A simulation study of the energy deposited in the DSSDwith the 90Sr source for the Belle II Experiment

Thong Q. Nguyen∗

The University of Texas at Dallas, Class of 2015 andAihara Laboratory, Department of Physics, The University of Tokyo

(Dated: August 21, 2014)

In the SVD testing experiment using 90Sr as the test source, the energy deposited by β-rays inthe double-side strip detector (DSSD) is difficult to determine experimentally. I develop a softwareto simulate the geometry and physics processes of the SVD testing experiment to study the energydeposited, using the GEANT4 toolkit [1]. Different thicknesses for the top scintillator in the testingexperiment are employed in the simulation to compare the corresponding trigger rates and energydistributions. The determined mean value of 144.1 ± 5.9 keV for the energy deposited in DSSDwith the 0.5 mm scintillator is stable with small scintillator thicknesses that are less than 1 mm.The correction factor for experiments using minimum ionizing particles (mips) is determined to be1.67, which can be used to calibrate the gain value of the APV25-readout chip. These results areimportant in the testing procedure of the upcoming SVD production, starting in October 2014.

I. INTRODUCTION

The primary physics goal of the Belle experiment at theKEKB collider is the systematic study of CP violatingasymmetries in the decay of B mesons to CP eigenstates,predicted by the theory of Kobayashi and Maskawa [2].After more than ten years of successful operation, theKEKB accelerator delivers a total integrated luminosityof 1 ab−1 [3]. While most results from the Belle ex-periment are in good consistency with the expectationfrom the Standard Model (SM), much larger data setsare needed to investigate whether a few measurementsthat show discrepancies at around three standard devi-ation level from the SM prediction are hints for NewPhysics models or merely statistical fluctuations. Theessential purpose of a super flavor factory, SuperKEKB,is to accumulate such high-statistics data sets from high-precision measurements that allow to confirm or denythe discrepencies from the SM predictions [4]. The Su-perKEKB’s designed luminosity is 40 times higher thanthe KEKB, and the integrated luminosity at the Belle IIexperiment is expected to be 50 ab−1 in about 5 yearsrunning [5].

Major upgrades of the Belle II detector include the Sil-icon Vertex Detector (SVD) that consists four layers ofDSSDs, fabricated from six-inch wafers. A readout chip,APV25, is employed to suppress the background hits.The fully assembled SVD ladder is tested to verify thefunctionality of every strip. Since using the beam testrequires tremendous work and preparation, the sourcetest, 90Sr, which emits β-rays with the maximum energyof 2.186 GeV, is chosen for this testing experiment. Onthe development of the β-ray system test, an accuratedetermination of the energy deposited in the DSSD isof significant interests. First, it allows to verify if thesignal value given by one strip is correct. Second, the

∗ thong.nguyen@utdallas.edu

energy deposited in the DSSD is amplified through theAPV25 readout chip, and then converted to digital sig-nal with the ADC before displaying on the PC. With theknown output value, determining the input value–the en-ergy deposited in the DSSD–provides the gain value ofthe APV25 readout chip. Third, the correction factor forthe testing experiments using mips is calculated based onthe energy deposited in the DSSD in testing experimentusing β-rays. However, this energy deposited is difficultto determine by experiment, since β-rays have broad en-ergy distribution at low energy. In addition, the experi-ment includes two trigger scintillation counters and flex-ible circuit surrounding DSSD. These materials changethe initial energy of the β-ray. Hence, a simulation studyis necessary to acquire the expected value of the energydeposited in the DSSD.

In this paper, I present a GEANT4 simulation studyof the β-ray testing system for the SVD using 90Sr as thetest source. The energy deposition of β-ray varies withdifferent thickness of the top scintillator in the testingsystem; therefore, a comparison of the energy depositedwith respect to various scintillator’s thicknesses is ana-lyzed. The energy deposited collected from the simula-tion result will be used to calculate the correction factorfor the testing experiments using mips.

