PHYSICAL REVIEW D 85, 052007 (2012)

Supernova relic neutrino search at super-Kamiokande
K. Bays,6 T. Iida,1 K. Abe,1 Y. Hayato,1,3 K. Iyogi,1 J. Kameda,1 Y. Koshio,1 L. Marti,1 M. Miura,1 S. Moriyama,1,3
M. Nakahata,1,3 S. Nakayama,1 Y. Obayashi,1 H. Sekiya,1 M. Shiozawa,1,3 Y. Suzuki,1,3 A. Takeda,1 Y. Takenaga,1
K. Ueno,1 K. Ueshima,1 S. Yamada,1 T. Yokozawa,1 H. Kaji,2 T. Kajita,2,3 K. Kaneyuki,2,3 T. McLachlan,2 K. Okumura,2K. P. Lee,2 K. Martens,3 M. Vagins,3,6 L. Labarga,4 E. Kearns,5,3 M. Litos,5 J. L. Raaf,5 J. L. Stone,5,3 L. R. Sulak,5W. R. Kropp,6 S. Mine,6 C. Regis,6 A. Renshaw,6 M. B. Smy,6,3 H. W. Sobel,6,3 K. S. Ganezer,7 J. Hill,7 W. E. Keig,7
S. Cho,8 J. S. Jang,8 J. Y. Kim,8 I. T. Lim,8 J. Albert,9 K. Scholberg,9,3 C. W. Walter,9,3 R. Wendell,9 T. Wongjirad,9T. Ishizuka,10 S. Tasaka,11 J. G. Learned,12 S. Matsuno,12 S. Smith,12 T. Hasegawa,13 T. Ishida,13 T. Ishii,13 T. Kobayashi,13
T. Nakadaira,13 K. Nakamura,13,3 K. Nishikawa,13 Y. Oyama,13 K. Sakashita,13 T. Sekiguchi,13 T. Tsukamoto,13
A. T. Suzuki,14 Y. Takeuchi,14,3 M. Ikeda,15 K. Matsuoka,15 A. Minamino,15 A. Murakami,15 T. Nakaya,15,3 Y. Fukuda,16Y. Itow,17 G. Mitsuka,17 M. Miyake,17 T. Tanaka,17 J. Hignight,18 J. Imber,18 C. K. Jung,18 I. Taylor,18 C. Yanagisawa,18
A. Kibayashi,19 H. Ishino,19 S. Mino,19 M. Sakuda,19 T. Mori,19 H. Toyota,19 Y. Kuno,20 S. B. Kim,21 B. S. Yang,21
H. Okazawa,22 Y. Choi,23 K. Nishijima,24 M. Koshiba,25 Y. Totsuka,25 M. Yokoyama,25,3 Y. Heng,26 S. Chen,26 H. Zhang,26
Z. Yang,26 P. Mijakowski,27 K. Connolly,28 M. Dziomba,28 and R. J. Wilkes28(Super-Kamiokande Collaboration)
1

2

Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu, 506-1205, Japan
Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan
3
Institute for the Physics and Mathematics of the Universe, Todai Institutes for Advanced Study, University of Tokyo,
Kashiwa, Chiba 277-8582, Japan
4
Department of Theoretical Physics, University Autonoma Madrid, 28049 Madrid, Spain
5
Department of Physics, Boston University, Boston, Massachusetts 02215, USA
6
Department of Physics and Astronomy, University of California, Irvine, Irvine, California 92697-4575, USA
7
Department of Physics, California State University, Dominguez Hills, Carson, California 90747, USA
8
Department of Physics, Chonnam National University, Kwangju 500-757, Korea
9
Department of Physics, Duke University, Durham, North Carolina 27708, USA
10
Junior College, Fukuoka Institute of Technology, Fukuoka, Fukuoka 811-0214, Japan
11
Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan
12
Department of Physics and Astronomy, University of Hawaii, Honolulu, Hawaii 96822, USA
13High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
14
Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan
15
Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan
16
Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan
17
Solar Terrestrial Environment Laboratory, Nagoya University, Nagoya, Aichi 464-8602, Japan18
Department of Physics and Astronomy, State University of New York, Stony Brook, New York 11794-3800, USA
19
Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan20
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
21
Department of Physics, Seoul National University, Seoul 151-742, Korea
22
Department of Informatics in Social Welfare, Shizuoka University of Welfare, Yaizu, Shizuoka, 425-8611, Japan
23
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
24
Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
25
The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
26
Department of Engineering Physics, Tsinghua University, Beijing, 100084, China
27
Institute of Experimental Physics, Warsaw University, 00-681 Warsaw, Poland
28
Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA(Received 19 November 2011; published 22 March 2012)
A new Super-Kamiokande search for supernova relic neutrinos was conducted using 2853 live days ofdata. Sensitivity is now greatly improved compared to the 2003 Super-Kamiokande result, which placed aflux limit near many theoretical predictions. This more detailed analysis includes a variety of improvements such as increased efficiency, a lower energy threshold, and an expanded data set. New combined
upper limits on supernova relic neutrino flux are between 2.8 and 3:1 e cm2 s1 > 16 MeV total
positron energy (17.3 MeV E ).
DOI: 10.1103/PhysRevD.85.052007

1550-7998= 2012=85(5)=052007(15)PACS numbers: 13.15.+g, 13.85.Rm, 97.60.Bw

052007-1

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PHYSICAL REVIEW D 85, 052007 (2012)

I. INTRODUCTION AND MOTIVATION
A. The SRN signal
With supernovae each releasing on the order of 1046 J ofenergy, 99% as neutrinos, the neutrino flux from eachsupernova event is enormous. In a galaxy such as theMilky Way, it is estimated a supernova will occur around2 or 3 times a century [1]. Although we would not see asignificant neutrino burst from a supernova farther away
than our galaxy and its satellites, all of the core collapse
supernovae that have exploded throughout the history of
the Universe have released neutrinos, which, in the absenceof unexpected physics, should still be in existence. These
neutrinos are herein called the supernova relic neutrino(SRN) signal (or simply relics, though care should betaken, since this terminology is also sometimes used forbig bang relic neutrinos), also sometimes referred to as the
diffuse supernova neutrino background.
Many astrophysicists have considered the SRN signal,
constructing models that predict both the flux and thespectrum. The first models were crafted even before
SN1987A [2–4]; then after SN1987A with increasing interest and sophistication with models such as Totani, Sato,and Yoshii’s constant SN rate model [5]; Malaney’s cosmic
gas infall model [6]; Woosley and Hartmann’s chemical
evolution model [7]; Kaplinghat, Steigman, and Walker’s
heavy metal abundance model [8]; Ando, Sato, andTotani’s large mixing angle (LMA) model [9,10];
Lunardini’s failed supernova model [11,12]; and the variable neutrino temperature formulation of Horiuchi,
Beacom, and Dwek(6 MeV and sometimes 4 MeV cases
10

