Search for Tens of MeV Neutrinos associated with Gamma-Ray Bursts in Super-Kamiokande

A search for neutrinos produced in coincidence with Gamma-Ray Bursts(GRB) was conducted with the Super-Kamiokande (SK) detector. Between December 2008 and March 2017, the Gamma-ray Coordinates Network recorded 2208 GRBs that occurred during normal SK operation. Several time windows around each GRB were used to search for coincident neutrino events. No statistically significant signal in excess of the estimated backgrounds was detected. The $\bar\nu_e$ fluence in the range from 8 MeV to 100 MeV in positron total energy for $\bar\nu_e+p\rightarrow e^{+}+n$ was found to be less than $\rm 5.07\times10^5$ cm$^{-2}$ per GRB in 90\% C.L. Upper bounds on the fluence as a function of neutrino energy were also obtained.

A search for neutrinos produced in coincidence with Gamma-Ray Bursts (GRBs) was conducted with the Super-Kamiokande (SK) detector. Between December 2008 and March 2017, the Gamma-ray Coordinates Network recorded 2208 GRBs that occurred during normal SK operation. Several time windows around each GRB were used to search for coincident neutrino events. No statistically significant signal in excess of the estimated backgrounds was detected. Theν e fluence in the range from 8 MeV to 100 MeV in positron total energy forν e + p → e + + n was found to be less than 5.07 × 10 5 cm −2 per GRB in 90% C.L. For all GRBs, upper bounds were obtained on the fluence as a function of neutrino energy. Additionally, for GRBs at known distances, upper limits were set for the neutrino energy emission at the GRB.

Introduction
Gamma-Ray Bursts (GRBs) are one of the most luminous phenomena in the universe, as an enormous amount of energy is released as gamma-rays over a very short time scale. GRBs were first discovered in 1967 [1]; since that time, detailed observations have revealed their main features, though the underlying astrophysical mechanism remains poorly understood.
Neutrinos may be able to advance our understanding of the burst mechanism, as they interact very weakly with matter and, thus, can promptly escape from high-density regions such as the inner core of a GRB progenitor. The observation of neutrinos from a GRB would enable a direct study of the entire burst process.
GRBs can be sub-divided into two categories, based on their duration. Long GRBs are believed to originate when the rotating core of a massive star collapses into a neutron star (NS) or a black hole (BH). Short GRBs may arise from a NS-BH merger, or from the merger of two NS [2]. Either in long or short GRBs, gamma-ray emission is thought to be produced by relativistic outflow. The central engine of GRBs may also emit a large amount of thermal neutrinos. A typical total energy of neutrinos is expected to be E ν,tot ∼ 2 × 10 53 erg [3], which gives a fluence at the Earth to be where E ν,tot is the total neutrino energy of the fireball, E ν is average neutrino energy at the source, and D is the distance to the GRB.
As yet, no clear evidence has been observed for a neutrino signal originating from a GRB.
This paper describes a new search with an increased number of GRBs and a longer exposure of SK data.
This paper is organized as follows. In Section 2, we describe the search method including the GRB catalog, the SK detector, data reduction, and analysis methods. In Section 3, we present the results of searches. Finally, in Section 4, we conclude the summary of the results.

Search Method
In order to search for a possible GRB neutrino signal, we looked for correlations between GRBs in the Gamma-ray Coordinates Network (GCN) database [14] and SK data taken from 2008 December 7 to 2017 May 31. We have adopted the GRBweb online catalog [15], which was developed for neutrino searches with the IceCube observatory. The catalog is compiled from GCN circulars that archive satellite reports. It contains important information about GRB events, including duration (t90), distance from Earth, trigger time (t0), start time (t1) and end time (t2). To avoid confusion with other variables, this paper will refer to the start and end times as t s and t e . GRB events with a t90 duration less than 2 seconds are defined as 'short GRBs', while GRBs with greater duration are classified as 'long GRBs'.
The catalog contains 2208 GRB events observed during the SK data-taking period considered for this analysis. However, fourteen of these GRBs are missing either t s or t e information and the remaining sample of 2194 GRBs is considered for variable timing window analysis discussed in Sec. 2.3.2.

