source: Backup NB/Talks/MEMPHYSetal/LAGUNA/EU I3/PhysicsLatex/Laguna-before-xarchiv/snv_det.tex

\section{Supernova neutrinos}
\label{sec:SN}
%\REDBLA{Version 0 by JEC 28/2/06: sort of summary of A. Mirizzi talk 16/2/06.}
%\REDBLA{update by A. Bueno 23/3/06}
%\REDBLA{update by A. Mirizzi 9/4/06}
%\REDBLA{update by T. M. Undagoitia  10/4/06}
%\REDBLA{update by M. Wurm  19/4/06}
%\REDBLA{update by J.E Campagne  3/5/06}
%\REDBLA{update by JEC + A. Tonazo 9/5/06}
%\REDBLA{update by A. Bueno 19/5/06}
%\REDBLA{update by JEC 16/10/06: this is a section now}
%\REDBLA{update by G. Raffekt 10/1/06}
%
%A.Mirizzi 9/4/06 START
A supernova (SN) neutrino detection represents one of the next
frontiers of neutrino astrophysics. It will provide invaluable
information on the astrophysics of the core-collapse explosion
phenomenon and on the neutrino mixing parameters. In particular,
neutrino flavor transitions in the SN envelope are sensitive to the
value of $\theta_{13}$ and on the type of mass hierarchy, and the
detection of SN neutrino spectra at Earth can significantly contribute
to sharpen our understanding of these unknown neutrino parameters.  On
the other hand, a detailed measurement of the neutrino signal from a
galactic SN could yield important clues on the SN explosion mechanism.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{SN neutrino emission and oscillations}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A core-collapse supernova marks the evolutionary end of a massive star
($M\gtrsim 8\,M_\odot$) which becomes inevitably instable at the end
of its life: it collapses and ejects its outer mantle in a shock-wave
driven explosion.  The collapse to a neutron star ($M \simeq M_\odot
$, $R\simeq 10$~km) liberates a gravitational binding energy, $E_B
\approx 3 \times10^{53}~{\rm erg} $, released at $\sim 99\%$ into
(anti)neutrinos of all the flavors, and only at $\sim$1\% into the
kinetic energy of the explosion. Therefore, a core-collapse SN
represents one of the most powerful sources of (anti)neutrinos in the
Universe.

In general, numerical simulations of supernova explosions provide the
original neutrino spectra in energy and time $F^0_{\nu}$. Such initial
distributions are in general modified by flavor transitions in SN
envelope, in vacuum (and eventually in Earth matter)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{equation}
F^0_\nu {\longrightarrow} F_\nu
\end{equation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
and must be convolved with the differential interaction cross section
$\sigma_e$ for electron or positron production, as well as with the
detector resolution function $R_e$, and the efficiency $\varepsilon$,
in order to finally get observable event rates:
%...............................................................................
\begin{equation}
\label{Conv}
N_e = F_\nu \otimes \sigma_e \otimes R_e \otimes \varepsilon\
\end{equation}
%...............................................................................
Regarding the initial neutrino distributions $F^0_{\nu}$, a SN
collapsing core is roughly a black-body source of thermal neutrinos,
emitted on a timescale of $\sim 10$~s.  Energy spectra parametrization
are typically cast in the form of quasi-thermal distributions, with
typical average energies: $ \langle E_{\nu_e} \rangle= 9-12$~MeV,
$\langle E_{\bar{\nu}_e} \rangle= 14-17$~MeV, $\langle E_{\nu_x}
\rangle= 18-22$~MeV, where $\nu_x$ indicates any non-electron flavor.

