# Proposal: JSNS2-II

S. Ajimura Research Center for Nuclear Physics, Osaka University, Osaka
565-0871, JAPAN  M. Botran  University of Michigan, Ann Arbor, MI, 48109, USA
J. H. Choi  Laboratory for High Energy Physics, Dongshin University, Chonnam
58245, KOREA  J  Department of Physics, Chonnam National University, Gwangju,
61186, KOREA  W. Choi  Department of Physics, Chonnam National University,
Gwangju, 61186, KOREA  M. K. Cheoun  Department of Physics, Soongsil
University, Seoul 06978, KOREA  T. Dodo  Research Center for Neutrino Science,
Tohoku University, Sendai, Miyagi 980-8577, JAPAN  H. Furuta  Research Center
for Neutrino Science, Tohoku University, Sendai, Miyagi 980-8577, JAPAN  J.
Goh  Department of Physics, Kyung Hee University, Seoul 02447, Korea  K. Haga
J-PARC Center, JAEA, Tokai, Naka Ibaraki 319-1195, JAPAN  M. Harada  J-PARC
Center, JAEA, Tokai, Naka Ibaraki 319-1195, JAPAN  S. Hasegawa  J-PARC Center,
JAEA, Tokai, Naka Ibaraki 319-1195, JAPAN  Advanced Science Research Center,
JAEA, Tokai, Naka Ibaraki 319-1195, JAPAN  Y. Hino  Research Center for
Neutrino Science, Tohoku University, Sendai, Miyagi 980-8577, JAPAN  T.
Hiraiwa  Research Center for Nuclear Physics, Osaka University, Osaka
565-0871, JAPAN  H. I. Jang  Department of Fire Safety, Seoyeong University,
Gwangju 61268, KOREA  J. S. Jang  Gwangju Institute of Science and Technology,
Gwangju, 61005, KOREA  M. C. Jang  Department of Physics, Chonnam National
University, Gwangju, 61186, KOREA  H. Jeon  Department of Physics,
Sungkyunkwan University, Suwon 16419, KOREA  S. Jeon  Department of Physics,
Sungkyunkwan University, Suwon 16419, KOREA  K. K. Joo  Department of Physics,
Chonnam National University, Gwangju, 61186, KOREA  J. R. Jordan  University
of Michigan, Ann Arbor, MI, 48109, USA  D. E Jung  Department of Physics,
Sungkyunkwan University, Suwon 16419, KOREA  S. K. Kang  School of Liberal
Arts, Seoul National University of Science and Technology, Seoul, 139-743,
KOREA  Y. Kasugai  J-PARC Center, JAEA, Tokai, Naka Ibaraki 319-1195, JAPAN
T. Kawasaki  Department of Physics, Kitasato University, Sagamihara, Kanagawa
252-0373, JAPAN  E. J. Kim  Division of Science Education, Jeonbuk National
University, Jeonju, 54896, KOREA  J. Y. Kim  Department of Physics, Chonnam
National University, Gwangju, 61186, KOREA  S. B. Kim111Co-spokesperson
Department of Physics, Sungkyunkwan University, Suwon 16419, KOREA  S. Y. Kim
University of Michigan, Ann Arbor, MI, 48109, USA  W. Kim  Department of
Physics, Kyungpook National University, Daegu 41566, KOREA  T. Konno
Department of Physics, Kitasato University, Sagamihara, Kanagawa 252-0373,
JAPAN  H. Kinoshita  J-PARC Center, JAEA, Tokai, Naka Ibaraki 319-1195, JAPAN
D. H. Lee  High Energy Accelerator Research Organization (KEK), Tsukuba,
Ibaraki 305-0801, JAPAN  S. Lee  Department of Physics, Kyung Hee University,
Seoul 02447, Korea  I. T. Lim  Department of Physics, Chonnam National
University, Gwangju, 61186, KOREA  E. Marzec  University of Michigan, Ann
Arbor, MI, 48109, USA  T. Maruyama222Spokesperson High Energy Accelerator
Research Organization (KEK), Tsukuba, Ibaraki 305-0801, JAPAN  S. Masuda
J-PARC Center, JAEA, Tokai, Naka Ibaraki 319-1195, JAPAN  S. Meigo  J-PARC
Center, JAEA, Tokai, Naka Ibaraki 319-1195, JAPAN  S. Monjushiro  High Energy
Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, JAPAN  D.
H. Moon  Department of Physics, Chonnam National University, Gwangju, 61186,
KOREA  T. Nakano  Research Center for Nuclear Physics, Osaka University, Osaka
565-0871, JAPAN  M. Niiyama  Department of Physics, Kyoto Sangyo University,
Kyoto 603-8555, JAPAN  K. Nishikawa333Deceased High Energy Accelerator
Research Organization (KEK), Tsukuba, Ibaraki 305-0801, JAPAN  M. Nomachi
Research Center for Nuclear Physics, Osaka University, Osaka 565-0871, JAPAN
M. Y. Pac  Laboratory for High Energy Physics, Dongshin University, Chonnam
58245, KOREA  J. S. Park  High Energy Accelerator Research Organization (KEK),
Tsukuba, Ibaraki 305-0801, JAPAN  S. J. M. Peeters  Department of Physics and
Astronomy, University of Sussex, BN1 9QH, Brighton, UK  H. Ray  University of
Florida, Gainesville, FL, 32611, USA  G. Roellinghoff  Department of Physics,
Sungkyunkwan University, Suwon 16419, KOREA  C. Rott  Department of Physics,
Sungkyunkwan University, Suwon 16419, KOREA  K. Sakai  J-PARC Center, JAEA,
Tokai, Naka Ibaraki 319-1195, JAPAN  S. Sakamoto  J-PARC Center, JAEA, Tokai,
Naka Ibaraki 319-1195, JAPAN  T. Shima  Research Center for Nuclear Physics,
Osaka University, Osaka 565-0871, JAPAN  C. D. Shin  Department of Physics,
Chonnam National University, Gwangju, 61186, KOREA  J. Spitz  University of
Michigan, Ann Arbor, MI, 48109, USA  I. Stancu  University of Alabama,
Tuscaloosa, AL, 35487, USA Y. Sugaya  Research Center for Nuclear Physics,
Osaka University, Osaka 565-0871, JAPAN  F. Suekane  Research Center for
Neutrino Science, Tohoku University, Sendai, Miyagi 980-8577, JAPAN  K. Suzuya
J-PARC Center, JAEA, Tokai, Naka Ibaraki 319-1195, JAPAN  M. Taira  High
Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801,
JAPAN  R. Ujiie  Research Center for Neutrino Science, Tohoku University,
Sendai, Miyagi 980-8577, JAPAN  Y. Yamaguchi  J-PARC Center, JAEA, Tokai, Naka
Ibaraki 319-1195, JAPAN  M. Yeh  Brookhaven National Laboratory, Upton, NY,
11973-5000, USA  I. S. Yeo  Department of Fire Safety, Seoyeong University,
Gwangju 61268, KOREA  C. Yoo  Department of Physics, Kyung Hee University,
Seoul 02447, Korea  I. Yu  Department of Physics, Sungkyunkwan University,
Suwon 16419, KOREA  A. Zohaib  Department of Physics, Chonnam National
University, Gwangju, 61186, KOREA

