Master Thesis:
Upgrade and Calibration of Super-Kamiokande’s
Inner Photodetectors(スーパーカミオカンデ光電子増倍管の改良型導入と較正)Xia, Junjie
Department of Physics
Graduate School of Science, University of Tokyo
Student ID: 35-176375
E-mail: seanxia@icrr.u-tokyo.ac.jp
Supervisor: Prof. Kajita, Takaaki
July, 2019

Abstract
In the year of 2018∼2019, Super-Kamiokande (Super-K) has completed a detector upgrade to its 5th running phase. One of the major improvements is the 136 new Photomultiplier tubes (PMT) of better photon detection efficiency that were installed to replace thebroken ones inside the tank. Those PMTs are designed for Hyper-Kamiokande (HyperK)—the next generation of large underground water Cherenkov experiment. Thus theiroperation in Super-K will be the very first step of realizing Hyper-K in the near future.
Other than the measurements and tuning of those new PMTs, this work has also improved
and developed new methods for the calibration of Super-K. The individual variance of
PMT’s charge response has been reduced by ∼75%, meanwhile the drift in photon multiplication factor has been corrected so that the present value is close to the initial one
over 10 years ago. In addition, the detector timing has been calibrated with lower systematic uncertainties. The results of these calibrations are now being implemented into
the physics analysis of Super-K. Meanwhile the framework and softwares developed thistime will serve as a sample reference for the next upgrade in 1∼2 years, when Super-K
will for the first time dissolve Gadolinium (Gd) salt into its water.

Acknowledgements
Throughout these 2 years there are many great people who have helped and guided mealong the path of research. First of all, I would like to express my sincere gratitude to
my advisor Prof. Takaaki Kajita who has always been patient and supportive. Other
than this great experience of working at Super-K, he has also always been encouraging
me to explore where my interests truly lie in. Studying and working with Prof. Kajita
is really joyful with absolutely 0 stress in all discussions or group meetings we had. At
the meantime I am grateful to Kimihiro Okumura-sensei and Chieko Mashima-san aswell, who helped with both my research and living in Japan when Prof. Kajita was notavailable given to his super busy schedule.

I could never achieve the results in this work without the help from people including
Prof. Shigetaka Moriyama, Yusuke Koshio-sensei, Yasuhiro Nishimura-sensei, Yasuhiro
Nakajima-sensei, Patrick de Perio, and Hidekazu Tanaka-sensei. Leading the Super-K
calibration group during this detector upgrade period, Prof. Moriyama was the goal
keeper of the whole Super-K calibration who did not let any problem pass his supervision. From the very beginning he has kindly helped me getting familiarized with theSuper-K system and working flows. Meanwhile throughout this calibration work, I havereceived tons of valuable suggestions from him, as well as Koshio-sensei, Nakajima-sensei,
Nishimura-sensei, and Tanaka-sensei to improve the analyses. This calibration was notan easy job, and I still remember those days when I stayed in the mine overnight taking
data with them. From them I have seen a physicist’s academic rigor and unyieldingness.
Patrick was truly a great mentor and friend of mine. Together we worked out a lot for
the new calibration software and I have learned so many in coding from him.

The life in Kamioka to be honest was not so amusing, especially when one needs to drive
more than 15 km for the nearest convenience store. But thanks to my friends: Akira
Takenaga-san, Takumi Suzuki-san, Kouhei Okamoto-san, Nobuyuki Kato-san, Toshiki
Mochizuki-san, Takeshi Okada-san, and Shuichi Imaizumi-san the time in Kamioka wasmemorable with free rides and parties and BBQs.

Last but not the least I would like to say thanks to all of the Super-K collaborators.
Working in such a large collaboration, I still feel connected to every other colleagues foreveryone was so warmhearted and easy to access. I really look forward to the future
journey here as a PhD student.

Contents
List of Figures

3

List of Tables

5

1 Introduction

6

2 Neutrinos

7

2.1

2.2

The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.1.1

Neutrino Interactions in the Standard Model . . . . . . . . . . . .

7

2.1.2

Higgs Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . .

8Neutrino Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

2.2.1

Three-Generation Mixing . . . . . . . . . . . . . . . . . . . . . . .

11

2.2.2

Derivation of Neutrino Oscillations . . . . . . . . . . . . . . . . .

12

2.2.3

Measurements of Neutrino Oscillations . . . . . . . . . . . . . . .

15

3 The Super-K and Hyper-K Experiments

16

3.1

Overview of Super-K . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

3.2

Cherenkov Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

3.3

ID and OD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

3.3.1

Optically Separated Water Tank . . . . . . . . . . . . . . . . . . .

19

3.3.2

The Super-K 50 cm Venetian Blind PMT . . . . . . . . . . . . . .

21

3.4

Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

3.5

Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

3.6

Prospects for Hyper-K . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

4 The Hyper-K 50 cm Box&Line PMT

26

4.1

The Box&Line Dynodes . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

4.2

High Photon Detection Efficiency . . . . . . . . . . . . . . . . . . . . . .

27

4.3

Charge and Time Responses . . . . . . . . . . . . . . . . . . . . . . . . .

28

4.4

Gain Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

4.5

Background Noises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

5 2018 Detector Upgrade
5.1

32

Pre-Calibration of Hyper-K 50 cm B&L PMTs . . . . . . . . . . . . . . .

32

5.1.1

Experiment Setting up . . . . . . . . . . . . . . . . . . . . . . . .

32

5.1.2

Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

5.1.3

Systematic Error Corrections . . . . . . . . . . . . . . . . . . . .

35

5.1.4

Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

1

5.2

5.3

Voltage Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

5.2.1

Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

5.2.2

New Voltage Determination . . . . . . . . . . . . . . . . . . . . .

44

5.2.3

No Change Channels . . . . . . . . . . . . . . . . . . . . . . . . .

49

5.2.4

New Voltage Results . . . . . . . . . . . . . . . . . . . . . . . . .

49

5.2.5

Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

Timing Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

5.3.1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

5.3.2

Time Peak Fitting . . . . . . . . . . . . . . . . . . . . . . . . . .

59

5.3.3

T-Q Curve Fitting . . . . . . . . . . . . . . . . . . . . . . . . . .

61

5.3.4

Global Timing Offset . . . . . . . . . . . . . . . . . . . . . . . . .

65

5.3.5

Timing Correction Quality Checks . . . . . . . . . . . . . . . . .

66

5.3.6

Bad Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

6 Inputs to Super-K Detector Simulation

70

6.1

SPE Charge Distribution for Hyper-K PMTs . . . . . . . . . . . . . . . .

70

6.2

Timing Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

7 Conclusions and Outlook

74

References

772

List of Figures
2.1

The Standard Model of Elementary Particles . . . . . . . . . . . . . . . .

2.2

The Feynman diagrams of neutrino interactions with Charged Current(left) by gauge boson W ± and Neutral Current (right) by Z. . . . . . . .

2.3

8
11

CPT, CP, and T transformations that relate different flavor transition
channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

3.1

Schematic view of Super-K tank and its surroundings . . . . . . . . . . .

17

3.2

A particle moving at speed βc emits Cherenkov light cone in a medium
with refractive index n > 1 . . . . . . . . . . . . . . . . . . . . . . . . . .

18

3.3

Cherenkov radiation spectrum in water . . . . . . . . . . . . . . . . . . .

19

3.4

Cross section of the Super-K water tank . . . . . . . . . . . . . . . . . .

20

3.5

Super module of PMTs . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

3.6

Super-K 50 cm PMT design and QE spectrum . . . . . . . . . . . . . . .

22

3.7

Venetian blind dynode display and the Monte Carlo simulation of secondary electron trajectories . . . . . . . . . . . . . . . . . . . . . . . . .

22

3.8

The Super-K water purification system . . . . . . . . . . . . . . . . . . .

23

3.9

Super-K water temperature in vertical direction . . . . . . . . . . . . . .

23

3.10 Neutrino mass hierarchy sensitivity after 10 years of Hyper-K data collection (1.9 Mton·year exposure . . . . . . . . . . . . . . . . . . . . . . . . .

25

3.11 Constraints on δCP after 10 years of Hyper-K exposure . . . . . . . . . .

25

4.1

Hamamatsu R12600 50 cm B&L PMT . . . . . . . . . . . . . . . . . . .

27

4.2

Box&Line dynode layout . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

4.3

Measured QE of six 50cm B&L PMTs . . . . . . . . . . . . . . . . . . . .

28

4.4

Hyper-K B&L PMT charge and time resolution. . . . . . . . . . . . . . .

29

4.5

B&L PMT linearity measurement . . . . . . . . . . . . . . . . . . . . . .

29

4.6

B&L PMT gain stability measurements. . . . . . . . . . . . . . . . . . .

30

4.7

Hyper-K B&L PMT dark hits . . . . . . . . . . . . . . . . . . . . . . . .

31

5.1

Schematic view of the dark room dark room . . . . . . . . . . . . . . . .

33

5.2

Residual magnetic field at the 7 PMT positions . . . . . . . . . . . . . .

33

5.3

Schematic plot of the electronic circuit . . . . . . . . . . . . . . . . . . .

34

5.4

Hyper-K 50 cm B&L PMT data samples . . . . . . . . . . . . . . . . . .

36

5.5

Channel variation measured by the reference PMT . . . . . . . . . . . . .

37

5.6

Pedestal fluctuation over time . . . . . . . . . . . . . . . . . . . . . . . .

38

5.7

Gain stability check with the reference PMT . . . . . . . . . . . . . . . .

39

5.8

Pre-calibration voltage scan example . . . . . . . . . . . . . . . . . . . .

40

5.9

Reference PMT afterpulse rate . . . . . . . . . . . . . . . . . . . . . . . .

40

5.10 Fitted and raw data PVR . . . . . . . . . . . . . . . . . . . . . . . . . .

41

3

5.11 Measurement and selection of 145 Hyper-K 50 cm PMTs . . . . . . . . .

42

5.12 Schematic view of voltage adjustment experimental set up . . . . . . . .

44

5.13 The spiky feature of SPE charge distribution . . . . . . . . . . . . . . . .

45

5.14 Effect of bin width on the spiky feature . . . . . . . . . . . . . . . . . . .

46

5.15 Super-K PMT SPE fitting example with exponential tail . . . . . . . . .

47

5.16 Super-K PMT SPE fitting example with error function skewed Gaussian48

5.17 Hyper-K PMT SPE fitting example with error function modified Gaussian48

5.18 Voltage scan examples for 3 generations of PMT . . . . . . . . . . . . . .

50

5.19 Example of rejected PMT from the voltage scan . . . . . . . . . . . . . .

50

5.20 Gain comparison for SK-IV and SK-V . . . . . . . . . . . . . . . . . . .

51

5.21 The average voltage curves of 3 PMT generations and the adjusted SK-V
voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

5.22 φ dependence check for SPE peaks . . . . . . . . . . . . . . . . . . . . .

53

5.23 Occupancy dependence check for SPE peaks . . . . . . . . . . . . . . . .

55

5.24 The systematic and statistical uncertainties from fitting of SPE peak. . .

56

5.25 SPE peak check from the 2 different processes . . . . . . . . . . . . . . .

56

5.26 Time walk effect demonstration . . . . . . . . . . . . . . . . . . . . . . .

58

5.27 Timing calibration set ups . . . . . . . . . . . . . . . . . . . . . . . . . .

58

5.28 Example of time-charge 2-D display . . . . . . . . . . . . . . . . . . . . .

60

5.29 The smearing effect to the time peak in the 2nd Q bin . . . . . . . . . .

61

5.30 The difference in time peak between the raw and smeared data . . . . . .

61

5.31 Examples of raw time data peak fitting . . . . . . . . . . . . . . . . . . .

62

5.32 T-Q curve fitting problem in empty Q bins . . . . . . . . . . . . . . . . .

62

5.33 Extrapolation example with PMT channel 9999 . . . . . . . . . . . . . .

64

5.34 Determination of the 0 order constant in T-Q curve. . . . . . . . . . . . .

64

5.35 Global timing difference between the 2 TQ maps . . . . . . . . . . . . . .

65

5.36 The difference between data and fitting in all Q bins of PMT 00014 . . .

66

5.37 Data&fitting agreement check of all ID PMTs . . . . . . . . . . . . . . .

67

5.38 Verification of the time walk effect correction . . . . . . . . . . . . . . . .

67

5.39 Comparison to LINAC data taken during SK-IV . . . . . . . . . . . . . .

68

5.40 Example of scattered distribution in T-Q 2-D display. . . . . . . . . . . .

69

6.1

Ni-Cf data of Hyper-K PMTs . . . . . . . . . . . . . . . . . . . . . . . .

71

6.2

Fitting the SPE charge distribution of Hyper-K PMTs with Ni-Cf data .

72

6.3

Fitting of the integrated timing distribution of Super-K and Hyper-K PMTs. 73

6.4

The timing resolutions of Super-K and Hyper-K PMTs . . . . . . . . . .

474

List of Tables
2.1

Latest measurements of the neutrino mixing angles and mass squared difference.

3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

The Super-K running periods. The last column shows the corresponding
front-end electronic system of each phase. . . . . . . . . . . . . . . . . . .

18

3.2

QBEE system specifications [20] . . . . . . . . . . . . . . . . . . . . . . .

24

4.1

Minimum requirements of the Hyper-K ID PMTs from [21]. . . . . . . . .

26

5.1

Currents and voltages applied to each pair of Helmholtz coils in all 3 spatial
directions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

5.2

The coordinates of the diffuser ball in the tank. . . . . . . . . . . . . . .

44

5.3

Run information of the SN-LD data. The 3rd column shows the voltage
difference of each PMT from the SK-IV setting. . . . . . . . . . . . . . .

45

5.4

The breakdowns of 62 no change PMTs in the voltage adjustment. . . . .

49

5.5

The voltage curve parameter averages of 3 PMT generations. . . . . . . .

51

5.6

Sinusoidal function fitting results of SPE peak φ dependences. . . . . . .

53

5.7

Systematic and statistical uncertainties in SPE peak for the 3 PMT generations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.8

55

The differences in average SPE peak calculated by charge peak - ADC
count converted peak. The first column represents the voltage setting foreach row. The 3 generations of PMT are also listed. The peak differences
are written in units of pC. . . . . . . . . . . . . . . . . . . . . . . . . . .

5.9

57

Averages of the fitted parameters from the time walk effect corrected TQ data of all ID PMTs. The standard deviation in each parameter was
assigned as the uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . .

68

5.10 PMT channels with similar feature to Figure 5.40. In the "largely scatterd"case the data were too scattered that no T-Q curve could be fitted. In the"less severe" case there were some small "blobs" of scatter but still a usable
T-Q curve could be fitted. . . . . . . . . . . . . . . . . . . . . . . . . . .