II. THE SIMULATION

A. The GEANT4 Toolkit

I use the Monte Carlo simulation package GEANT4,which is widely used in experimental high-energy physicsfor simulating the passage of particles through mat-ter. GEANT4 library include the all the establishedphysics processes that take place in the actual exper-iment. GEANT4 processes individual simulated parti-cles one by one and carries them through the materi-als. When a particle is initiated, GEANT4 calculates themean free path of all the separated physics processes im-

mailto:thong.nguyen@utdallas.edu

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Layer Material Density (g/cm3) Thickness Quantity

Top Scintillator Plastic EJ212 1.03 0.5 mm 1

Bottom Scintillator Plastic EJ212 1.03 8.0 mm 1

DSSD Silicon 2.33 320 µm 1

Glue Epoxy resin 1.15 50 µm 3

Polyimide Kapton 1.413 210 µm 2

Copper Copper 8.96 27 µm 2

TABLE I: Specification of layers in the SVD testing experiment.

plemented, calculates a random distance associated witheach process, and selects that with the shortest distanceto be implemented. It then determines the physics prop-erties of the particle that occur within the process, calcu-lates the state of its new position, and records the trackof the particle until it has no remaning kinetic energy,leaves the volume, or reaches a low-energy threshold [6].Further details about GEANT4 can be found in Ref. [1].

B. The Geometry

FIG. 1: The actual SVD testing experiment.

Figure 2 indicates the schematic design of the SVDtesting experiment. A β-ray, emitted from 90Sr source,hits the two scintillators, triggering the APV25 readoutchip. Consequently, the readout chip obtains the valueof the energy deposited in the DSSD, amplifies and sendit to the ADC. The actual SVD testing experiment isshown in Figure 1.

The SVD consists multiple layers, which are describedin Table I. The two scintillators are also included. Thesespecifications are used in the modeling of the SVD test-ing experiment with GEANT4. Figure 3 shows the visu-alization of the GEANT4 simulation. The distance is notscaled proportionally for presentation purpose. All speci-fications of the simulation, including material, width, anddensity, accurately match the actual experiment’s.

To reduce the energy loss of the passing particles, the

top scintillator should be as thin as possible. However,the thinness can also reduce the scintillator’s efficiency.Therefore, the simulation is repeated with various topscintillator’s thicknesses to study the changes in the trig-ger rate of the two scintillators with respect to differenttop scintillator’s thicknesses. This result can also be usedfor the validation of the simulation with the actual ex-periment.

C. Physics Processes

1. Energy Loss

The energy deposited of particles traveling in the mat-ter due to collision is calculated with the Bethe-Blochformula[8].

−dEdx

= 2πNar2emec

2ρZ

A

1

β2

[ln

τ2(τ + 2)

2(I/mec2)2+ F (τ)− δ − 2C

Z

]where

τ : the kinetic energy of the particle in units of mec2

F (τ) = 1 − β2 +τ2

8−(2r+1)ln2(τ+1)2

for e−

re: classical electron radius = 2.817 × 10−13 cmme: electron massNa: Avogadro’s numberI: mean excitation potentialZ: atomic number of absorbing materialA: atomic weight of absorbing materialρ: density of absorbing materialz: charge of incident particle in units of eβ: v/c of the incident particle

γ: 1/√

1 − β2δ: density correctionC: shell correction

The Bethe-Bloch formula indicates that the energy de-posited of the particle in the material is proportional tothe Z/A ratio. Thus, most materials chosen for the SVDhave the low Z/A ratio to reduces the loss of the particle’skinetic energy.

According to Ref. [8], at low energy, the energy lossdue to collision dominates the process and energy loss dueto Bremsstrahlung radiation is negligible. Figure 4 shows

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FIG. 2: The schematic design of the scintillator trigger system in the SVD testing experiment.

FIG. 3: The visualization of the GEANT4 simulation of the SVD testing experiment.

FIG. 4: Radiation loss vs. collision loss for electronsand protons in copper [8].

the comparison between radiation loss and collision forelectrons. Since the β-rays emitted from 90Sr have themaximum energy of 2.2 MeV, it is safe to ignore the

Bremsstrahlung radiation in the simulation.

