PHYSICAL REVIEW D 93, 012004 (2016)

First measurement of radioactive isotope production through cosmic-ray
muon spallation in Super-Kamiokande IV
Y. Zhang,33 K. Abe,1,30 Y. Haga,1 Y. Hayato,1,30 M. Ikeda,1 K. Iyogi,1 J. Kameda,1,30 Y. Kishimoto,1,30 M. Miura,1,30
S. Moriyama,1,30 M. Nakahata,1,30 T. Nakajima,1 Y. Nakano,1 S. Nakayama,1,30 A. Orii,1 H. Sekiya,1,30 M. Shiozawa,1,30
A. Takeda,1,30 H. Tanaka,1 T. Tomura,1,30 R. A. Wendell,1,30 T. Irvine,2 T. Kajita,2,30 I. Kametani,2 K. Kaneyuki,2,30,*
Y. Nishimura,2 E. Richard,2 K. Okumura,2,30 L. Labarga,3 P. Fernandez,3 J. Gustafson,4 C. Kachulis,4 E. Kearns,4,30
J. L. Raaf,4 J. L. Stone,4,30 L. R. Sulak,4 S. Berkman,5 C. M. Nantais,5 H. A. Tanaka,5 S. Tobayama,5 M. Goldhaber,6,*
G. Carminati,7 N. J. Griskevich,7 W. R. Kropp,7 S. Mine,7 A. Renshaw,7 M. B. Smy,7,30 H. W. Sobel,7,30 V. Takhistov,7
P. Weatherly,7 K. S. Ganezer,8 B. L. Hartfiel,8 J. Hill,8 N. Hong,9 J. Y. Kim,9 I. T. Lim,9 A. Himmel,10 Z. Li,10
K. Scholberg,10,30 C. W. Walter,10,30 T. Wongjirad,10 T. Ishizuka,11 S. Tasaka,12 J. S. Jang,13 J. G. Learned,14 S. Matsuno,14
S. N. Smith,14 M. Friend,15 T. Hasegawa,15 T. Ishida,15 T. Ishii,15 T. Kobayashi,15 T. Nakadaira,15 K. Nakamura,15,30
Y. Oyama,15 K. Sakashita,15 T. Sekiguchi,15 T. Tsukamoto,15 A. T. Suzuki,16 Y. Takeuchi,16,30 T. Yano,16 S. Hirota,17K. Huang,17 K. Ieki,17 T. Kikawa,17 A. Minamino,17 T. Nakaya,17,30 K. Suzuki,17 S. Takahashi,17 Y. Fukuda,18 K. Choi,19
Y. Itow,19 T. Suzuki,19 P. Mijakowski,20 K. Frankiewicz,20 J. Hignight,21 J. Imber,21 C. K. Jung,21 X. Li,21 J. L. Palomino,21
M. J. Wilking,21 C. Yanagisawa,21 H. Ishino,22 T. Kayano,22 A. Kibayashi,22 Y. Koshio,22 T. Mori,22 M. Sakuda,22 Y. Kuno,23
R. Tacik,24,32 S. B. Kim,25 H. Okazawa,26 Y. Choi,27 K. Nishijima,28 M. Koshiba,29 Y. Suda,29 Y. Totsuka,29,*
M. Yokoyama,29,30 C. Bronner,30 M. Hartz,30 K. Martens,30 Ll. Marti,30 Y. Suzuki,30 M. R. Vagins,30,7 J. F. Martin,31
P. de Perio,31 A. Konaka,32 S. Chen,33 and R. J. Wilkes34(Super-Kamiokande Collaboration)
1

Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka,
Gifu 506-1205, Japan
2
Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo, Kashiwa,
Chiba 277-8582, Japan3
Department of Theoretical Physics, University Autonoma Madrid, 28049 Madrid, Spain
4
Department of Physics, Boston University, Boston, Massachusetts 02215, USA
5
Department of Physics and Astronomy, University of British Columbia, Vancouver,
British Columbia V6T1Z4, Canada
6
Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
7
Department of Physics and Astronomy, University of California, Irvine, Irvine,
California 92697-4575, USA
8
Department of Physics, California State University, Dominguez Hills, Carson, California 90747, USA
9
Department of Physics, Chonnam National University, Kwangju 500-757, Korea
10
Department of Physics, Duke University, Durham North Carolina 27708, USA
11
Junior College, Fukuoka Institute of Technology, Fukuoka, Fukuoka 811-0295, Japan
12
Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan
13
GIST College, Gwangju Institute of Science and Technology, Gwangju 500-712, Korea
14
Department of Physics and Astronomy, University of Hawaii, Honolulu, Hawaii 96822, USA
15High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
16
Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan17
Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan18
Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan
19
Solar Terrestrial Environment Laboratory, Nagoya University, Nagoya, Aichi 464-8602, Japan
20
National Centre For Nuclear Research, 00-681 Warsaw, Poland
21
Department of Physics and Astronomy, State University of New York at Stony Brook,
New York 11794-3800, USA
22
Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan
23
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
24
Department of Physics, University of Regina, 3737 Wascana Parkway, Regina,
Saskatchewan S4SOA2, Canada
25
Department of Physics, Seoul National University, Seoul 151-742, Korea
26
Department of Informatics in Social Welfare, Shizuoka University of Welfare, Yaizu,
Shizuoka 425-8611, Japan
27
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
28
Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
29
The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan

2470-0010=2016=93(1)=012004(12)012004-1© 2016 American Physical Society

Y. ZHANG et al.

PHYSICAL REVIEW D 93, 012004 (2016)30

Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes
for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan
31
Department of Physics, University of Toronto, 60 St., Toronto, Ontario M5S1A7, Canada
32
TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T2A3, Canada
33
Department of Engineering Physics, Tsinghua University, Beijing 100084, China
34
Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA(Received 27 September 2015; published 15 January 2016)