5

69

1

Introduction

Neutrino, a neutral lepton that only interacts through the weak coupling and gravitational
force, has been one of the most popular topics of particle physics study for generationsof people. Thanks to its low interaction rate, a neutrino may survive an extremely long
distance to an observer, which makes it a good messenger of astrophysical sources whereother particles are easily scattered and absorbed along the track. However, the exact
same merit also makes it incredibly hard to detect. Over the past several decades, theprogress in neutrino physics study was prominent. The observation of Supernova 1987A’s
neutrino by Kamiokande experiment [1] has manifested the great potential of neutrinos
in astrophysics research. Later on the neutrino oscillation proven by Super-K experiment[2] and SNO experiment [3] has opened a gate to new physics beyond the Standard Model.
Started in 1996, Super-K has been pioneering in neutrino observation for more than
20 years. In 2018, it has ended its longest running period, which lasted for more than
10 years, for a full scale detector upgrade. One of the major purposes was to prepareSuper-K for the future operation with Gd dissolved water, or so called SK-Gd. The upgrade started in June 2018 and ended in January 2019, with a variety of refurbishments
finished including a new water circulation system, leakage proof upgrading, rust and dust
removal inside the tank, PMT replacement, etc. In total there were 136 PMTs installed
to replace the dead channels of Super-K Inner Photodetector (ID). Those new PMTs are
Hamamatsu R12860 50cm Box&Line PMTs, which are designed for the next generation
experiment—Hyper-Kamiolande (Hyper-K).
Chapter 2 gives a summary of the Standard Model, the Higgs mechanism and Electroweak
symmetry breaking, and the theoretical background and experimental measurements ofneutrino oscillations.
Chapter 3 briefly introduces the Super-K experiement and its successor Hyper-K, with
their design and detection mechanism. Meanwhile Chapter 4 focuses on various advantages of the new 50cm B&L PMT.
A detailed description about the 2018 detector upgrade is given in Chapter 5. section
5.1 describes the measurement and quality check of 50cm B&L PMTs before their installation. Section 5.2 and 5.3 talk about the major calibration tasks involved in this work
respectively—the voltage adjustment and timing calibration of all ID channels after the
installation of new PMTs.

6

Finally Chapter 6 talks about the application of calibration data from this work to SuperK’s Monte Carlo (MC) simulation and its implication for the future analysis.

2

Neutrinos

This section introduces the physics and mathematical backgrounds of the Standard Modeland neutrino oscillation. Most of the discussion follows the books by C. Giunti and C.
W. Kim [4], M. Srednicki [5], and M. Thompson [6].

2.1

The Standard Model

The Standard Model of particle physics is the theory describing three fundamental forces:
the electromagnetic, weak and strong couplings, and the elementary particles involved inthese interactions. As shown in Figure 2.1, the particles composing matters are named
fermions meanwhile the fundamental force carriers are named bosons. In the family offermions the particles can be further divided into 2 groups according to their electriccharges, i.e. quarks with fractional charges (+2/3 or -1/3) and leptons with integer
charges (-1 or 0). Besides the 12 fermions shown in Figure 2.1, each has its own antiparticle with exactly opposite electric charge except for neutrinos. Therefore all the
charged fermions are known as Dirac fermions given to the discrepancy between theirantiparticles and themselves, while it is still unclear whether neutrinos are Majorana or
Dirac fermions.
2.1.1

Neutrino Interactions in the Standard Model

For the lepton sector of the Standard Model, 2 fundamental forces are available: electromagnetic interaction mediated by photon and weak by W± and Z bosons. The aforementioned 4 gauge bosons arises from the spontaneous symmetry breaking of electroweak
symmetry SU (2) × U (1) through the Higgs Mechanism. After the symmetry breaking,electromagnetic interaction acts on a particle’s charge eigenstate, while weak interaction
acts on flavor. Therefore due to the lack of a finite charge, neutrinos can only interact
through the weak forces as shown by Figure 2.2, in which the l∓ represents all 3 generations of the charged leptions (anti-leptons) and νl (ν̄l ) represents the corresponding
neutrino (anti-neutrino). To conserve the lepton number in one interaction, neutrino
νl can only interact with lepton l− , while anti-neutrino ν̄l is only associated with anticharged lepton l+ .

7

Figure 2.1: The Standard Model of Elementary Particles [7]2.1.2

Higgs Mechanism

To understand why such interactions shown in Figure 2.2 are so "weak", we can startwith the minimal Higgs model of 2 complex scalar fields in weak isospin doublet:
 +


φ
1 φ1 + iφ2
φ==√φ0
2 φ3 + iφ4(2.1)

where φ0 is a neutral scalar field and differs from the charged field φ+ by 1 unit of charge.
The Lagrangian for this doublet is

L = (∂µ φ)† (∂ µ φ) − V (φ)
where V (φ) is the Higgs potential

V (φ) = µ2 φ† φ + λ(φ† φ)2

8

(2.2)

For negative µ2 , at the potential minimum the fields satisfies
1v2µ2
φ† φ = (φ21 + φ22 + φ23 + φ24 ) =
=−
2
2
2λ
Since photon after symmetry breaking is massless, the minimum of the Higgs potential
must be non-zero for the neutral field φ0 . Expanding this field about the minimum
with the Higgs field h(x) while removing the Goldstone fields by gauge transformation
gives


0
1
φ(x) = p(2) v + h(x)To find the masses of gauge bosons and the interaction terms in the resulted Lagrangian,or Salam-Weinberg model, first switch the derivative in Eq.2.2 to a covariant one∂µ → Dµ = ∂µ + igW T · Wµ + ig 0

Y
Bµ
2

(2.3)

where T = 21 σ are the SU (2) symmetry generators. According to the Glashow-SalamWeinberg model, the hypercharge of Higgs doublet Y = 1. From1
Dµ φ = p
2 (2)

(3)

(1)

(2)

2∂µ + igW Wµ + ig 0 BµigW [Wµ − iWµ ](1)2∂µ − igW Wµ + ig 0 Bµ

(2)

(3)

igW [Wµ + iWµ ]

!


0
v+h

(2.4)

the (Dµ φ)† (Dµ φ) term in the Lagrangian that determines gauge bosons masses turns out
to be

 1


1 2 2
v gW Wµ(1) W (1)µ + Wµ(2) W (2)µ + v 2 gW Wµ(3) − g 0 Bµ gW W (3)µ − g 0 B µ
|8
{z
} |8
{z
}
W±

(2.5)

Z, γ

Through the symmetry breaking W (1) and W (2) Goldstone bosons combine into the W ±bosons of weak interaction, and W (3) and B ended up with the Z boson and photom γ.
Since the mass term of scalar field in the Lagrangian are1
1 2
mW Wµ(1) Wµ(1) and m2W Wµ(2) Wµ(2)229the mass of the W Goldstone boson is therefore
1
mW = gW v
2(2.6)

which is determined by the coupling constant of the SU (2)L gauge interaction gW andthe Higgs field vacuum expectation value. The two W Goldstone bosons construct thebasis of charged W ± bosons through a linear combination:1
W ± = √ (W (1) ∓ iW (2) )2
Meanwhile the masses of the other 2 Goldstone bosons can be found by diagonalizing thematrix2
gW−gW g 0−gW g 0g 02!

After diagnolization the second part in Eq. 2.5 can be rewritten in the diagonal basis(Aµ , Zµ ) by
00
1 2v Aµ Zµ )280 gW + g 02

!

Aµ
Zµ



where

(3)

Aµ =

g 0 Wµ + gW Bµp2
gW+ g 02= cos θW Bµ + sin θW Wµ(3)
(3)

Zµ =

gW Wµ − g 0 Bµp2
gW
+ g 02= − sin θW Bµ + cos θW Wµ(3)Relating the interaction term from the diagonal basis to the corresponding mass term in
the Lagrangian and find1
mA = 0 and mZ = v
2

q

2
gW
+ g 02(2.7)

which can be identified as the massless photon and massive Z boson in the flavor basis.

10Thus as shown by Eq. 2.6 & Eq. 2.7, the weak interaction gauge bosons W ± and Z
gain their masses from the Higgs field. With the experimental measurements for thetwo masses at around 80 GeV and 91 GeV respectively, the coupling constant of weakinteraction is accordingly much smaller than that of the electromagnetic interaction due
to the −q21−m2 dependence of the propagator.
νl (ν̄l )l∓l∓ , p, nW∓νl (ν̄l )l∓ , p, nZl∓νl (ν̄l )νl (ν̄l )Figure 2.2: The Feynman diagrams of neutrino interactions with Charged Current (left)
by gauge boson W ± and Neutral Current (right) by Z.

2.2

Neutrino Oscillations

The Standard Model has predicted neutrinos as massless, left handed fermions. However,with multiple experiments having verified the non-zero probability of neutrino oscillations,
it becomes obvious that neutrinos are massive particles. So far the neutrino oscillation
has remained as the only experimentally verified phenomenon beyond the scope of theStandard Model.
2.2.1

Three-Generation Mixing

The reason of neutrino oscillation originates from the difference in 2 eigenbases. In theStandard Model, there are 3 flavor eigenstates of neutrinos forming a complete orthonormal basis: νe , νµ , and ντ , labeled according to their partner charged leptons in a Charged
Current (CC) weak interaction. Meanwhile, one can also construct a mass eigenbasis forthe free particle Hamiltonian: ν1 , ν2 , and ν3 . It has been verified that these 2 bases are
not the same. The rotation matrix linking on to the other can be written as
  
 
νe
Ue1 Ue2 Ue3
ν1
  
 
νµ  = Uµ1 Uµ2 Uµ3  ν2 
  
 
ντ
Uτ 1 Uτ 2 Uτ 3
ν3
11

(2.8)

where the mixing matrix U is named the PMNS matrix after Pontecorvo, Maki, Nakagawa, and Sakata in reverence to their contributions to the neutrino mixing model.
In Eq.2.8, only 3 generations of neutrino are considered. Note that the degree of theeigenbasis can be larger than 3 with the existence of sterile neutrinos, which are candidate sources of the neutrino masses. In the three-generation case of the Standard Model,
the PMNS matrix can be further parameterized by 3 mixing angles θ12 , θ23 , θ13 , and 1
CP-violating δCP phase in the case of Dirac neutrinos or 2 phases λ2 , λ3 of Majorana
neutrinos.



Ue1 Ue2 Ue3






U =
U
U
U
µ1
µ2
µ3


Uτ 1 Uτ 2 Uτ 3



−iδCP
c12 c13s12 c13
s13 e
1
0
0



λ2
−i
iδ
iδ



CP
CP
= −c23 s12 − s23 c12 s13 e
c23 c12 − s23 c12 s13 e
s23 c13  0 e 2
0 

λ
−i 23
iδCP
iδCP
s23 s12 − c23 c12 s13 e−s23 c12 − c23 s12 s13 e
c23 c13
0
0
e
 




1
0
0
c12 s12 0c13
0 s13 e−iδCP
1
0
0
 




 −s12 c12 0 0 e−i λ22


=
0
1
0
0
c
s
0
23
23
 




λ3
0
0 1
−s13 e−iδCP 0
c13
0 −s23 c23
0
0
e−i 2
|
{z
}

exists only if Majorana neutrinos

where cij = cos θij and sij = sin θij for (i, j = 1, 2, 3).
2.2.2

Derivation of Neutrino Oscillations

Since the neutrino mass states |νk i are eigenstates of Hamiltonian with energy eigenvalue
Ek , the Schrodinger equationid|νk (t)i = H |νk (t)idt

implies that the neutrino mass evolve in time as plane waves:|νk (t)i = e−iEk t |νk i (k = 1, 2, 3)(2.9)

Yet since the flavor eigenstates are the observables, applying the PMNS matrix on themass eigenstates to map to the flavor states12

|να (t)i =X∗ −iEk t
Uαke|νk i (α = e, µ, τ )(2.10)ksuch that|να (t = 0)i =

X

∗
Uαk
|νk i = |να ikUsing the unitary relation U † U = 1 and rewrite the mass states as a combination offlavor states|νk i =

X

Uαk |να i(2.11)

∗ −iEk t
Uαke
Uβk |νβ i(2.12)α

Substituteing Eq.2.10 with Eq.2.11 gives|να (t)i =X X
β=e,µ,τ

kThus, the initial single flavor state |να i becomes a superposition of different flavor states
at t > 0 given to the non-diagonality of the PMNS matrix U . The transition probability
is thenPνα →νβ (t) = | hνβ |να (t)i |2
X
∗
∗
Uαk
Uβk UαjUβj e−i(Ek −Ej )t=(2.13)k,j −i∆m2 t 
kj
∗
∗
=
Uαk
Uβk Uαj Uβj
exp
2E
k,j
X

where in the case of ultra-relativistic neutrino

Ek =

q

m2k
2
2
p + mk ≈ E +2E

E = |p|∆m2kj = m2k − m2j
However since a neutrino’s travel time is usually unknown in experiment, it is practicalto substitute t = L since the speed of neutrino’s approximates the speed of light c.
Thus

13

Pνα →νβ (L, E) =

 −i∆m2 L 
kj
∗
∗
exp
Uβk Uαj Uβj
Uαk
2E
k,j

X

(2.14)

Therefore by observing the non-zero probability of neutrino oscillations, one can measure
the 3 mixing angles θ12 , θ23 , and θ13 of the PMNS matrix as well as the mass squared
difference ∆m2ij among the 3 neutrino generations.
The oscillation of anti-neutrinos can be derived in a similar way. Again starting from therotation between flavor and mass eigenbasis of anti-neutrinos|ν̄α i =X

Uαk |ν̄k i(2.15)k

one can finally achieve the transition probability of anti-neutrinos asPν̄α →ν̄β (L, E) =

 −i∆m2 L kj∗∗
Uαk UβkUαjUβj exp
2Ek,jX(2.16)The difference between neutrino and anti-neutrino oscillation probabilities can be seen
easily if rearranging Eq.2.14 and Eq.2.16 intoPνα →νβ (L, E) = δαβ − 4hi −i∆m2 L kj∗∗
Re UαkUβk Uαj Uβj
sin2
4E
k>j

X

h
i
 −i∆m2 L 
kj
∗
∗
+2
Im UαkUβk Uαj Uβj
sin
2E
k>j

(2.17)Xandi
 −i∆m2 L 
h
kj
∗
∗
2
Pν̄α →ν̄β (L, E) = δαβ − 4Re Uαk Uβk Uαj Uβj sin
4E
k>j
X

−2

X

Im

h

∗
∗
Uαk
Uβk Uαj Uβj

k>j

i

sin

 −i∆m2 L (2.18)kj

2E

As shown in Figure 2.3, the CP transformation changes the να → νβ to ν̄α → ν̄β . Since the
PMNS matrix is complex, it will naturally lead to the violation of CP symmetry for α 6= βas the imaginary part differs between the Pνα →νβ and Pν̄α →ν̄β in Eq.2.17 and Eq.2.18. Sucha violation can be checked by comparing the appearance and disappearance of neutrino
14

Figure 2.3: CPT, CP, and T transformations that relate different flavor transition channels. [4]and anti-neutrino in the same flavor transition channel, with precise measurement of theenergy and momentum of particles.
The CP asymmetry can be written asACPαβ = 4hi
 −i∆m2 L kj∗∗
Im UαkUβk Uαj Uβj
sin
2E
k>j

X

(2.19)

which only depends on the Dirac phase δCP in the mixing matrix since E and L canbe controlled as the same for neutrino and anti-neutrino. Therefore it is another mixing
parameter that is under intense study at present.
2.2.3

Measurements of Neutrino Oscillations

In general, the current facilities being used for neutrino oscillation measurement can be
categorized by the origin of target. One is for the atmospheric, solar, and cosmic neutrinos
that are generated in nature, the other is for the artificial neutrinos from nuclear reactor
or particle accelerators. For example, Super-K simultaneously collects solar, atmosphericand beamline neutrino data, meanwhile keeps monitoring the neutrino outburst from supernovae, γ-ray bursts, and other cosmic sources. For any of the neutrino sources, thedeterminant factor of sensitivity to the mass squared difference ∆m2 is the ratio of EL
as shown in Eq.2.14. For example, the transition baseline of solar neutrinos will be thedistance between the sun and the earth, which is about 1011 m. Meanwhile the solar
neutrinos are typically of an energy range of 0.1∼10 MeV [8], which gives a sensitivity to∆m2 ' 10−12 eV2 .
As mentioned in Section 2.2.2, the mixing angles θij and Dirac phase δCP are sensi15

sin2 θ12

0.307 ± 0.013

2(2.12 ± 0.08) × 10−2sin θ130.421+0.033−0.025 (IH, quad. I)
0.592+0.023−0.030 (IH, quad. II)2sin θ230.417+0.025−0.028 (NH, quad. I)
0.597+0.024−0.030 (NH, quad. II)(7.53 ± 0.18) × 10−5 eV2

∆m221
∆m232

(−2.56 ± 0.04) × 10−3 eV2 (IH)
(2.51 ± 0.05) × 10−3 eV2 (NH)

Table 2.1: Latest measurements of the neutrino mixing angles and mass squared difference.
tive to the neutrino oscillations and have been measured by a variety of experiments.
Table 2.1 summarizes the latest constraints on the mixing angles and mass squared difference from [9]&[10]. The precise result of the mixing angles θij plays a critical role inthe determination of neutrino mass hierarchy, i.e. either it is a Normal Hierarchy (NH)where m1 < m2 < m3 or an Inverted Hierarchy (IH) m3 < m1 < m2 . On the other hand,the possible CP violation may be the key to understand the Baryonic asymmetry of theuniverse. Although still with some ambiguity, recently T2K experiment has excluded the
CP-conserving value of δCP by 2σ confidence level [11].