SK detector
Super-Kamiokande is a 50 kton water Cherenkov detector located in the Kamioka mine [16]. A rock overburden of 1000 meters (2700 meters water equivalent) reduces the flux of cosmic ray muons by five orders of magnitude. The SK detector is a right cylinder with a diameter of 39.3 m and height of 41.4 m. A stainless steel frame divides the detector into two optically separated volumes, an inner detector (ID) and outer detector (OD). The steel frame provides both the optical barrier and a support structure for photo-multiplier tubes (PMTs).
The OD serves as both a passive shield and active veto for external particles. It contains a 2.5 m thick layer of water and is instrumented with 1885 8 inch PMTs. The water stops gamma rays from the surrounding rock, while the PMTs enable the OD to tag particles originating from outside of the detector.
The ID contains 32.5 kton of water, which is viewed by 11,129 20 inch PMTs for a total photocathode coverage of 40%. In areas that are close to the ID wall, the background rate is very high. For this analysis, a 22.5 kton fiducial mass is defined as the water contained in a virtual volume that is at least 2 m from the ID wall. This region of the detector is called the fiducial volume (FV).

Data reduction
Super-Kamiokande has performed two different analyses for neutrinos with energies below 100 MeV. The solar neutrino analysis [17] focuses on high levels of background reduction to enable precision measurements of 8 B solar neutrinos. The supernova relic neutrino (SRN) analysis [18] is optimized to search for electron antineutrinos interacting via the inverse beta decay (IBD) reaction (ν e + p → e + + n).
In the energy region of this analysis (8 MeV to 100 MeV in positron total energy), the dominant reaction is the IBD reaction [19] assuming that the neutrino flux from a GRB is distributed approximately equally among all neutrino flavors; therefore, this study adopts the data reduction of the SRN analysis. Expected signals are single particle electron-like events.
A detailed description of the event reconstruction and the data reduction can be found in [18]. The selection cuts below were tuned following an upgrade to the detector electronics in 2008. First, non-physical events are removed, as well as decay electrons identified with cosmic ray muons, and events near the ID wall; a summary of the selection is listed here: • Calibration event cut: Periodic calibration events induced by laser and Xe light during normal data taking are identified by a trigger tag and removed.
• Noise event cut: Events caused by electronic noise are removed.
• OD cut: Charged particles originating from outside of the detector are identified by their signal in the OD and removed.
• Time difference cut: Decay electrons and noise events produced by PMT ringing after cosmic ray muons are removed via a 50 µs cut following each event.
• Fiducial volume cut: Radioactive backgrounds emanating from PMTs and the steel frame are identified by their proximity to the ID wall and removed.
• Goodness cut: The energy, vertex and direction of neutrino candidate events are reconstructed according to the method described in [17]. Candidate events that are reconstructed poorly are removed.
• Energy cut: Neutrino candidate events with reconstructed energy below 8 MeV are outside the range of this analysis and are therefore removed.
After this sequence of data reduction (called 'first reduction' hereafter), the dominant background source in the energy range below 20 MeV is the radioactive decay of unstable nuclei. These nuclei are created by spallation-induced by cosmic ray muons. In the energy range above 20 MeV, the dominant background originates from atmospheric neutrino interactions, which can take the form of pions, muons, gamma-rays (via neutral current interactions), and decay electrons produced by the decay of muons with energies below the Cherenkov threshold.
To remove these backgrounds, additional selection criteria are applied. These are • Spallation cut: The removal of spallation products relies on several factors. Both the time difference to a muon event, and the transverse distance from a muon track are considered. Additionally, the maximum value of energy deposited by the muon in a 50 cm bin along muon track, and the longitudinal distance from the spallation point where energy deposit of the muon is maximum (Fig. 1) are used. To identify spallation-induced events in the detector, these variables are calculated for muons observed within a 30 sec window prior to the neutrino candidates.
• Gamma cut: A more stringent cut of events originating from outside of the detector is implemented by using the reconstructed travel distance from the ID wall. It is calculated from the vertex position and the event direction.
• Pion cut: The sharpness of the Cherenkov ring is evaluated and used to remove charged pions created in atmospheric neutrino interactions.
• OD correlated event cut: Incoming events without an explicit OD trigger are identified and removed by searching for correlations between the ID hits and the OD hits.
• Multi-ring cut: Atmospheric neutrino interactions can sometimes produce both a charged lepton and a charged pion; such events have two Cherenkov rings. To reduce this background, events with an angle between rings that is greater than 60 degrees are removed from the data sample.
• Solar events cut: The direction to the sun, as well as total energy and anisotropy of the PMT hit patterns is used to remove solar neutrinos from the data sample.
• Pre/Post activity cut: Events with > 12 hits for pre-activity or > 15 hits for post-activity within the time range from -5 µsec to +35 µsec are removed. Such activities are expected in low energy atmospheric interactions which produce muons at or below the Cherenkov threshold [18].
• Cherenkov angle cut: Low energy atmospheric muon neutrinos can produce low energy muons via charged current interactions. These muons will be close to the Cherenkov threshold and, thus, have a smaller Cherenkov angle than that of a highly relativistic charged particle. Neutral current interactions and nuclear de-excitations can produce events comprising multiple gamma-rays. These reconstruct as if they had a large Cherenkov angle, due to an artifact of the fitting algorithm. By placing a constraint of 38 degrees to 50 degrees on the reconstructed Cherenkov angle, both of these backgrounds can be removed.
• µ/π cut: Residual muon and pion events remaining after the pion cut and the Cherenkov angle cut are removed by using the ratio of PMTs with large charge.
These events deposit a large amount of energy along a short track, causing one PMT to observe many photoelectrons.
• N16 cut: Low energy muons may be captured by 16 O to produce 16 N. The 16 N will decay by emitting a γ and/or an electron. Spatial and timing correlations between low energy events and stopping muons are used to remove this background.
The method described in [18] is used to determine the efficiency of the signal retained by the spallation cut, with the resulting number given in [20]. The signal efficiency for the other reduction steps described above are calculated using a Monte Carlo simulation of events generated at typical energies within the range of this analysis. The generated events are positrons distributing uniformly in the 32 kton ID in isotropic direction. By combining these procedures, we obtain the total signal efficiency as a function of positron energy in the fiducial volume, which is shown in Fig. 2.