###### Contents

  1. 1 Introduction
  2. 2 Advantage of two detector configuration
  3. 3 Recent status of sterile neutrino searches
    1. 3.1 World-wide status
      1. 3.1.1 $\nu_{\mu}\to\nu_{e}$ appearance mode
      2. 3.1.2 Disappearance mode
    2. 3.2 The current JSNS2 experiment
  4. 4 The second detector
  5. 5 Signal and backgrounds
  6. 6 Energy spectra of signal and backgrounds
  7. 7 Fit methods and uncertainties
    1. 7.1 Normalization uncertainty
    2. 7.2 Fit method
      1. 7.2.1 Binned likelihood method
      2. 7.2.2 Treatment of systematic uncertainties
  8. 8 Expected sensitivity
  9. 9 Timescale and cost
  10. 10 Acknowledements

##  1 Introduction

This proposal describes the goal and expected sensitivity of the JSNS2-II at
J-PARC Materials and Life Science Experimental Facility (MLF).

The JSNS2-II is the second phase of the JSNS2 experiment (J-PARC Sterile
Neutrino Search at J-PARC Spallation Neutron Source) [1, 2] with two detectors
which are located in 24 m and 48 m baselines to improve the sensitivity of the
search for sterile neutrinos, especially in the low $\Delta m^{2}$ region,
which has been indicated by the global fit of the appearance mode [3]. Note
that the experiment with two detectors were proposed in the JSNS2 proposal
[1], and 25th J-PARC PAC strongly recommended to make the two detector
configuration [4] (2018) as shown in Fig. 1 even though we started the JSNS2
with one detector during the first phase.

Figure 1:  The 25th J-PARC PAC’s recommendation.

Based on the J-PARC PAC’s recommendation, the JSNS2 collaboration has put a
lot of effort in securing the grant, and the Grant-in-Aid for Specially
Promoted Research was awarded in 2020. Therefore, the funding is now available
to build the second detector.

The JSNS2 aims to have a direct test of the LSND experiment [5] using the same
neutrino source ($\mu$ Decay-At-Rest), neutrino target (proton), and detection
principle (Inverse-Beta-Decay: IBD) but uses the short-pulsed 3 GeV proton
beam and Gd-loaded liquid scintillator (GdLS). Therefore, 100 times better
signal-to-noise ratio is given compared to the LSND experiment. Please see the
reference [2] for more details such as the current setup and sensitivity of
the JSNS2 experiment.