2. Radioactive Decay Process

The 90Sr source has two β-decay channels due to theprocesses:

90Sr →90 Y + β−90Y →90 Zr + β−

(1)

The β-ray emitted in the 90Sr decay, whose the half-lifetime is 28.79 years, has the maximum energy of 0.5 MeV.The 90Y decay emits a β-ray with the maximum energyof 2.2 MeV[7] and has the half-life time of 64 hours. Theradioactivity of the Sr90 source used in the SVD testingexperiment is 1.614 MBq.

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FIG. 5: The range-energy curve [9].

3. Mean Range of Particles Traveling in Matters

The mean range of particle is calculated as:

R(T0) = R0(Tmin) +

T0∫Tmin

(dE

dx

)−1dE

where Tmin is the minimum energy at which the dE/dxformula holds, and R0(Tmin) is an empirically deter-mined constant which accounts for the remaining lowenergy behavior of the energy loss [8]. Previously ex-perimental work done by L. Katz and A. S. Penfold [9]establishes a range-energy relation as shown in Figure 5.For a 2.2 MeV electrons in silicon with the density of 1.03g/cm3, the mean range is determined to be 4.5 mm.

D. Detectors and Hits

1. The Sensitive Detector Regions

In order to appreciate the hit pattern in the simulatedSVD it is necessary to describe the sensitive detector re-gions, which include the two scintillators and the DSSDlayer. The top scintillator, which should be thin to re-duce the energy loss of the passing β-rays and maximizethe trigger rate, is made of an 0.5 mm plastic. The bot-tom scintillator is made of the same material with thethickness of 8 mm. Note that the bottom scintillatordoes not need to be thin because it is placed under theDSSD; therefore, its thickness does not affect the energyof the β-ray passing through the DSSD.

The distance between the two scintillators is 30 mm.The DSSD is positioned 9.6465 mm below the top scintil-lator. Every time a particle passing through a sensitivedetector in the simulation, a hit is recorded in a “collec-tion hit,” which contains the information of the passingparticle, including particle ID, track ID, kinetic energy,deposited energy, et cetera. At the end of one event,the collection hit corresponding to each detector is ana-lyzed. If a same track passing through the two scintilla-tors in one event, the energy deposited in the DSSD ofthe track’s particle is stored.

E. Energy Distribution of β-Decays of 90Sr

FIG. 6: GEANT4 simulation of the energy distributionof β-decays from 90Sr.

Figure 6 shows the simulation of the energy distri-bution of the β-rays emitted from 90Sr, generated byGEANT4 using the Monte-Carlo method. Note that90Sr has two β-decay channels, as explained in SectionII C 2. The particles are generated using GEANT4’s Gen-eral Particle Gun. 90Sr particles are “injected” randomlyin the cylindrical space of the 90Sr source, shown in thevisualization in Figure 3. The 90Sr particle decays andemits β-rays, beginning one event.

III. SIMULATION RESULTS AND DISCUSSION

The energy deposited in the DSSD, as shown in Figure7, is fitted with a Landau function. The most probablevalue (MPV), represented by the peak, is 0.103 ± 1.88 ×10−4 MeV. Due to the asymmetric distribution of Landaufunction, the MPV is smaller than the mean value, whichis 0.144 ± 5.91 × 10−4 MeV.

In other SVD testing experiments which use mips asthe test source, the energy deposited in the DSSD is de-termined to be 86 keV. With the mean value of 144 keVdetermined from the simulation with the 90Sr source, acorrection factor of 144/86 = 1.67 can be applied to cal-ibrate the gain value of the APV25 readout chip.

Figure 8 shows the change of trigger rates of the twoscintillators with respect to different top scintillator’sthickness, ranging from 0.5 mm to 5.5 mm. It is ob-served that the rate decreases exponentially as the topscintillator thickness increases. This plot is obtained byinitiating 50 million events in each simulation with differ-ent top scintillator’s thickness and counting the numberof trigger. With the given radioactivity of the 90Sr sourceto be 1.614 MBq, the time it takes for 50 million 90Srparticles to decay is calculated to be 30.97 seconds. The

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FIG. 7: Energy deposited in the DSSD, fitted with aLandau function.

FIG. 8: The trigger rate of the two scintillators withrespect to different top scintillator’s thicknesses. The

plot is fitted with an exponential function.

number of trigger for each top scintillator’s thickness isdivided by 30.97 to obtain the trigger rate.

