of detector techniques can be chosen to improve the PID at intermediate momentum range, namely time-of-flight (TOF) and Cherenkov detector.

A TOF utilizes the difference mass, thus difference velocity at a given momentum, to distinguish the particle species. Excellent time resolution is crucial to extend PID by TOF to high momentum. The basic formulae for TOF PID are listed below,

,

where T is the time of light, b is the velocity, m is the particle mass and p is the momentum. DT, Db and Dm² are the differences of T, b and m² between different particle species. Thus

where L is the path length of the particle trajectory and c is the speed of light in vacuum. As shown in Fig. 1, L may be down to 1m.

For p/K and K/p at p=2GeV/c, the time difference DT are around 0.1 and 0.27ns. So to achieve 3s p/K/p separation an overall TOF time resolution better than 30/90ps is needed. Considering the available choice on detector technology, a TOF alone cannot identify p/K to p=2GeV/c.
4.2.2 Cherenkov detector

The Cherenkov radiation is commonly used in high-energy experiments to identify particles at high momentum. This specific radiation happens if a charged particle travels faster than the speed of light in the medium, as illustrated in Fig. 1. By choosing different types of medium, often called Cherenkov radiator, particle species can be distinguished in a range from several to hundreds GeV, depending on the refractive index of the radiator. As shown in Fig. 1 is the principle of Cherenkov radiation. With a refractive index n of the radiator and particle speed v=bc, the Cherenkov radiation emits at an angle _c relative to the particle moving direction. Some relevant formulae are listed below.

,

where and is the Cherenkov emission angle;

which denote the threshold velocity and Lorentz factor for Cherenkov radiation emission; and the differential Cherenkov photon yield is expressed as:

a) to check if there exists Cherenkov radiation at given momenta, i.e. if the particle has reached its threshold velocity. In this way the detector is called threshold Cherenkov detector, which is usually technically simple to build but often applicable limited;

b) to determine the Cherenkov emission angle precisely, and compare to expected values of different particle species to find the most possible candidate. In this case the momentum vector when the particle hits the Cherenkov detector must be known with good precision, and the spatial resolution of the Cherenkov light detector should be good enough. The detector design is usually more complex than the threshold Cherenkov detector, but with much wider kinematic coverage and more diverse PID capability. There exist various methods to experimental realize such kinds of Cherenkov detector, such as the ring imaging Cherenkov detector (RICH) and the detection of internally reflected Cherenkov light (DIRC).

Fig. 2: The separation of different particle species by Cherenkov angle and momentum measurements.

Shown in Fig. 2 is the idea to separate different type of particles through Cherenkov emission angle and momentum measurements. The blue lines in the plot denote the expectations of charged particles e, , K and p due to the equation below,

.
the grey bands in Fig. 2 simulate the experimental results, with an uncertainty estimation of

.
with the two parameters and , the PID capability can be evaluated. The right vertical coordinate shows the number of Cherenkov photon , where is XXX and T is the thickness of the radiator.

Options for the PID detector

RICH is a suitable Cherenkov detector for PID at barrel. To avoid space consumption and relatively complex optical design, the proximity-focusing RICH is found to be an appropriate candidate. Due to the limited space, the proximity gap should not be very large. A 10cm gap is considered here. Without TOF, the dE/dx measurement only (7% resolution) can separate /K to p=0.8GeV/c. To ensure full PID coverage, the Cherenkov radiation measurement should be applicable at this momentum, indicating that the refractive index of the Cherenkov radiator must be larger than 1.18. This requirement practically removes all gas mixture and aerogel as Cherenkov radiator, leaving only liquid and solid radiator material.

An alternative PID detector technique involves TOF. As discussed earlier, a TOF system with an overall time resolution of ~90ps provides required performance for K/p separation. However for /K separation the needed ~30ps time resolution is very challenging to achieve. One of the reasons is the precise determination of the collision time (start time), which is roughly 55ps at BESIII. So with TOF alone it’s not sufficient to identify all charged hadrons in the kinematic range at HIEPAF.