The approved Proton-On-Target (POT) of the current JSNS2 with one detector
from the J-PARC PAC is 1.114$\times$1023 (1 MW $\times$ 3 years), while we aim
to have 1 MW $\times$ 5 years for the JSNS2-II. Considering the constraints in
the MLF and the Japanese Fire Law, the baseline of the second detector is 48 m
from the target. To get a better sensitivity, the second detector which has 35
tons of fiducial weight, locates outside of the MLF as shown in Fig. 2. On the
other hand, the current existing detector stays at the location of 24 m
baseline even after the second detector construction.

Figure 2:  The location of the 2nd detector in the JSNS2-II. The orange circle
in the picture shows the location of the detector.

We already started to discuss the issues regarding the Japanese Fire Law and
MLF and there have been no show-stoppers thus far.

##  2 Advantage of two detector configuration

The detector located in the longer baseline can search for the neutrino
oscillations with the lower $\Delta m^{2}$ region in general. However, in
addition, there are a few large advantages to use two detectors compared to
that uses one detector as follows:

  1. 1.

If sterile neutrinos exist, the observed oscillation pattern as a function of
energy will be changed because the neutrino oscillation probability is changed
as functions of the flight length and energy of neutrinos as:
$P(\bar{\nu_{\mu}}\rightarrow\bar{\nu_{e}})=\sin^{2}2\theta\sin^{2}(\frac{1.27\cdot\Delta
m^{2}(eV^{2})\cdot L(m)}{E_{\nu}(MeV)})$. Figure 3 shows the difference of the
oscillation probabilities as a function of the energy with two different
baselines with the different oscillation parameters.

(a) 24m (LSND best fit) (b) 48m (LSND best fit) (c) 24m (JSNS2 best fit case)
(d) 48m (JSNS2 best fit case)

Figure 3:  Oscillation probabilities at 24 m (left) and 48 m (right) with two
different oscillation paramaters. Top: LSND best fit parameters ($\Delta
m^{2},sin^{2}(2\theta)$)=(1.2, 0.003), bottom: the JSNS2 single detector best
fit case. ($\Delta m^{2},sin^{2}(2\theta)$)=(2.5, 0.003)

  2. 2.

The background rates are different between two detectors because the
backgrounds induced from the beam are reduced as a function of distance (1/r2:
r is the distance from the mercury target), while backgrounds induced by
cosmic rays does not depend on the distance. This makes much better
understandings of the backgrounds compared to the one-detector scheme.

  3. 3.

Systematic uncertainties such as normalization of neutrino fluxes are canceled
out using two detectors. This effect will be shown later (section 8).

It might be ideal to use two identical detectors. However JSNS2-II aims to
look for the $\bar{\nu}_{\mu}\to\bar{\nu}_{e}$ appearance and the requirements
to the systematic uncertainties are relatively small. Therefore, after the
detailed understanding of the detector, it is possible to achieve our goals
even using the different size detectors.

##  3 Recent status of sterile neutrino searches

The situation up to 2015 was described in the JSNS2 Technical Design Report
(TDR) [2]. There have been several new results since then. Here we explain the
relevant ones, but please see the reference which reviews them in details [3].

###  3.1 World-wide status

####  3.1.1 $\nu_{\mu}\to\nu_{e}$ appearance mode

The MiniBooNE experiment updated their results recently: Their latest
publication [6] mentioned that the significance of the
$\bar{\nu_{\mu}}\to\bar{\nu_{e}}$ signal compared to background only is
4.7$\sigma$ now. However, as the MicroBooNE experiment [7] pointed out, the
observed excess of events in the low-energy region could be due to single
$\gamma$ production interactions, which are poorly understood in the current
theory, therefore the MiniBooNE cannot distinguish between the oscillation
signal and this background because it is a Cherenkov detector. The MicroBooNE
uses a liquid argon TPC detector and they can distinguish the oscillation
signal and single $\gamma$ events. They are expected to publish their results
in near future.

The far detector of the Short Baseline Neutrino experiment (SBN) at FNAL, the
ICARUS detector, is ready to take data. They are already fully filled with
liquid argon [8], and are waiting for beam. The SBN experiment will provide
direct confirmation or refutal of MiniBooNE anormaly.

####  3.1.2 Disappearance mode

If the neutrino oscillation due to fourth or more mass eigenstates (i.e.
sterile neutrino(s)) exist, the $\nu_{e}\to\nu_{s}$ and $\nu_{\mu}\to\nu_{s}$
are also happened accordingly. Especially, three active plus one sterile
neutrino model have a simple relationship between appearance and disappearance
modes, as shown in our TDR [2] and many other publications (see for example
[3]).