The oscillated neutrino fluxes arriving at Earth may be
written in terms of the energy-dependent ``survival probability''
 $p$ ($\bar{p}$) for neutrinos (antineutrinos) as~\cite{Dighe:1999bi}
\begin{eqnarray}
F_{\nu_e} & = & p F_{\nu_e}^0 + (1-p) F_{\nu_x}^0  \nonumber \\ 
F_{\bar\nu_e} & =  &\bar{p} F_{\bar\nu_e}^0 + (1-\bar{p}) F_{\nu_x}^0 \label{eqfluxes1-3} \\
4 F_{\nu_x} & = & (1-p) F_{\nu_e}^0 + (1-\bar{p}) F_{\bar\nu_e}^0 +
(2 + p + \bar{p}) F_{\nu_x}^0 \nonumber
\end{eqnarray}
where $\nu_x$ stands for either $\nu_\mu$ or $\nu_\tau$.  The
probabilities $p$ and $\bar{p}$ crucially depend on the neutrino mass
hierarchy and on the unknown value of the mixing angle $\theta_{13}$
as shown in \refTab{tab:Phys-SN-Flux}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table}
                \caption{\label{tab:Phys-SN-Flux}Values of the $p$ and $\bar{p}$ parameters used in
 Eq.~\ref{eqfluxes1-3} in different scenario of mass hierarchy and  $\sin^2 \theta_{13}$.}

                \begin{tabular}{cccc} \hline\hline
                Mass Hierarchy        & $\sin^2\theta_{13}$ & $p$     & $\bar{p}$ \\ \hline
                Normal                & $\gtrsim 10^{-3}$              & 0        & $\cos^2 \theta_{12}$ \\ 
                Inverted                          & $\gtrsim 10^{-3}$              & $\sin^2 \theta_{12}$ & 0 \\
                Any                   &  $\lesssim 10^{-5}$             & $\sin^2 \theta_{12}$ & $\cos^2 \theta_{12}$ \\ \hline\hline
                \end{tabular}
\end{table}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
\subsection{SN neutrino detection}
%
Galactic core-collapse supernovae are rare, perhaps a few per century. 
Up to now, supernova neutrinos have been measured only once
during SN~1987A explosion in the Large Magellanic Cloud ($d=50$~kpc).
Due to the relatively small masses of the detectors operative at that time,  only few events were detected
(11 in Kamiokande \cite{Hirata:1987hu,Hirata:1988ad} and 8 in IMB \cite{Aglietta:1987we,Bionta:1987qt}). 
The  three proposed large-volume neutrino detectors with a broad range
of science goals might guarantee continuous exposure for 
several decades, so that  a high-statistics supernova 
neutrino signal may eventually be observed.

Expected number of events for GLACIER, MEMPHYS and LENA
are reported in \refTab{tab:Phys-SN-DetectorRates}, for a typical galactic SN distance
of $10$~kpc. In the upper panel it is reported the total number of events,
while  the lower part refers to the $\nu_e$ signal detected
during the prompt neutronization burst, with a duration of
$\sim 25$~ms, just after the core bounce. 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table*}
                \caption{\label{tab:Phys-SN-DetectorRates} Summary of the expected neutrino interaction 
rates in the different detectors for a $8 M_\odot$ SN located at 10~kpc (Galactic center). 
The following notations have been used: I$\beta$D, $e$ES and pES stands for Inverse $\beta$ Decay, 
electron and proton Elastic Scattering, respectively. The final state nuclei are generally unstable and decay either 
radiatively (notation ${}^*$), or by $\beta^-/\beta^+$ weak interaction (notation ${}^{\beta^{-,+}}$).
The rates of the different reaction channels are listed, and for LENA they have been obtained by scaling
the predicted rates from \cite{Cadonati:2000kq, Beacom:2002hs}.}
%
                \begin{tabular}{cccccc} \hline\hline
                \multicolumn{2}{c}{MEMPHYS} & \multicolumn{2}{c}{LENA} & \multicolumn{2}{c}{GLACIER} \\
                Interaction    & Rates  & Interaction    & Rates  & Interaction    & Rates  \\ \hline
                $\bar{\nu}_e$ I$\beta$D & $2 \times 10^{5}$ &
                $\bar{\nu}_e$ I$\beta$D & $9 \times 10^{3}$ &
                $\nu_e^{CC}({}^{40}Ar,{}^{40}K^*)$ & $2.5 \times 10^{4}$ \\
%               
                $\nunubar{e}{}^{CC} ({}^{16}O,X) $ & $10^{4}$ &
                $\nu_x$ pES  & $7 \times 10^{3}$ &
                $\nu_x^{NC}({}^{40}Ar^{*})$ & $3.0 \times 10^{4}$ \\             
%               
                $\nu_x$ $e$ES  & $10^{3}$ &
                $\nu_x^{NC} ({}^{12}C^{*})$ & $3 \times 10^{3}$ &
                $\nu_x$ $e$ES & $10^{3}$ \\
%
                & & 
                $\nu_x$ $e$ES & $600$ &
                $\bar{\nu}_e^{CC}({}^{40}Ar,{}^{40}Cl^*)$ & $540$ \\
%               
          &             &
                $\bar{\nu}_e^{CC} ({}^{12}C,{}^{12}B^{\beta^+})$ & $500$ & &\\
%               
                & &
                $\nu_e^{CC} ({}^{12}C,{}^{12}N^{\beta^-})$ & $85$  & & \\
%
                \hline\hline
                \multicolumn{6}{l}{Neutronization Burst rates}\\
                  MEMPHYS & 60 & ${\nu}_e$ eES & & & \\
                    LENA & 
                    % M Wurm 23-08-06 BEGIN 
                    $70$ & $\nu_e$ eES/pES & &  & \\
                    % M Wurm 23-08-06 END
                    & $\nu_e^{CC} ({}^{12}C,{}^{12}N^{\beta^-})$ & &  & \\
                    