3

The Super-K and Hyper-K Experiments

This chapter describes the Super-K detector in details and also the design plan of HyperK experiment. The two experiments share the same scientific goal—searching for proton
decay and observing neutrinos from both natural and artificial sources as mentioned in
Section 2.2.3. But Hyper-K is expected to be over 8 times more efficient in statistic
accumulation than Super-K.

3.1

Overview of Super-K

The Super-K detector lies about 1000 m beneath the peak of Mt. Ikenoyama, Gifu
Prefecture, Japan. The overburden rock shields cosmic rays of energy lower than 1.3
TeV, helping to reduce the background noise in the detector [12]. The stainless steel
cylindrical water tank has a diameter of 39 m and height of 42 m, containing in total
50,000 tons of water. Figure 3.1 illustrates the schematic view of the Super-K facilities.
To mitigate the geomagnetic field in the tank, which can cause systematic bias in the16measurement, 26 sets of horizontal and vertical Helmholtz coils are mounted to the tank’s
inner suface. With the current applied in the Helmholtz coils, the average magnetic field
inside the tank has been reduced from 450 mG to 50 mG measured in air [12].

Figure 3.1: Schematic view of Super-K tank and its surroundings [13].
There were 4 running periods done in Super-K and the 5th current one is therefore called
SK-V. A chronological summary of the Super-K running period prior to SK-V is given in
Table 3.1. During the water refilling in 2002 after the maintenance work, an implosion ofa single ID PMT happened under water and destroyed more than half of the PMTs by theshock wave. This caused the ID Photo-Coverage rate dropping to 19% during the SK-II
period, during which only about half of the PMTs were operating. The replacement of
all broken PMTs was finished by 2006. To prevent such a tragedy from happening again,a Fibre-reinforced plastic (FRP) case was attached to each PMT for protection. In 2008,
the front-end electronics has been upgraded from Analog-Timing-Module (ATM) to QTC(charge to time)-Based Electronics with Ethernet (QBEE). The latter is currently in use
in SK-V.

3.2

Cherenkov Radiation

To detect the particle interaction happening inside the water tank, Super-K searches forlight cones that causes rings of hits in the PMTs. From the topological feature of the ringand its number of photons, the incoming particle’s direction, vertex position, and momentum can be reconstructed. Such a light cone that provides crucial information of physics
observation originates from the Cherenkov radiation of moving charged particles in water.
17

SK-I

Apr, 1996 - Jul, 2001

40% ID Photo-Coverage

ATM

SK-II

Oct, 2002 - Oct, 2005

19% ID Photo-Coverage

ATM

SK-III

Jul, 2006 - Sep, 2008

40% ID Photo-Coverage

ATM

SK-IV

Sep, 2008 - Jun, 2018

40% ID Photo-Coverage

QBEE

Table 3.1: The Super-K running periods. The last column shows the corresponding
front-end electronic system of each phase.

Although the speed limit of moving objects by the speed of light c in vacuum is wellestablished [14], it is still possible that an ultra-relativistic charged particle can movefaster than light in some medium like water since c is reduced in this case. The signatureof such a phenomenon is a conical wave front of light emitted from the particle as shownin Figure 3.2, which was first predicted by Oliver Heaviside in the 19th century [15]. The
experimental observation was first done by the Soviet physicist Pavel Cherenkov in 1934[16], and therefore named after him.

Figure 3.2: A particle moving at speed βc (direction indicated by the red arrow) emits
Cherenkov light cone (blue arrows) in a medium with refractive index n > 1 [17].
From Figure 3.2 the relation of Cherenkov light cone opening angle and the speed ofparticle can be related ascos θC =

1
nβ

(3.1)

where β is the ratio of particle’s speed to the speed of light in vacuum. It is clear to see
18that opening angle can only be greater than 0 in the limit ofnβ > 1
Therefore the ability of a particle to produce Cherenkov radiation in a medium is determined by its own kinetic energy. In the case of pure water whose refractive index isn ≈ 1.34, the Cherenkov light cone produced by an ultra-relativistic particle with β ≈ 1is roughly 42◦ .
The number of photons emitted per unit length per unit wavelength is formulated by
 2πα
d2 N
2πα 
1
= 2 1− 2= 2 sin2 θC
(3.2)
dLdλ
λ
β n(λ)2λwhere α is the fine structure constant, L the distance traveled by the particle, and λ thewavelength. The Cherenkov radiation spectrum in water of wavelength range 300∼600
nm is shown in Figure 3.3.

Figure 3.3: Cherenkov radiation spectrum in water from [13].

3.3

ID and OD

The Super-K tank is optically separated into the ID and OD (stands for Outer-Photodetector).
This section will discuss the reason of this design and how the ID and OD work together
for physics observation. Most of the details in this chapter from this section are takenfrom ref. [12].
3.3.1

Optically Separated Water Tank

A cylindrical stainless-steel frame, mounted with 11,146 inward-facing 50 cm PMTs
(Hamamatsu R3600) called ID and 1885 outward-facing 20 cm PMTs (Hamamatsu R1408,
19

partially replaced during the 2018 detector upgrade) called OD, divides the tank into 2
sections with water freely flow in between. This is to further improve the selection of
Cherenkov radiating particle originated in the tank aprart from the through going cosmic
muons, which will be also detected and vetoed by the OD. The inner section is 33.8 m
in diameter and 36.2 m in height, meanwhile there is slightly more than 2.5 m of wateroutside each surface of the frame. The region with more than 2 m away from the frame
inside ID is a special section, because only the interactions in this region are "fully contained (FC)" events being used for real physics analysis. The FC section contains 22,000
tons of water. On the other hand, since the PMT-supporting frame itself is about 55 cm
thick, it causes a dead zone that is not monitored by either the ID or OD. Figure 3.4
shows the schematic view of ID and OD inside the tank.

Figure 3.4: Cross section of the Super-K water tank [12]The ID PMTs are grouped into 3×4 arrays in one super module of the stainless-steel
frame as shown in Figure 3.5. On the side of ID PMTs, opaque black polyethylene telephthalate sheets are used to prevent the light leaking from the inner tank into the outer.
At the same time they also help to absorb the residual photons from the radioactivity inthe back of PMTs. On the side of OD, each PMT is attached with a Wavelength-Shifting(WS) plate made by acrylic to enhance its light collection efficiency. Meanwhile all of the
OD frame surface is covered with a reflective layer made from Tyvek R sheets. The reflection rate was measured to be on the order of 90% near the peak wavelength of PMT’s
sensitivity.
20

Figure 3.5: Super module of PMTs [12].
3.3.2

The Super-K 50 cm Venetian Blind PMT

A schematic demonstration of the Super-K 50 cm PMT is shown in Figure 3.6 (a). Oneof the key characters of a PMT is quantum efficiency (QE), which means the probability
the photocathode will emit an electron by absorbing an incoming photon. The bialkali(Sb-K-Cs) photocathode used in the Super-K 50 cm PMT was measured to have peak
QE of about 21∼22% at 360-400 nm as shown in Figure 3.6 (b).
The phrase "venetian blind" stands for the PMT dynode structure, which is illustrated
in Figure 3.7. It was noticed that a venetian blind dynode structure may cause thephotoelectron missing the next stage dynode plate and results in the underperformanceof a PMT’s photon Collection Efficiency (CE). Sophisticated study was done to regularize
the electron multiplication process in the Super-K 50 cm PMTs so that its CE was
improved by about 50% compared to other venetian PMTs of the similar size [18]. In
Super-K, the gain of ID PMTs, i.e. the photon multiplication factor, was set to the orderof 107 so that they would be sensitive to supernova neutrinos.

21

(a) PMT schematic drawing(b) QE spectrum

Figure 3.6: Super-K 50 cm PMT design and QE spectrum [12].

Figure 3.7: Venetian blind dynode display and the Monte Carlo simulation of secondary
electron trajectories [18].

3.4

Water

The water quality is essentially critical for the success of Super-K, for an over-abundanceof dust in the water will cause too much scattering and absorption of Cherenkov lightthat decreases the detector sensitivity. Another big contamination in water comes fromthe dissolved radon gas, which is common for underground facilities and may cause false
signal by its radioactivity. Other contaminations include micro creatures and bacterias,
as well as heavy particles from the impurity. To remove these contaminations, SuperK adapts both water and air purification systems. The water is circulated in Super-K
through series of filters at a rate of 60 tons/hour as shown in Figure 3.8. Meanwhile fresh
air from outside is continuously pumped into the tank to reduce the underground radon
concentration.
Since the major part of a PMT’s dark noise is from its thermal electron emission, it is22

Figure 3.8: The Super-K water purification system [13].
necessary to keep the water temperature low and stable. The heat exchangers in thewater purification systems maintain the water temperature at ∼13◦ C, monitored by thethermometers inside the tank. Meanwhile a full convection is achieved in the bottom ∼10
m, which keeps the temperature uniform in that region. Due to the lack of convection in
the higher part of the tank, a 0.2◦ C top-bottom asymmetry in temperature was observed
as shown in Figure 3.9.

Figure 3.9: Super-K water temperature in vertical direction [19].

23Number of inputs

24∼ 900 ns/cycle

Processing speed of QTC
Number of ranges

3 (small, medium, large)

Discriminator-0.3 to -14 mV (small range)

Charge dynamic range

0.2 to 2500 pC

Charge resolution∼0.2 pC (small range)

Charge Linnearity<0.1%
0.3 ns (2 pC input)

Timing resolution< 0.2 ns (> 10 pC input)

Power consumption< 1 W/ch

Table 3.2: QBEE system specifications [20].

3.5

Data Acquisition

At the beginning of SK-IV in 2008, the data acquisition (DAQ) system was updated to
QBEE, which can process 100 times more events in a 10 s interval than its predecessor:
the ATM system [20]. The specifications of QBEE are listed in Table 3.2. An analog PMT
signal is first digitized by the QBEE system to get the hit time and charge information.
Meanwhile online PCs continuously collects the "hits" into a software trigger buffer, inwhich an event trigger will be issued once the total number of PMT hits within 200 ns
interval has exceeded a preset threshold. The events accompanied by a trigger are treatedas physics data and saved on disk for analyses.

3.6

Prospects for Hyper-K

This section introduces briefly the plan and physics goal of Hyper-K following the description in the 2018 Hyper-K design report [21]. The water tank design of Hyper-K is similar
to the Super-K one described in Section 3.3, but much larger—74 m in diameter and 60 m
in height. Thus the FC section of real physics analyses in Hyper-K will be 8 times as big
as that of Super-K’s. As a result Hyper-K is expected to accumulate data much faster,which helps to push forward the neutrino oscillation studies which is currently limited by
the lack of statistics. Same with Super-K, Hyper-K will have 40% Photo-Coverage as well.
With the cavern excavation to be started in 2020, Hyper-K is expected to start its firstdata collection in about a decade from now. It has a great physics potential in neutrino and nucleon decay observation. For neutrino oscillation study, Hyper-K is expected
to finalize measuring the mixing angle and Dirac phase mentioned in Section 2.2 and24

hence determine the mass hierarchy and CP violation problem. Predictions of Hyper-K’s
sensitivity to this two quantities are given in Figure 3.10 and Figure 3.11 respectively.

Figure 3.10: Neutrino mass hierarchy sensitivity after as a function of the true value ofsin2 θ23 after10 years of Hyper-K data collection (1.9 Mton·year exposure. The blue (red)band denotes the NH (IH), with the bad width representing the uncertainty from δCP[21].

Figure 3.11: Constraints on δCP after 10-year-long Hyper-K exposure. Different neutrino
sources are denoted with different colors. Cyan and blue lines show the constraints fromatmospheric neutrino sample and beam neutrino sample individually, The red curve isthe combination of the 2. The left (right) figure assumes δCP = 0◦ (δCP = 90◦ ), withsolid (dashed) curves representing NH (IH) [21].

25Requirements

Value

Based onConditions

Photon detection effi-

26%

Avg.

QE × CE at wavelength ∼ 400

ciencynm(10%)(including Photo-Coverage on
the inner detection area)

Timing Resolution

5.2 ns

FWHM, Avg.

Single Photoelectron (SPE)Charge resolution

50%

σ, Avg.

SPE

Signal window

200 nsMax.

Time window covering morethan 95% of total integrated
charge2

Dynamic range

2 photon/cm

Min.

Gain

107 ∼ 108

Avg.

Afterpulse rate

5%

Max.

Per detection area on wall
For SPE, relative to the primary pulse

Rate tolerance

10 MHzMin.

SPE pulse, within 10% changeof gain

Magnetic field toler- 100 mG

Min.

Within 10% degradation

anceLife time

20 years

Min.

Less than 10% dead rate

Pressure rating

0.8 MPaMin.

Static, load in water

Table 4.1: Minimum requirements of the Hyper-K ID PMTs from [21].