Cosmic-ray-muon spallation-induced radioactive isotopes with β decays are one of the major backgrounds for solar, reactor, and supernova relic neutrino experiments. Unlike in scintillator, production
yields for cosmogenic backgrounds in water have not been exclusively measured before, yet they are
becoming more and more important in next generation neutrino experiments designed to search for raresignals. We have analyzed the low-energy trigger data collected at Super-Kamiokande IV in order todetermine the production rates of 12 B, 12 N, 16 N, 11 Be, 9 Li, 8 He, 9 C, 8 Li, 8 B, and 15 C. These rates wereextracted from fits to time differences between parent muons and subsequent daughter β’s by fixing the
known isotope lifetimes. Since 9 Li can fake an inverse-beta-decay reaction chain via a β þ n cascade decay,
producing an irreducible background with detected energy up to a dozen MeV, a dedicated study is neededfor evaluating its impact on future measurements; the application of a neutron tagging technique using
correlated triggers was found to improve this 9 Li measurement. The measured yields were generally foundto be comparable with theoretical calculations, except the cases of the isotopes 8 Li=8 B and 9 Li.
DOI: 10.1103/PhysRevD.93.012004

I. INTRODUCTION
Cosmic-ray muon spallation induced radioactive isotopes with β decays are one of the major backgrounds forsolar, reactor, and supernova relic neutrino experiments.
Although the production yields for spallation backgrounds
have been extensively measured in liquid scintillator
experiments [1–3], there has been a lack of measurementsof these isotopes produced in water. In this case, it isunderstood that cosmic-ray muons and their subsequent
showers interact with 16 O nuclei to produce isotopes, whichusually have a lifetime up to tens of seconds and canundergo a cascade decay with β energy ranging from a few
MeV to a dozen MeV. For neutrino interactions in thisenergy range, these events can form a background inplanned next-generation water Cherenkov detectors [4–8],
which are designed for detecting signals such as solar
neutrino-electron elastic scattering or inverse beta decay(IBD; ν̄e þ p → eþ þ n) of antineutrinos from reactors or
core-collapse supernovae.
Previous studies at Super-Kamiokande (SK)—where thecosmic-ray muon rate is around 2 Hz—developed cuts toremove the spallation backgrounds produced in water byusing the event time offset and distance to the preceding
muon as well as the muon’s light production in relation to
its path length [9–12]. However, many long-lived isotopes
still survived and affected the search for a low-energy
upturn of the solar 8 B neutrino spectrum as well as the huntfor evidence of supernova relic neutrinos (SRNs), also
known as diffuse supernova neutrino background (DSNB),*

Deceased.

emitted from past core-collapse supernovae. Recently,
theoretical progress has been made in the calculation of
the production and properties of these backgrounds inwater, shedding light on practical improvements in spallation background rejection [13–15]. Providing experimental
data should help improve knowledge in this area.
In addition, certain spallation products in water are ofparticular interest for antineutrino detection, as decays fromthese isotopes can mimic the IBD signature. This affects thesearch for reactor neutrinos as well as for SRNs. The SRN
search is particularly vulnerable to the spallation background since its expected signal event rate is quite low. We
find that of the potential spallation isotopes only the decayof 9 Li can have a significant contribution through the βenergy tail to the “golden” SRN search window of
9.5–29.5 MeV in positron kinetic energy, in which thecontribution from both reactor neutrino and atmospheric
neutrino backgrounds is relatively small. Theoretically, the9
Li isotope is known to be not directly produced by the
primary muon, but rather by the secondary π − interactingwith the 16 O nucleus: π − þ 16 O → α þ 2p þ n þ 9 Li,
where 9 Li has a lifetime of 0.26 s and decays into β þ nwith a probability of 50.8%  0.9% [16]. This feature canbe exploited to separate the 9 Li candidates from otherisotope events and give a better measurement on thecorresponding yield, if the delayed neutrons are tagged
as was done in the SK-IV SRN search [17].
In this article, the study of cosmogenic isotopes produced in SK-IV is described in detail. Section II introduces
the SK detector and performance. Section III describes
the definition and classification of cosmic-ray muons.
Section IV presents the measurement of production rates

012004-2

FIRST MEASUREMENT OF RADIOACTIVE ISOTOPE …

II. EXPERIMENTThe SK experiment, a cylindrical, 50-kton water
Cherenkov detector with 2700 meter water equivalent
overburden, consists of two volumes: an outer detector(OD) and an inner detector (ID) [18]. The OD is viewed by1885 outward-pointing photomultiplier tubes (PMTs),
which are used to tag charged particles originating fromoutside (or exiting) the ID. An OD trigger is issued when
the number of OD PMT hits within 200 ns exceeds 22. The
ID has a diameter of 33.8 m and a height of 36.2 m and issurrounded by 11,129 inward-pointing PMTs, which areused to detect the Cherenkov light from charged particles
traveling in the ID.
At SK, low-energy events are triggered by the number ofcoincident ID PMT hits within 200 ns, in which an ID PMT
hit is defined as one having a recorded charge over 0.25
photoelectrons. In the summer of 2008, a new electronics
and online system was successfully installed to enhance thedata-processing capability of SK [19]. The running period
after that time is referred to as SK-IV, during which thetrigger threshold for low-energy events was consequently
lowered to 3.5 MeV. Physics analyses for solar neutrinos
and other low energy phenomena are performed with thistrigger. In addition, the new online system allowed theintroduction of a correlated trigger scheme. Low-energy
events with a threshold over 9.5 MeV (reduced to 7.5 MeV
after the summer of 2011) were followed by a forced trigger
500 μs long to record all the PMT hits, including those
fired by the subtle 2.2 MeV γ emitted from a neutron
capture on hydrogen (n þ p → d þ γ). Due to the readoutconfiguration of the new online system, data for normal
triggers were taken for 40 μs ranging from −5 to 35 μs withrespect to the time when the triggers were issued.
Therefore, delayed 2.2 MeV γ signals can be searched
for up to 535 μs after the primary event time. This study
used data collected from October 2008 to October 2014.
Reconstruction, energy, and position calibrations for
low-energy events in SK are carefully performed as
described in Ref. [11]. The vertex resolution is about
65 cm for a 7.5 MeV electron or positron (indistinguishable
in SK) and improves as energy increases. The energy of anevent is reconstructed from the number of detected
Cherenkov photons. That number (approximately proportional to the energy of a charged particle) is estimated by
the number of PMT hits within 50 ns and corrected for latehits, dark noise, bad PMTs, photocathode coverage, andwater transparency. In this paper, the energy we use is the
kinetic energy of the electron (positron).
III. COSMIC RAY MUON DATA
The reconstruction of cosmic-ray muons is of criticalimportance in both tagging spallation backgrounds andselecting cosmic μ-e decays. Muon candidates are required
to have both an ID and an OD trigger. In addition, thenumber of photoelectrons (p.e.s) collected should begreater than 1000 (∼140 MeV) in the ID. In this study,
we only analyzed muons within 30 seconds around thelow-energy events. These muon candidates were reconstructed with a dedicated muon fitter. Details about thealgorithm of the muon fitter can be found elsewhere[20,21]. The muon fitter categorized the cosmic ray muons
into four classes(i) Single through-going muons: those with a track
penetrating the ID. (84.1%  0.3%) of all muons(ii) Multiple muons: events inconsistent with a single
straight track in the ID are fit to several parallel
tracks. (6.9%  0.2%)(iii) Stopping muons: those with a track that entered but
did not leave the ID. (4.6%  0.2%)(iv) Corner-clipping muons: those with a track length
shorter than 7 m inside the ID. (4.1%  0.1%)
The remaining 0.3% of the muon events were not
identified by the muon fitting algorithm due to an
insufficient number of PMT hits after the selection cuts.
These events were referred to as nonfitted muons. In
addition, we observed that 1.2% of the muons among thefour classes had a poor quality of fit and were thusclassified as poorly fitted muons. The nonfitted andpoorly fitted muons were still used in the studies of
the time distributions even though the transverse distance4000