1

2

Flux /cm /sec/MeV

10

10

-1

-2

LMA 0310-3

6 MeV 09
Failed SN 09

10

Cosmic Gas 97-4

Heavy Metal 00
Chemical Evolution 97
10

-5

10

20

30

40

50

60

Neutrino energy (MeV)

FIG. 1 (color online). Examples of theoretical SRN spectra.
Flux is  e only. For heavy metal abundance model, average
metal yield of one solar mass is assumed.

considered) [13]. Some examples of theoretical spectra areshown in Fig. 1. Although the normalizations vary, thegeneral shape and slope of the predicted spectra are relatively similar.
The SRN signal has never been seen. A paper was
published in 2003 detailing the first search for the SRN
events at Super-Kamiokande (SK) [14]. The basic method
was to eliminate as many backgrounds as possible, thenattempt to model the spectrum of the remaining backgrounds. A 2 fit was performed on the energy spectrumof the final data sample, with two background components
and one signal component. From this fit, a final modelindependent flux limit of 1:2 e cm2 s1 for  e energy>19:3 MeV was extracted, which was 100 times more
stringent than the previous world’s best limit [15]. This
study is an update to that 2003 result, with more live time,
lower energy threshold, and significantly increased sensitivity. Other experiments have also produced SRN limits,such as SNO [16] (a neutrino search) and KamLAND [17](an antineutrino search). Recent models predict a SRN fluxthat is on the cusp of discovery [13,18], motivating further
efforts.
B. The SK detector
The Super-Kamiokande detector is a 50 kton water
Cherenkov detector located in the Kamioka mine inJapan. The inner detector (32.5 ktons, 22.5 ktons fiducial)has an inner surface lined with 11 100 ( 5200 for
SK-II) 50 cm Hamamatsu photomultiplier tubes (PMTs).
More information on the hardware and experimental
setup of the detector, including calibration details, isprovided by the following references: [19–21].
The SK detector began data taking in April 1996, andwas shut down for maintenance in July 2001. This period isreferred to as SK-I (1497 days live time). While refilling
after the maintenance, on November 12, 2001, a major
accident [22] destroyed 60% of the PMTs. The surviving
tubes were redistributed to cover the entire detector while
replacement tubes were manufactured, and data taking was
resumed in December 2002, running until October 2005
with reduced cathode coverage. This is the SK-II period(794 days). After the replacement tubes were installed, andthe detector was back up to its nominal 40% coverage, datataking again continued from July 2006 until August 2008,
marking the SK-III period (562 days). Finally, the detector
electronics were upgraded [23,24], and data taking since
September 2008 is referred to as SK-IV. This study considers SK-I, SK-II, and SK-III data.
The SK detector has many different triggers. Whenenough PMTs observe light within 200 ns (approximately
the longest time it can take light to traverse the innerdetector) a detector trigger occurs. Inner detector (ID)electronics triggers include the high energy (HE) trigger(about 33 PMTs), low energy (LE) trigger (about 29 PMTs,
100% efficient at 6.5 MeV), and super low energy (SLE)052007-2

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triggers (variable threshold between 17 and 24 PMTs).
SLE events have the lowest threshold (which has changed
over time), and occur orders of magnitude more often thanLE triggered events ( 1 KHz as opposed to 10 Hz),requiring dedicated hardware for filtering and reducing theSLE data flow to manageable levels. The SLE trigger
enables SK to see the lowest energy events. The outerdetector (OD) also triggers if 19 or more OD PMTs firewithin 200 ns.
SK primarily sees SRN events via inverse beta decay( e þ p ! n þ eþ ). The next most visible mode for SRN
interactions is about 2 orders of magnitude less frequent.
The inverse beta decay cross section used is described inRefs. [25,26].

C. Fiducial volume cut

II. DATA REDUCTION
A. Cuts
Each SK PMT fires with a dark rate of 3–5 kHz;
cosmic ray muons penetrate the detector at 2 Hz, and25 atmospheric and solar neutrino events are identified
every day. Many of these act as backgrounds to the SRN
signal. With an expected rate of only a couple of SRN
events a year, careful background reduction is necessary.
Most backgrounds are removable, but a few remain after
all cuts and must be understood. The events that can beremoved, and the cuts used to remove them, are describedin this section.
The software tools used for reconstructing event vertex,
direction, and energy information are the same as used in
the long-standing SK solar neutrino analysis [27,28].
Some cuts (most notably the spallation cut) could not be
fully represented using Monte Carlo (MC), and therefore
the data were used to help understand and tune the cuts. All
cuts were tuned prior to any fits being done or results being
extracted, however.
B. Noise reduction
Many noise events can be separated from the main
sample easily. These preliminary cuts are the same as thoseused for the long-studied SK solar analysis [27], and arecollectively called ‘‘noise reduction.’’Calibration events are labeled as such and are immediately removed. Events which trigger the OD are also
removed, as these events have a charged particle entering
the detector from outside, while relic events should be fully
contained. Electronics noise events are also cut using timing and charge considerations, with a signal efficiency ofalmost 100%.
The total charge deposited in the detector by the event isa quick criterion useful for separating out muons. Muons
are in general much brighter than inverse beta decay positrons, and deposit much more charge in the detector. Any
event with more than 800 photo electrons is removed (400p.e. for SK-II), quickly eliminating most of the muons.

The SK ID is filled with 32.5 ktons of pure water.
Radioactive events occur in the detector from sources
such as the surrounding rock wall and radioactive isotopes
in the PMT glass itself. Most of these events are eliminatedby definition of a fiducial volume (FV). In the relic analysis, we have implemented the standard SK FV cut ofremoving the volume within 2 m of the walls, leaving a
FV mass of 22.5 ktons.
D. Spallation cut
The analysis lower energy threshold is determined byspallation, which is the process of a nucleus emitting
nucleons when struck by a highly energetic particle.
Cosmic ray muons interacting with an oxygen nucleus
cause radioactive spallation which mimics a real SRN
signal. At lower energies, the unstable nuclei tend tohave longer lifetimes, making them harder to tag throughmuon correlation. Eventually tagging becomes too inefficient for the remaining data to be useful, thus determining
the lower energy threshold of the analysis. Spallation constitutes the bulk of the SRN background after the noise
reduction cut. Elimination of spallation events is complex
and quite costly in terms of signal efficiency, making it
perhaps the most important removable background.
To remove spallation, we correlate relic candidates topreceding muons. If the muon is responsible for the event,then the event should be located near the muon track, bothin location and time. The main spallation cut utilizes alikelihood method:First, the muon tracks are reconstructed and categorizedas (i) single muons that travel through the detector ( 83%
of muon events); (ii) multiple muons bundles ( 8%);(iii) muons that enter from outside but stop within the ID(stopping muons, 5%); and (iv) short track length muons,
usually just clipping the corner of the detector ( 4%).
Each of these muon types was found to produce spallationdifferently, and is thus treated independently.
A dE=dx profile of each muon track is constructed byprojecting back the amount of light seen by each PMT anddetermining where along the muon track it originated according to the measured arrival time of the light at the PMT.
This profile of charge emitted along the muon track tends topeak for spallation producing muons approximately at theposition along the track the spallation occurred (Fig. 2).
Although the exact mechanism responsible for this peak is
not known, the correlation is unmistakable in our data.
Four spallation tagging variables are considered. The
first spallation variable, t, is simply the amount of timeby which the muon preceded the relic candidate. The
second variable, LTRANS , is the transverse, or perpendicular, distance from the muon track to the relic candidate (seeFig. 3). The center of the nine consecutive bins (4.5 m
distance) with the largest combined charge in the dE=dx
histogram corresponds to a position along the muon track