4The Hyper-K 50 cm Box&Line PMTAmong the many upgrades of Hyper-K from Super-K, the ID PMT is one of those mostimportant. Aiming to finally solve the mass hierarchy and CP violation problem thathas been challenging physicists for decades, Hyper-K is in need of an advanced PMTthat is competent for the demanding nature of precise neutrino oscillation observation.
The minimum requirements for Hyper-K’s photosensors are listed in Table 4.1, There aremany candidates, and the Hamamatsu R12860 50 cm Box&Line (B&L) PMT (Figure4.1) is one of them. This chapter demonstrates some of its key characteristics, most ofwhich can also be found in the ref. [21].

4.1

The Box&Line Dynodes

The Box&Line stands for the specific dynode arrangement of this PMT as shown in
Figure 4.2. The first dynode plate, which is larger than any others, is called the "Box"26

Figure 4.1: Hamamatsu R12600 50 cm B&L PMT
and is known for large photon coverage. Meanwhile the series of small plates is called the"line" and helps to improve PMT’s linearity.

Figure 4.2: Box&Line dynode layout with electron trajectories. Electrons enter from thebottom at where the photocathode locates [21].

4.2High Photon Detection Efficiency

The profoundest improvement of the B&L PMTs compared to the Super-K Venetian blind
ones is its superior photon detection efficiency, which is QE × CE in Table 4.1. Figure
4.3 compares the QE between the Hyper-K B&L and Super-K Venetian blind PMTs. At
the peak wavelength of ∼390 nm, the former has a typical QE of 30% whereas the latterhas only 21∼22% as aforementioned in Section 3.3.2.
Although great efforts were made to improve the Super-K Venetian blind PMT’s CE by27

Figure 4.3: Measured QE of six 50cm B&L PMTs (solid lines) and Super-K Venetian
Blind PMTs (dashed lines) [21].
large, it still remained at 73% within the 46 cm cross section of the photocathode. In
comparison, the Hyper-K B&L PMT has 95% CE in the same area and as high as 87%
within the full size of 50 cm. It was achieved by the new B&L dynode structure as wellas the optimized glass curvature and focusing electrode. At SPE level, the CE of B&L
PMT was measured to be 1.4 times that of the Venetian blind PMT’s, and hence resulted
in an improvement in QE×CE by a factor of 1.9.

4.3

Charge and Time Responses

Thanks to the large photon coverage of the "Box" dynode, the SPE hit rate has increased
in a B&L PMT largely and therefore improved the SPE charge resolution, which is definedby the ratio of SPE pulse width in σ to its peak position. The B&L PMT’s SPE charge
resolution was measured to be 30.8% and the Venetian blind 60.1% as shown in Figure
4.4(a). On the other hand, the rise time of SPE pulse in a B&L PMT is ∼40% faster thanthe Venetian blind PMT, meanwhile the former’s Transit Time Spread (TTS) caused bydifferent electron traveling time was measured to be 1.23 ns in σ, which is over 50% better
than latter’s at 2.86 ns (Figure 4.4(b). The aforementioned comparison results of SPE
charge resolution and TTS are based on a measurement done in the Super-K site with
145 B&L PMTs and 6 Venetian blinds, at a gain of 1.4 × 107 [22].

4.4Gain Stability

The PMT’s charge response range is crucial for observing a wide energy range of particles.
It is possible that a large number of photons hitting the PMT simultaneously may fully
dissipate the available electrons in the photocathode and cause saturation in the PMT

28

A.U.

A.U.

1.6
HK PMT

1.4

1

HK PMTSK PMTSK PMT

0.8

1.2
1

0.6
0.8
0.4

0.6
0.4

0.2
0.2
0
−2

0

2

4

6

0
−20

8
Charge [pC](a) SPE charge resolution in σ

−15

−10

−5

0

5

10

15
20
Time [ns](b) SPE time resolution in σ

Figure 4.4: Hyper-K B&L PMT charge and time resolution, with blue (red) curves denoting the Super-K (Hyper-K) PMT.
output, i.e. charge no longer increases with light intensity. To confirm that the B&L
PMT is suitable for the physics tasks of Hyper-K, a measurement on charge linearity wasdone and verified that the B&L PMT’s charge output is in 95% agreement with expectedvalue up to a signal of 470 photo-electrons (PEs) as shown in Figure 4.5. Moreover, thesaturation level was measured to be more than 1,000 PEs. Therefore for the signal lower
than 1,000 PEs the charge output will be reliable with the correction from the non-linear
effect derived from Figure 4.5.

Figure 4.5: Measured charge output linearity of B&L PMT. The red dotted line represents
the perfect linear case [21].
Since these PMTs are designed for over 20 years of life span, it is also important to make29

sure that the PMT’s performance does not degrade too much with aging. To confirm
this, the gain of 3 B&L PMT samples was monitored over 2 years in a 200 ton watertank in the Super-K site, which was originally constructed for the feasibility study of Gd
dissolved water. The result turned out to be good, with negligible change and only 1%(at RMS) fluctuation in all 3 tubes. A 2-month window snapshot of this monitoring isshown in Figure 4.6.

Figure 4.6: The relative charge output of 3 B&L PMTs over 2 months operation. The 3
tubes were monitored inside a 200 tons water tank with a Xenon light source [21].

4.5Background Noises

There are 2 major sources of background noises that may affect the physics observation.
One is the dark hit from the PMT itself through electron thermal emissions at the photocathode. The dark hit may cause fake signals if they happen to be over the signal
selection threshold after being integrated. Since the dark hit pulse is usually small inenergy, it will affect the most the low energy observation, for example supernova andsolar neutrinos. The dark hit rate is sensitive to many factors including the material’s
working function, the environmental temperature, the voltage applied to the PMT, thetime for stabilization with minimum light exposure, etc. For the Hyper-K B&L PMTs,
the dark hit rate (8.3 kHz in 15◦ C water after 1 month stabilization) is higher than the
Super-K Venetian blind ones (4.2 kHz) as a side-effect of its higher QE.
It has been noticed that a substantial portion of the dark hit in a B&L PMT is not theusual "singularly-pulsed" electron thermal emission, but some bursting pulses as shownin Figure 4.7. The source of such a feature, suspected to be the radioactive isotopes
in the PMT glass, is under investigation. A solution to avoid the false triggering fromthe bursting dark pulses has already been worked out by [23], meanwhile currently large
efforts are being made to suppress such kind of bursting dark hits in the B&L PMTs.
30

Dark Rate (kHz)(a) The waveform of bursting dark hits from ref. [23]Total Dark Rate

22

Dark Rate Excluding Chain Peaks

20
18
16
14
12
10
8
1500

1600

1700

1800

1900

2000

2100
HV (V)(b) The rates of all dark hits and bursting pulses excluded ones

Figure 4.7: The dark hits of Hyper-K B&L PMT’s. In panel (a) is a 1 µs snapshot fromoscilloscope showing the typical waveform of the bursting pulses. Panel (b) shows thescanned total dark hit rate and the rate (red) after excluding the bursting pulses (blue)at room temperature after 1 day of stabilization. The x-axis shows the corresponding
high voltage (HV) of each measurement.
Another noise source is the PMT afterpulse, which is caused by the ionized residual gases
drifting to the photocathode and releasing electrons not related to the incoming photons. Different gas elements will have different delay in time, ranging from tens of ns
to several µs. A large afterpulse rate in PMT can result in mis-reconstruction for delayed interactions. The afterpulse rate of the Hyper-K B&L PMTs’ was measured to beless than 5% relative to the main pulse at SPE, which is comparable to the Super-K tubes.

31

52018 Detector Upgrade

As mentioned in Chapter 1, Super-K has completed the 2018 detector upgrade by January 2019. A variety of refurbishments have been finished, including a new water cycling
system for Gd parallel to the current one as shown in Section 3.4. To make sure that NO
Gd from the experiment will leak outside, better leakage proof has been achieved andchecked carefully.
Besides the upgrade of water system, there were 136 dead ID channels replaced by the
new Hyper-K 50 cm B&L PMTs. After January 2019, a complete calibration for the
upgraded Super-K tank started. This work focuses on the refurbishments and calibration tasks related to the ID PMTs, which include both the Super-K and Hyper-K 50 cm
PMTs.

5.1

Pre-Calibration of Hyper-K 50 cm B&L PMTs

Before the installation, the Hyper-K 50 cm B&L PMTs have gone through a series ofquality checks in the Super-K site with a newly constructed experiment. This section
will describe the measurements and results of those new tubes in details. Meanwhile abrief summary can be also found in [24].
5.1.1

Experiment Setting up

In March 2018, 145 newly produced Hyper-K 50 cm B&L PMTs arrived at the Super-K
site. An experiment to measure those tubes was set up in an underground laboratory at
about 100 m away from the Super-K tank. A dark room large enough for 7 PMTs wasconstructed using PVC frames and light proof black curtains. The PMTs were placed on
the specially designed carts so that all the first dynodes were held facing up at around 60
cm above the floor. Figure 5.1 shows a schematic top-view of the dark room and PMTs
in carts denoted as 7 channels.
To mitigate the geo-magnetic field that distorts the photoelectrons inside the PMTs
and thus causes systematic uncertainties, 6 Helmholtz coils were divided into 3 pairs
surrounding the whole dark room in the x, y, and z directions denoted in Figure 5.1.
Furthermore, all the PMTs in the dark room are aligned in the same direction—with thefirst dynode plate "Box" in +y direction and the second "Line" in the -y. However, themagnetic field inside the dark room was not uniform and large variation by positions wasobserved. Therefore it was not possible to bring the field distribution inside the darkroom to uniform in all 3 spatial directions with the coils being used. Since the PMTs
32

Figure 5.1: Schematic view of the dark room. The entrance is from the bottom in the
figure.
were facing upward and thus the photoelectron would propagate in the z direction, mostconstraints were then applied to the x and y directions in which the magnetic field has
the biggest effect on the experiment. Figure 5.2 shows the residual magnetic field at the
7 PMT positions after the correction, with fluctuation less than ±100 mG in the x andy directions. The currents and voltages applied in each pair of coils are shown in Table

Magnetic Field [mG]

5.1.

250

B(x)
B(y)
B(z)

200
150
100
50
0
−50
−100
0

1

2

3

4

5

6

7

8
ChannelFigure 5.2: Residual magnetic field after correction at the 7 PMT positions.

During the experiment 7 PMTs were measured simultaneously. The correspondence be-33

Ix (A)

Iy (A)Iz (A)

8.49

17.26

4.49

Vx (V)Vy (V)Vz (V)

16.10

20.78

9.86

Table 5.1: Currents and voltages applied to each pair of Helmholtz coils in all 3 spatial
directions.
tween the channel number in the electronic DAQ system and the PMT positions is shownin Figure 5.1. A NIM Analog-to-Digital Converter (ADC) module was used to record
the amplified charge information of the PMTs’, meanwhile a Time-to-Digital Converter(TDC) module for timing. At the same time a scaler was used to count the dark hits ofeach PMT. At the 7 PMT positions, a laser light source was hanging from the ceiling in
the dark room at about 50∼60 cm above the PMT glass dome. The laser was set with a
150 mA amplitude and 150 ps width, so the occupancy in each PMT was as low as 0.09
photoelectron/hit and generated almost only SPE signals. A NIM clock was attached totrigger both the laser and DAQ system. A schematic plot of the electronic circuit of the
pre-calibration is shown in Figure 5.3.

Figure 5.3: Schematic plot of the electronic circuit.

34

5.1.2

Data Collection

The data collection was done on a daily base by shifts. Everyday in the morning 6 PMTs
in the dark room measured on the previous day will be replaced. One PMT was fixed
throughout the whole experiment period at channel 7 as marked out in red in Figure 5.1.
This reference PMT was used to determine whether if there is any systematic difference
between the beginning and end. After 1∼2 hours of stabilization in the dark room with
voltage on, the first data would be taken by the shift members. Two voltage settings were
tested. One was the value given by the Hamamatsu producer that corresponds to 107
gain. The other was the tuned voltage corresponds to 1.4 × 107 gain calculated by thevoltage scan conducted during this experiment. For simplicity, the lower voltage at 107
gain is called "HK Voltage" in this work, and the higher voltage at 1.4 × 107 is called "SKvoltage". Besides the voltage scan, the dark hit rate at different discriminator thresholds
was also scanned. Then during the midnight after ∼10 hours of stabilization, the system
was designed to automatically take another set of data for comparison. This process was
repeated for all 145 Hypre-K PMTs and 6 Super-K ones that were temproarily taken outof the tank during the detector upgrade period. Since those 6 Super-K PMTs would besoon re-installed inside the tank, the FRP covers were kept attached to the PMTs forprotection and contamination proof.
The function used to fit the SPE charge distribution was

2
!
x−p
x − p x − p 
− √ 1
4
1
2p2
f (x) = p0 · e+ 0.5 · p3 · erf
− erf
{z
}
|
p5
p2
SPE Gaussian peak
{z
}
|

(5.1)

Back scattering

where the SPE Gaussian peak and back scattering are represented by the green and cyan
curves in Figure 5.4(a) respectively.
On the other hand the equation for timing distribution was

f (x) = 0.5 · λ · γ · e0.5·λ·

2·µ+λ·σ 2 −2x· µ + λ · σ2 − x √
1 − erf
2σ

!
(5.2)

which represents the red dashed curve in Figure 5.4(b).
5.1.3

Systematic Error Corrections

As mentioned in Section 5.1.1, large variation existed in the residual magnetic field amongthe 7 PMT positions. Meanwhile there were also other uncertainties from the electronics such as the variation of amplification factor at different channels, the different noise35

(a) SPE charge distribution with fitting curves(b) SPE timing distribution with fitting curves(c) SPE dark hit rate scanFigure 5.4: Hyper-K 50 cm B&L data samples
levels in TDC channels, etc. that might bias the experimental results. Therefore it wasnecessary to reduce the systematic errors that arouse from different PMT positions andchannels.
This was accomplished by measuring the reference PMT at all other 6 positions andthe corresponding channels. The voltage was set to "HK voltage". Figure 5.5 shows
the measurement of the gain, TTS, SPE resolution, single photoelectron hit rate (SHR),
dark hit rate, and peak-to-valley ratio (PVR) at 7 channels with the reference PMT. The
SHR was calculated by the ratio of SPE hits to the integrated hits of SPE + pedestal,meanwhile the PVR was defined as the ratio of SPE peak height to he lowest point between the SPE and pedestal. Multiple measurements were taken at the same position
for an estimation of statistical uncertainties. For the charge related quantities like thegain and SHR, a correction by scaling among the 7 channels was applied since it was
the amplification factor considered as the major error source. Whereas for TTS a simple
offset was added to each channel to correct the different background noise level. For
36

quantities such as SPE resolution and PVR, no correction was applied since by taking
the ratio it was assumed that the error could be cancelled out. Last but not the least, nocorrection was applied to the dark hit rate either because it is mostly affected by otherfactors as mentioned in Section 4.5 and in principle should not depend on PMT positionor channel.

Hit Ratio

Gain

6

× 10
12.8

EA3595-E

0.4
0.35

EA3595-E

0.3

12.6

0.25
0.2

12.4

0.15
12.2

0.1
0.05

12

0

1

2

3

4

5

6

P/V Ratio

Resolution (%)− 0.05Weighted EA3595-E Gain Among Channels: 1.231e+07 ± 8.077e+03[stat] ± 4.917e+05[std].