singlemultiple
stopping
corner-clipping

3500
3000

Events/100 cm

of spallation isotopes from fits to the lifetime distributions.
Section V describes a modification of the neutron tagging
and gives the improved measurement for 9 Li. Section VI
gives results and discussions, focusing on a comparison
with the theoretical calculations and the impact on future
experiments using the water Cherenkov technique.
Section VII contains a summary.

PHYSICAL REVIEW D 93, 012004 (2016)

2500
2000
1500
1000
500
0

0

1000

2000
3000
Path length(cm)

4000

5000

FIG. 1. The path-length distributions for single through-going(solid), multiple (dashed), stopping (dotted), and corner-clipping(dot-dashed) muons, respectively.

012004-3

Y. ZHANG et al.

PHYSICAL REVIEW D 93, 012004 (2016)

cut defined in the following section could not be applied,since the entrance position for cosmic-ray muon was notdetermined by the muon fitter. Here, we only used themost probable track information for multiple muons in
the analysis. Figure 1 shows the path length distribution
for each muon category. The distributions reflect theeffects due to the geometry of the detector and the zenith
angle distribution of the cosmic-ray muons. The peaks
around 36 m are from muons traveling vertically downward through the detector. The muon rate Rμ and theaverage path length for muons Lμ were found to be Rμ ¼
2.00  0.01 Hz and Lμ ¼ 2200  4 cm, respectively.
IV. MEASUREMENT OF ISOTOPE RATESThe candidates for radioactive decays from spallation
events were selected using cuts on both the temporal andspatial relationship between the low-energy events andthe preceding muons. The live time of the data set used
for this study is 1890 days. The time distribution of lowenergy events up to 30 s after each muon was used to extract
the production rate of radioactive nuclei (in the spallation
backgrounds). Table I lists the possible radioactive isotopes
induced by cosmic-ray muon spallation at SK [13,22,23].
A. Data reduction
The cuts for selecting the signal of spallation products
from the low-energy events are described in this section.

1. First reduction
We applied a first event reduction to remove nonphysicalevents using the following criteria [10,12].
(i) Events with a noise ratio greater than 0.55 were
removed, where the noise ratio is defined as thefraction of PMT hits with charge lower than 0.5
photoelectrons compared to the total number of
PMT hits.
(ii) Events with a reconstructed position less than 2 mfrom the ID wall were removed.
(iii) Events within 50 μs of a preceding muon were
rejected in order to remove cosmic μ-e decays, aswell as to eliminate events due to after pulsing of
the PMTs.
Using a Geant 3.21-based Monte Carlo (MC) simulation
package [24], the efficiency for the dominant spallation
products passing the first reduction cuts was estimated to begreater than 99%  1%.
2. Energy
For this analysis, events were required to have a detectedenergy above 6 MeV since below this energy threshold
nonspallation events dominate. The efficiency for spallation events passing the energy cut is assessed individuallyfor each isotope using the corresponding β energy spectra.
In this article, all the theoretical spectra for the isotopes
were obtained from Ref. [23]. It should be noted that theTABLE I. Possible radioactive isotopes induced by cosmic-ray muon spallation at SK [13,22,23]. The fourth column lists the end
point kinetic energy (Ekin .). The fifth column lists the primary generation process of the radioactive isotopes.
τ (s)Decay mode

Ekin . (MeV)

11 Be

19.9

β−

16

N

10.3

15

C

3.53

Li

1.21
1.11
1.08
0.26

11.51
9.41 þ 2.1ðγÞ
10.44
4.27 þ 6.13ðγÞ
9.77
4.51 þ 5.30ðγÞ
∼13.0
∼13.9
∼4
13.6
∼10
3–15
9.67 þ 0.98ðγÞ

Radioactive isotope

8

8B
16

C
9
Li
9

C
He

0.18
0.17

12 Be

0.034
0.029
0.025
0.02
0.016
0.013
0.012

8

12

B
13
B
14 B
12
N
13
O
11
Li

β− γ
β−
β− γ
β−
β− γ
β−
βþ
−
β þn
β−
−
β þn
βþ þ p
β− γ
−
β þn
β−
β−
β−
β− γ
βþ
þ
β þp
β−
−
β þn

11.71
13.37
13.44
14.55 þ 6.09ðγÞ
16.38
8–14
20.62
∼16

012004-4

Primary process16Oðn; α þ 2pÞ11 Be
16
16

Oðn; pÞ16 N

Oðn; 2pÞ15 C

16 Oðπ − ; α þ 2 H þ p þ nÞ8 Li
16

Oðπ þ ; α þ 2p þ 2nÞ8 B
18
Oðπ − ; n þ pÞ16 C
16 Oðπ − ; α þ 2p þ nÞ9 Li
16Oðn; α þ 4nÞ9 C