Fixed timing window analysis
A 2000 sec window of SK data is selected that occurs within ±1000 sec around the GRB trigger time. The inner 1000 sec (±500sec) is the search window and the outer 1000 sec is used for background estimation. This search window was selected by considering the time scale of GRB models and the arrival time delay between gamma-rays and neutrinos caused by neutrino mass. For core-collapse supernovae, the neutrino emission is expected to begin within 1 sec of the explosion, and continue for ∼10 sec [21,22]. For neutron star mergers, the neutrino emission is expected to have a duration ranging from a few tens of msec [23] to a few sec [24] following the merger. In case of the cosmic string model [5], the difference between the emission time of gamma-rays and neutrinos is predicted to be less than ∼10 sec.
The width of the search window was determined by consideration of several parameters.
Relative to photons, neutrinos experience a time-of-flight delay of where m ν is neutrino mass, E ν is neutrino energy and T γ is gamma-ray time of flight. We can estimate m ν in this equation from observations of baryon acoustic oscillations, the cosmic microwave background (CMB), and CMB lensing. A combined analysis of these observations can be used to limit the sum of neutrino masses to ≤ 0.23 eV [25]. By combining these results with those from neutrino oscillation experiments, which measure the difference in the square of the masses, we can determine that the upper limit on the heaviest neutrino is 0.087 eV. In addition to m ν , we also need the gamma-ray time-of-flight. To date, the most distant GRB observed is GRB090429B, which has a redshift of 9.4 [26] and corresponds to a time-of-flight of 13 × 10 9 years. Using these values together with the lower energy threshold of this search , we find the maximum neutrino time-of-flight to be delayed by about 24 sec relative to the gamma-ray. This justifies using ±500 sec as a conservative search window.  from the GRBweb online catalog [15]. These GRBs are used for the variable time window analysis.

Neutrino search for stacked data
To enhance the statistical power of this search, a study was performed in which the data from all 2208 GRBs were stacked. In this way, the sensitivity to detect an excess above the background will be improved. By accumulating data for many GRBs, only a statistical excess can be observed; even so, this method provides sensitivity for the case where the number of expected events is too small to detect neutrinos in correlation with individual GRBs. This method is called the "stack analysis". The signal and background windows are defined in the same way as in the fixed timing window analysis (Sec. 2.3.1). In general, the distribution of the observed number of events is consistent with background. The probability of more than 225 GRB with one neutrino event is obtained from the Poisson distribution with an average value of 224.6. The probability is 0.50. Those of more than 11 GRBs with two neutrino events and more than one GRB with three neutrino events are 0.73 and 0.38, respectively. For one GRB (GRB140616A), three neutrino candidate events are found in the fixed search window. Additional checks were performed to determine whether these events constituted a signal. We found that the energy distribution and the transverse distances of these three events are consistent with those of spallation products;

Neutrino search for individual
thus, we concluded that these events are most likely to be residual spallation events (see Fig. 6 and Table 1).  Table 1: Properties of neutrino candidate events remaining in the signal window around GRB140616A after the data reduction is applied. The time difference and spatial distances listed are relative to the most likely parent muon. Transverse distance and longitudinal distance are described in Fig. 1.