11.8

7

85

− 0.1
9

Weighted EA3595-E Hit Rate Among Channels: 9.301e-02 ± 1.000e-06[stat] ± 4.209e-02[std].
1

2

3

4

5

6

7

8

80

7

75

6
5

70

4
65
3
60
2
55

1

Weighted EA3595-E Resolution Among Channels: 7.089e+01 ± 1.000e-06[stat] ± 1.395e+01[std].
50

1

2

3

4

5

6

Weighted EA3595-E P/V Ratio Among Channels: 4.433e+00 ± 3.977e+00[stat] ± 1.785e+00[std].
0

7

1

2

3

4

Channel567Channel(a) Gain (top) and SPE resolution (bottom)(b) SHR (top) and PVR (bottom)(c) Dark hit rate at 1mV threshold(d) TTS

Figure 5.5: Channel variation measured by the reference PMT. The weighted mean isshown by red dashed line in each panel.
Some big source of uncertainty other than the channel difference is the ADC pedestal
fluctuation. The pedestal kept changing over time in all 7 PMT and would cause large
uncertainties if not subtracted correctly. This fluctuation is purely caused by uncertainties in the electronics and not related to the photon multiplication process in PMTs, butwill affect determining the SPE peak. Figure 5.6 shows the pedestal fluctuation over thewhole experiment period, which was about 1 month.
37

Charge (pC)

Pedestal_Long_Term_Stability
0.4

CH1_Ped
CH2_Ped
CH3_Ped
CH4_Ped
CH5_Ped
CH6_Ped0.3

CH7_Ped
CH8_Ped

0.2
0.1
0
−0.1
−0.2
−0.3

6

1522

1523

1524

1525

1526

1527

1528

1529

×10
1530 1531
Unixtime (s)Figure 5.6: Pedestal fluctuation over time with the empty channel 8 (no fluctuation) asa reference.
Since even at the same voltage, a PMT’s gain is sensitive to many other factors including
environment temperature, stabilization status, etc, it was also necessary to confirm thatthe gain was stable in this experiment. From the reference PMT, both the long term andday-and-night gain stability were checked. The room temperature was monitored to bestable around 25◦ C and hence no clear difference was seen in the gain from the daytime
and late-night measurements. On the other hand, throughout the 1-month experimentperiod there appears to be a 0.8% difference in the gain of reference PMT, but it wasmuch smaller than the day-by-day fluctuation and not so convincing for unstable gain asshown in Figure 5.7(a).
The fitting function for long term gain stability check was
f (x) =N+At − tof f set(5.3)

A stronger time dependence can be seen in the bottom panel of Figure 5.7(a), whichshows the SPE peak position before the pedestal subtraction. The trend resembles whatis shown in Figure 5.6 a lot. The gain in the top panel was calculated after subtracting
the pedestal from the SPE peak position, and has merely no time dependence. Meanwhile
for the day-and-night difference in gain was as small as 0.5%. Therefore, the gain wasverified to be stable over both long and short terms by the reference PMT.
38

CH7 Gain vs. Time at 1823V
χ2 / ndf
Prob
Norm
Shift

CH7 Gain

6

13.5

×10

13

3.171e+05 / 87
01.323e+11 ± 6.026e+08
1.227e+07 ± 324.9

12.5

Gain Change

11.5

6

11

×10
1523

1524

1525

1526

1527

1528

1529

30

Charge (pC)

0.02669 / 87
19.801e+04 ± 6264
1.872 ± 0.003152

20

−0.4

10

−0.6

2

−0.8

1.9

−1

1.8

−1.2

1.7

0
−10
Gain Change Mean = 8.114e+03

−1.4
6

1.6

40

0.2

−0.2
χ2 / ndf
Prob
Norm
Shift

2.1

50

1530
Unixtime (s)CH7 Peakx vs. Time at 1823V
2.2

×10
0.4

×10
1523

1524

1525

1526

1527

1528

1529

30000

1530
Unixtime (s)(a) Long term gain stability (top) and SPE

Gain Change [%]

6

12

−20

Gain Change Percent Mean = 0.05%

35000

40000

45000

50000

55000

60000

65000 70000
Unixtime [s](b) Day-and-night gain difference

peak (bottom) without pedestal subtraction

Figure 5.7: Gain stability check with the reference PMT.
5.1.4

Measurements

One of the motivations of this experiment was to verify that these Hyper-K 50 cm B&L
PMTs were qualified to be installed inside the Super-K tank. According to the operationand detection requirements of Super-K, 4 criteria was made based on the voltage range
for the target gain, the TTS that represents timing resolution, the dark hit rate, and theSPE resolution.
In this experiment, we set the target gain to 1.4 × 107 . The corresponding "SK Voltage"
were found by the voltage scan at 12 points ranging from 1500 V to 2250V. At eachvoltage, the PMT’s SPE peak was recorded and used to fit the peak-voltage relation
represented by the functionµ(V ) = α · (V − Vof f )β(5.4)

where µ(V) stands for the corresponding gain at voltage V. An example of Eq 5.4 isshown in Figure 5.8(a). The voltage of all 145 Hyper-K 50 cm PMTs at the "SK Voltage" is shown in Figure 5.8. The results of "HK Voltage" in this experiment were slightly
different from the values by the PMT producer. This was because of the different fitting
function Eq 5.1 we used, in which the back scattering part will affect the SPE peak position.
Other than these 4 quality checks, a few measurements on different quantities were also
made. But the result was not representative and limited by either the hardware or analysis method so that they could not serve for quality checks. For example, the afterpulse
39Reference PMT (EA3595-E) HV-Curves at All 7 Channels

×10

Gain

6

45
40
35

CH01
CH02
CH03
CH04
CH05
CH06

30

CH07

25
20
15
HV at 1.4e7 gain : 1863.6± 0.1(stat)± 2.1(sys) [V]

10
5
1600

HV at 1e7 gain : 1759.6± 0.1(stat)± 2.9(sys) [V]

1700

1800

1900

2000

2100
2200
2300
Voltage Supply [V]Figure 5.8: Pre-calibration voltage scan example by the reference PMT.
rate was measured in this experiment and turned out to be less than 1%. However, due
to the low intensity light source being used, it was unclear whether this low rate is a
result of the lack of ionization or residual gas. Moreover, Figure 5.9 shows that with thereference PMT, a 5% afterpulse rate would be observed in some channels whereas 0 in
some others such that a channel-by-channel correction was not possible. Given to thesereasons, we decided not to include the afterpulse rate as a checking criterion.

Ch3 EA3595-E 1823.0V Run5828

Ch5 EA3595-E 1823.0V Run5832

h102

After Pulse
5.1 ± 0.9 [%]

−5000

0

Entries 1919483
Mean 1.268e+04
RMS

h104

104

CountsCounts104

After Pulse
0.0 ± 18.7 [%]1.383e+04−5000

5000 10000 15000 20000 25000 30000 35000 40000
Time [ns](a) Reference PMT afterpulse at channel 30

Entries 1647814
Mean 1.545e+04
RMS

1.392e+04

5000 10000 15000 20000 25000 30000 35000 40000
Time [ns](b) Reference PMT afterpulse at channel 5

Figure 5.9: The afterpulse rate of reference PMT’s at different channels.
The other quantity excluded was the PVR. During the analysis we have found that insome PMTs the data points were scattered in the SPE "valley". A larger disagreement
between the data and fitting was found compared to the other regions in the charge distribution. More specifically, in such a scattered case the fitting tends to find the lowest
point that turned out to be an outlier. This discrepancy between the fitted PVR and40

the PVR from the data average is shown in Figure 5.10 where a large portion of PMTs
have inconsistent results. Therefore a different PVR in this experiment does not directly
mean the PMT’s SPE peak is different. Hence the criterion provided by the producer

Raw PVR

could not be applied.

10

P/V Comparison

HK Voltage

Number of PMTs

SK Voltage

8146

SK Fitted PV

4.659 ± 0.970

SK Raw PV

3.890 ± 0.765

HK PV Dev

1.094

SK PV Dev

1.339

6

4

2

0
0

2

4

6

8

10
Fitted PVR

Figure 5.10: The comparison of the fitted and raw data PVR at "HK voltage" and "SKvoltage". The entry number is larger by 1 because a PMT was accidentally measured
twice.
At last, the selection was then made only based on the aforementioned 4 quantities. The
selection range for voltage was determined to be 1500∼2350V, for TTS to be 1∼4 ns
in FWHM, for SPE resolution to be 20%∼70% as measured by σ of the peak, and therange for dark hit rate to be 2∼30 kHz. The measured value of these quantities from all
145 PMTs are shown respectively in Figure 5.11, where the selection range is plotted indotted vertical lines in each panel. All 145 PMTs have satisfied those selections and in
the end 136 were randomly picked to be installed in Super-K.
Please note that the allowed range for dark hit rate was significantly large (30 kHz
compared to 4.2 kHz in Super-K), but had been used before in the Hyper-K PMT gainstability check that was mentioned in Section 4.4. This was because during the experiment we kept exchanging the PMTs and the stabilization time was only several hours.
In addition the room temperature was more than 10◦ C higher than the Super-K watertemperature. The dark hit rate selection made in this experiment does not aim to determine the dark noise level of these Hyper-K PMTs, but just as a quick check for broken
or flasher tubes if any.
41

20
18

TTS at 1.4E7 Gain

Entries

145

Mean

1931

CountsCounts

HV at 1.4E7 Gain

25

Std Dev 117.6

Entries

145

Mean

2.59

Std Dev 0.1293

16
20
14
12
15
10
8

10

6
4

5

2
0

0
0

1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

1

2

3

4

5

(a) Voltages at 1.4 × 107 gain(b) TTS at 1.4 × 107 gain

Dark Rate at 1.4E7 Gain

1.4E7 Gain Resolutions (σ)

Entries

145

Mean

14.94

30

14

Std Dev 3.123

25

6

TTS [ns]

CountsCountsHV [V]

Entries

145

Mean

28.61

Std Dev 4.026
12
10

20

8
15
6
10
4
5

0
0

2

10

20

30

40

50

0
10

60

Dark Rate at 1mV (kHz)(c) Dark hit rate (1mV threshold) at 1.4 × 107

20

30

40

50

60

70

80

SPE Resolution (σ) [%](d) SPE resolution at 1.4 × 107 gain

gain

Figure 5.11: Measurement and selection of 145 Hyper-K 50 cm PMTs.

42

5.2

Voltage Adjustment

With 136 ID channels in Super-K replaced by the Hyper-K 50 cm B&L PMT, new voltage
settings were needed since these PMTs have different charge responses. Meanwhile, it wasobserved that the ID gain kept drifting during the SK-IV phase. It had been a big concern
for a long time since the gain drift would cause larger channel-by-channel variation in
charge responses, and hence extra systematic uncertainty in physics analyses. Taking
the chance of 2018 detector upgrade and ID PMT replacement, we decided to retune thevoltage for all ID PMT channels. This chapter will explain the voltage adjustment withthe experimental method, adjustment results, and underlying systematic uncertainties indetails.
5.2.1

Data Collection

Previously in Super-K, the voltage of each ID channel was determined using a Xenon
source, which emits large intensity of isotropic light triggering multi-PE signals in the
PMTs. There were 420 Super-K 50 cm PMTs precisely calibrated outside and evenly
distributed in the tank [19]. Those PMTs severed as a reference of the expected charge
response for the PMTs at the same distances to the Xenon source. A relation between
the number of hits in each PMT and the applied voltage was found to determine thevoltage for the target gain.
However, this time there was no such a group of "reference PMT" anymore. Those
420 PMTs’ gain has changed along with all the others throughout the SK-IV phase andthus can no longer be used as a guidance. Moreover, the old hanging system for Xenon
source was broken and no substitution was available. Therefore we had to find a new
method to tune the ID voltages. Meanwhile, there was also another request to investigate the Super-K detector’s energy lower limit threshold cut. Hence a weaker light source
other than the Xenon is preferred. Taking all of these into account, this time we useda laser diode Hamamatsu PLP-10 that has low intensity and peak wavelength at 404
nm. Since this source was at first used for supernova study, it is also called SN-LD. On
the other hand, since both the number of hits and mean value of charge distribution are
sensitive to the energy threshold cut, we used the fitted SPE peak as the reference for a
PMT’s gain similar to the pre-calibration mentioned in Section 5.1. More details about
the SPE peak fitting will be discussed in Section 5.2.2.
Figure 5.12 shows a schematic view of the experimental set up for voltage adjustment in
the Super-K tank. The SN-LD light was injected into the tank through a diffuser ball43x (cm)y (cm)z (cm)

35.35-70.70

0.00

Table 5.2: The coordinates of the diffuser ball in the tank.
near the center. The coordinates are given in Table 5.2. A NIM clock was used to trigger
the SN-LD and the DAQ. The coincidence with the SN-LD signal in channel 15024 was
required for triggering the DAQ. Since the LD pulse rate was tuned to 2 kHz, an extra
cut was applied to the data selection that any 2 consecutive signals should be separated
by ∼0.5 ms. This was to remove the potential false DAQ triggering by other sources.
The time window for DAQ was at -400 to 0 ns from the trigger. Moreover, a piece of
background (-800 to -400 ns) taken outside of the trigger time window in each PMT was
subtracted from the "on-time" signal to reduce the dark noise. On February 7th, 2019 7
sets of data were taken with the SN-LD at different voltages for each PMT as shown in
Table 5.3.

Figure 5.12: Schematic view of voltage adjustment experimental set up.

5.2.2

New Voltage Determination

To find the new voltage for each PMT, a similar method to the pre-calibration of HyperK 50 cm PMTs as mentioned in Section 5.1 was used. From the 7 sets of data taken at
voltages ranging -75 V to +75 V from the SK-IV value, a relation between a PMT’s SPE
peak and its gain was found. To extract the charge information from the ADC counts ateach channel, a polynomial function representing count-to-charge conversion was appliedin the data reduction process of Super-K. Depending on the target charge range, it would
either be a linear or higher order function. In addition to that, the temperature effect
44

Run#

Duration (s)Voltage

80249

1393

0

80254

994

+75 V

80263

1221

+50 V

80265

1291

+25 V

80269

1087

0

80275

1349

-25 V

80278

1075

-50 V

80282

1082

-75 V

Table 5.3: Run information of the SN-LD data. The 3rd column shows the voltage
difference of each PMT from the SK-IV setting.
Cable550_Charge

Cable550_ADC_Pedestalh_spe_on_550
Entries
47265
Mean
33.57
23.78
Std Dev

1200

1000

1000
800

800

600

600

400

400

200

200

0

h_spe_on_550
Entries
47265
Mean
3.509
Std Dev
2.27

1200

0

50

100

150

0
−5

200
Count

(a) Temperature corrected ADC count distri-

0

5

10

15
20
Charge [pC](b) Converted SPE charge distribution

bution (after pedestal subtraction)

Figure 5.13: The spiky feature of SPE charge distribution that comes from the count-tocharge conversion.
of QBEE signal read out was also corrected. However, it was noticed that the resulted
charge distribution had some spiky feature as shown in Figure 5.13. The cause of thiswas considered to be the rounding and binning issue when converting from integer ADC
counts to decimals. For each channel 1 ADC count corresponds to some long digits
decimal number of charges, i.e. some number like 0.113xxxxxxx... Figure 5.14 showsthat by simply changing the bin width from 0.1 to 0.11 pC, such a spiky feature would tosome extents disappear. Although the actual count-to-charge correspondence is different
for each channel, the 0.11 pC bin width was the leading term in decimals for all channels
and thus helped to solve the issue. Then the spikes were further reduced by rebinningthe histograms.
Since the Super-K and Hyper-K PMTs have different SPE charge response, the fitting
45

Figure 5.14: By changing the bin width from 0.1 pC (red) to 0.11 pC (blue), the spikes
in charge distribution to some extents disappeared.