16 Oðπ − ; 3 H þ 4p þ nÞ8 He
18 Oðπ − ; α þ p þ nÞ12 Be
16Oðn; α þ pÞ12 B

16 Oðπ − ; 2p þ nÞ13 B
16

Oðn; 3pÞ14 B
Oðπ þ ; 2p þ 2nÞ12 N
16 Oðμ− ; μ− þ p þ 2n þ π − Þ13 O
16
Oðπ þ ; 5p þ π 0 þ π þ Þ11 Li
16

FIRST MEASUREMENT OF RADIOACTIVE ISOTOPE …

PHYSICAL REVIEW D 93, 012004 (2016)0.5

single0.6

multiple

0.5

Normalized likelihood

Normalized likelihood

0.4
stopping
non-fitted

0.4
0.3
0.2

0.3

0.2

0.1
0.1
0

0

0.05

0.1

0.15
dt (s)

0.2

0

0.25

0

50

100 150 200 250 300 350 400
lt (cm)FIG. 2. The normalized dt (left panel) and lt (right panel) distributions for the spallation signal events with single through-going
muons (solid points), multiple muons (open squares), stopping muons (open triangles), and nonfitted muons (open circles), respectively.
The dt and lt distributions for corner-clipping muons are flat and are therefore not shown. Since there is no muon tracking information
for nonfitted muons, no corresponding lt distribution is shown. See text for more details.

detected energy might include energy from γ’s in addition
to the expected β energy. This was taken into account in thesimulation.
3. Distance and time
In previous SK analyses, the transverse distance (lt)between a muon track and a low-energy event was used
as a powerful cut to remove the spallation background. Thiscut was reinvestigated for spallation events. In this analysis,a correlated muon event was defined as a muon recorded lessthan 30 s prior to a low-energy event, while an uncorrelated
muon event was defined as a muon recorded less than
30 s after a low-energy event. The muon along with the
low-energy events corresponding to the correlated anduncorrelated muon classes comprise the spallation andnonspallation samples, respectively. The absolute timedifference dt was calculated from the muon time and thelow-energy-event time. Under these definitions, we statistically obtained the distributions for the spallation signal
events from a subtraction of the nonspallation sample fromthat of the spallation sample. This helped us to have a better
understanding to the mechanism of muon spallation.
Figure 2 shows the subtracted distributions of dt and lt
for all the muon categories except for the corner clippingmuons. We normalized the distributions to unity in order togive a shape comparison. Since the isotopes produced bycorner-clipping muons either were removed by data reduction or escaped from the ID, the dt and lt distributions forthese muons were dominated by the nonspallation muons.
The dt distributions are similar for each fitted muon class,and so we conclude that there is no correlation between thetype of muon and the resulting spallation isotope. However,
we observed that the lt distribution for multiple muons wasbroader than the others. This was understood to be dueto the choice of evaluating lt from the most probable trackout of several parallel muon tracks in each bundle.
Consequently, a cut on lt had different impacts on themuons and should be studied carefully.
To reject nonspallation muons, we required that lt <200 cm for all the muons except for the nonfitted andpoorly fitted muons, which had no or no reliable muontrack information as described in Sec. III. The efficiency ofthe lt cut for all the combined spallation muon categories
was directly evaluated from the data. The total number ofspallation signal events was obtained from the number of
events in the spallation sample subtracted by that in thenonspallation sample. The fraction of spallation signal
events surviving the lt cut gave the efficiency to be
78.8%  0.6%, where the error is statistical only. We
investigated the systematics by applying different dt cuts
and checked if these cuts could affect the contribution fromthe isotopes with different lifetimes. We found the relative
variation was within 4.8%, which was assigned as thesystematic uncertainty for the lt cut.
B. Production rates
We used the spallation sample to measure the production
rates of the isotopes. Table II lists the measured major
radioactive isotopes induced by the spallation at SK withlifetimes varying from 0.016 s to 19.9 s (see Table I).

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Y. ZHANG et al.

PHYSICAL REVIEW D 93, 012004 (2016)

TABLE II. The measured production rates (Ri ) over the entire
energy spectrum for spallation-induced radioactive isotopes using
the fit in the full time range. The first column lists the names ofradioactive isotopes, the second column lists the selection
efficiency ϵi, and the third column lists the production rates ofradioactive isotopes from the fit. The first and second uncertainties in Ri represent the statistical and the systematic uncertainties,
respectively. The systematic uncertainties include contributions
from the data reduction and the maximum deviation of rates
observed by changing the relative fraction of 8 Li from 0 to 1. The
fitted rates of 8 He=9 C, 11 Be, and 15 C are consistent with zero, so
we set upper limits at 90% confidence level (C.L.).

FðtÞ ¼X Niiτie−dt=τi þ const;

ð1Þ

where τi is the lifetime of the ith radioactive isotope andconst is the expected number of accidental events, whichgive a flat time distribution. We can obtain each N i value by
fitting the experimental dt spectrum with the function.
2. Fits to subtime ranges

Fitting the time distributions using discrete time ranges
simplified the procedure for extracting the initial production rates of the spallation isotopes.

Since the lifetimes of the isotopes differ significantly, we
can divide the full time range into four parts and obtain N i ’s
which can then be used as initial values for the final fit to
the full time range. The subtime ranges given below arearranged according to the fitting sequence.
(i) Time range from 50 μs to 0.1 s: i ¼ 12 B and 12 N.
(ii) Time range (6–30) s: i ¼ 16 N and 11 Be.
(iii) Time range (0.1–0.8) s: i ¼ 9 Li, 8 He=9 C and 8 Li=8 B
by fixing the N i ’s of 12 B, 12 N, 16 N, and 11 Be
obtained above. Since the N i of 8 He could not be
decoupled from that of 9 C due to their similar
lifetimes as shown in Table I, only the sum of bothwith an equal fraction was fitted. The same treatment
was also applied to 8 Li and 8 B.
(iv) Time range (0.8–6) s: i ¼ N i ’s of 15 C and 16 N wereobtained by fixing the N i of 8 Li=8 B obtained fromthe measurement in the range of 0.1–0.8 s.