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PHYSICAL REVIEW D 85, 052007 (2012)µ track

8000

6000

peak ofdE/dx plot

LLONG

4000

LTRANS

2000

0

5
10
15
20
25
30
Distance along muon track in ID (m)35

FIG. 2 (color online). Example of a dE=dx plot. The red line
indicates where along the muon track the candidate was reconstructed. This example has particularly good correlation.

where the spallation is expected to have occurred. The
distance along the muon track from where the spallation
is expected to occur to where the relic candidate exists isthe third likelihood variable, longitudinal distance LLONG .
Lastly, the value of the combined charge in the largest nineconsecutive bins of the dE=dx histogram is our fourth
likelihood variable, QPEAK . The more charge in the peak,
the more likely the muon is to be making spallation.
Probability density functions (PDFs) are formed foreach of the four spallation variables. For each muon categorization, the relic candidates were correlated to muonspreceding the candidate in time (the ‘‘data sample’’), andcorrelations were examined. A random sample was formedby taking the same correlations to muons immediately
following the relic candidate in time. The random sample
histograms were subtracted from the data histograms(yielding a ‘‘spallation sample’’), for each muon categorization. These profiles were parametrized, resulting infunctions representing spallation (from the spallation sample) and accidental correlation background (from the random sample). These parametrizations, once normalized,
are the PDFs, which are multiplied together to give thelikelihood (for example, see Fig. 4).
For each muon categorization, a cut on the likelihood
was instituted. Cut values were tuned until no statisticallysignificant difference existed in the distributions of the dataremaining after the cut compared to the random sample forthe t and LTRANS variables. The spallation contamination
remaining after the spallation cut is difficult to estimate
due to the large statistical uncertainties, but no evidence
for remaining background was found. For the SK-I/III
combined sample, we could see any excess with a resolution of about 4 events; and for SK-II, with a resolutionof about 2 events.

FIG. 3 (color online).
distance variables.
10

Schematic explanation of spallation-2
spallation data
spallation likelihood
random sample data

10
normalized likelihood0

relic candidate

10-3

random sample likelihood

-4

100

x 10

200

-2

300
1000
LTRANS (cm)

2000

3000

0.18

normalized likelihood

Light deposited in detector (photo electrons)

10000

0.16

spallation data

0.14

spallation likelihood

0.12

random sample data

0.1

random sample likelihood

0.08
0.06
0.04
0.02
0

-2000

-1000

0

1000

2000

LLONG (cm)FIG. 4 (color online). SK-I/III data with likelihood functions
overlaid for single through-going muons. Top shows transverse
distance; bottom shows longitudinal distance.

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11

Be

10
16

10

5

N

Data Sample
Random Sample

15

C

C

8

Half-life (s)

1

9

10

-1

Li

number of events

8

16

B

9

Li

C

8

He

12

B

12

Be

10

-2

6

8

10

13

B

12
14
16
Energy (MeV)

12

14

N
13

18

O

B
11
Li

20

10

4

10

3

10

2

-15

22

-10

-5

0

5

10

15

Likelihood

FIG. 5 (color online). Half-lives and event end-point energies
of spallation products expected to occur in pure water. Lower
energy events trend to longer decay times.

SK-I and SK-III use the same spallation cut. Becauseof the differences in cathode coverage, SK-II required
separate likelihoods and tuning. The lower energy
threshold of the cut is the energy below which keeping
the sample free of any definite spallation contamination
becomes too inefficient to be viable. Figure 5 shows thehalf-life and maximum energy of spallation products in
SK; as spallation products decrease in energy, they tend
to have longer half-lives, and are more difficult to tag.
Taking into account energy resolution, events at 14 MeV
such as 9 Li can reconstruct up to 16 MeV. The final
energy threshold of the analysis, for which no evidenceof spallation remains in the final sample, is 16 MeV
positron energy (or 17.3 MeV  e energy) for SK-I/III,and 17.5 MeV for SK-II.
The cut need not be applied at all energies. The cut’s
upper energy bound is determined by the highest energy
spallation products, 11 Li and 14 B, each with an end-point
energy of 20.6 MeV and a half-life of around 0.01 seconds.
The SK-I/III spallation cut is applied up to 24 MeV
positron energy, and the SK-II cut up to 26 MeV, which
is about 1:5 of energy resolution away from 20.6 MeV.
The cut is split into two energy regions: a more stringent
selection for the lower energies, which has many more
spallation events and is most critical for the analysis, anda looser selection at the higher energies, which has fewer
spallation events, many of which are 11 Li and are easily
removed considering its short half-life. Thus, for SK-I/III,
the cut from 16–18 MeV is different than from 18–24 MeV,
and in SK-II, the cut from 17.5–20 MeV is different thanfrom 20–26 MeV.
For all muons, a timing cut rejecting events with t <4 seconds (8 s) was implemented on the most energetic ofFIG. 6 (color online). Comparison of likelihood distributionsof data sample and random sample for single through-going
muons in SK-I/III. The data sample contains spallation events,
while the random sample does not. The high likelihood valuesof the spallation excess show the effectiveness of the cut. The
SK-I/III 16–18 MeV cut value of 3 is shown; everything to theright of the line is rejected.

muons, those over 400 000 (800 000) p.e., as these events
are rare and almost always create spallation.
For multiple muon type events, the secondary track is
usually well fit, so the dE=dx profile of secondary tracks
was calculated, and a separate secondary track likelihood
tuned. Additional tracks do not have trustworthy dE=dx
profiles, and a likelihood for these cases was constructedbased only on t, LTRANS , and the total amount of light
deposited by the muon in the detector.
Finally, for single through-going muons, 1:5% of thetime the muon fitter was unable to correctly fit the track. A
dedicated alternate fitter was developed for these misfit
events, which correctly fit approximately 75% of the misfit
single through-going muons. For the remaining 25% of
misfits, a 2 s detector veto was implemented to prevent
spallation contamination.
Figure 6 demonstrates the power of this method to tag
spallation events. Table I shows the cut signal efficiency. In
the published 2003 SK analysis, in order to be spallation
free the spallation cut was 37% inefficient from 18 to
34 MeV. Now, for the same SK-I data, the cut is only 9%
inefficient from 18 to 24 MeV, and furthermore the

TABLE I. Spallation cut signal efficiencies.
Efficiency

SK-I/IIISK-II

Low energy
High energy

81.8% (16–18 MeV)
90.8% (18–24 MeV)