For the $\nu_{e}\to\nu_{s}$ searches using the $\nu_{e}$ disappearance, there
have been (super-)short baseline reactor experiments, such as Daya-Bay [9],
RENO [10], DANSS [11], NEOS [12], Neutrino-4 [13], PROSPECTS [14], Stereo
[15]. They typically put the scintillator detectors with the baseline of
$\sim$10 meters. The Neutrino-4 experiment declares that they observed a clear
oscillation pattern, while other experiments showed the exclusion regions for
the two-dimensional mixing angles and $\Delta m^{2}$ plane although some of
allowed regions are remained.

$\nu_{\mu}\to\nu_{s}$ searches using the $\nu_{\mu}$ disappearance have been
developed by IceCube [16], Super-Kamionkande [17], MINOS/MINOS+ [18] and T2K
[19] recently. Their results showed no sterile neutrinos, and there is clear
tension between the apperance and the disapperance modes.

###  3.2 The current JSNS2 experiment

Under the current situation, the experiments that provide direct tests for the
apperance modes are getting crucial. For the direct test of MiniBooNE,
MicroBooNE itself and SBN are important. On the other hand, for the direct
test of LSND, the JSNS2 plays an important role. The second detector of the
JSNS2 must be constructed in a timely fashion because the funding to build the
second detector was granted in 2020 as recommended by J-PARC PAC.

The JSNS2 has started data taking from June 2020 [20]. Currently, we are
checking the background rates in the data. We will show some concrete
background numbers in the presentation at the next J-PARC PAC.

Currently, we assume that the amount of backgrounds in the second detector is
the same as the current one although we expect that they are much smaller
backgrounds because the beam-related background, such as gamma rays from MLF
third floor concrete, will be reduced drastically compared to the current
JSNS2 [2].

##  4 The second detector

The location of the second detector is shown in Fig. 2. In this location, we
can have a 8 m $\times$ 8 m space to satisfy the Japanese Fire Law constraint,
which requires an empty space of 5 m from the edge of the detector.

The second detector has a similar structure as the existing JSNS2 detector,
which is already working. The conceptual design of the detector is shown in
Fig. 4. As shown here, the detector is placed outside the MLF building and no
specific buildings for the detector is made, therefore, we will make a
stainless roof on the top of the detector. The electronics, PMT cables and
slow monitor/control system are put here.

Figure 4:  The structure of the 2nd detector in the JSNS2-II.

To compensate for the reduction of the neutrino flux due to the distance from
the mercury target, the target mass of the GdLS, which is the Linear
AlkylBenzene (LAB) based liquid scintillator, inside the acrylic vessel is
increased to 35 tons. On the other hand, the detector located at the longer
distance is better at searching in the lower $\Delta m^{2}$ region of the
neutrino oscillation.

Similar to reactor experiments such as Daya-Bay [9], RENO [21], Double-Chooz
[22], we will have double stainless tank structure. The inner stainless
structure makes the sepration of gamma catcher (dark brown) and veto (light
brown) regions. In veto region, the same reflector sheets (REIKO LUIREMIRROR
[23]) as the existing JSNS2 detector will be used. The gamma catcher and veto
regions are filled with pure liquid scintillator (LS), which is also based on
the LAB. The total weight of the pure LS is about 130 tons.

To keep the same photo coverage of the detector as the first detector, we will
surround the acrlyic vessel with the 240 PMTs.

All details of this detector structure will be described in the Technical
Design Report (TDR) of the JSNS2-II. Some of GdLS and pure LS (and PMTs if
possible) could be donated from the Daya-Bay experiment. The JSNS2 has started
and will continue to negotiate for this donation.

##  5 Signal and backgrounds

Based on the JSNS2 TDR [2], only the following three data samples must be
considered to calculate the sensitivity. Other background components are
negligible. The realistic estimation of the background components with the
real data taken by the existing detector will be shown in the PAC
presentation.

  1. 1.

signal : $\mu^{+}\to
e^{+}+\nu_{e}+\bar{\nu}_{\mu}:\bar{\nu}_{\mu}\to\bar{\nu}_{e}$.

  2. 2.

intrinsic background : $\mu^{-}\to e^{-}+\nu_{\mu}+\bar{\nu}_{e}$.

  3. 3.

accidental backgrounds

Hereafter, we will assume that the numbers of events with the event selection
efficiency are the same as those in the TDR if the time exposure, detector
size, and the baseline of the location are identical, but scaled as function
of exposure time and detector fiducial volume for the accidental background,
and scaled by 1/r2 in addition to the time exposure and detector size, for the
intrinsic background.