1. Fitting formula

3. Fit to full time range

Assuming the initial amount of ith radioactive isotope as
N i , the dt spectrum can be described with the following
function:

After all the initial N i ’s of radioactive isotopes wereobtained from the separated time distributions, they wereused as inputs to a fit to the full time range, where the N i ’sϵiRi (kton−1 day−1 )

45.5%
56.2%
45.0%
38.1%
39.2%
22.2%, 50.2%
42.8%, 51.3%
31.8%

19.8  0.1  1.0
2.8  0.1  0.1
39.7  3.3  2.8<16.9
0.9  0.3  0.3<1.4
8.3  0.3  0.3
<6.7

12 B

12 N
16

N
Be
9 Li
8 He=9 C
8
Li=8 B
15
C
11

total
12
B
12
N
9
Li
8
Li
8
B
15
C
16
N
11
Be
8
9
He, C
const

107

Events/0.006 s

106
5

10

104
103
102

1000

500

Residual of (data-fit)

Radioactive isotope

0

-500

-1000

10
-1500
1

-3

10

10-2

10-1
dt(s)

1

-3

10

10

10-2

10-1
dt(s)

1

10

FIG. 3. Left panel: The fit result in the full time range with a χ 2 =ndf ¼ 5167.7=4991 using the low energy data above 6 MeV. The
points represent the data. The lines denote the radioactive isotope contributions as obtained from the fit. The flat line represents theconstant rate of the accidental events. Right panel: The fit residual (data-fit) as a function of time difference (dt). The result is gaussian
distributed around zero. For the purpose of display, bins are combined for equal bin width in log scale.

012004-6

FIRST MEASUREMENT OF RADIOACTIVE ISOTOPE …

of the isotopes were completely free. Figure 3 shows thefit result with parameters for the nine isotopes and aparameter for the accidental background. The χ 2 =ndf
was 5; 167.7=4; 991, corresponding to a p-value of
4.0%. To further illustrate the fit quality, we also show
the fit residual (data—fit) in Fig. 3. The result is gaussian
distributed around zero. The small p-value was due to thefact that some points have large statistical deviation asshown in Fig. 3 (right panel).

With the fitted N i for each isotope, the corresponding
production rate Ri was calculated byNi;
FV · T · ϵiprobability that a background event would be misidentified
as a neutron. This method incorporated eight separate cuts
to distinguish the 2.2 MeV γ rays from the accidental
coincidence of PMT noise fluctuations. As the yield of 9 Li
is low compared to other spallation backgrounds (which do
not produce neutrons), this neutron capture selection was
retuned and improved to get a larger rejection of accidental
coincidence background.
1. Discriminating variables for 2.2 MeV γ’s

4. Production rates

Ri ¼

PHYSICAL REVIEW D 93, 012004 (2016)

ð2Þ

where FV is the effective fiducial mass, which was
22.5 kton. ϵi is the selection efficiency, including thecontribution from the first reduction, energy cut, and lt
cut, for the ith radioactive isotope. The first reduction
efficiency varies by 0.5% across the fiducial volume, theenergy cut by 4%, and the lt cut by 5%. The summary islisted in Table II. T is the live time. Table II lists themeasured Ri ’s of radioactive isotopes over the entire energy
spectrum. The Ri of 9 Li was found to be strongly
anticorrelated with both 8 He and 9 C due to their similar
lifetimes. This issue can be addressed by applying theneutron tagging method described in Sec. V, since both 9 C
and 8 He are unlikely to produce a neutron, especially if theenergy is greater than 7.5 MeV [23]. The relative fractionsof 8 B and 8 Li could affect the fit; however the Ri of 8 B and
8
Li could not be decoupled due to their similar lifetimes
and endpoint energies (∼13 MeV for 8 Li and ∼14 MeV for
8B). In the fit, the fractions of 8 B and 8 Li were assumed tobe equal. By changing the relative fraction of 8 Li from 0 to
1, the differences in the Ri ’s were calculated and were
included in the systematic uncertainty.
V. IMPROVEMENT OF THE
Li YIELD MEASUREMENT9

The 9 Li β þ n decay has the same signature as the IBD
reaction, so this irreducible cosmogenic background can
only be statistically subtracted from the low energy IBD
sample. Therefore, a precise measurement will greatly
benefit searches for the IBD signal. As the measurementof 9 Li yield (see Sec. IV) had large uncertainties, we
improved it by tagging the neutrons from 9 Li β þ n decays
using the 2.2 MeV γ ray emitted by the neutron capture onhydrogen.
A. Neutron tagging
Reference [17] introduced a neutron tagging methodwith a ∼20% neutron detection efficiency and a ∼1%

The PMT hits in the time range between 50 ns and535 μs after the prompt event were used to search for the
2.2 MeV γ rays from neutron captures. Each PMT hit time
was corrected by the time of flight (TOF) of the photon
from the vertex of the prompt event to the PMT. (Using theprompt event vertex as an approximation for the neutron
capture vertex is reasonable since the displacement of athermal neutron is much smaller than the vertex resolution
at 10 MeV, and it is difficult to fully reconstruct low lightyield events.) A 2.2 MeV γ candidate was required to havemore than 7 hits within 10 ns.
Besides the eight variables described in Ref. [17], fiveother variables were also developed as follows:(i) The mean value of the number of collected photoelectrons for the hit distribution;(ii) The root-mean-square (rms) of the number ofcollected photoelectrons for the hit distribution;(iii) The number of PMT hits inside a 20° cone aroundthe sum vector of all PMT hit directions as seenfrom the vertex;(iv) The number of PMT hits with collected charge
above three photoelectrons, and(v) The rms value of the angle between the individual
and sum of hit direction vectors.
2. Optimization of neutron tagging
To optimize the neutron tagging, we adopted the multilayer perceptron (MLP) method [25,26]. Unlike the previous analysis, the MLP method combined all thediscriminating variables into one single output variable;
the resulting accidental background level for the sameacceptance was much lower than [17]. To train the MLP, wedefined a background sample from a random trigger data
regularly taken for the purpose of evaluating the realtime
noise level. A MC simulation of 2.2 MeV γ rays with aneutron capture time of 200 μs incorporating noise fromthe random trigger data served as the signal sample.
pﬃﬃﬃ
We maximized the significance defined as s= b wheresðbÞ is the signal (background) level assuming an initialsignal/noise ratio of 1. The optimal signal (background)
efficiency was found to be 9.6% (0.070%). Both values
refer to the time range from 50 ns to 535 μs. Comparedwith the previous neutron tagging method, this modified
method suppressed accidental background by a factor of 16

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Y. ZHANG et al.