46

Figure 5.15: An example of Super-K’s SPE at SK-IV voltage fitted by Eq. 5.5.
function for their SPE peaks were different. For the Super-K tubes, depending on the SPE
spectrum the software was designed to pick the better fit from the 2 options available.
The first option with higher priority was a gaussian plus exponentially modified error
function as shown in Eq. 5.5−

fgexp (x) = p0 · e(x−p1 )2
p2

+ 0.5 · ep5 +p6 ·xx − p3 x − p1 
· erf
− erf
p4
p2


(5.5)

where pi for i = 0,1,2,3,4,5,6 is the fitting parameter and erf stands for the Gaussian
error function. p1 represents the peak position. An example of this fitting result is shownin Figure 5.15. The upper limit of fitting range was set to 3σ right to the fitted SPE
peak. This was to avoid the potential distortion from 2 PE peak.
However, in some cases where the voltage was lowered, a Super-K PMT’s SPE peakslightly edged the energy threshold cut that left no visible exponential tail to the left. This
would much likely cause the fitting with fgexp in Eq. 5.5 to fail. Under this circumstance,a second fitting function of error function skewed Gaussian as shown by Eq. 5.6 would
be used.

−fgskew (x) = p0 · e(x−p1 )2p2

x − p1 · 1 + p3 · erf
p2

(5.6)

which is demonstrated with an example in Figure 5.16.
It was noticed that the fitted peak p1 of fgskew from Eq. 5.6 was always much to theleft of the actual function peak due to the skewness, therefore in the case of Eq 5.6 thex value corresponding to the function maximum was used as the SPE peak. The fitting
47

Figure 5.16: An example of Super-K’s SPE at -50 V from SK-IV voltage fitted by Eq.
5.6.

Figure 5.17: An example of Hyper-K’s SPE at SK-IV voltage (for the channel) fitted by
Eq. 5.7.
range was kept same as 3σ.
On the other hand, the Hyper-K PMTs do not have any exponential tail in their SPE distribution and a fitting function similar to what has been used during the pre-calibration
was introduced:

fHK (x) = p0 · e−(x−p1 )2p2

x − p4 
x − p1 · 1 + 0.5 · p3 erf− ·erfp5p2
An example of the Hyper-K PMT fitting is given in Figure 5.17.

48

(5.7)

Dead Channel

Blank Channel

Rejected Fitting

Flasher

Voltage out of Ranges

24

17

11

5

5

Table 5.4: The breakdowns of 62 no change PMTs in the voltage adjustment.
From the fitted SPE peak in units of pC at each voltage in Volts, the correlation wasdetermined by fitting a power function relating the peak with voltage. Because there wasa ∼ 3 order of magnitude difference between the 2 values, a natural logarithmic function
as shown in Eq 5.8 was actually used.
log(p(V )) = log(α) + β · log(V )(5.8)

where p(V ) is the SPE peak corresponding to voltage V , and α and β are the normalization factor and power index to be determined.
Inside Super-K, there are actually 3 generations of PMTs including the Hyper-K tubes.
The oldest generation is named SK2 PMTs, which were produced in the late 1990s. The
second generation is SK3 PMTs that were produced after the accident in 2000s. And thelast is Hyper-K (HK) PMTs produced in 2018. Since these 3 generations of PMT havedifferent voltage dependences of gain, they were treated separately this time. Figure 5.18
shows an example of the voltage scan for each generation of PMT. The error in peak
was assigned by the fitting error of the corresponding parameter. In general the Hyper-K
tubes have the smallest error size.
5.2.3

No Change Channels

The voltage scan and SPE peak fitting results of all ID PMTs were checked individuallyby eyes. Those tubes with bad fitting results were kept as the same as SK-IV value. An
example of the bad fitting is shown in Figure 5.19. Meanwhile we set the safety range ofthe new target voltage to be 1400∼2450 V, which was 200 V higher than the Super-K
safety lower limits and 50 V lower than the upper. Any PMT with the resulted target
voltage beyond this range was also not changed. In total 62 channels including thoseblank ones without a PMT attached were separated from the voltage adjustment. The
breakdowns of those tubes are listed in Table 5.4.
5.2.4

New Voltage Results

The target gain for this voltage adjustment was decided to be 1.65 × 107 , which was
the initial setting for SK-III phase. Multiplied by the elementary charge, the SPE peak49

(a) SK2 PMT voltage scan example(b) SK3 PMT voltage scan example(c) Hyper-K PMT voltage scan example

Figure 5.18: Voltage scan examples for 3 generations of PMT.

Figure 5.19: This SK3 PMT 2532 merely shows any voltage dependence of the SPE peak,meanwhile large uncertainty can be seen in the fitted result.

50Figure 5.20: The SPE peak for all ID PMTs before the voltage adjustment (red) andafter (blue). The peak average has decreased from 3.17 pC to 2.72 pC, corresponding to
the gain changes from 1.98 × 107 to 1.70 × 107 . The RMS has also decreased from 0.38
pC to 0.10 pC. The dashed lines represent SK2 (green), SK3 (pink), and Hyper-K PMTs
(violet).
α [pC/ Vβ ]βSK2 PMT

1.977 × 10−26

7.960

SK3 PMT

−28

1.748 × 10

8.783

Hyper-K PMT

5.721 × 10−20

5.971

Table 5.5: The voltage curve parameter averages of 3 PMT generations.
position corresponding to the target gain was 2.635 pC. On February 14th, 2019, thefirst data set at the new voltage was taken with the SN-LD. By checking the new SPE
peak position after the voltage adjustment, we have confirmed that the average gain was
brought down by 14.3% from the SK-IV phase, which corrected the increment over a
decade. Meanwhile the gain difference among individual PMTs was also decreased toonly 26.3% of the variance during SK-IV. This result is shown in Figure 5.20.
The voltage curve of each PMT generation is shown in Figure 5.21(a), with the meanvalue of α and β from Eq. 5.8 listed in Table 5.5. Meanwhile the new voltage settings of
all PMTs is shown in Figure 5.21(b). On average the SK2 PMTs’ voltage decreased by
31.7 V from the SK-IV value and SK3 40.5.V.

51

HighGainHV

SK3 New Voltage

SPE Peak [pC]

Average_HV_Curves

200

HK
10

150

83.78

Entries
Mean

4940
1923

RMS

118.3

Entries
132
Mean
1972
RMS
102.8

100

4

RMS

HK New Voltage

8

6

6035
1620

SK2 New Voltage

SK2
SK3

Entries
Mean

50

2

0
0
1400

1600

1800

2000

2200

1500

2000

Voltage [V]2400
HV [V](a) Average voltage curve of 3 PMT generations(b) Tuned result of SK-V voltages for 3 PMT
generations

Figure 5.21: The average voltage curves of 3 PMT generations and the resulted SK-V
voltages. In the right panel the SK2 PMTs are plotted in red, SK3 in blue, and Hyper-K
in pink.
5.2.5

Uncertainties

In Super-K, the charge response of each PMT is corrected by the average gain in thetank and the relative difference of each individual tube, both of which were determined
separately by other calibrations. Thus the uncertainties in the voltage adjustment result
would be covered. Therefore this section does not aim to reduce the systematic uncertainties arouse in the voltage adjustment, but just to clarify the possible sources andestimate the scale.
As aforementioned in Section 5.2.1, previously in Super-K the voltage of each PMT
channel was determined by the number of ADC counts. However, this old method would
have a large systematic uncertainty from the water quality since the number of photon
reaching each PMT is sensitive to absorption and scattering rate and the light source is
not at the exact center of tank. It was noticed before that there was a ∼4% asymmetry inthe horizontal angle φ for QE, which means the number of photon in the far end is ∼4%
smaller than the near end. This asymmetry would then cause a systematic bias in thegain tuning. Nevertheless this time the SPE peak was used instead, which is in principal
not affected by water quality. Although we did not know about the water transparency
when this work was done, Figure 5.22 hardly shows any φ dependence of the SPE peak.
In addition, a sinusoidal function was fitted to the φ distribution of SPE peaks. The
52

(a) SK2 PMT SPE peak φ dependence(b) SK3 PMT SPE peak φ dependence(c) Hyper-K PMT SPE peak φ dependence

Figure 5.22: The SPE peak of all 3 PMT generations merely shows any φ dependence.
Amplitude [pC]

Phase [◦ ]Y-axis Offset [pC]

SK2 PMT0.003 ± 0.002−91.73 ± 0.67

2.706 ± 0.001

SK3 PMT0.002 ± 0.002−21.64 ± 0.83

2.722 ± 0.001

Hyper-K PMT

0.020 ± 0.008−24.35 ± 0.48

2.705 ± 0.006

Table 5.6: Sinusoidal function fitting results of SPE peak φ dependences.
fitting results are summarized in Table 5.6.

Another potential source of distortion to a PMT’s SPE charge spectrum is the occasional
multiple hits, which can be checked by the PMT occupancy. If by coincidence 2 or more
photons are absorbed by a PMT’s photocathode within a short time window, the PMT
occupancy will be enlarged and the resulted photoelectron will have the sum of photon
energy if neglecting loss in photoelectric process. This will result in a higher charge in53

the PMT signal output and thus distort the charge spectrum. But since we have strictly
limited the fitting range as discussed in Section 5.2.2, the multi-PE hits should not toaffect our SPE peak result. To verify this 3 sets of data with different light intensities
were taken with the SN-LD, from which we fitted a linear function relating SPE peak to
occupancy. The fitted slope of each PMT is plotted in Figure 5.23. As expected there isno systematic occupancy dependence.
Besides the potential bias in data, another source of systematic uncertainties is fromthe fitting and measurement errors. To estimate the uncertainty of voltage curve, thecovariance matrix of parameter α and β was generated for each PMT. Since the voltage
was set by other systems with high precision, the V in Eq. 5.8 was assumed to be aconstant with negligible error. Therefore, the variance from the fitting uncertainty ofSPE peak at a certain voltage can then be written as2222σlog(p(V)) = σα + log (V )σβ + 2 · log(V )σαβ

(5.9)

where σαβ stands for the covariance of the 2 parameters. Due to the error propagationof
σlog(p(V )) =σp(V )∂log(p(V ))σp(V ) =∂p(V )p(V )the result from Eq. 5.9 directly represents the percentage of peak variance. The dataat the adjusted new voltage taken on February 14th, 2019 was used to generate Figure5.24(a). On average the voltage curve uncertainty resulted in a ∼5.07% variance in thefitted peak, which corresponds to ∼0.14 pC.
On the other hand, the statistical uncertainty was checked by 2 sets of data at the
new voltage taken more than 1 week apart. Figure 5.24(b) shows this comparison. No
systematic difference was observed since the mean was as small as 0.004 %. Meanwhile√
the individual uncertainty was RMS/ 2 = 2.58% that corresponds to 0.07 pC. The details of 3 PMT generations are summarized in Table 5.7.
Last but not the least, the binning effect shown in Figure 5.13(b) may have also causeda systematic error in the fitting even though it had been to some extents removed. To
check such a possibility, the same fitting functions of SPE peak were first applied tothe temperature corrected ADC count profile, which was "spike-free" as shown in Figure5.13(a). The ADC count to charge conversion was then applied to the fitted peak. Sucha process did not involve the uncertainties from the spiky structures and rebinning of the
PMT signal spectrum. Figure 5.25 shows the comparison of the peak from the 2 different
54(a) SK2 PMT SPE peak occupancy dependence(b) SK3 PMT SPE peak occupancy dependence(c) Hyper-K PMT SPE peak occupancy dependence

Figure 5.23: The systematic occupancy dependence for SPE peak is verified to be negligible with the slope of peak-occupancy relation averaging at 0. The spread comes fromthe larger uncertainties in lower occupancy tubes.
PMT Type

Systematic Error

Statistical Error

Hyper-K

3.80%

1.33%

SK2

4.07%

2.75%

SK3

5.94%

2.45%

Table 5.7: Systematic and statistical uncertainties in SPE peak for the 3 PMT generations.
55

Gain_Uncertainties

Entries

11108

Mean

0.003528

RMS

3.647

150
HK
SK2

100

SK3

50

0

-10

0

10

Peak Uncertainty [%](a) Peak variance from the voltage curve un-(b) Statistical uncertainty of SPE peakcertainty

Figure 5.24: The systematic and statistical uncertainties from fitting of SPE peak. The
SK2, SK3, and Hyper-K PMTs are in blue, pink, and red respectively.
Peak

600

400

200

0
1

2

3

4

5

6

SPE Peak [pC](a) SPE peak from charge (ADC count) in red(b) Peak differences between the 2 processes(blue)

Figure 5.25: SPE peak check from the 2 different processes.
processes on the data taken at SK-IV voltages.
Several data at different points of voltage scan was checked as well as the data taken at
the new SK-V voltage. The result is summarized in Table 5.8. It shows that the discrepancy in the peak was larger at higher voltage than the lower, which would give rise to a

56

All

SK2

SK3

Hyper-K

SK-IV -75 V-0.082-0.068-0.094-0.029

SK-IV +0 V

-0.098-0.092-0.105-0.057

SK-IV +75 V-0.101-0.101-0.102-0.070SK-V-0.009-0.006-0.0120.009

Table 5.8: The differences in average SPE peak calculated by charge peak - ADC countconverted peak. The first column represents the voltage setting for each row. The 3
generations of PMT are also listed. The peak differences are written in units of pC.
smaller slope in the fitted voltage curve. Nevertheless the difference in the peaks at the
new voltage was surprisingly small. Therefore the discrepancy at the high voltage in thepeaks fitted from charge and ADC count may help to explain the offset in the resulted
peak average of the tank. Since the slope of voltage curve was underestimated, it would
result in an insufficient correction in the voltage to achieve the target gain and thus alarger average peak value.

5.3

Timing Calibration

The timing of each ID PMT is essential to event reconstruction and various physics
analyses. To understand whether the hits in multiple PMTs are connected to a single
interaction, one needs a precise time measurement free of systematic biases. In Super-K,
this is achieved by applying a correction in time for different signal charges. The analysis
framework of timing calibration was first developed by [25], with several modifications
and updates from this work. This chapter describes in details how the timing calibration
was done for SK-V.
5.3.1

Overview

The 2 major sources of timing systematic biases are the differences in electronics processing time and the time walk effect at the timing gate threshold in TDC. As shown in
Figure 5.26, the time walk effect originates from the difference in signal charges since thehigher charger signal will rise more rapidly and causes a fake "early arrival" relative tothe lower charge signal.
Figure 5.27 shows the experimental set ups for timing calibration. A USHO-KEC100
nitrogen-dye laser was used as the light source. The wavelength was shifted from 337
nm to 398 nm by the dye, which is roughly the peak wavelength of PMTs. There were 2

57

Figure 5.26: The time walk effect caused by different pulse amplitudes at the threshold[26].