Table 1 summarizes the number of events in the TDR and those in this proposal
configuration. The 1 MW $\times$ 5 years are assumed here to conclude LSND
region with 3 sigma confidence level.

| Contents |  Current JSNS2 | near(24m) | far(48m)
---|---|---|---|---
|  | 17tons | 17tons | 35tons
|  |  5000h/y$\times$3y |  5000h/y$\times$5y |  5000h/y$\times$5y
| $sin^{2}2\theta=3.0\times 10^{-3}$ |  |  |
| $\Delta m^{2}=2.5eV^{2}$ | 87 | 145 | 24
| $sin^{2}2\theta=3.0\times 10^{-3}$ |  |  |
| $\Delta m^{2}=1.2eV^{2}$ | 62 | 103 | 77
| (Best fit values of LSND) |  |  |
|  $\overline{\nu}_{e}$ from $\mu^{-}$ | 43 | 72 | 36
| ${}^{12}C(\nu_{e},e^{-})^{12}N_{g.s.}$ | 3 | 5 | 2
background | beam-associated fast n |  $\leq$2 |  $\leq$3 |  $\leq$2
| Cosmic-induced fast n | negligible | negligible | negligible
| Total accidental events | 20 | 33 | 67
Table 1:  Summary of the number of events based on the reference [2]. Summary
of the event rate for 5000 h/y$\times$3 years for one 17-ton detector (left:
[2]) and those with 5000 h/y$\times$5 years for the near (24 m) and far (48 m)
detectors. Note that the rate of the beam-related background components has
been changed as function of the fiducial mass, the exposure time and the
distance from the target. Cosmic ray related backgrounds are changed as
function of the fiducial mass and exposure time only.

The expected energy spectra of the background will be described in the next
section.

##  6 Energy spectra of signal and backgrounds

As described in the JSNS2 proposal [1], the energy spectra of the signal and
background are used to separate them. The beam timing can select the neutrino
production from muon (plus) decay-at-rest ($\mu$DAR) from others. Note that
the Michel spectrum of $\mu$DAR is well known thanks to the huge efforts made
by the elementary particle physicists’ so far [24].

To make the fitting templates, we used the official JSNS2 simulation (RAT) and
reconstruction (JADE) tools. For example, the energy loss in the acrylic
vessel is very well simulated using GEANT4 [25].

Figure 5 shows the true $\bar{\nu_{e}}$ energy and reconstructed energy
spectra for the signal (with high $\Delta m^{2}$ region). The event vertices
are uniformly randomized in the acrylic vessel region of the detector. The
difference of the spectra between the true $\bar{\nu_{e}}$ energy and observed
reconstructed energy is mainly due to the energy loss in the acrylic vessel.
However, some of them are due to IBD interaction [26].

Figure 6 shows the 2D plot between the true positron energy and the true
$\bar{\nu_{e}}$ energy (left), and that between the reconstructed energy and
the true $\bar{\nu_{e}}$ energy (right). You can see the effects from the IBD
neutrino interaction, the energy reconstruction and the energy loss inside the
acrylic vessel.

(a) The energy spectrum of signal (b) The reconstructed energy of signal
events

Figure 5:  True $\bar{\nu}_{e}$ energy (left) and the reconstructed energy
(right).

(a) True $\bar{\nu}_{e}$ vs True Positron Energy (b) True $\bar{\nu}_{e}$ vs
Reconstructed Positron Energy

Figure 6:  True energy of $\bar{\nu}_{e}$ (horizontal axis) and true energy of
positrons (vertical) simulated one (left). True energy of $\bar{\nu}_{e}$
(horizontal axis) and reconstructed energy of positrons (vertical) (right).

Figure 7 shows the true and reconstructed energy spectra for the intrinsic
background ($\bar{\nu}_{e}$ from $\mu^{-}$). Event vertices are uniformly
randomized in the acrylic vessel region.

(a) The energy spectrum of intrinsic $\bar{\nu}_{e}$ background (b) The
reconstructed energy

Figure 7:  True $\bar{\nu}_{e}$ energy (left) and the reconstructed energy
(right).

Figure 8 shows the reconstructed energy spectrum for the accidental
background. The background of the prompt IBD region is dominated by the gamma
rays induced by cosmic rays. As pointed out by [27], the gamma rays are
generated on the surface of the stainless steel tank.

Figure 8:  The reconstructed energy of the accidental background.

The expected energy spectra with the LSND best fit parameters of neutrino
oscillations ($\Delta m^{2},sin^{2}(2\theta)$)=(1.2, 0.003)) are shown in Fig.
9, The energy spectrum of the $\overline{\nu}_{e}$ generated by the
oscillation at 48m baseline is significantly different from that of the
intrinsic $\overline{\nu}_{e}$ background.

(a) The energy spectrum of 24m detector (b) The energy spectrum of 48m
detector

Figure 9:  Expected observed energy spectrum in the JSNS2-II in two detectors
in the LSND best fit case for the 24 m detector (left) and the 48 m detector
(right).

##  7 Fit methods and uncertainties

The important difference between the JSNS2 [2] and the JSNS2-II is the ability
of JSNS2-II to use different energy spectra information with two different
baselines.

Figure 10 shows the expected energy spectra in 24 m detector and 48 m detector
for the case with no neutrino oscillations in the JSNS2-II. To make the
sensitivity plots, this pseudo-data is used.