PHYSICAL REVIEW D 93, 012004 (2016)

Source X (cm) Y (cm) Z (cm) ϵn ðAm=BeÞ (%) ϵn ð MCÞ (%)
A
B
C

35.3 −70.7
0.
35.3 −1201.9 0.
35.3 −70.7 1500.

10.1  0.2
12.0  0.4
11.3  0.4

10.2
10.2
11.3

at a cost of reducing the neutron tagging efficiency by
only a factor of 2. This signal efficiency ϵn was used in
calculating the 9 Li production rate.
3. Neutron tagging uniformity and validation
The time variation in the accidental background levelwas 23% for the period of SK-IV and was mostly due toincreasing PMT gain and noise rate. We assigned thisvariation as the systematic uncertainty.
To test the neutron tagging uniformity, we subdivided thefiducial volume into 10 bins in square of radius and 11 binsin height (for definitions, see Ref. [11]). The variation insignal (background) efficiency was found to be 20% (30%).
The time distribution of events selected by the neutron
tagging from the random trigger data was observed to beflat, and differs from the expected exponential distribution
from neutron captures in water.
To validate the neutron tagging efficiency as well as its
position dependence, an Am/Be source was deployed atthree different positions with source A at the center of theID, source B close to the barrel of the ID, and source C
close to the top of the ID. More description of theexperimental setup and other details can be found elsewhere [17,27]. Table III lists the detailed positions of thesources, together with a comparison between the neutron
tagging efficiency ϵn ðAm=BeÞ obtained from the Am/Be
neutron source and that obtained from the MC simulation.
The combined neutron capture time in water wasmeasured to be (202.6  3.7) μs, which was in good
agreement with the ð204.7  0.4Þ μs in Ref. [28].
Combining the neutron tagging efficiencies of the threesource positions gave a weighted average of 10.6% 
0.2%, which was compared to the neutron tagging efficiency ϵn in Sec. VA. The maximum percent difference
between the optimal signal efficiency found in Sec. VA(9.6%) and the neutron tagging efficiency determined using
the Am/Be source was calculated to be 10.4%. This value
was used as the overall systematic uncertainty for theneutron tagging efficiency.
B. 9 Li rate and yield
After validating the modified neutron capture selection,
we selected 9 Li decay candidates with a β þ n pair from thespallation sample with a 7.5 MeV trigger threshold for the
low-energy events associated with the preceding muons:(i) Triplets (μ, β, n) must pass the first reduction
described in Sec. IV.
(ii) Events should satisfy 0.05 s < dt < 0.5 s and lt <200 cm to reject accidental coincidences and longerlived spallation backgrounds.
(iii) No additional muon within 1 ms was allowed toremove most of multiple neutron events induced by
the preceding muons.
(iv) Detected energy was required to be between 7.5 and14.5 MeV.
1. The β energy
The lower bound of the detected energy range waslimited by the trigger threshold. The live time for thissample is 998 days. In total, we observed 116 candidates
for the decay of 9 Li. No event with multiple neutrons wasobserved in these candidates. Among these candidates, weestimated the number of events without neutrons to be 38.2
with the total 54, 963β events scaled by the accidental
background level of 0.070% introduced by the neutron
tagging (see Sec. VA). This approximative calculationneglected the small component from the 9 Li β þ n decays
in the β event sample. We also treated the spectrum for theaccidental background in the same manner. Figure 4 shows
the detected β energy spectrum for all the 9 Li β þ n decay
candidates. Also shown are the expected spectrum from thesum of both the signal and accidental background spectra.
The observed and the expected spectra were consistent
within the uncertainties. We found a clear event excess
compared with the background-only scenario (points over
60

data
bkg.
50

expected

40
Events/MeV

TABLE III. The positions of Am/Be for sources A, B, C. The
last two columns give a comparison between the neutron tagging
efficiency ϵn ðAm=BeÞ obtained from the Am/Be neutron source
and that obtained from the MC simulation. See text for moredetails.

30

20

10

8

9

10
11
12
Energy (MeV)

13

14

FIG. 4. Detected β energy spectrum (points) for all the 9 Li β þ
n decay candidates. Also shown are the expected spectrum(shaded areas with dashed lines) using the electron spectrum
from 9 Li β þ n decay modes and the spectrum of accidental
background.

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FIRST MEASUREMENT OF RADIOACTIVE ISOTOPE …

PHYSICAL REVIEW D 93, 012004 (2016)

the shaded areas with dotted line). The number of 9 Li β þ ndecay events was estimated to be ð77.8  10.8Þ events,
which was obtained by subtracting the estimated number of
events without neutrons from the number of 9 Li candidates.
The systematic uncertainty due to the accidental background estimate was evaluated to be 8.8 events, which gave
a relative difference of 11.2%.

data

3. The 9 Li lifetime
Another cross-check was the 9 Li lifetime, which was
defined by the time difference between the preceding muonand the β for the 9 Li β þ n decay candidates. Figure 6
shows the 9 Li lifetime distribution. All the accidental
background sources were understood to be from 12 B,
12N, 15 C, 8 Li=8 B, 16 N, 11 Be, and 8 He=9 C decays together
with the 9 Li β decay without a neutron. We calculated the

Events/0.03 s

total

10

1

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
dt (s)

FIG. 6. The distributions of the time difference between thepreceding muon and the β for the 9 Li β þ n decay candidates. The
points represent the data. The lines correspond to various radioactive isotopes and their total. The contributions from 15 C, 16 N,
11 Be, and 8 He=9 C are not shown, since they are tiny as indicatedin Table IV.

number of events for each background source based on Ri
from Table II using
N b ¼ Ri · FV · T · ϵb ;ð3Þ8where T is the live time of the data. ϵb is the remaining
background level after the first reduction, dt cut, lt cut,energy cut, and neutron tagging cut. The quantities of thevariables in Eq. (3) can be found in Table IV. The total
number of 34.7 expected events from the eight backgroundsources given in Table IV was in good agreement with theestimate given in Sec. V B. Fixing the lifetimes of background isotopes listed in Table I and their expected events
given in Table IV, we performed a one-parameter fit to thelifetime distribution (dt) with eight exponentials. The fitted
lifetime of 9 Li was ð0.23  0.06Þ s, which was also in good
agreement with the expected 0.26 s. This indicated that the
9 Li events were observed via the neutron tagging method at
SK-IV.