76.2% (17.5–20 MeV)
88.2% (20–26 MeV)

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16–18 MeV region is now opened up for study withan inefficiency of 18%, all spallation free.
E. Solar angle cut
Solar neutrinos elastically scatter off electrons, creatingrecoil electrons that look like SN relic positrons. To discriminate such events, we use the angle between the reconstructed direction vector of the event and the direction
vector from where the sun was in the sky at the time of theevent (sun ).
Although the direction of the recoil electron closely
follows that of the incoming solar neutrino (usually within10 degrees), multiple Coulomb scattering (MCS) of therecoil electron smears out the peak in the cosðsun Þ distribution at cosðsun Þ ¼ 1. This long tail in the distribution
makes cutting solar neutrino events using cosðsun Þ inefficient, especially since the end points for 8 B and hep solar
neutrinos are right at the critical lower energy edge of theanalysis, where inefficiency impacts the relic sensitivity
the most. In order to maximize sensitivity, we used anenergy-dependent cut coupled with an estimate of MCS.
MCS was estimated using a PMT hit by PMT hit Houghtransform that reconstructs the direction and returns a
goodness value corresponding to the amount of MCS.
The correlation of this MCS goodness to the shape of thecosðsun Þ distribution can be seen in Fig. 7. The candidate
sample is split into various MCS goodness bins, and the cut
value for each MCS goodness bin is separately tuned, in
1 MeV energy bins, by use of the following significancefunction:pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
Significance ¼ = S þ ;(1)goodness < 0.4

1

0.4 ≤ goodness < 0.5
0.5 ≤ goodness < 0.6

Integrated fraction

0.8

0.6 ≤ goodness
0.6

0.4

0.2

0
0.2

where  is the cut efficiency, S is the number of solar
neutrino events,  is the reduction effectiveness of thecut (such that   S is the number of solar neutrino events
remaining after the cut is applied), and  represents thenonsolar neutrino background.
The solar neutrino spectrum is modeled using SK MC,
which is a mix of 8 B and hep with a mixing ratio determined by the SSM. The solar neutrino flux was normalizedusing real SK data below energy threshold (14–16 MeV),
with all cuts applied [except the one on cosðsun Þ]. To
normalize, it was assumed that all events withcosðsun Þ < 0 were not solar neutrino events, and that
all nonsolar remaining events had no cosðsun Þ dependence. Thus, simply subtracting the number of eventswith cosðsun Þ < 0 from the number of events withcosðsun Þ > 0 allows us to estimate the number of solar
neutrino events at a particular energy, and then extrapolate the number of solar neutrino events at all energies.
The dominant nonsolar neutrino background was assumed to be decay electrons from atmospheric  charged
current (CC) events, as decay electrons are our largest SRN
background (see Sec. III). For the purpose of tuning thesolar cut, the decay electron spectrum was modeled using asample of data that was identified as decay electrons bytiming and spatial correlation to a preceding muon that had
no OD trigger (a fully contained muon from a muon
neutrino interaction). The normalization of the decay electron background was determined by fitting to the data.
As with many of the cuts, SK-I and SK-III used one cut,
and a separate version of the cut was tuned for SK-II. The
SK-II cut criteria are simply the SK-I/III cut with theenergy bins shifted by þ6% to reflect the poorer energy
resolution. The cut is MCS goodness bin dependent forE < 19 MeV (SK-I/III, <20:14 MeV SK-II), while for
19–20 MeV (20.14–21.2 MeV SK-II) there is a simple,
MCS goodness bin-independent cut that eliminates eventswith cosðsun Þ > 0:93. More cut details can be found in
Table II. Note that the cut values in the table mean thatevents with cosðsun Þ> cut value are rejected. Also notethat the inefficiencies are already weighted by the fractionof events in that MCS goodness bin, so that they can be
simply added for the total.
After the cut, MC estimates limit the number of remaining neutrino events in the combined SK-I/II/III final data
sample to <2, and no statistically significant cosðsun Þ
excess can be seen in the final sample.
TABLE II.

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Integrated cos(θsun)

FIG. 7 (color online). SK-I/III solar MC integrated cosðsun Þ
distributions by multiple Coulomb scattering goodness bin.

SK-I/III solar cosðsun Þ cut value (inefficiency).

MCS Goodness

16–17 MeV

17–18 MeV

18–19 MeVg < 0:4
0:4  g < 0:5
0:5  g < 0:6
0:6  gTotal

0.05 (7.2%)
0.39 (9.7%)
0.59 (6.7%)
0.73 (2.4%)
26.2%

0.35 (5.0%)
0.61 (6.4%)
0.73 (4.5%)
0.79 (2.0%)17.9%

0.45 (4.3%)
0.77 (3.8%)
0.81 (3.2%)
0.91 (1.0%)
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F. Incoming event cut

G. Decay electron cut

The FV cut eliminates most of the radioactivity events
that enter from detector edges, but not all. Instead of
reducing the FV, it is more efficient to separate the remaining radioactive background by position and direction
considerations.
We use an effective distance parameter, deff , which isdefined identically as in the SK solar neutrino analysis(where this is referred to as the ‘‘gamma ray cut’’ [27]).
The event direction and position are reconstructed; then,starting at the event vertex, the distance projected backwards along the event direction is calculated until a wall ishit. This distance is deff .
The radioactive backgrounds targeted by the incoming
event cut are energy dependent, and much more prevalent
at lower energies. However, some background exists at allenergies. Thus, the cut has two pieces. A 300 cm deff cut isapplied at all energies, for all three SK phases. The lower
energy part of the cut is tuned separately for each SK
phase.
For SK-I, sufficient statistics existed to allow an energydependent tuning of the cut, to maximize efficiency (seeFig. 8). The shielding added to the PMTs at the start of
SK-II to prevent another serious accident produces radioactive backgrounds, and thus the SK-I tuning could not be
used for other phases. Furthermore, the reduced cathodecoverage of SK-II makes it different. Each phase is tuned
separately, but for SK-II and SK-III, the statistics were
not sufficient for energy-dependent tuning. Instead, a cut
was implemented below 22 MeV, at deff < 500 cm for
SK-II, and deff < 450 cm for SK-III.

The SK electronics saves PMT signals in a 1:3 swindow. Sometimes, a muon decays into an electron
quickly enough that the light from both particles is captured in the same event. These events are eliminated bysearching for a multipeak structure in the timing information of the event.
More commonly, the muon and resultant decay electron
are in separate events. For each relic candidate, all SK data
are searched up to 50 s before the candidate (in case thecandidate is a decay electron), and up to 50 s after the
event (in case the candidate is actually a low charge muonfrom an atmospheric neutrino interaction, or one of two
decay electrons).
When searching for preactivity, finding any LE or HE
triggered event within the 50 s causes the candidate to be
rejected. Since SLE events are much more frequent, afurther vertex correlation requirement of 5 m is requiredin order to improve efficiency. When searching for postactivity, the 5 m vertex correlation is required of all events,
whether HE, LE, or SLE.