In order to further distinguish /K, additional detectors may be required. A possible candidate is the threshold Cherenkov detector, which is relatively simple to build. In Fig. 4 the threshold momenta of , , K and p are plotted as a function of the refractive index n. It’s clear with n~1.03  and K can be identified in the momentum range of 0.6-2GeV/c by checking whether the Cherenkov radiation happens.

A practical example of such approach is the TOF+ACC (aerogel Cherenkov counter) PID system in the BELLE experiment. Sufficient p/K separation in 0.8-2.5GeV/c with n=1.03 and separation in 1.0-3.5GeV/c with n=1.01 have been experimentally verified. Both TOF and ACC are technically easy to realize, but need adequate space to accommodate all the detector components. The gap between MDC and EMC need be increased to ~30cm to fit this PID option. The influence on outer detectors, performance and cost, should be taken into account.

Time of propagation (TOP) technique is a recent progress in the field of Cherenkov detector. The principle of this technique is illustrated in Fig. 5. It makes use of the total reflection inside the fused silica (served as radiator as well as Cherenkov light guide) and precision measurement of both the 2-D hit position and the timing information at the one or both ends of the radiator. In this way the final 2-D spatial and 1-D time structure is combined to identify the particle species. This technique is to some extent similar to the DIRC approach, but with 1-D spatial measurement replaced by 1-D timing measurement. The modification of readout method makes TOP an impact Cherenkov detector. The challenge in measuring simultaneously the photon hit position and time with good precision is well within the capacity of modern photon sensors.

Similar to the RICH used in the barrel, this technique is applicable at the endcap region. Due to longer track length in the MDC, the energy loss resolution may be improved, thus allowing wider identification range by dE/dx only. If the dE/dx resolution is good enough so that /K separation can go up to ~1GeV/c, there will be more choices to realize the RICH. According to Fig. 4, kaon starts to generate Cherenkov radiation at p~1GeV/c with n~1.13. Such a refractive index may be obtained by aerogel technique, adding more radiator candidates to those introduced previously for the barrel. Furthermore, this RICH serves as a threshold Cherenkov detector for proton identification since the threshold momentum for proton at n=1.13 is close to 2GeV/c.

The PID method with threshold Cherenkov detector and TOF is relevant in the endcap region, just similar to that in the barrel. However, to ensure good time resolution the endcap TOF (ETOF) should be carefully designed. Plastic scintillator coupled with fast PMT is used in the endcap at the BESIII experiment. The data taken in e⁺e^- collisions reveals that the TOF resolution is around 110-130ps for charged particles other than electron. To get better time resolution the new type gaseous multi-gap resistive plate chamber (MRPC) is proposed to replace the current ETOF. Beam test has proven the choice and an overall TOF resolution <80ps is foreseen. If successfully operated in BESIII, this technique can be adapted to the experiment at HIEPAF.

Considering all the detector options and technical advancement, the baseline design of the PID detector at HIEPAF is illustrated in Fig. 7. The basic structure is similar to that of the ALICE HMPID, but with MWPC in the photon detection part replaced by triple gaseous electron multiplier (GEM) layers. The GEM readout is mechanically easier to maintain, meanwhile the position resolution and rate capacity are much better than the MWPC. The surface of the first GEM layer is doped with a CsI layer of several hundred nanometers thick to convert the Cherenkov photon to electron (called photo-electron, or p.e.). The electric field in the ionization gap is reversely biased so that most of the electrons from charged particle ionization are removed. In this way the background noise is significantly suppressed. This readout method has been used in the PHENIX hadron blind detector (HBD), also proposed for the PANDA particle ID.

The radiator thickness and the proximity gap should be tuned to optimize the performance and the cost of the PID detector. At n=1.3 and p=2GeV/c, the /K separation requires ~120mrad Cherenkov angle resolution . Take a photon yield of 10 and a proximity gap of 10cm, the estimated photon sensor size is around 1-1.5cm, which should be straightforward to achieve.

According to the requirements on PID imposed by the physics program at HIEPAF, various detector techniques applicable at this experiment are discussed. The baseline design is presented and the estimated performance fulfills the PID capability target.