6

TABLE IV.

4

Radioactive isotope

14
12
Events / 25μs

Li
B
12
N
8
Li, 8B
12

2. The neutron capture time
As a cross-check to the background estimate given
above, we studied the neutron capture time from the timedifference between the β and the 2.2 MeV γ for the 9 Liβ þ n decay candidates. A fit with a fixed neutron capture
time at 200 μs and a free background level was performed
to the distribution of time differences, giving a fitted
background of 55.6  16.7 events which agreed with theestimate given in Sec. V B within one standard deviation.
As shown in Fig. 5, we also conducted an unbinned
maximum likelihood fit with an exponential plus a constantbackground estimate (see Sec. V B). The fitted capture timewas ð281.2  77.5Þ μs, which was consistent with the
expectation, indicating that events with β þ n pairs wereobserved.

9

10

9

2
0

Li w/o n
B
12
N
15
C
8
Li=8 B
16N
11Be
8 He=9 C
Total
12

100

200

300
Δ T(μs)

400

500

FIG. 5. The distribution of time differences between the β andthe 2.2 MeV γ for the 9 Li β þ n decay candidates (points). The
solid line shows the fit result, while the shaded region represents
the expected backgrounds without neutrons.

012004-9

The quantities of the variables in Eq. (3).
ϵbNb

1.1 × 10−4
3.5 × 10−5
1.4 × 10−5
7.8 × 10−6
5.3 × 10−5
5.2 × 10−6
3.1 × 10−6
3.9 × 10−5


2.3
15.6
0.9
0.6
9.9
4.6
0.4
0.4
34.7

Y. ZHANG et al.

PHYSICAL REVIEW D 93, 012004 (2016)8

We noted that the cosmic-ray muon induced He also hasa β þ n decay mode with a branching ratio of ∼16% [16].
However, the fraction of β from the 8 He β þ n decays
above the trigger threshold was <1%, and thus was
ignored. The contribution of muon-induced 9 C was also
ignored because there is no neutron produced in this decay.
4. 9 Li production rate
After performing cross-checks using both the neutron
capture time and 9 Li lifetime distributions, we calculated
the rate using
R9 Li ¼

N 9 Li;
FV · BR · T · ϵ9 Li

ð4Þ

VI. RESULTS AND DISCUSSIONS

9

where N9 Li is the number of Li decay events in Sec. V B,
BR ¼ 50.8% is the branching ratio for the 9 Li β þ n decay
mode [16]. ϵ9 Li is the efficiency, including 16.3% for thefraction of electrons above the trigger threshold from the9
Li β þ n decays; 4.9% for the first reduction, dt and lt
cuts, and neutron tagging cuts. The 9 Li production rate was
finally measured to be−1

R9 Li ¼ ð0.86  0.12stat Þ kton

−1

day :

ð5Þ

5. Systematic uncertainties
The systematic uncertainties are summarized in Table V.
The uncertainties on the live time calculation and theefficiency of first reduction were taken from Ref. [12].
Since the precision of the time measurements is much better
than the uncertainty of the 9 Li lifetime, the uncertainty on
the dt cut was ignored. As for the lt cut, the efficiency
varies for different muon classes due to their different lt
distributions as already shown in Fig. 2. In particular, the lt
distribution of multiple muons is much wider than theothers. According to the theory [14], all the spallation
isotopes including 9 Li were made in muon showers. In
addition to the systematic study in Sec. IVA, we studied the
production rate specifically for the multiple muon events.
We observed that about 40% of 9 Li’s are indeed producedby these events. The systematic uncertainty related to the lt
TABLE V. The break down of relative systematic uncertainties
for the 9 Li measurement with the neutron tagging.
SourceLive timeFirst reduction
lt reduction
Energy thresholdn-tag efficiency
Background estimate
BR
Total

cut is estimated using data, as discussed in Sec. IVA. The
systematic uncertainties for the neutron tagging efficiency
and the accidental background level were estimated inSecs. VA and V B. Since we had an energy threshold cut on
the 9 Li energy tail, the difference between the true and thesimulated energy spectra could vary with the water transparency, PMT gain and dark noise, etc. These effects weretaken into account in MC simulation; the maximum relative
deviation in the efficiency for the energy threshold wasfound to be 8.0% and assigned as the systematic uncertainty. The uncertainty of BR was obtained from Ref. [16].
The total systematic uncertainty was added in quadrature
and was found to be 18.1%.

Systematic uncertainty
0.1%
1.0%
4.8%
8.0%
10.4%
11.2%
1.8%
18.1%

With the quantities listed in Sec. III, Sec. IV B, andTable II, the yield of the ith radioactive isotope (Y i ) is
calculated by
Yi ¼