2500

deff (cm)

2000

1500

1000

H. Pion cut
Some of the higher energy events in our sample (usually>30 MeV, reconstructed assuming event is an electron)
are charged pions from atmospheric neutrino interactions.
One way to distinguish between charged pions and electrons is by looking at the ‘‘fuzziness’’ of the resulting
Cherenkov ring. This is because pions are quickly capturedby an oxygen nucleus, while electrons tend to travel farther
and MCS more. This MCS causes the electron direction tochange as it travels, causing the Cherenkov ring to be morepoorly defined. Pions are also heavier, and deflect lesswhen scattering.
Quantitatively, this difference can be used to construct atool for discriminating pions and electrons. When the
Cherenkov angle for an event is calculated, a distributionof three-hit combinations (or triplets) is formed. Eachcombination of three-hit PMTs forms a cone, and an
opening angle. The distribution of these opening angles
has a peak that is narrower for pions than for electrons.
Using this logic, a pion ratio variable was constructed,
where pion likelihood is defined as follows (using thetriplet distribution):
RPION ¼500

0#triplets  3 from peak:ð#triplets  10  #triplets  3 Þ

(2)

By looking at MC compared to data, the cut criterion
was determined to be 0.58 for all SK run periods.
20

25

30
35
40
Energy (MeV)45

50

I. Cherenkov angle

FIG. 8 (color online). SK-I data distribution showing energydependent incoming event cut. Events below the line arerejected.

Charged particles traveling in pure water at a velocity
close to the speed of light in vacuum emit Cherenkov lightin a cone shape with an opening angle of about 42 degrees.

052007-7

K. BAYS et al.

PHYSICAL REVIEW D 85, 052007 (2012)
TABLE III. Cut signal efficiency (systematic error).

Number of Events

4000
3500

SK-I/III relic MC

3000

SK-II relic MC

Cut

SK-I

SK-II

SK-III

Noise reduction
99% (1%)99% (1%)99% (1%)
Spall + solar
88% (1%)87% (1.4%)
89% (1%)
Incoming event
98% (0.5%) 95% (0.3%) 96% (0.3%)
Pion
98% (0.2%) 97% (0.5%) 98% (0.5%)
Cherenkov angle 95% (0.4%)
88% (3%)94% (0.3%)
Other cuts
98% (2%)98% (2%)98% (2%)
Total
78.5% (2.5%) 69.2% (4.0%) 76.7% (2.5%)

2500
2000
1500
1000

Heavier particles, such as muons, pions, and protons, may
have a velocity that is smaller if their energies are relatively
small, producing Cherenkov light with an opening angle
that is less than 42 degrees. Figure 9 shows the Cherenkov
angle distribution of SN relic MC (all models are very
similar). The Cherenkov angle used is the peak of the
distribution of three-hit combination opening angles. The
signal region is determined to be between 38 and 50 degrees. Events at other Cherenkov angle values are notdiscarded, but instead they are kept to help extrapolate
backgrounds into the signal region, as discussed in thefollowing section.

ones listed in Table III are from the LMA model. The
systematic error of most cuts was calculated by comparing
LINAC[20] MC to LINAC data, or by using the values
established in the solar analyses when the cuts are similar(noise reduction, incoming event cut). The OD correlated
cut uses a random sample of cosmic ray muon data for OD
hit information for determining efficiency. The efficiencyof the spallation cut is a function of position (efficiency isgreater near the edges of the detector, where the candidate
can be correlated to fewer muons), and the vertex distribution of relic MC is used to estimate the average efficiency. The error on this estimation is likely dominated by
the statistics of our relic MC and spallation random sample, and is rounded up to be conservative. The efficiency ofthe solar angle cut is mostly geometric and exact; the only
source of systematic error comes from the ratio of events
falling in each multiple Coulomb scattering goodness bin,as determined from solar MC. Values of the systematic
errors, along with the cut efficiencies, can be seen in
Table III, and the SK-I signal efficiency as a function ofenergy compared to that of the 2003 analysis is shown in
Fig. 10.

J. Other cuts

III. REMAINING BACKGROUNDS

Occasionally events traveling through the OD do not
deposit enough light to cause an OD trigger, but still causea few OD PMT hits. OD hit clusters are compared in timeand space to ID hits and the reconstructed event vertex, andif sufficient correlation exists, the event is rejected.
The multiring cut uses ring counting software developed
for atmospheric neutrino and proton decay analyses [29]. If
the software finds that more than one Cherenkov ring exists
in the event, the angle between the two rings is calculated,
as sometimes the fuzziness of low energy electron
Cherenkov rings can cause the event to be mistakenly
identified as having more than one ring. False 2-ring resultsreconstruct as having a small relative angle. A 2-ring result
separated by more than 60 degrees is judged to be a realmultiring event, and such events are rejected.

A. Background sources
Even after all cuts, some backgrounds remain that must
be modeled. The remaining background can be categorized
into four main groupings. Atmospheric  and e CC
backgrounds were considered in the 2003 SK publishedSRN paper, and now additional atmospheric neutrino backgrounds are also considered. Although remaining backgrounds other than the four listed below were found toexist (for example, from multiple and neutral pion production), their contributions were small and their spectrum
shapes well described by linear combinations of our fourmodeled backgrounds. Thus, any contribution from thesesources will be absorbed into the four backgrounds below
during the fit.

K. Efficiency and systematic error

1. Atmospheric  CC events

Most cut efficiencies were calculated using relic MC.
Each relic model has slightly different efficiencies; theThis is the largest remaining background in our sample.
Atmospheric  ’s and   ’s interact in the water of the

500
0

0

10

20

30

40

50

60

70

80

90

Cherenkov Angle (degrees)

FIG. 9 (color online). Expected Cherenkov angle distributionof SRN events. This is expected to be model independent; shownis Ando, Sato, and Totani’s LMA [9] relic MC.

052007-8

SUPERNOVA RELIC NEUTRINO SEARCH AT SUPER- . . .

B. Background modeling

0.9

All our backgrounds are modeled using the SK MC,
based on GEANT 3 and NEUT [30]. Hadronic interactions
are simulated using a combination of CALOR and custom
SK code. For the Michel spectrum (used for the  CC),
we measure the spectrum of decay electrons from cosmic
ray muons. The spectra of the other three remaining backgrounds are determined from the MC, as is the Cherenkov
angle distribution of all four backgrounds. The SN relicsignal itself is modeled separately, with its own MC. Manydifferent models are considered, and different results arecalculated for each model.
Figure 11 shows the energy spectrum of the four remaining backgrounds taken from the MC. Figure 12 shows the
Cherenkov angle of the four backgrounds, with no
Cherenkov angle cut applied (from MC); it can be seenthat the MC has a shape quite similar to the data. Also,
while the CC backgrounds have a Cherenkov angle distribution similar to that of SN relics (38–50 degrees), the NC
elastic background mostly reconstructs at high angles(where the Cherenkov angle reconstruction algorithm,
which assumes a single ring, misreconstructs events withmultiple gammas and roughly isotropic distributions oflight), and the = leakage mostly reconstructs at lower
angles (as expected from heavier, low energy particles).
Because of these distributions, we have split the data into
three regions: one is the signal region (38–50 degrees); theother are the two background regions, or ‘‘sidebands,’’
consisting of the low (20–38 degrees) = region andhigh (78–90 degrees) NC elastic region. The sidebands

