Perspectives of DSNB neutrino researches in modern detectors

Studies of diffuse supernova neutrino background (DSNB) by modern underground detectors are reviewed. DSNB neutrino fluxes, their spectra and current experimental limits on their flux are discussed. Currently the best upper limit on DSNB neutrino flux is 2.9 cm-2s-1. Also posibilities to improve upper limits on future detectors and perspectivies of DSNB neutrino detection are discussed.


Diffuse Supernova Neutrinos
The Diffuse Supernova Neutrino Background (DSNB) is the flux of neutrinos and antineutrinos, which were emitted by all core-collapse supernovae in the Universe. Total rate and spectral shape of DSNB neutrinos could give new information about supernova core-collapse rate and neutrino emission from supernova.

Spectrum
The DSNB flux spectrum at the Earth can be written as [1]: where N Sn -neutrino emission spectrum from each individual supernova, R SN -cosmic supernova rate (it is a function of redshift and star formation rate), H 0 -Hubble constant, Ω m = 0.3, Ω Λ = 0.7 -the relative densities of the matter and dark matter in the Universe.

Astrophysical inputs
DSNB predictions are dependent from astrophysical inputs: the cosmic supernova rate, the star formation rate(SFR), the neutrino emission spectra from core-collapse supernova. Star formation rate is defined by the mass of the formed star in a volume unit. The SFR function can be written in the form [2]: (1 + z) 3.28 , z < 1; (1 + z) −0.26 , 1 < z < 4.5; (1 + z) −7.8 , 4.5 < z; (2) The energy spectrum for neutrino of each flavour is expected to be thermal near the surface of the supernova and can be parametrized as: where E -neutrino energy, L ν -expected luminosity of individual flavour of ν, E 0ν -average energy, β ν -pinch factor ∼ 2 − 5 describing the shape of the spectrum. Currently, there are several MC calculations performed by different groups, predicting the neutrino spectral shape: Lawrence-Livermore National Laboratory group(LL) [3], Keil, Raffelt, Janka (KRJ) group [4] and Thompson, Burrows, Pinto (TBP) group [5]. General difference between models is in time of bursts simulation.
Neutrino energy spectrum is thermal and neutrinos average energy is ∼ 10 − 20 MeV, ν e and ν e will have colder spectra with respect to ν µ and ν τ .
Studies of DSNB neutrinos were performed on several detectors but diffuse neutrinos from supernovae were not detected yet, nevertheless some upper limits for diffuse neutrino flux were obtained.

Super-Kamiokande
Super-Kamiokande detector is a 50 kton water Cherenkov detector located in the Kamioka mine in Japan. More information about the detector can be found in [6].
Super-Kamiokande detects electron antineutrinos via inverse beta decay reaction: In 2012 upper limit for DSNB electron antineutrino was set on. Limit is 2.9ν e cm −2 s −1 in E > 16 MeV (17.3 MeV E ν ) energy range [6]. In the paper [7] SK collaboration lowered neutrino energy threshold from 17.3 MeV to 13.3 MeV by including neutron tagging. In further researches the collaboration expects that the energy threshold will be lowered to 10 MeV.

KamLAND
The KamLAND is liquid scintillator detector located in underground laboratory Kamioka Observatory in Japan.
Results of searches for extraterrestrial electron antineutrino sources were published in 2012. As a result of these researches, limit for diffuse supernova electron antineutrino flux was obtained and its value is 139 cm −2 s −1 in 8.3 < E < 31.8 MeV energy range [8].

SNO
SNO is one kton the water-Cherenkov detector, which used heavy water as a target. It is located in the Inco, Ltd. Creighton nickel mine near Sudbury, Ontario, Canada at a depth of 6010 m water equivalent.

Borexino
Borexino is a large volume liquid organic scintillator detector located in the underground national laboratory Gran-Sasso, Italy. DSNB electron antineutrinos detect in Borexino via inverse beta decay reaction. Borexino collaboration has published the limit forν e from unknown sources in the energy range 1.8 < E < 17.8 MeV [11]. This limit value is 760 cm −2 s −1 .
Summary of all detectors results for all antineutrino extraterrestrial sources are shown in figure 1.  Diffuse supernova neutrinos will be detected by inverse beta-decay reactions. Expected DSNB rate is 1.5 -2.6 events per year. Expected upper limit for diffuse electron antineutrino flux in absence of signal is shown on the figure 2 together with Super-Kamiokande results for comparison.
The collaboration expects upper limit value will be 0.2 cm −2 s −1 after 10 years in energy range above 17 MeV [12].

Conclusion
Modern results limit neutrino fluxes in energy range from 8.3 MeV to 40 MeV. Since Borexino detector has the least energy threshold, this low-background detector has an unique chance to set the upper limit for DSNB neutrinos in the low-energy area.