Ri · FV;Rμ · ρ · Lμ

ð6Þ

where ρ is the density of water. The 9 Li yield measurement
using the neutron tagging is calculated from the 9 Li
production rate given in Eq. (5) and the corresponding
systematic uncertainties are listed in Table V. The measured
results and a theoretical calculation are given in Table VI.
The theoretical calculation is given by Ref. [13], which isbased on the simulation code FLUKA [29,30].
This is the first measurement of the radioactive isotope
yields produced by cosmic-ray muons in underground water
detectors. The mean values of the 12 B, 12 N and 16 N
theoretical yield calculations are inside the two-sigma
confidence interval of the respective measurements. The
best-fit 12 B yield is only 2.5% smaller than the calculation
while the corresponding 8 Li yield measurement [2] (seeTable VI) in scintillator is 42% below expectation. The bestfit 12 N yield is 23% larger than the calculation while thecorresponding 8 B yield measurement in scintillator exceeds
the calculation by 47%. The best-fit 16 N yield is 30% larger
than the calculation, the corresponding 12 B yield measurement in scintillator exceeds the calculation by 54%. The
upper limit of the 8 He=9 C yield is only 10% lower than thetheoretical prediction while the upper limits of 11 Be and 15 C
are consistent. However, we found that the yields of thespallation ejecting many nucleons of the 16 O into 8 Li=8 B
and 9 Li are a factor of 3.6–4.1 and 3.1–4.7 below thecalculations. There is no corresponding spallation of the 12 C
nucleus in scintillator, since 4 Li is very short-lived, and 4 H
and 5 H do not exist. The larger discrepancy could be owed tothe spallation ejecting many nucleons, or a feature of theπ-initiated reaction. While scintillator measurements show
agreement for those isotopes within a factor of 2, isotopes
produced by spallation ejecting many nucleons of 12 C are

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FIRST MEASUREMENT OF RADIOACTIVE ISOTOPE …

PHYSICAL REVIEW D 93, 012004 (2016)

TABLE VI. Measured spallation-induced radioactive isotope yields (Y i ’s) in SK. The fitted yields of 8 He=9 C, 11 Be, and 15 C areconsistent with zero, so we set upper limits at 90% C.L. The yields from a theoretical calculation [13] are shown in the third column.
KamLAND’s experimental and simulation results [2] are listed in the fourth and fifth columns, respectively. The unit is10−7 μ−1 g−1 cm2 .
Isotope
12 B

12 N
16

N
Be
9 Li w/o n-tag
9 Li w/ n-tag
8
He=9 C8
Li=8 B,
15 C
11

Y i in water

Expected [13]Y i in scintillator [2]Expected [2]11.7  0.1  0.6
1.6  0.1  0.1
23.4  1.9  1.7<10.0
0.5  0.2  0.2
0.51  0.07  0.09
<0.9
4.9  0.2  0.2
<3.9

12
1.3
18
0.81
1.9
1.9
1.1
18.8
0.82

42.9  3.3
1.8  0.4
1.1  0.2

27.8  1.9
0.77  0.08

0.84  0.09

2.2  0.2
0.7  0.4=3.0  1.2
12.2  2.6=8.4  2.4-

3.16  0.25
0.32  0.05=1.35  0.12
21.1  1.4=5.7  0.4-

not measured. We also note that the two different measurements on the 9 Li yield in SK are in good agreement, and theone with neutron tagging is better because of the strong
background suppression.
Since the production rates of the radioactive isotopes
depend on a power law of the muon energy [2], the measured
yields, especially the 9 Li yield, can be directly applied to theevaluation of the spallation background in SK and future
experiments, such as the Super-Kamiokande gadolinium
project (SuperK-Gd) [31], Hyper-Kamiokande [5], etc.
In SuperK-Gd, the neutron tagging efficiency will be
increased to about 80% (90% capture and 90%
reconstruction efficiencies) when 0.2% of Gd2 ðSO4 Þ3 bymass is added into the SK water. Assuming 80% IBD
detection efficiency, we expect 0.5–8.1 SRN signal events/22.5 kton/year in 9.5–29.5 MeV positron kinetic energy
range for various theoretical models [32–41]. From ourmeasurement on the 9 Li yield, assuming 80% neutron
tagging efficiency and 0.5% probability of the muoninduced 9 Li event leakage after the spallation cuts, theexpected background events from the cosmogenic 9 Li
would become 0.5  0.1  0.2 events/22.5 kton/year in
the same energy window.
Furthermore, as the spectral shapes of the 9 Li background and the SRN signal differ—most of the 9 Li eventsare found in the bottom three 1 MeV bins, while thepredicted SRN spectra are much flatter—the signal to noise
ratio can be significantly optimized by adjusting the lower
edge of the allowed energy range upward slightly. Such anenergy cut will also serve to shield against occasional
highly upward-fluctuated reactor antineutrinos. The study
presented herein therefore demonstrates for the first timethat spallation-induced 9 Li will have a negligible effect on
SuperK-Gd’s SRN search.
VII. SUMMARY
In summary, the first measurement of the yields ofradioactive isotopes produced by cosmic-ray muons in

an underground water Cherenkov detector was performed
using time distributions in SK-IV data. The path length
distribution of cosmic-ray muons, the relative time anddistance distributions between parent muons and daughter
isotopes, the energy distribution of 9 Li β þ n decays, andso on are expected to facilitate further insights into themechanism of spallation in water, which should be useful indeveloping a more practically powerful tool to reject
cosmogenic backgrounds in solar, reactor and supernova
relic neutrino experiments. Finally, the yield of 9 Li was more
precisely measured by tagging neutrons. This information
regarding an important potential background source could
aid in the design and optimization of future water Cherenkov
detectors that aim to search for SRNs. Agreement of the datawith theoretical calculations is in general much better inwater than in scintillator; only those isotopes produced asa result of ejecting many nucleons of 16 O significantly
deviate—by about a factor of 4—from predictions.
ACKNOWLEDGMENTS
We gratefully acknowledge the cooperation of the
Kamioka Mining and Smelting Company. The SuperKamiokande experiment has been built and operated fromfunding by the Japanese Ministry of Education, Culture,
Sports, Science and Technology, the U.S. Department ofEnergy, and the U.S. National Science Foundation. Someof us have been supported by funds from the Research
Foundation of Korea (BK21 and KNRC), the Korean
Ministry of Science and Technology, the National
Research Foundation of Korea (NRF- 20110024009), theEuropean Union FP7 (DS laguna-lbno PN-284518 and ITN
invisibles GA-2011-289442), the Japan Society for the
Promotion of Science, the National Science and Engineering
Research Council (NSERC) of Canada, and the Scinet andWestgrid consortia of Compute Canada; This work is also
supported by the National Natural Science Foundation ofChina (Grant No. 11235006). We wish to thank John
Beacom and Shirley Li for many helpful discussions.

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