0.8

Signal efficiency

PHYSICAL REVIEW D 85, 052007 (2012)1

0.7

Signal Efficiency

0.62003 Efficiency
unnormalized LMA flux

0.5
0.4
0.3
0.2
0.1
0

20

30

40

50

60

70

80

90

Energy (MeV)

FIG. 10 (color online). Signal efficiency of new analysis compared to 2003 study. An unnormalized LMA spectrum is overplotted to show the importance of the improvements.

detector and create a muon via a charged current reaction.
This muon is very low energy, often below Cherenkov
threshold, in which case its decay electron cannot be
removed like other decay electrons (by correlation to thepreceding muon), since the muon is invisible. This background’s energy spectrum is the well-known Michel spectrum, slightly modified by resolution effects, and is quite
different from the SN relic spectrum.

6

2. e CC events

Decay-eNumber of events in SK-I final sample

This background also originates from atmospheric cosmic ray interactions. Atmospheric e ’s and  e ’s are indistinguishable from SN relic  e ’s on an individual basis.
Their spectrum is quite different, however.
3. Atmospheric  neutral current (NC) elastic events
NC elastic events have an energy spectrum that rises
sharply at our lower energy bound, similar to SN relics.
Most are removed by Cherenkov angle reconstruction, butsome still leak into our final sample and must be modeled.
With the lowering of the energy threshold from 18 MeV to
16 MeV, this background has become much more relevant.
4. =

production from atmospheric 

NC Elastic
µ/π

4

3

2

1

0

This last category is a grouping of two different things,
both heavier particles. First, NC reactions produce charged
pions >200 MeV=C, some of which survive the pion cut.
These remaining events must be modeled. Included withthem, since the spectrum and Cherenkov angle distribution
are relatively similar, are surviving muons above
Cherenkov threshold.

νe CC

5

20

30

40

50

60

70

80

90

Energy (MeV)

FIG. 11 (color online). Spectra of the four remaining backgrounds in the signal Cherenkov angle region with all reduction
cuts applied. The  CC channel is from decay electron data; theother three are from MC. All are scaled to the SK-I LMA best fit
result.

052007-9

K. BAYS et al.
250

PHYSICAL REVIEW D 85, 052007 (2012)µ/π
regionsignalregion0NC
region-0.25

150

SK-I final sample-0.5

νµ + νe CC-0.75

Likelihood

number of events

200

µ/π
NC elastic

100

-1

SK-I
SK-II

-1.25

SK-III
Combined

-1.5

50
-1.75

0
20

-2

30
40
50
60
70
80
90
SK-I final sample Cherenkov angle (degrees)

FIG. 12 (color). Cherenkov angle of SK-I combined final data(all cuts except Cherenkov angle cut applied) overlaid with
distributions of the four remaining backgrounds from SK-I
MC (same cuts applied). The division of Cherenkov angle
regions is also pictured.

are used to normalize the NC elastic and = backgrounds
in the signal region, where the SN relic signal would occur.
IV. LIMIT EXTRACTION

i¼1



e

P5
j¼1

cj



5
X

cj pdfj ðEi Þ;

(3)

j¼1

where c is the coefficient for parameter j representing thenumber of events for that channel present in all three
Cherenkov angle regions combined, which modifies the
PDF for that channel, pdfðEÞ. The likelihood in each
Cherenkov angle region is separately calculated, but maximized in conjunction. The likelihood is maximized foreach SK phase separately. Toy MC studies found no significant bias in the fitter.
The 90% C.L. flux limit is extracted from the likelihood
curve (maximum likelihood as a function of number of

4

6
8
10 12
SNR events/year

14

16

relic events). The likelihood curves of SK-I, II, and III are
first multiplied together (see Fig. 13), and then the 90%
C.L. point limit90 is determined by the following simple
relationship, where r represents the number of SN relic
events:Z 1
Z limit90
LðrÞdrLðrÞdr ¼ 0:9:
(4)
0

The relic best fit and upper flux limit are determined by
performing an unbinned maximum likelihood fit. A simultaneous fit is done in all three Cherenkov angle regions. For
each of the Cherenkov angle regions the spectrum of eachof the five parameters (SN relic þ4 backgrounds) is parametrized into an analytical function, which is used as the
PDF for that parameter. Each possible reasonable combination of parameters is checked (although no parameter isallowed negative), and the best fit is the combination thatmaximizes the likelihood, which is determined by thefunctionNY
events2

FIG. 13 (color online). Example likelihood curves from the
LMA model. Vertical lines represent best fit and 90% C.L.
results for the combined fit.

A. Likelihood fit

L ¼

0

0

B. Systematic error
Four systematic errors are considered. Each systematic
error is applied to the likelihood by a Bayesian integration
method, similar to that described in Eq. (33.28) in the
PDG [31].
1. Energy scale and resolution uncertainty
The energy scale and energy resolution systematic uncertainties are considered to be uncorrelated. They areseparately calculated, then added in quadrature. The
amount of the energy scale and energy resolution systematic errors are based on the SK solar analyses [27,28], thenincreased due to the broader energy range and higher
energies, and to cover slight uncertainties in the MC. Theenergy resolution systematic uncertainty used in our study
is 3%, while the energy scale uncertainties used are 2% for
SK-I and SK-III, and 3% for SK-II. Inclusion of thissystematic error was not found to have an appreciable
effect on the results.
To take the energy scale systematic uncertainty into
account, the PDFs for four of the five channels (the 
CC was taken from decay electron data, and is thus not
MC, and not susceptible to this error) were shifted by the052007-10

SUPERNOVA RELIC NEUTRINO SEARCH AT SUPER- . . .