From the actual experiment, it is determined that noiserate of the trigger, also known as the background, is ap-proximately 0.1 × 10−3 Hz. For most top scintillator’sthicknesses, the trigger rate is much higher than the noiserate. Therefore, the background in the SVD testing ex-periment is negligible.

Figure 9 shows the energy distribution of the energydeposited in the DSSD corresponding to different topscintillator’s thicknesses. As the top scintillator’s thick-ness increases, the number of events decreases since lessβ-rays can pass through the top scintillator and have

FIG. 9: Energy distribution of the energy deposited inthe DSSD with different top scintillator’s thicknesses.

FIG. 10: Mean and MPV of the energy distributionwith respect to different top scintillator’s thicknesses.

enough energy to hit the bottom one. The peaks of dif-ferent distributions, however, do not vary much. Figure10 verifies if the change of the top scintillator’s thicknesscould affect the MPV and mean value of the distribu-tion of the energy deposited. A slight upward trend isobserved as the thickness increases from 0.5 to 5.5 mm.However, the value does not change much for small thick-nesses that are less than 1 mm.

IV. CONCLUSIONS

I have developed a GEANT4 program to simulate theSVD testing experiment and provide the expected valuefor the energy deposited in the DSSD by the β-rays emit-

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ted from 90Sr. The simulation results show that the en-ergy deposition distribution has the mean value of 0.144± 5.91 × 10−4 MeV and the most probable value of 0.103± 1.88 × 10−4 MeV. These values are relatively stablewith small scintillator’s thicknesses that are less than 1mm. A correction factor of 1.67 can be applied to cal-ibrate the gain value of the APV25 readout chip. Thesimulation can be validated with experimental work us-ing the plot of trigger rates corresponding to different topscintillator’s thicknesses.

V. ACKNOWLEDGMENTS

I would like to thank Professor Hiroaki Aihara for pro-viding me with an opportunity to participate in his re-search group. I owe my gratitude to my advisor, Pro-fessor Yoshiyuki Onuki, for his wisdom and patience inexplaining the theories behind the experimental work.Also invaluable was the lecture series in high energyphysics given by Dr. Denis Epifanov. Special thanksgo to my labmates, Jin Yifan, Junya Sasaki, NobuhiroShimizu, Fuminao Hosomi, Hiroko Niikura, and NaruhiroChikuma for valuable discussions. I appreciate the pro-fessional support of the staff members of the Universityof Tokyo Research Internship Program (UTRIP), whohost this program. Last but not least, I am indebted toFriends of UTokyo, Inc. (FUTI) for the generous schol-arship award that financially supports my research.

[1] S. Agostinelli et al., Nucl. Instrum. Meth. A 506, 250(2003).

[2] M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49,652 (1973).

[3] T. Kuhr, (2011), arXiv:1101.1916 [hep-ex].[4] A. G. Akeroyd et al., (2009), arXiv:1002.5012 [hep-ex].[5] T. Abe et al. (Belle II Collaboration), (2010),

arXiv:1101.0352 [physics.ins-det].

[6] S. Tang and D. M. Smith, ApJ 721 (2010).[7] Nuclear Data Sheets (Brookhaven National Laboratory,

2013).[8] W. R. Leo, Techniques for Nuclear and Particle Physics

Experiments: A How-to Approach, 2nd ed. (Springer-Verlag Berlin Heidelberg GmbH, 1993).

[9] L. Katz and A. S. Penfold, Reviews of Modern Physics 24(1952).

http://arxiv.org/abs/arXiv:1101.1916 [hep-ex]http://arxiv.org/abs/arXiv:1002.5012 [hep-ex]http://arxiv.org/abs/arXiv:1101.0352 [physics.ins-det]

A simulation study of the energy deposited in the DSSDwith the 90Sr source for the Belle II ExperimentAbstractIntroductionThe SimulationThe GEANT4 ToolkitThe GeometryPhysics ProcessesEnergy LossRadioactive Decay ProcessMean Range of Particles Traveling in Matters

Detectors and HitsThe Sensitive Detector Regions

Energy Distribution of -Decays of 90Sr

Simulation Results and DiscussionConclusionsAcknowledgmentsReferences