5. 1 General Consideration

The electromagnetic calorimeter (EMC) is an array of scintillating crystals readout by photo-sensors. It has a barrel EMC and two endcap EMCs to maximize the coverage towards 4It measures the energy and direction of photons, electrons and discriminates between electrons and charged hadrons. It is also helpful for the identification of hadrons including anti-neutrons. To accomplish these jobs, the EMC is required to have good energy and position/angular resolution. It is also helpful if it has good timing resolution.
In the high luminosity era, the background in the EMC region is significantly higher than the EMC currently operating in electron-positron colliders, such as the EMC of BaBar, Belle and BESIII. The high background, on one hand, results in radiation damage of the crystals. This radiation damage degrades the light yield of the crystal thus worsen the EMC energy resolution. Furthermore, the degradation of the crystal light yield is a function of radiation dose, or the running time. This will requires much more efforts on the timely calibration and potentially introduce larger systematic uncertainty. On the other hand, the high rate of photon background produces lots of pile-up in EMC. They energy deposited in EMC by the high rate of photon background fluctuates frequently with time. These noises will definitely affect the energy and position resolution of the EMC.
With the new challenge in the high luminosity era, the EMC is required to have a crystal with short decay time thus a short signal shaping time and charge integration time is adequate to get high statistics of fluorescence photons. The crystal is also required to be radiation hard. In the reality that the fast crystal in the market usually has much less light yield than that of CsI(Tl) used by BaBar, Belle and BESIII EMC, to construct a EMC with fast crystal and good energy resolution, a photo sensor with high photon detection efficiency, high gain and small excess noise factor is needed.
5.2 Crystal Options

The properties of crystal significantly impact the performance of EMCs. Tabel 1 lists the properties of various crystals including doped CsI and pure CsI, BSO, PbWO₄ and LYSO crystal. The doped CsI crystal CsI(Tl) has very high light output. It is widely used in electron-positron collision experiments such as CLEO, BaBar, Belle and BESIII. Very good energy resolution was achieved. The major difficulty to use it in the high luminosity era is to deal with its long decay time, as large as microsecond. The small radiation resistance also prevents it to be used at a high background region. The superB experiment think the radiation damage of CsI(Tl) is affordable at barrel and proposed to reuse Babar barrel EMC as its barrel EMC, but pay the price of higher noise equivalent energy due to shorter shaping and integration time. The Belle2 experiment also decides to reuse Belle barrel EMC and upgrade the electronics to Flash ADC to suppress the pile-up effects.

Pure CsI is much faster than doped CsI, which make it a candidate of crystal at high luminosity era although its light output is significantly lower than doped CsI. The major difficulty is to find an appropriate photosensor with high quantum efficiency at the wavelength of ~300 nm.

The LYSO crystal has relatively high light output (about half of doped CsI), short decay time (about 40 ns) and high radiation hardness (upto 10⁸ rad). These properties make it an ideal candidate of the EMC crystal at high luminosity era. However, the high melting point makes it too expensive to be affordable for a big detector array.

PbWO₄ crystal is also a fast crystal. It has a major component with decay time of 30 ns and a smaller component with decay time of 10 ns. It has been used in CMS experiment and provides good energy resolution at high energy. However, the low light output limits it to be used at an electron-positron collision experiment where the energy resolution at low and intermediate energy is important. The Panda experiment at GSI is working with crystal vendors to improve the light output of the PbWO₄ crystals and a 2 to 3 times of light output improved is achieved. They also proposed to work at a temperature as low as -25 ^oC to further increase the light output.