As mentioned above, we have two background components. One is from the
accidental backgrounds, and the other is from the intrinsic $\bar{\nu}_{e}$
from $\mu^{-}$.

(a) The energy spectrum of 24m detector (b) The energy spectrum of 48m
detector

Figure 10:  Expected observed energy spectrum in the JSNS2-II in two
detectors: 24 m detector (left), and 48 m detector (right).

The fitter considers what is the best mixture of the three components among
(a) oscillated signal, (b) accidental background, (c) intrinsic
$\bar{\nu}_{e}$ from $\mu^{-}$ to explain the energy spectra in Fig. 10. Of
course, it is crucial how accurately the normalization factors of these three
components are known, therefore the systematic uncertainties of the factors
will be discussed later.

###  7.1 Normalization uncertainty

For the fit of the oscillation parameters, $\Delta m^{2}$ and
$\sin^{2}(2\theta)$, constraints of the background normalization are
important. However, $\bar{\nu}_{e}$ from $\mu^{-}$ has a very poor
normalization constraint from the external information since the production
rates of charged pions are not well known due that there have never been any
experiments to study the interactions between 3 GeV protons and mercury
target. Therefore, 50$\%$ of the uncertainty of the normalization factor for
this background is used.

On the other hand, the cross section for the $\nu_{e}+^{12}C\rightarrow
e+^{12}N_{gs}$ reaction is known at a 10$\%$ level [28]. The lifetime of
$N_{gs}\beta$ decay and the $e^{-}$ energy spectrum are also well known. The
measurement of the reaction provides the normalization factor for the
oscillated signal ($\bar{\nu_{e}}+p\rightarrow e^{+}+n$) since the parent
particle for the oscillated signal is $\bar{\nu_{\mu}}$ from $\mu^{+}$ decays
($\mu^{+}\rightarrow e^{+}+\bar{\nu_{\mu}}+\nu_{e}$). Note that the
determination of the normalization factor can be done at the 10$\%$ level.

Finally, the normalization factor of the accidental background can be very
well determined by data since the main background of the IBD prompt region is
gamma rays induced by the cosmic rays and the IBD delayed background is caused
from the beam related gamma rays from the floor and gamma rays induced by the
cosmic rays which have small time structure of the rate. So, we don’t need the
specific systematic uncertainty on this background normalization.

###  7.2 Fit method

To get the exclusion region, we use the sum of the backgrounds (intrinsic
$\bar{\nu}_{e}$ and accidental backgrounds) as the pseudo-data as mentioned
above. In this scheme, the maximum likelihood always obtains $\sin^{2}2\theta$
= 0, regardless of the $\Delta m^{2}$.

####  7.2.1 Binned likelihood method

A binned maximum likelihood method is used for the analysis. The method fully
utilizes the energy spectrum of each background and signal components, thus
the amount of the signal components can be estimated efficiently.

For this purpose, the following equation is used.

$\displaystyle L$ $\displaystyle=$ $\displaystyle L_{1}\times L_{2}$ (1)
$\displaystyle=$
$\displaystyle\displaystyle\left[\Pi_{i}P_{1}(N_{exp}|N_{obs})_{i}\right]_{1}\times\left[\Pi_{i}P_{2}(N_{exp}|N_{obs})_{i}\right]_{2}$
(2) $\displaystyle P(N_{exp}|N_{obs})$ $\displaystyle=$
$\displaystyle\frac{e^{-N_{exp}}\cdot(N_{exp})^{N_{obs}}}{N_{obs}!}$ (3)

where, $L_{1}$ and $L_{2}$ are the likelihoods of the first and second
detectors, the index $i$ refers to the $i$-th energy bin, $N_{exp}$ is
expected number of events in $i$-th bin, $N_{obs}$ is number of observed
events in $i$-th bin. Energies between 20 and 60 MeV are only considered
because the energy cut above 20 MeV is applied for the primary signal as
explained before. Note that $N_{exp}=N_{sig}(\Delta
m^{2},\sin^{2}2\theta)+\displaystyle\sum N_{bkg}$, and $N_{sig}(\Delta
m^{2},\sin^{2}2\theta)$ is calculated by the two flavor neutrino oscillation
equation as shown before:
$P(\bar{\nu_{\mu}}\rightarrow\bar{\nu_{e}})=\sin^{2}2\theta\sin^{2}(\frac{1.27\cdot\Delta
m^{2}(eV^{2})\cdot L(m)}{E_{\nu}(MeV)})$.

The maximum likelihood point gives the best fit parameters, and 2$\Delta lnL$
provides the uncertainty of the fit parameters. As shown in the PDG [24], we
have to use the 2$\Delta lnL$ for 2 parameter fits to determine the
uncertainties from the fit.