PHYSICAL REVIEW D 85, 052007 (2012)amount of the uncertainty. To take into account the energy
resolution systematic uncertainty, the energy resolutionfunction from Ref. [28] was applied to the likelihood
functions to distort them.
Finally, the full uncertainty was incorporated into thelikelihood calculation algorithm as follows. Let  be avariable representing the amount of spectral distortion,such that an  of 1 represents a 1 deviation in the energy
scale and resolution, and let LðÞ be the likelihood evaluated with the likelihoods distorted by an amount . Thenthe new final likelihood L0 is
1 Z 1 2 =2
L 0 ¼ pﬃﬃﬃﬃﬃﬃﬃeLðÞd;(5)
1
2

physical boundary at 1. Thus, we applied the error
asymmetrically from 1 to þ3.
For the e CC channel, the relative normalization across
Cherenkov angle regions is not a concern, as more than
99% of the events fall into the signal region, so instead a
distortion of the spectrum in the signal region was considered. The e CC PDF in the signal region was distorted asfollows:
0:5ðE  16Þ
PDF new ¼ PDFold  N 1 þ;(6)
74 MeVsuch that the originally calculated likelihood L is now
simply the  ¼ 0 case.
2. Atmospheric  background systematic errors
Three of the four remaining backgrounds are modeledby SK MC (the exception being the  CC background,which is modeled by decay electron data). The SK MC iswell verified above 100 MeV; however, in the lower energy
region of 16–100 MeV that is relevant to our study, the MC
accuracy is less well studied. Little data exist to compare to
the MC, especially for the NC elastic mode. To incorporate
these concerns into the analysis, two systematic errors on
the e CC and NC elastic backgrounds were included.
These systematics were designed to cover any remaining
uncertainties in the MC. As for the other two backgroundchannels, the  CC comes from real data and therefore is
not vulnerable to MC inaccuracies, and the = channel isby far the least relevant of the four channels, and therefore
the safest to neglect.
For the NC elastic channel, the greatest potential for
error lies in the relative normalization across Cherenkov
angle regions. The amount of NC elastic found in the 78–
90 degree region determines the amount of the fit in thesignal region. If the ratio of the amount of NC elastic in thehigh angle region compared to the signal region as determined by MC is off by some factor, this will tend to have alarger influence on the result than a distortion of thespectrum of the NC elastic in the signal region by thesame factor.
For SK-I, the NC elastic MC has 7.4% of events occur inthe signal region, while 87% of events occur in the highangle region. Considered is a 100% change in the normalization of the number of NC elastic events in the signal
region, with all changes to be correspondingly balanced bya change in the normalization of the high angle region.
Thus, a þ1 effect would be for 14.8% of events to occur
in the signal region, and 79.6% of events to occur in thehigh angle region, while a 1 effect would be for no NC
elastic events to occur in the signal region, and 94.4% of
the events to occur in the high angle region. As we cannot
have less than 0 events in the signal region, there is awhere E is the energy (MeV),  is the magnitude of thespectral distortion, and N is a constant such that the new
PDF is normalized the same as the old.
A 2 effect would reduce the PDF to 0 at 90 MeV.
This was considered to be unphysical, and thus a 1effect was considered the physical lower bound, forcing us
to apply this error in the same asymmetric manner as theNC elastic, from 1 to þ3.
We applied the background channel systematics using
an integral method with a weighting function (Bayesianprior). However, as our error is applied over an asymmetricregion ( 1 to þ3), we could not use a symmetric
Gaussian (such as we use in the next section) without
introducing a bias in our result. Instead, we used aweighted Gaussian that as closely as possible maintained
the properties of the symmetric Gaussian.
Specifically, in the case of a symmetric error (i.e., 1 to1), a normal Gaussian would have the following properties: (1) expectation value (first moment) = 0, (2) variance(second moment) = 2 . Our weighted Gaussian was constructed such that its properties (integrated over  from 1to 3) were the same as the symmetric case. This weighted
Gaussian was normalized to 1 and used in both the e CC
and NC elastic cases, as their integration ranges wereidentical.
The integral method of applying the systematic error is
as follows. Let GðÞ be our weighted Gaussian function
described above. Let Lðr; Þ be the likelihood as a function of SN relic events and whichever systematic error isunder consideration. Then, the likelihood after the application of the systematic error of either of the backgroundchannels is
Z3L ðrÞnew ¼Lðr; Þold GðÞd:(7)
1Inclusion of the atmospheric  background systematics
changed the result (towards a less stringent limit) by lessthan 6%.
3. Energy-independent efficiency systematic error
The energy-independent portion of the efficiency systematic error is assumed uncorrelated. The systematic errorof each cut, as shown in Table III, is added in quadrature, to
get the total efficiency systematic error of the reduction.

052007-11

K. BAYS et al.

PHYSICAL REVIEW D 85, 052007 (2012)20

TABLE IV. Total efficiency systematic error.
Error source

SK-I

SK-II

relic

18

SK-III

all background
νµ CC

16

3.1%
1.3%
1.0%
0.1%
3.51%

4.4%
1.1%
1.0%
0.1%
4.65%

3.1%
1.0%
1.0%
0.1%
3.41%

14
number of events

Cut reduction
Fiducial volume
Cross section
Live time
Total

νe CC

SK-II

NC elastic

12

µ/π

10
8
6

The total efficiency systematic error also includes theuncertainty in the fiducial volume cut, inverse beta crosssection, and live-time calculation, as shown in Table IV.
The fiducial volume and live-time calculation systematic errors are the same as, and taken from, the SK solar
analyses [27,28].
To apply this systematic error, the likelihood curve(likelihood as a function of number of SN relic events) is
modified. The modification for each value of the likelihood
is as follows, where  is the efficiency,  is the efficiency
systematic error, PðÞ is a probability function in the shapeof a Gaussian centered on 0 with width 0 , r is thenumber of relic events seen in the data, and R is the numberof relic events actually interacting in the detector, such thatr ¼ R:L 0 ðRÞ ¼Z1
¼0

LðRÞPðÞd(8)This error is applied last, after all other calculations arecomplete. Inclusion of this systematic error changed theresult (making the limit less stringent) by a few percent.
V. THE RESULT
Figures 14–16 show the final sample data, overlaid withthe best fit results for the LMA model. For SK-I, the relic
best fit is negative and unphysical (for all models), so zerorelic contribution is shown. However, for all models SK-II

4
2
0

25

50

75

20-38 degrees (MeV)

25

50

75

38-50 degrees (MeV)

25

and SK-III find a positive indication (not significant) of arelic component. The 90% C.L. upper flux limits differ foreach model, and are summarized in Table V.
A. Comparison to previous study
The new analysis has a lower energy threshold than the2003 study, so the results are not immediately comparable.
Furthermore, the previous study presented its result in amodel-independent fashion due to the similarity of theresults. Although we verified that with an 18 MeV energy
threshold the SK-I results were similar enough to justify amodel-independent approach, the lower energy thresholdand new data required model-dependent results. For comparison purposes, we consider the LMA model. The limit is
2:9 cm2 s1 > 16 MeV (positron energy), which isequivalent to 2:0 cm2 s1 > 18 MeV positron energy.

all background
νe CC

νµ CC

SK-I
20

Number of events

νe CC
NC elastic
µ/π

15

νµ CC

12

all backgroundNumber of events

relic

relic

25

75

FIG. 15 (color). SK-II LMA best fit result. The relic best fit is3.05 events per year interacting in the detector (before reduction
efficiencies).

14
30

50

78-90 degrees (MeV)10

SK-IIINC elastic
µ/π

8
6
4

10

2
5

0
0

25

50

75

20-38 degrees (MeV)

25

50

75

38-50 degrees (MeV)

25

50

25

50

75

20-38 degrees (MeV)

75

25

50

75

38-50 degrees (MeV)

25

50

75

78-90 degrees (MeV)

78-90 degrees (MeV)

FIG. 14 (color). SK-I LMA best fit result. The relic best fit isnegative, so a relic fit of 0 is shown.