Figure 5.27: The set ups for timing calibration.
signal outputs from the laser. One was going into a 2-inch monitor PMT placed outside
the tank. To trigger a DAQ from the laser pulse one and only one hit in the monitor PMT
was required. The charge and timing from the monitor PMT were separately recorded
in QBEE channel 15001 and 15009. In the other output, the laser light passed a neutral
filter before entering the tank via the diffuser ball. The filter is a rotating plate of differential transparency that allowed us to control the intensity of light being injected into
the tank remotely. The position of the diffuser ball was the same as in Table 5.2.
The relative time in each PMT can be then written as
Ti = −ti + tofi + tlsr
58

(5.10)

where the tlsr is the time stamp of a laser signal, tofi is the "time-of-flight" that neededby light to travel from the diffuser ball to PMT i in water, and ti is the time stampof the hit in that PMT in response to the laser light. An implicit term in Eq. 5.10 is
the time for signal traveling in each cable and being processed in each QBEE channel,
which are contained by ti . Meanwhile to correct for the time walk, the relative timing
Ti was calculated at different charges of signal ranging from 0 to 3981 pC. It was foundthat the filter position ∼3500 would give the maximum light intensity, meanwhile 3950
the minimum. A piecewise polynomial function so-called "T-Q curve" was fitted foreach PMT so that the delay caused by the time walk effect at different charges can be
estimated. Then, by applying the relative timing correction Ti to the real data given theircharge information we can trace back on the interaction vertex and time with improved
precision.
5.3.2

Time Peak Fitting

The time and charge information of each PMT were first used to generate a 2-D display as
shown by Figure 5.28. As a Super-K convention, the earlier hits are of larger numbers in
the y-axis. There are 384 time bins between 1100 and 1300 ns. Each time bin spans 1/1.92
ns, which is the same as the TDC resolution. Along the x-axis the charge is grouped into
180 Q bins. The conversion is linear in the low charge region and logarithmic in the highas denoted in Eq. 5.11.

# Q bin =5 · Q(0 < Q ≤ 10 pC)

50 · log (Q)10(10 < Q ≤ 3981 pC)(5.11)In this work, the charge in each PMT channel was calculated directly from its raw ADC
counts. To find the peak in time, a time slice was taken from each Q bin and re-plotted
into a 1-D histogram. Due to the distortion from scattered hits, pre-, and late pulses, thetime distribution turned out to be an asymmetric peak. A damped Gaussian function
was used for fitting as shown by Eq. 5.12.
 1 + tmp − exp(tmp) f (T ) = max · exp
ef f Asy 2
where
tmp = ef f Asy ·(5.12)

T − TpeakσT

In Eq. 5.12, the amplitude max, peak Tpeak , width σT , and damping factor ef f Asy are
the fitting parameters. In the limit of small damping factor that corresponds to the nearly59

Figure 5.28: An example of the time-charge 2-D display. The low (medium, high) charge
range is plotted in pink (red, blue). The scattering such as pre-pulses and late pulses
were excluded from this analysis.
symmetric case, the fitting approximates to a pure Gaussian function if only considering
up to the 2nd order derivative in Taylor expansion. For asymmetric cases, practicallyderivatives up to 4th order were included in calculation.
Previously in SK-IV, a smearing was applied (Figure 5.29) to the time distribution ineach Q bin before fitting. The smearing was first introduced to solve the pedestal fluctuation problem happened to the ATM modules. It was then done by summing over thetime bins’ entries assuming gaussian distributions. However, this would, especially in the
low charge region, cause the smeared peak deviated from the original one, as well as abroadening effect that would affect the determination of detector time resolution. Figure5.30 shows the difference between the raw data peak and smeared peak against Q bins.

Since there is no pedestal fluctuation issue in the QBEE system meanwhile the raw data
had no problem with the fitting, the smearing process was removed from the timing
calibration this time. As a result, the fitted time peaks in the small Q bins were expected
to be more accurate. An example of the fitting on raw data is given in Figure 5.31.
Meanwhile due to finite time bin width, the peak in the histogram can be differed fromthe true peak by up to 0.5/1.92 ns. Such a shift was estimated and corrected by checking
the change in mean every time an entry was added.

60

tqpeak_002_00001
Entries

669

Mean

1192

RMS

30

9.106

χ 2 / ndf

74.35 / 54

Prob0.03455
23.22 ± 1.25

maxAsy1195 ± 0.4

tpkAsy20smooth @ QBin 002 Cable 00001

Entries per 0.52 ns

Entries per 0.52 ns

tqpeak @ QBin 002 Cable 00001

sigAsy5.026 ± 0.193

effAsy0.8213 ± 0.1617

10

20

15

smooth_002_00001
Entries

668

Mean

1192

RMS
χ 2 / ndf

9.835
0.01348 / 23

Prob
maxAsy18.35 ± 1.29

1

sigAsy1194 ± 1.3
6.448 ± 0.968

effAsy0.4558 ± 1.5381

tpkAsy

10

5

0
1150

1200

0
1150

1250

1200

T (ns)

1250

T (ns)(a) Raw data without smearing(b) Smeared data

Figure 5.29: The smearing effect to the time peak in the 2nd Q bin.

Peak Diff [ns]TPeak Diff

0.5

0

-0.5

-1
0

50

100

150

Qbin
Figure 5.30: The average peak difference from Traw − Tsmear across the Q bins. Error bars
stand for the standard deviation among ID PMTs. The red (blue, pink) dots represent
SK2 (SK3, Hyper-K) PMTs.
5.3.3

T-Q Curve Fitting

From the binning shift corrected Tpeak ’s, a polynomial curve as defined in Eq. 5.13 wasused to determine the charge dependence of relative hit time in each PMT.

pol3(x)
0 ≤ x ≤ 10

T (x) = T (10) + (x − 10)[T 0 (10)|x=10− + (x − 10)pol3(x − 10)] 10 < x ≤ 50
T (50) + (x − 50)pol6(x − 50)
50 < x ≤ 180(5.13)
where x is the Q bin number and polN (x) represents the polynomial function of order61

tqpeak @ QBin 120 Cable 00012

tqpeak_014_00012
Entries
3968
Mean
1190
RMS
4.312
χ2 / ndf
35.29 / 31
maxAsy228.9 ± 5.1
tpkAsy1192 ± 0.1
sigAsy2.943 ± 0.043
effAsy0.6519 ± 0.0592

200

200

Entries per 0.52 ns

Entries per 0.52 ns

tqpeak @ QBin 014 Cable 00012

tqpeak_120_00012
Entries
577
Mean
1204
RMS
0.6291χ2 / ndf
1.452 / 3
maxAsy195 ± 10.6
tpkAsy1204 ± 0.0
sigAsy0.6061 ± 0.0223
effAsy0.1551 ± 0.1579

150

100

100
50

0

1180

1190

1200

0

1210

1200

1205

T (ns)1210

T (ns)(a) Fitting on raw data in Q bin #14(b) Fitting on raw data in Q bin #120

Figure 5.31: An example of raw time data peak fitting.
tqhistN_00010
Entries 331767
1600
Mean x89.75
Mean y
1207
RMS x
45.25
1400
RMS y
5.945

T (ns)

tqhistN @ cable # 00010

1220

1200
1000
1200

800
600
400

1180
0

200
50

100

0

150

QBin

Figure 5.32: In the empty Q bins the T-Q curve tended to bend down. Attempts weremade to extend the data tail over Q bin 170 but the issue still remained.
N . However, it happened that the data could not span full 180 Q bins even with the
maximum light intensity passing through the neutral filter. This caused a difficulty in thefitting of the largest 5∼10 Q bins. As shown in Figure 5.32, the high order polynomial
tended to bend down in the empty Q bins, which causes a big uncertainty in the fitted
T-Q curve.
A solution to this issue was extrapolation. A Spline5 and Newton series were applied
respectively to predict the data points in the empty Q bins based on the existing ones.
First a Spline5 interpolation was applied to the full dataset in each PMT, which assumes
differentiability and same curvature at each junction point asq 0 (xi ) = q 0 (xi )ii+1q 00 (x ) = q 00 (x )
i

i

i+1

(5.14)iwhere 1 ≤ i ≤ n − 1 is the ith point in a total set of n. Based on the right most data62

point, an extrapolation was done assuming the derivative does not change. However, due
to the natural fluctuation in the data points the derivative between 2 consecutive points
is usually much different from the average trend of the group. Since the data usually saturated in the large charge region that caused a "shooting up" in the last several points,
the Spline5 extrapolation would easily exaggerate the real case. Therefore a second hand
was introduced to kill the divergent effect from the large derivatives.
Newton’s series can be written as
f (x) =

X x−a
k=0

k!

!
∆k |f |(a)(5.15)

where ∆k is the kth order difference counted backward from the point a and!
x−a(x − a)(x − a − 1)(x − a − 2)...(x − a − k + 1)=k!
k!
Thanks to the fact that the data points had integer uniform step sizes in x-axis: 1 Q
bin, the binomial coefficient and k! are cancelled out since we always considered the casewhere x = a + 1 for extrapolation. Meanwhile to suppress the extreme derivatives in theextrapolation, a weight negatively related to each ∆k term was included. The maximum
order of difference was taken to be 4. Effectively, the Newton series extrapolation as
given by Eq. 5.16 would lead to a "flatter" prediction than the real case. Therefore bytaking the average of the 2 extrema: Spline5 and Newton series extrapolations, it was
hoped that the extrapolated points would approximate the reality better.
f (x) =

4X
(1 − ∆k |f |(xk ))∆k |f |(xk )P
2 · 4j=0 ∆j |f |(xj )k=0(5.16)

Moreover, since a larger charge will have faster rising and hence "fake" earlier hit, it
is unnatural for the extrapolated points to curve down. Thus in such a case where anegative slope was extrapolated in the empty Q bins, a linear extrapolation based on thedata of Q bin range 120∼end would be used instead. Figure 5.33 gives an example of theextrapolation to Q bin 180.
On the other hand, another problem rouse in the low charge region. Due to this time theaverage gain has been lowered in the tank as discussed in Section 5.2.4, it was difficult
to accumulate enough statistics for Q bin #1, which is close to the 0.25 PE energy
threshold cut. Many channels did not have a time peak fitted in this Q bin because of
the low signal-to-noise ratio. In such cases, similarly a Spline5 extrapolation was applied
63

Time [ns]Extrapolation of Channel 09999
1190

1180
P3_0
P3_1
P3_2
P3_3
P5_2
P5_3
P5_4
P5_5
P7_1
P7_2
P7_3
P7_4
P7_5
P7_6
P7_7

1170

1160
0

50

100

χ 2 / ndf = 798.4 / 164
1159 ± 0.0
2.283 ± 0.001-0.1188 ± 0.0001
0.001609 ± 0.000004-0.0202 ± 0.0001
0.0006887 ± 0.0000016-1.144e-05 ± 1.224e-08
6.71e-08 ± 1.40e-09
0.1169 ± 0.0010-0.0002319 ± 0.0000190-8.286e-07 ± 9.423e-08
5.792e-09 ± 8.824e-10
4.139e-11± 3.574e-12-8.436e-14 ± 6.992e-14-8.209e-16 ± 3.559e-16

150

Qbin

Figure 5.33: An example of extrapolation. The fitted time peak from the original datais plotted in red, while the extrapolated prediction is in blue.
tqhistN @ cable # 00006

Entries10886

T (ns)

600
500
50
400
300

0

200
-50

0

100
50

100

150

0

QBin
(a) 2-D display after T-Q curve subtraction(b) In the right panel the timing averages of thesubtracted 2-D display

Figure 5.34: The time axis offsets after subtracting the preliminary T-Q curve for all
channels is plotted in red. The result after offset correction with the final T-Q curve isplotted in blue.
(as shown in Figure 5.33 and when the extrapolated slope was not positive a linear fit
based on the average trend was instead used. Another problem about Q bin #1 wasthat the low statistics caused a large uncertainty in determining the constant term in the
T-Q curve function Eq. 5.13. To solve it a preliminarily fitted T-Q curve was at first
subtracted from the raw data. After doing so the time-charge 2-D display would become
a flat curve centering around 0 in the time axis. Then the offset in time was calculated
and added into the preliminary T-Q curve. Figure 5.34 illustrates this process.

64

htdiff
Entries

11099

Mean

0.01279

RMS

2.461

1000

500

0

-40

-20

0

20

40

Timing Difference [ns]Figure 5.35: An agreement up to 0.01 ns was achieved between the 2 TQ maps after the
global timing offset correction.
From the final T-Q curve, a list called "TQ map" of the 15 parameters used in thefitting was made for all ID PMT channels. The "TQ map" is what would be used in theupcoming various physics analyses and new Monte Carlo simulations (MC).
5.3.4

Global Timing Offset

Besides the relative timing difference in each individual PMT channel, there was a global
timing offset in all channels first observed when upgrading from ATM to QBEE in SuperK. However, unfortunately the source of such a time shift in the QBEE system remained
unclear. As a temporary solution, a constant shift was added to the 0 order term in the
SK-IV TQ map so that it matched up with the previous one in SK-III. And this has
also been done this time. A shift averaged at 52.8 ns was observed between the SK-V
and SK-IV TQ maps. Comparing to the previous value at 40 ns, the major part in the
difference may be the time offset caused by the new discriminator for the monitor PMT.
Figure 5.35 shows the global timing difference between the new TQ map and the previous
one of SK-IV after a correction of 52.8 ns.
However, this correction by aligning the 2 generations of TQ maps will carry the errors
from the previous to the next. Since the alignment is based on the 0 order constants
that has the lowest statistics, this error propagation may be a severe problem. Thus adetailed investigation on the global timing offset in the electronics is urgently needed.
An independent method (from the TQ map itself) to correct this shift will prevent theaccumulation of errors after many generations.
65Entries

Data - Fit (ns)tqcurv_00014_resabs

180

2

1

0

-1

-2
0

50

100

150

Qbin
Figure 5.36: The difference between data and fitting in all Q bins of PMT 00014. Larger
discrepancy exists in the low charge region.
5.3.5

Timing Correction Quality Checks

The T-Q curve fitting quality was checked by the difference in the time peak and fitted
value as shown in Figure 5.36. Except for the slightly larger discrepancy in the charge
region < 1 pC due to the low statistics, the data and fitted curves agreed with each otherwithin 1 time bin width. Figure 5.37 shows the average and standard deviation of the
data&fitting difference in Q bin range 5∼end for all ID PMTs.