####  7.2.2 Treatment of systematic uncertainties

Equation 1 takes only statistical uncertainty into account, therefore the
systematic uncertainties should be incorporated in the likelihood.
Fortunately, energy spectrum of the oscillated signal and background
components are well known, thus the error (covariance) matrix of energy is not
needed. Note that the uncertainty on the energy scale does not affect to the
sensitivity if we achieve the 1$\%$ systematic error as described in [29] (See
Fig.121 therein).

In this case, the uncertainties of the overall normalization of each component
have to be taken into account, and the assumption is a good approximation.

In order to incorporate the systematic uncertainties, the constraint terms
should be added to Equation 1 and the equation is changed as follows.

$\displaystyle L$ $\displaystyle=$
$\displaystyle[\Pi_{i}P(N_{exp}^{{}^{\prime}}|N_{obs})_{i}]\times
e^{-\frac{(1-f_{1})^{2}}{2\Delta\sigma_{1}^{2}}}\times
e^{-\frac{(1-f_{2})^{2}}{2\Delta\sigma_{2}^{2}}}$ (4)

where $f_{j}$ are nuisance parameters to give the constraint term on the
overall normalization factors. $N_{exp}^{{}^{\prime}}=f_{1}\cdot
N_{sig}(\Delta m^{2},\sin^{2}2\theta)+f_{2}\cdot N_{intrinsic\hskip
2.84544ptbkg}+N_{accidental\hskip 2.84544ptbkg}$. $\Delta\sigma_{i}$ gives the
uncertainties on the normalization factors of each components. In this
proposal, the profiling fitting method is used to treat the systematic
uncertainties. The method is widely known as the correct fitting method as
well as the marginalizing method. The profiling method fits all nuisance
parameters as well as oscillation parameters.

As mentioned above, the flux of the $\bar{\nu}_{e}$ from $\mu^{-}$ decays
around the mercury target has very poor constraints from the external
information. For this situation, the uncertainty of this background component
is assigned to be 50$\%$.

Table 2 shows the summary of the uncertainty of the normalization factors for
the signal and background components. They are regarded as inputs of
$\Delta\sigma$ although only $\bar{\nu}_{e}$ from $\mu^{-}$ and the accidental
background are used as mentioned above.

components | uncertainty | comments
---|---|---
signal |  10$\%$ |  normalized by $\nu_{e}$ from $\mu^{+}$
$\bar{\nu_{e}}$ from $\mu^{-}$ |  50 $\%$ |
cosmic / beam | negligible | well known from calibration source
Table 2:  Summary of uncertainties on the normalization factors. Note that
only $\bar{\nu}_{e}$ from $\mu^{-}$ and accidental backgrounds are used in the
fitting since they are dominant ones in TDR.

##  8 Expected sensitivity

Figure 11 shows the sensitivity of the JSNS2-II. We assume that the starting
point of the JSNS2-II is after 3 years of running of the current JSNS2
experiment. For the reference, the sensitivity of the current JSNS2 experiment
[2] is also shown.

The sensitivity becomes better, especially in the low $\Delta m^{2}$ region,
which has been indicated by the global fit of the appearance mode [3] because
of the longer baseline. The 3$\sigma$ C.L. line nicely covers most of LSND
indicated regions.

Figure 11:  The sensitivity of the JSNS2-II (right). For the comparison, the
sensitivity of the current JSNS2 is also shown in the left.

To understand the power of the sensitivity of each detector (24 m and 48 m
baselines) and combination of the signal and background understanding, Figs.
12 compare the sensitivity with each detector only and JSNS2-II. Below 1 eV2,
the second detector effects are large as expected. Also we can see the
cancellation effects of the systematic uncertainties on the neutrino flux
normalizations, espaecially at lower $\Delta m^{2}$. In the lower $\Delta
m^{2}$ region, the energy spectra between the oscillation signals and the
intrinsic background are getting closer due to the oscillation pattern. In
that case, the cancellation effects of the normalization error on the
intrinsic background due to two detectors are large.

(a) near (24 m) (b) far (48 m) (c) each detector/combined

Figure 12:  The sensitivity of the near and the far detectors. (a): the near
(24 m) detector only. (b): the far (48 m) detector only. (c): overlaid plots
for each detctor and the JSNS2-II.

##  9 Timescale and cost

The possible timescale of the JSNS2-II is shown in Fig. 13.

Figure 13:  The timescale of the JSNS2-II.

Whilst running the current JSNS2 experiment, the second detector will be
built, and the JSNS2-II will start data taking from FY2023.

Table 3 shows the cost estimation of the second detector. These numbers are
based on the experience of the 1st detector construction. Note that the Grant-
in-Aid for Specially Promoted Research in Japan is adpoted in FY2020,
therefore 480M Yen was granted to this project. We assume some of components
could be donated from the foreign experiment(s) here.