                    GLACIER & 380 & $\nu_x^{NC}({}^{40}Ar^{*})$ & & & \\
                \hline\hline
                \end{tabular}
\end{table*}
%\begin{figure}
%\begin{center}
%\epsfig{figure=./figures/snevents.eps,width=8cm,height=8cm}
%\caption{% Figure to be redone for 440 kt! 
%The number of events in a 400 kt water \v{C}erenkov detector (left scale)
%and in SK (right scale) in all channels and in the individual
%detection channels as a function of distance for a supernova
%explosion \cite{Fogli:2004ff}.}
%\label{fig:SN}
%\end{center}
%\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
One can  realize that $\bar{\nu}_e$ detection by Inverse $\beta$ Decay (I$\beta$D) 
is the golden channel for MEMPHYS and LENA. 
%T. M. Undagoitia  10/4/06 START
%and updated by J.E.C 13/4/06 to be upto date with the new text by A. Mirizzi
%A 8~M$_{\odot}$ supernova exploding in the centre of the milky way
%typically will induce in LENA a total signal rate of
%$\sim20~000$~events. This would include neutrinos and antineutrinos of
%all flavours. The rates of the different reaction channels are listed
%JEC 13/10/04 see table caption for the mention of the scaling method
%in ~\ref{tab:Phys-SN-DetectorRates} and have been obtained by scaling
%the predicted rates from~\cite{Cadonati:2000kq}\cite{Beacom:2002hs} to LENA. A
%discrimination between electron neutrinos and electron antineutrinos
%would be possible by the interaction of antineutrinos via inverse beta
%decay
In addition, the electron neutrino signal can be detected in LENA
thanks to the interaction on $^{12}$C.  The three charged current
reactions will deliver information on $\nu_e$ and $\bar{\nu}_{e}$
fluxes and spectra while the three neutral current reactions,
sensitive to all neutrino flavours will provide information on the
total flux.
%T. Marrodan Undagoitia 10/4/06 END
GLACIER has also the opportunity to see the $\nu_e$ by charged current
interactions on ${}^{40}\rm{Ar}$ with a very low threshold.  The
detection complementarity between $\nu_e$ and $\bar{\nu}_e$ is of
great interest and would assure a unique way to probe SN explosion
mechanism as well as neutrino intrinsic properties.  Moreover, the
huge statistics would allow spectral studies in time and in energy
domain.

We stress that it will be difficult to establish SN neutrino
oscillation effects solely on the basis of a $\bar\nu_e$ or $\nu_e$
``spectral hardening'' relative to theoretical
expectations. Therefore, in the recent literature the importance of
model-independent signatures has been emphasized.  Here we focus
mainly on the signatures associated to: the prompt $\nu_e$
neutronization burst, the shock-wave propagation, the Earth matter
crossing.