FIG. 16 (color). SK-III LMA best fit result. The relic best fit is
6.9 events per year interacting in the detector (before reduction
efficiencies).

052007-12

SUPERNOVA RELIC NEUTRINO SEARCH AT SUPER- . . .
90% C.L. flux limit ( cms ), E > 17:3 MeV.

SK-I

SK-II

SK-IIIAll

Predicted

Gas infall (97)
Chemical (97)
Heavy metal (00)LMA (03)
Failed SN (09)
6 MeV (09)

<2:1
<2:2
<2:2
<2:5
<2:4
<2:7

<7:5
<7:2
<7:4
<7:7
<8:0
<7:4

<7:8
<7:8
<7:8
<8:0
<8:4
<8:7

<2:8
<2:8
<2:8
<2:9
<3:0
<3:1

0.3
0.6
<1:8
1.7
0.7
1.5

3

Excluded (E>16MeV)
νe→e+ (90%C.L.)

53

Model

SK 1497+794+562 Days
SN νe Energy in 10 erg

TABLE V.

PHYSICAL REVIEW D 85, 052007 (2012)

2 1

2

IMB

1
Kamioka0
2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Tν in MeV

FIG. 18 (color online). Results plotted as an exclusion contourin SN neutrino luminosity vs neutrino temperature parameter
space.
The
Irvine-Michigan-Brookhaven
(IMB)
and
Kamiokande allowed areas for 1987A data are shown (originallyfrom [35]) along with our new 90% C.L. result. The dashed line
shows the individual 90% C.L. results of each temperature
considered separately, which is not a true two-dimensional
exclusion contour. Results are in the form of Fig. 6 from [32].

B. Typical SN  emission limit
Most of the elements involved in a comprehensive prediction of the SRN flux are now fairly well-known [32](e.g., initial mass functions, cosmic star formation history,
Hubble expansion, etc.), and thus we can parametrize
typical supernova neutrino emission using two effective

e candidates>16MeV/22.5kton year

It is notable that this result is less stringent than the 2003
result of 1:2 cm2 s1 positron energy >18 MeV. There
are multiple reasons for this.
First, a 0th order approximation of the inverse beta crosssection was then used. Now, the full cross section from [25]is used. This raises the limit by about 8%. If events withpostactivity are also removed, the old-style analysis limit
becomes 1:35 cm2 s1 . Furthermore, the binned 2method used assumed Gaussian statistics, while
Poissonian statistics are more appropriate considering thelow statistics. This alone would change the limit from 1.2
to 1:7 cm2 s1 . When all these corrections are combined,
the original analysis result of 1:2 cm2 s1 instead becomes 1:9 cm2 s1 .
With our improved analysis, if we neglect atmospheric 
background systematics (which were not fully included in
the 2003 study), the SK-I only LMA result is
1:6 cm2 s1 (> 18 MeV positron energy), which ismore stringent than the published analysis with these corrections. However, the SK-II and SK-III data show a hint ofa signal, which causes the limit to become less stringent
when all the data are combined, for the final LMA result(with all systematics) of 2:0 cm2 s1 > 18 MeV positron energy, or 2:9 cm2 s1 > 16 MeV positron energy.

0.3

3MeV
4MeV
5MeV
0.2

6MeV
7MeV

0.15

8MeV
0.1

0.05

0
10

15

20

25

30

35

40

45

50

8
7

SK 1497+794+562 Days
Excluded (E>16MeV)
νe→e+ (90%C.L.)

6
5
4

HMA

LMA

3

6 MeV

2
CE

1

4 MeV

FS

CGI

+

Event Rate (/22.5kt yr MeV)

0.25

9

55

60

Positron Energy (MeV)

FIG. 17 (color). True positron spectra in SK for each neutrino
temperature, from 3 to 8 MeV in 0.5 MeV steps (SN  eluminosity of 5  1052 ergs assumed).

0
3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Tν in MeV

FIG. 19 (color online). Exclusion contour plotted in a parameter space of SRN event rate vs neutrino temperature. The red
shaded contour shows our 90% C.L. result. The dashed line
shows the individual 90% C.L. results of each temperature
considered separately, which is not a true two-dimensional
exclusion contour. CGI is cosmic gas infall model, HMA isheavy metal abundance model, CE is chemical evolution model,
LMA is large mixing angle model, FS is failed supernova model,
and the 6 and 4 MeV cases are from [13]. For the 4 and 6 MeV
cases a total uncertainty is provided and shown, and the HMA
model gives a range which is shown. Other models have no given
range or uncertainty and are represented by a star.

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PHYSICAL REVIEW D 85, 052007 (2012)

TABLE VI. Summary of limit values.
 e temperature (MeV)
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0

53

Energy ( 10

ergs)

9.0
4.8
2.9
2.1
1.5
1.3
1.1
0.92
0.82
0.75
0.70

parameters [13,33]:  e luminosity from a typical supernova
and average emitted  e energy.
To calculate this result, SRN MC samples were createdwith a Fermi-Dirac emission spectrum at multiple temperatures (see Fig. 17). The Ando, Sato, and Totani model[9] corresponds to a Fermi-Dirac spectrum of close to
6 MeV and a  e luminosity of 7  1045 J. MC was createdfrom 2.5 to 8 MeV in 0.5 MeV steps. PDFs were made ofthese spectra, and the final data sample was fit, as previously described, with these new likelihoods in the place ofthe other SRN models. The following constants were assumed: m ¼ 0:3,  ¼ 0:7, and c=H0 ¼ 4228 Mpc.
The result is independent of the initial mass function used.
Our result is shown in Figs. 18 and 19. Also plotted forconvenience is the one-dimensional line representing theresults of each neutrino temperature analyzed separately(the numerical values are given in Table VI).
VI. CONCLUSION AND FUTURE
In summary, we have made large improvements to the2003 SK relic analysis. The cuts have been optimized,
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lowering the energy threshold down to 16 MeV. New
remaining backgrounds are now considered and modeled,
and we have almost twice as much data in our final sample.
A new maximum likelihood fit with multiple Cherenkov
angle regions is utilized to extract a set of model-dependent
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Although our limit is tantalizingly close to the best
theoretical predictions, no signal has so far been detected.
While SK is expected to continue data taking for many
more years, future sensitivity improvements will be slow,
since SK-I/II/III’s exposure is already 176 kt years, and theanalysis is now highly optimized. Fifty kt years of SK-IV
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ACKNOWLEDGMENTS
We gratefully acknowledge the cooperation of the
Kamioka Mining and Smelting Company. The SuperKamiokande experiment has been built and operated
from funding by the Japanese Ministry of Education,
Culture, Sports, Science and Technology, the UnitedStates Department of Energy, and the U.S. National
Science Foundation. Some of us have been supported byfunds from the Korean Research Foundation (BK21), theNational Research Foundation of Korea (NRF20110024009), the Japan Society for the Promotion of
Science, and the National Natural Science Foundation ofChina (Grants No. 10875062 and No. 10911140109).

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