To verify that the time walk effect has been successfully corrected in all ID PMTs, a pol6function was used to fit the T-Q curve subtracted 2-D display for each PMT as shown in
Figure 5.34(a) as an example. The fitted results have confirmed that the subtracted 2-D
displays were flat with negligible curvature as shown in Figure 5.38 and Table 5.9.

corr
For the consistency check of TQ maps, the time peak in this data set Tpeak
corrected by

the SK-V TQ map was compared to the previous Linear Accelerator (LINAC) data hit
times corrected by the SK-IV TQ map. A discrepancy was seen in the charge range < 1
PE, which corresponds to the first few Q bins. Figure 5.39 gives a few examples of thiscomparison at several charge ranges.
It remained unsolved why the USHO-KEC100 laser data has broader width in the time
distribution compared to the LINAC data as shown in Figure 5.39a. The PMT time66

h_resabs

h_resabsmean
Entries

11099

Mean

-0.0005408

RMS

0.005498

800

2000

Entries

11099

Mean

0.1572RMS

0.06928

600

400
1000
200

0
-0.1

-0.05

0

0.05

0
-1

0.1

-0.5

Data - Fit Mean (ns)

0

0.5

1

Data - Fit StdDev (ns)(a) Average data-fitting differences of all ID(b) Standard deviation of data-fitting difference

PMTs

of all ID PMTs

Figure 5.37: The data and fitted results show good agreement in Q bin 5∼end.

(a) 0 order constant of the pol6 fitting(b) coefficient of the 2nd order term in the pol6
fitting

Figure 5.38: The fitting on the T-Q curve subtracted 2-D display shows flat distribution.
All 7 coefficients are centered at 0.

67

p0

−0.02 ± 0.73

p1

−0.02 ± 0.09

p2

(0.09 ± 0.6) × 10−2p3(−0.02 ± 0.37) × 10−3p4

(0.16 ± 0.90) × 10−5p5(−0.02 ± 1.19) × 10−7p6

(0.06 ± 4.67) × 10−10

Table 5.9: Averages of the fitted parameters from the time walk effect corrected T-Q
data of all ID PMTs. The standard deviation in each parameter was assigned as theuncertainty.

(a) Hit time comparison for 0.2(b) Hit time comparison for 0.8(c) Hit time comparison for 1.6< Q < 0.4 PE< Q < 1.0 PE< Q < 1.8 PE

Figure 5.39: The black curves are the LINAC corrected hit times. The red represent the
corr
Tpeak
taken this time. The blue are the corrected time peak from the smeared data thatwere NOT used for the timing calibration but plotted just to show the broadening in thetiming resolution.

68Entries

T (ns)

tqhistN @ cable # 01674
1250

260066

200
180
160
140
120

1200

100
80
60
40
20

1150
0

50

100

0

150

QBin

Figure 5.40: An example of scattered distribution in T-Q 2-D display.
Largely Scattered

Less Severe

202

1674

4418

4641

4778

2267

2532

4825

5336

6744

2882

4070

7404

9061

9195

9506

9691

10356

4572

Table 5.10: PMT channels with similar feature to Figure 5.40. In the "largely scatterd"case the data were too scattered that no T-Q curve could be fitted. In the "less severe"case there were some small "blobs" of scatter but still a usable T-Q curve could be fitted.
resolution is related to the signal charge and for low charges the resolution tends to beworsen. But this feature was not seen in the LINAC data. An investigation on this issue
will be carried out soon. Nevertheless, the 2 data sets still showed great consistency for
Q > 1 PE.
5.3.6

Bad Channels

In total 47 PMT channels (including the 17 blank ones with no PMT) were identified
to be bad channels. Those PMTs either showed no response to the laser light or had anarrow charge output range up to only ∼ 100 PE. Most of them have also been identified by other studies. These channels will not be used in the physics analyses during SK-V.
Besides the already known bad channels, there were some others having scattered distribution in the 2-D display that no clear T-Q curve can be fitted as shown by the example
in Figure 5.40. These PMTs have not been listed as bad channels yet since attempts torecover them are to be made. A list of this kind of PMT channels is summarized in Table
5.10.

69

6

Inputs to Super-K Detector Simulation

The Super-K Detector Simulation (SKDETSIM) is a GEANT3 based Monte Carlo simulation program. With the calibration results, SKDETSIM was tuned to match theenvironmental set-ups of each Super-K phase. In the new SK-V environment, the major
contributions from this work to SKDETSIM are the Hyper-K PMT charge response andthe new Super-K detector timing resolution.

6.1

SPE Charge Distribution for Hyper-K PMTs

To determine Hyper-K PMT’s SPE charge model, a Ni-Cf source that can emit isotropic
γ-rays stably at SPE level was used. As mentioned before, the actual charge response in
PE of each PMT channel was determined by 2 constants: the average conversion factor
from pC to PE in the tank and the relative ratios among PMTs. The average conversion
factor was found to be 2.447 pC/PE for Hyper-K PMTs.
There were 2 sets of data taken at different gains and energy threshold cuts with the
Ni-Cf source. One was at the gain after the voltage adjustment as mentioned in Section
5.2.4 with the default energy threshold at -0.69 mV, which corresponds to roughly 0.25
PE. The other was at a higher gain level about 1.6 time larger and energy threshold at-0.40 mV. The reason for the second data set at higher gain lower threshold was to checkthe SPE profile being cut out below the -0.69 mV threshold. In the case of Super-K
PMTs, the higher gain data set would have a more profound exponential peak around
0 that helped the extrapolation below the energy threshold. However, in the case ofHyper-K PMT as shown by Figure 6.1, no clear peak was seen around 0 even after thegain was increased.
Based on the data shown in Figure 6.1(b), a preliminary fit without considering thethreshold effect was generated using Eq. 6.1. Since the gain was increased, the 2PE peak
was also taken into account. The fitting result is shown in Figure 6.2. In SKDETSIM,
the SPE charge distribution model was sliced into 5000 bins in the range of 0∼50 PE
and the integrated area of each slice was used to decide whether to keep the randomly
generated charge for downstream simulation or not.

70

0.04

A.U.

A.U.

0.06

Hyper-K PMT
Entries 4739515
Mean

1.019

RMS

0.4128Hyper-K PMT
Entries

836320

Mean

1.483

RMS

0.656

0.03
0.04
0.02
0.02
0.01

0
-2

0

2

0
-2

4

0

2

Q [p.e.]4

Q [p.e.](a) Hyper-K PMT Ni-Cf data at normal gain(b) Hyper-K PMT Ni-Cf data at higher gain

normal thresholdlower threshold

Figure 6.1: No clear peak emerged at around 0 after increasing the gain and lowering thethreshold cut. Both peaks were normalized by the number of events.


−

x−p1
√
2p2

f (x) = p0 · e
|
{z

2


−

}

SPE Gaussian peak

x−p4
√
2p5

+ p3 · e
|
{z

2
}

2PE Gaussian peak!
x − p x − p 7
11+ 0.5 · p6 · p0 · erf
− erf
p8
p12
{z
}
|
SPE Back scattering!
x − p x − p 1113+ 0.5 · p9 · p3 · erf
− erf
p12
p14
|
{z
}
SPE-2PE Back scattering!
x − p x − p 7
13+ 0.5 · p10 · p3 · erf
− erf
p8
p14
|
{z
}

(6.1)

2PE Back scattering

Besides the missing part below the energy threshold, another correction to the SPE
charge model is the smearing effect due to the QBEE channel resolution around the edgeof threshold cut. This effect can be seen in Figure 6.1(a)&(b) as the left side of theSPE profiles are not perfectly vertical. Previously in SK-IV, this smearing effect wasestimated by comparing difference in the data taken by ATM module and QBEE system.
However, for Hyper-K PMTs no ATM data is available. Thus a new method to determine

71

(a) Fitting on the Hyper-K SPE charge distri-(b) Fitting on the Hyper-K SPE charge distri-bution from Ni-Cf databution from Ni-Cf data in logarithmic scale

Figure 6.2: The fitting of the SPE charge distribution of Hyper-K PMTs with Ni-Cf data.
The blue curve represents the SPE peak, green the 2PE peak, and cyan the integrated
back scattering components. The red curve shows the overall fitting result.
the energy threshold smearing effect as well as the extrapolation below that threshold iscurrently under investigation.

6.2

Timing Resolution

At each Q bin, the timing resolution of ID PMTs was determined by integrating all
relative timing corrected on-time hits triggered by the USHO-KEC100 laser. Similar
to SK-IV, this time the integrated timing distributions were fitted by an asymmetric
Gaussian function as defined in Eq. 6.2.

A1 · exp(−(t − Tpeak )2 /σ 2 ) + B1 (t > Tpeak )1f (t) =
A · exp(−(t − T )2 /σ 2 ) + B (t ≤ T )
2

peak

2

2

(6.2)

peak

where the Ai , Bi and σi (i = 1, 2) are the fitting parameters. Continuity and differentiability are also required at the boundary t = Tpeak . SInce the Super-K and Hyper-K
PMTs are very different in timing resolution, they were treated separately this time. To
avoid the potential bias from different statistical sizes, i.e. the number of hits gets larger
when light intensity gets larger, the integrated timing distributions were normalized bytheir number of events respectively. Figure 6.3 shows the examples of fitting with Eq 6.2.
The new timing resolution at SPE (Q bin = 14) agreed with the SK-IV value for Super-K
72

(a) Integrated Super-K PMTs’ timing distribu-(b) Integrated Hyper-K PMTs’ timing distribu-

tion and fitting at Q bin = 14

tion and fitting at Q bin = 14

Figure 6.3: Fitting of the integrated timing distribution of Super-K and Hyper-K PMTs.
The events from each PMT were corrected by the TQ map before being summed up. The
x-axis has the reversed time direction, i.e. larger number means earlier hit in time. σr(l ) is the parameter σ1 (σ2 ) in Eq. 6.2.
PMTs within the range of TDC resolution. But since the voltage setting of SK-V is lower
than SK-IV, this agreement means that the SK-V timing resolution is effectively better
since a PMT’s time response will degrade with lower voltage.
The σi ’s of the Super-K and Hyper-K PMTs’ in the charge range if 0.01∼1000 PE are
shown in Figure 6.4. Compared to the Super-K PMT, the Hyper-K one has stronger
pre-pulses in the large charge > 1000 PE and are closer to the main peak in time. Therefore the contamination from the pre-pulses is severer for the Hyper-K tubes, which is thereason of an increment in their σ1 in the large charge region. Meanwhile another featureof Hyper-K PMTs different from the Super-K ones is the "bump" at Q∼2 PE. At thischarge region, the timing resolution does not improve with increasing signal strength but
goes in the opposite direction. Such a trend can also be seen in the Super-K tubes, butinstead of totally reversing the trend it only results in a slower decrement. The cause ofsuch a "bumpy" feature in the timing resolution is still under investigation.
The timing resolutions shown in Figure 6.4 are input into SKDETSIM to generate the
PMT response time using the probability density function73

(a) The timing resolution of Super-K PMTs(b) The timing resolution of Hyper-K PMTs

Figure 6.4: The timing resolution of Super-K and Hyper-K PMTs with respect to charge
Q in PE.

q
(t−t0 )2 
2

exp
−
(t < t0 )2π(σ1 +σ2 )2σ12f (t) = q(t−t0 )2
2
 π(σ +σ(t ≥ t0 )2 exp −
2σ 2
1
2)

(6.3)

2

where t0 is the injection time of a photon into a PMT. To verify the validity of the newtiming resolutions for SK-V environment, the MC simulated events will be compared tovarious data samples including the LINAC and the thru-going cosmic muons. On theother hand, due to a discrepancy between the MC and LINAC event in the timing of low
charge hits, some fitting method other than Eq. 6.2 to generate the timing resolution
parameters is also under studies. These tests are expected to be done after when the
upgrades of LINAC and SKDETSIM are finished.

7

Conclusions and Outlook

In the year 2018-19, Super-K has completed a full scale detector upgrade to SK-V. A variety of refurbishments were done, for example, a new water cycling system was installedin parallel to the existing one. This new system will be used to add Gd into the Super-K
tank in a year or two. Regarding this work, many improvements and updates were madeto the ID PMTs, among which were the 136 50 cm Hyper-K B&L PMTs used to replace
the dead channels from SK-IV. Before the installation, each Hyper-K tube was checked
carefully in an underground laboratory neighboring the Super-K tank. Those PMTs were74

confirmed to be of good quality by the measurement done in the air. The charge andtiming resolutions of Hyper-K PMTs were roughly twice as good as that of Super-K ones.
Meanwhile the measurements after installation in Super-K water also verified this. This
result and the future data of Hyper-K PMTs will serve a critical role in realizing theupcoming Hyper-K project.
The 2 major calibration tasks done by this work are the adjustment of all ID PMTs’
voltages and the new correction table of relative timing difference in each ID PMT channel. Throughout the SK-IV running phase, it was noticed that the average gain of ID
PMTs continuously drifted up. Meanwhile the gain increment varied among individual
PMTs, which resulted a larger spread in the PMT charge responses. To correct this systematic uncertainty, the new voltages targeting at the SK-III initial gain of 1.65 × 107
was determined by a voltage scan for each PMT using a laser diode at the center of thetank. At each voltage in the scan, the SPE charge peak of each PMT was fitted. It was
the first time in Super-K that the SPE charge peak of each individual PMT’s is used todetermine the voltage setting. Such a method is independent of the water quality andhas less bias from the occasional multi-PE signal contamination. After the adjustment,
the Super-K ID gain average has decreased down to 1.70 × 107 , which is ∼85.6% of thegain before adjustment. The ∼3% offset in gain average from the target value was due tothe uncertainty when converting the ADC count into charges, which resulted in a slightly
insufficient adjustment. On the other hand, the spread among ID PMTs has decreased
from 12% to 4% of the average value. The remaining 4% individual difference comesfrom the systematic and statistical error in the voltage curve fitting, which was on average 5.07% and 2.58% respectively. Nevertheless, the real gain and individual difference ofeach ID PMT were further measured by some other works and will be taken into accountin the data reduction and analyses of Super-K.
The relative timing difference in each ID PMT mainly comes from the electronics processing time. Meanwhile the PMT time response is different by signal strengths, which
is known as the time walk effect. These 2 systematic uncertainties were corrected by the
T-Q curves. To generate a T-Q curve, a laser source was enlightened at the tank centerand the timing of each PMT at a certain charge in the range of 0∼3981 pC was fitted.
Then in total ∼180 of such points were used to find the relation between PMT’s charge
and timing, or so-called T-Q curve. By applying the T-Q correction, the PMT’s timingof an event free of the time walk effect can be predicted from its charge. Meanwhile thedifference in electronics processing time was also measured and corrected by calculating
the time lag between the laser flash and PMT hits. Moreover, the detector timing resolu75

tion was also calculated from the T-Q curve corrected laser data. Super-K and Hyper-K
PMTs were treated separately this time. In the case of Super-K PMTs, the new timing
resolution is roughly equivalent to the previous value in SK-IV. However since the voltage
setting has been decreased, the detector timing resolution is effectively improved.
With a lower average voltage, the ID PMTs are expected to have lower dark hit ratethat strongly affect the study of low energy physics. There lies a possibility that Super-K
may lower its energy threshold, which improves its sensitivity to multiple target particles
such as solar and supernova neutrinos. At the mean time, the data collected during thiscalibration will be used to update SKDETSIM to SK-V environment, which helps to improve the physics event reconstruction and neutrino oscillation analyses. Last but no theleast, the calibration framework and software developed this time will be a great sample
for the upcoming calibration of SK-Gd phase, which will happen in 1∼2 years. All ofthese updates and improvements combined together will help to evolve this 20-year-longexperiment to a higher stage of physics studies.

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