The analysis of the time structure of the SN signal during the first few tens of milliseconds
after the core bounce can provide a clean indication if the full $\nu_e$ burst is present or
absent and therefore allows one to distinguish between different mixing scenarios as indicated by the
third column of \refTab{tab:Phys-SN-SummaryOscNeut}. For example, if the mass
ordering is normal and the $\theta_{13}$ is large, the $\nu_e$ burst
will fully oscillate into $\nu_x$.  If $\theta_{13}$ is measured
in the laboratory to be large, for example by one of the forthcoming
reactor experiments, then one may distinguish
between the normal and inverted mass ordering.  

As discussed, MEMPHYS is mostly sensitive to the I$\beta$D, although
the $\nu_e$ channel can be measured by the elastic scattering reaction
$\nu_x+e^-\to e^-+\nu_x$ \cite{Kachelriess:2004ds}. Of course, the
identification of the neutronization burst is cleanest with a detector
using the charged-current absorption of $\nu_e$ neutrinos, like
GLACIER.  Using its unique features to look at $\nu_e$ CC it is
possible to probe oscillation physics during the early stage of the SN
explosion, and using the NC it is possible to decouple the SN
mechanism from the oscillation physics \cite{Gil-Botella:2004bv,
Gil-Botella:2003sz}. 
%A. Bueno had included also the Gil-Botella:2004bv reference 23/3/06.

A few seconds after core bounce, the SN shock wave will pass the
density region in the stellar envelope relevant for oscillation matter
effects, causing a transient modification of the survival probability
and thus a time-dependent signature in the neutrino signal
\cite{Schirato:2002tg,Fogli:2003dw}.  It would show a characteristic
dip when the shock wave passes \cite{Fogli:2004ff}, or a double-dip
feature if a reverse shock occurs \cite{Tomas:2004gr}. The
detectability of such a signature has been studied in a Megaton \WC\
detector like MEMPHYS by the I$\beta$D \cite{Fogli:2004ff}, and in a
Large liquid Argon detector like GLACIER by Ar CC interactions
\cite{Barger:2005it}. The shock wave effects would be certainly
visible also in a large volume scintillator like LENA. Of course,
apart from identifying the neutrino mixing scenario, such observations
would test our theoretical understanding of the core-collapse SN
phenomenon.

One unequivocal indication of oscillation effects would be the
energy-dependent modulation of the survival probability $ p(E)$ caused
by Earth matter effects \cite{Lunardini:2001pb}. The Earth matter
effects can be revealed by wiggles in energy spectra and LENA benefit
from a better energy resolution than MEMPHYS in this respect which may
be partially compensated by 10 times more statistics
\cite{Dighe:2003jg}.  The Earth effect would show up in the
$\bar\nu_e$ channel for the normal mass hierarchy, assuming that
$\theta_{13}$ is large (\refTab{tab:Phys-SN-SummaryOscNeut}). Another
possibility to establish the presence of Earth effects is to use the
signal from two detectors if one of them sees the SN shadowed by the
Earth and the other not. A comparison between the signal normalization
in the two detectors might reveal Earth effects~\cite{Dighe:2003be}.
The shock wave propagation can influence the Earth matter effect,
producing a delayed effect $5-7$~s after the core-bounce, in some
particular situations~\cite{Lunardini:2003eh}
(\refTab{tab:Phys-SN-SummaryOscNeut}).

Exploiting these three experimental signatures, by the joint efforts
of the complementarity SN neutrino detection in MEMPHYS, LENA, and
GLACIER it would be possible to extract valuable information on the
neutrino mass hierarchy and to put a bound on $\theta_{13}$, as shown
in \refTab{tab:Phys-SN-SummaryOscNeut}.

% G. Raffelt 10/1/07 START: <optional short comment>
As an important caveat we mention that very recently it has been
recognized that nonlinear oscillation effects caused by
neutrino-neutrino interactions can have a dramatic impact on the
neutrino flavor evolution for approximately the first 100~km above the
neutrino sphere~\cite{Duan:2006an,Hannestad:2006nj}. The impact
of these novel effects on the observable oscillation signatures has
not yet been systematically studied. Therefore, our description of
observable oscillation effects may need revision in future as a
better understanding of the consequences of these nonlinear effects
develops.
%  G. Raffelt 10/1/07 END
 
Other interesting ideas has been also studied in the literature, ranging
from the pointing of a SN by neutrinos~\cite{Tomas:2003xn},
% G. Raffelt 10/1/07 START: <optional short comment>
determining its distance from the deleptonization burst that 
plays the role of a standard candle \cite{Kachelriess:2004ds},
%  G. Raffelt 10/1/07 END
an early
alert for SN observatory exploiting the neutrino
signal \cite{Antonioli:2004zb}, and the detection of neutrinos from
the last phases of a burning star \cite{Odrzywolek:2003vn}.