Results of the variable timing window analysis
The distribution of N ev versus t e − t s width is shown in Fig. 7. Fig. 8    To generate each individual MC set, we used the following procedure: • For a particular GRB, the number of SK events in a ±1000 sec window, N 2000 , is determined from a Poisson distribution of the background rate, 0.114 events/1000 sec.
• N 2000 time differences from the GRB trigger time are randomly allocated in 2000 sec with flat distribution (t 1 , t 2 , ..., t N 2000 ).
• t 1 , t 2 , t N 2000 in the t e − t s window is counted. This is the N ev for the simulated GRB.
• The probability of N ev is calculated as in the data analysis.
• Repeat the above process for all 2190 GRBs where t s and t e data is available.
• Use the results to make the probability distribution.
Using 10,000 sets of MC generated by this procedure, we were able to evaluate the significance of GRB events with small probability.
In the data, 1 GRB has N ev with a corresponding probability of less than 0.001, and 5 GRBs have N ev with a probability less than 0.01. In our simulation, 25.7% of the toy MC sets have 1 or more GRBs with a probability less than 0.001 (Fig. 9), and 60.5% of these sets have 5 or more GRBs with a probability less than 0.01 (Fig. 10). Therefore, we find that the data are statistically consistent with the expected background.

Results of the stacked data analysis
The time distribution of SK events, relative to the GRB trigger time, is shown in Fig. 11.
This figure contains all SK events that occurred within a ±1000 sec window around any of the 2208 GRB trigger times. No excess of events is seen within the ±500 sec signal window, relative to the background. The energy distribution of events within the signal window was compared to those within the off-time background window. As can be seen in Fig. 12, the two distributions are consistent. No excess of events was observed, and so we calculated the fluence limit from the stacked data. The stacked data leads to the best expected limit. The calculation method is described in [6]: Using a Poisson distribution with the background rate, N 90 , the 90% C.L. limit on the number of neutrino events in the signal window can be calculated as where N bg is the expected number of background events, N obs is the number of observed events and Poisson(N obs , x ) is the Poisson probability for N obs events with mean of x. When N bg is expected and N obs is observed, the probability that the number of neutrino events is less than N 90 , is 90%. For the limit calculation, events within an energy window of 8-100 MeV are used. We find N obs = 218 and N bg = 221; using these values and equation 3, we find the 90% C.L. limit N 90 = 23.9.
Once N 90 has been determined, it can be used to obtain the fluence limit Φ via this equation: where N T is the number of target nuclei within the 22.5 kton fiducial volume, λ is the neutrino spectrum normalized to unity, σ is the total neutrino cross section as a function of neutrino energy, and is the detector efficiency as a function of positron energy. The neutrino spectrum λ is assumed to be constant with respect to energy. The cross-section for inverse beta-decay from Strumia and Vissani [19] was used for σ(E ν ). The positron total energy is related to the neutrino energy by E ν − E e 1.293 MeV. The detector efficiency is calculated as Fig. 2 by applying the data reduction process to both the MC sample and the random sample [20]. In the energy window between 8 MeV and 100 MeV, the fluence limit per GRB (Φ / 2208) was found to be 5.07 × 10 5 cm −2 .
For 189 GRBs whose distance from Earth are known, the total energy carried away from the source by neutrinos was calculated. Assuming that the neutrino emission at the source is isotropic, the total energy E iso is where D is the distance from Earth. Fig. 13 shows E iso with the assumption that the energy spectrum is flat from 8 MeV to 100 MeV. Fig. 14 shows E iso with the assumption of a Fermi-Dirac spectrum with an average energy of 20 MeV [3]. The smallest upper limits on E iso are obtained with GRB150906 at z=0.0124 [27]; those limits are 2.8 × 10 56 erg and 6.0 × 10 56 erg for the flat and Fermi-Dirac spectra, respectively. We also calculated the fluence limit as a function of energy, using positron energies of 8, 10, 12, 15, 28, 38, 53, 65, and 80 MeV. Around each target energy, we used events within an energy window to calculate the fluence limit for that energy. The width of that window was determined by using the energy distribution of an MC sample. For each target energy, the reconstructed energy distribution is fitted with a Gaussian