Item | Unit price | Quantity | Total
---|---|---|---
* PMTs & Electronics system : | 500Ky/ch | 240 ch | 50My
Tanks & Acrylic Vessels : | 120My/set |  | 120My
Gd-LS, Buffer-LS |  |  | 10My
Fluid handling and infrastructure | 50My/set | 1 set | 50My
Miscellaneous |  |  | 50My
Grand Total |  |  | 280My
Table 3: Cost estimation (the second (far) detector). Donations from other
foreign experiment(s) are assumed.

##  10 Acknowledements

We thank the J-PARC staff for their support. We acknowledge the support of the
Ministry of Education, Culture, Sports, Science, and Technology (MEXT) and the
JSPS grants-in-aid (Grant Number 16H06344, 16H03967, 20H05624), Japan. This
work is also supported by the National Research Foundation of Korea (NRF)
Grant No. 2016R1A5A1004684, 2017K1A3A7A09015973, 2017K1A3A7A09016426,
2019R1A2C3004955, 2016R1D1A3B02010606, 2017R1A2B4011200, 2018R1D1A1B07050425,
2020K1A3A7A0908 0133 and 2020K1A3A7A09080114. Our work has also been supported
by a fund from the BK21 of the NRF. The University of Michigan gratefully
acknowledges the support of the Heising-Simons Foundation. This work conducted
at Brookhaven National Laboratory was supported by the U.S. Department of
Energy under Contract DE-AC02-98CH10886. The work of the University of Sussex
is supported by the Royal Society grant no.IES\R3\170385

## References

  * [1] M. Harada, $\it{et}$ $\it{al}$. arXiv:1310.1437 (2013)
  * [2] S. Ajimura, $\it{et}$ $\it{al}$. arXiv:1705.08629 (2017)
  * [3] M. Dentler, $\it{et}$ $\it{al}$. arXiv:1803.10661 (2018)
  * [4] https://j-parc.jp/researcher/Hadron/en/pac_1801/PAC25thMinutes_approved.pdf
  * [5] A. Aguilar, $\it{et}$ $\it{al}$. Phys. Rev. D $\bf{64}$, 112007 (2001).
  * [6] A. A. Aguilar-Arevalo $\it{et}$ $\it{al}$. (MiniBooNE Collaboration) Phys. Rev. Lett. $\bf{121}$, 221801 (2018)
  * [7] https://microboone.fnal.gov/
  * [8] https://indico.fnal.gov/event/43209/contributions/187821/attachments/130738/159560/Neutrino2020_Betancourt_.pdf
  * [9] F. P. An, $\it{et}$ $\it{al}$, Phys. Rev. Lett. $\bf{117}$ 15 151802 (2016).
  * [10] J. H. Choi, $\it{et}$ $\it{al}$, arXiv:2006.07782 (2020)
  * [11] I. Alekseev $\it{et}$ $\it{al}$, arXiv:1804.04046 (2018)
  * [12] Y. Ko $\it{et}$ $\it{al}$, Phys. Rev. Lett. $\bf{118}$ 12 121802 (2017).
  * [13] A. P. Serebrov, $\it{et}$ $\it{al}$. arXiv:1809.10561 (2018)
  * [14] M. Andriamirado, $\it{et}$ $\it{al}$, arXiv:2006.11210 (2020)
  * [15] H. Almazán $\it{et}$ $\it{al}$, Phys. Rev. $\bf{D102}$, 052002
  * [16] https://icecube.wisc.edu/news/view/749
  * [17] R. Wendell, $\it{et}$ $\it{al}$. Phys. Rev. $\bf{D81}$ 092004 (2010)
  * [18] P. Adamson, $\it{et}$ $\it{al}$. Phys. Rev. Lett. $\bf{122}$ 9, 091803 (2019)
  * [19] K. Abe, $\it{et}$ $\it{al}$. Phys.Rev. $\bf{D99}$ 7, 071103 (2019)
  * [20] https://indico.fnal.gov/event/43209/contributions/187854/attachments/129166/159526/Neutrino2020_JSNS2_v3.pdf
  * [21] J. K. Ahn, $\it{et}$ $\it{al}$. Phys. Rev. Lett. $\bf{108}$ 191802 (2012)
  * [22] Y. Abe, $\it{et}$ $\it{al}$. Phys. Rev. Lett. $\bf{108}$ (2012) 131801
  * [23] http://www.reiko.co.jp/eng/product_film.html
  * [24] https://pdg.lbl.gov/
  * [25] https://geant4.web.cern.ch/
  * [26] P. Vogel and J. F. Beacom, Phys. Rev. $\bf{D60}$ 053003\.
  * [27] M. Harada, $\it{et}$ $\it{al}$. arXiv:1502.02255 (2015).
  * [28] E. Kolbe, K. Langanke, G. Martinez-Pinedo, P .Vogel, J. Phys. G29 2569 (2003)
  * [29] https://research.kek.jp/group/mlfnu/JSNS2_rerevisedTDR_180517.pdf