Recently, a new type of crystal, BSO, is being developed. Its performance is between doped CsI and PbWO₄. The density is higher than CsI(Tl) and close to that of PbWO₄. Its radiation length and Moliere radius are about 40% lower than doped CsI(Tl) and close to PbWO₄. This allows a more compact EMC with higher granularity, which is import to improve the position/augluar resolution and suppress the pile-up effect as the area of surface of single crystal is significantly reduced. Its decay time is about 100 ns, an order or magnitude smaller than that of CsI(Tl) and a few times larger than that of pure CsI, PbWO₄ and LYSO crystals. Its light output is about a factor of 50 lower than CsI(Tl), but about 10 times higher than PbWO₄. The light output of the crystals within a window of 100 ns is also listed in table 1 for comparison. Note that although the light output of CsI(Tl) within 100 ns is still high to be able to give good statistics, the long decay time will produces significant pile-up to the upcoming events and significantly reduce the EMC performance. The radiation hardness is also reported to be as high as of 10^5-7 rad. It turns out that the BSO crystal is a very good candidate for the high intensity electron-positron collision experiment. One concern is that this crystal has not been widely used in high-energy experiments and the mass production capability is not proven yet. However, the Shanghai Institute of Ceramics, Chinese Academy of Sciences (SICCAS) has successfully produced 9 crystals for us for properties test. Figure 1 shows the 9 crystals with size of 2x2x20 cm³. Figure 2 shows the light output measured with a PMT XP2262 at room temperature. A good trend is observed that the light output increases with production time. The last 3 crystals have light output of around 90 photoelectrons per MeV deposited by a -ray. This light output is comparable to the improved PbWO₄ at operation temperature of -25 ^oC. The right panel of Fig. 2 shows that the decay time of BSO is about 100 ns. Figure 3 shows the normalized light output as a function of time in the presence of  irradiation source at different dose rate. There is still room to improve the radiation hardness.

Table 1 Properties of different crystals

Figure 1 BSO crystals produced by SICCAS.

Figure 2: The light output of the 9 BSO crystals and as a function of charge integration time.

At low and intermediate energy, the energy resolution is not dominantly determined by the statistics of photon produced in the crystal. For example, A BSO crystal with light output of 100 p.e./MeV produces about 10,000 photoelectrons when hit by a 100 MeV photon and gives energy resolution of 1%. The noise from the electronics plays an important role in the energy resolution and high signal-to-background ratio is essential to achieve good energy resolution at the energy range of tens MeV to a few GeV. The signal-to-background ratio depends on the light output of the crystal and the gain of the readout photosensor. A crystal with high light output readout by a photosensor with high gain gives high signal-to-background ratio and, as a consequence, gives small equivalent noise energy. To achieve good energy resolution, the noise from the photosensor itself is also required to be small.

Silicon photodiodes (PD) are widely used in high-energy physics as light detectors, such as BaBar, Belle, BESIII, CLEO, L3. Its quantum efficiency can exceed 90%. However, its gain is only 1. Low-noise amplifiers are necessary and low signal-to-background ratio is expected anyhow, unless the crystal has light output as high as CsI(Tl).

In comparison with PD, the avalanche photodiodes (APD) have high gain (~10-1000) .This can suppress the equivalent noise energy caused by the electronics. However, the APD itself have large noise thus large excess noise factor (ENF) and substantial cooling is often necessary.

Figure 4 shows the charge spectrum measured by a 3x3 mm² SiPM (Hamamatsu S10362-33-050C) coupled to a 3x3x15 mm³ BGO crystal irradiated by a ¹³⁷Cs and ²²Na  radioactive source, respectively. The SiPM has 3600 pixels in total. The number of fired pixels as a function of the -ray energy is shown in the left panel of Fig. 5. The right panel shows the corrected number of detected photons according the formula:

.

The numbers shown in the figures indicate the deviations of the last data point from the expectation based on the data points below 700 MeV. The uncertainty of the expectation is estimated to be 2.5% and 3.8% for BGO and CsI(Tl) crystals, respectively. The energy resolution as a function of energy and number of fired pixels are shown in Fig. 6. A few percent energy resolution is achieved at energy about 1 MeV. Our LYSO+SiPM results are similar as LYSO+PMT results shown in SuperB Technical Design Report. A BSO+SiPM is to be tested in the near future. The new generation of SiPM produced by Hamamatsu is to be pursued and tested to verify the improvements on the suppression of dark noise, after pulse and radiation hardness.

Figure 5 The linearity of the SiPM.

Figure 6 The energy resolution of crystals readout by SiPM.

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