distribution to obtain the peak (E peak ) and the RMS of the energy distribution (σ). The width of the energy window for that target energy is 3σ around E peak . An example can be found in Fig. 15, which shows the energy distribution of the 28 MeV MC sample after the full data reduction has been applied. The energy peak E peak is at 28.02 MeV, and the deviation is 2.89 MeV; therefore, the energy range for this target energy is 19.35 -36.69 MeV. Table 2 shows the energy peak and the RMS for each MC sample, and Table 3  Above 38 MeV, it was necessary to enlarge the background window to include the entire data taking period outside of the GRB signal windows (±1000 sec around t0). As shown in Table 3, the number of expected background events N exp in the usual background window is zero; the enlarged background window is required to obtain an estimate of the background.
The live time of the enlarged background window is 2826 days.
The N obs events are not unique to individual energy regions. Due to the finite energy resolution, there is overlap between some regions. For instance, the same four events constitute N obs for the 38 MeV and 53 MeV regions (see Table 3 Table 2: The relation of MC energy and reconstructed energy. The efficiency is for events in the FV. E gen is generated positron energy, E peak is energy peak after reduction.
the 65 MeV and 80 MeV regions. For all energy regions, N obs is consistent with the expected background.
The fluence limit using data associated with all GRBs is listed in Table 3. Our sample consists of 1813 long GRBs and 323 short GRBs. Fluence limits were calculated for each of these subsamples. Table 4 and Table 5 show the number of observed events, the number of expected background events (assuming that the background rate is same for both long and short GRB subsamples), N 90 , and the neutrino fluence limit for long and short GRBs, respectively. We compare our limits using data associated with all GRBs divided by number of GRB to those obtained from previous studies at SK [4] and Borexino [8]. This comparison is shown in Fig. 16. It can be seen that this analysis gives better fluence limits in the energy region of 28-80 MeV. In the previous SK study, N 90 was obtained by counting the number of events in the fixed energy range from 7 MeV to 80 MeV; this was done to get the limit at each energy point. As a result, the N 90 reported in the previous analysis has a larger value than in the current analysis. This effect is more pronounced in the larger energy region (>28 MeV). The fluence limit at neutrino energy E ν is obtained by replacing λ(E ν ) in eq. 4 by a delta function δ(E ν − E ν ).

Conclusion
A correlation analysis was used to search for neutrinos associated with GRBs. In this study, SK data from December 2008 to March 2017 was searched for neutrino candidates in coincidence with a set of 2208 GRBs. After applying the event reduction to the SK data sample, 250 candidate events remained in a fixed search window of ±500 sec around each GRB trigger time. This search window corresponds to a total livetime of 25.6 days. The background expected in each 1000 sec search window was estimated to be 0.114 events.
No statistically significant excess was observed within the search window, and the energy distribution of the events is consistent with background. Three candidate events observed in coincidence with GRB140616A seem to be caused by the spallation of oxygen nuclei by cosmic ray muons.
In addition to the fixed-window analysis, we utilized a variable search window that was determined by the GRB duration time. The number of SK candidate events occurring between the GRB start and end time was used to calculate a probability for each GRB.
By examining the probability distribution with toy MC, we concluded that the observed   A stacked analysis was performed statistically to search for excess events. This analysis combined the fixed-window data from all 2208 GRBs to create a sample with large statistics. No significant excess was observed in the stacked data, and so we used this sample to calculate the upper limit to the neutrino fluence. The fluence limit per GRB from 8 MeV to 100 MeV is 5.07 × 10 5 cm −2 . For 189 GRBs whose distance from Earth are known, the upper limits on the total energy emitted by neutrinos at the source was calculated as a function of the distance to these GRBs. An energy-dependent fluence limit was also calculated for the full set of GRBs as well as subsets based on GRB duration. The high detection efficiency and large statistics sample used in this study resulted in a world-leading fluence limit between 28 MeV to 80 MeV.