Up to now, we have investigated SN in our Galaxy, but the calculated
rate of supernova explosions within a distance of 10~Mpc is about 1
per year. Although the number of events from a single explosion at
such large distances would be small, the signal could be separated
from the background with the request to observe at least two events
within a time window comparable to the neutrino emission time-scale
($\sim 10$~sec), together with the full energy and time distribution
of the events \cite{Ando:2005ka}. In a MEMPHYS detector, with at least
two neutrinos observed, a supernova could be identified without
optical confirmation, so that the start of the light curve could be
forecasted by a few hours, along with a short list of probable host
galaxies. This would also allow the detection of supernovae which are
either heavily obscured by dust or are optically dark due to prompt
black hole formation.
%
\begin{table*}
                \caption{\label{tab:Phys-SN-SummaryOscNeut}Summary
 of the neutrino properties effect on $\nu_e$ and $\bar{\nu}_e$ signals.}
%
                \begin{tabular}{ccccc}\hline\hline
                \parbox[b]{2cm}{\center{Mass\\ Hierarchy}}   & $\sin^2\theta_{13}$ & \parbox[b]{3cm}{\center{$\nu_e$ neutronization\\peak}} & Shock wave & Earth effect \\[2mm] \hline
                Normal    & $\gtrsim 10^{-3}$ & Absent  & $\nu_e$   & \parbox[b]{3cm}{\center{$\bar{\nu}_e$\\$\nu_e$ (delayed)}} \\
                Inverted    & $\gtrsim 10^{-3}$ & Present  & $\bar{\nu}_e$   & \parbox[b]{3cm}{\center{$\nu_e$\\$\bar{\nu}_e$ (delayed)}} \\
                Any    & $\lesssim 10^{-5}$ & Present  & -   & \parbox[b]{3cm}{\center{both $\bar{\nu}_e$ $\nu_e$}} \\[2mm]
\hline\hline
                \end{tabular}
\end{table*}
%
\subsection{Diffuse Supernova Neutrino Background} 
%
% T. Marrodan Undagoitia  10/12/06 START 
% Some corrections and some paragraphs replaced
%\REDBLA{
A galactic Supernova explosion will be a spectacular source of
neutrinos, so that a variety of neutrino and SN properties could be
determined.  However, only one such explosion is expected in 20 to 100
years.  Alternatively, it has been suggested that we might detect the
cumulative neutrino flux from all the past SN in the Universe, the so
called Diffuse Supernova Neutrino (DSN) Background\footnote{We prefer
the word "Diffuse" rather than "Relic" not to confuse with the
primordial neutrinos produced one second after the Big Bang.}.  In
particular, there is an energy window around $10-40$~MeV where the
DSN signal can emerge above other sources, so that proposed detectors
may measure this flux after some years of exposure times.

\begin{table*}
        \caption{\label{tab:Phys-SN-DiffuseRates}DSN expected
        rates. The larger numbers are computed with the present limit
        on the flux by SuperKamiokande collaboration. The lower
        numbers are computed for typical models. The background coming
        from reator plants have been computed for specific locations
        for MEMPHYS and LENA. For MEMPHYS, the SuperKamiokande
        background has been scaled by the exposure. More studies are
        needed to estimate the background at the new Fréjus
        laboratory.}

        \begin{tabular}{cccc}\hline \hline
        Interaction & Exposure     &  Energy Window &  Signal/Bkgd \\ \hline \\[-2mm]
        %JEC 3/5/06 START scale to 1 shaft MEMPHYS only filled with Gd + 5 years
\multicolumn{4}{c}{1 shaft MEMPHYS + 0.2\% Gd (with bkgd Kamioka)} \\[-4mm]
\parbox{3cm}{\center{$\bar{\nu}_e + p \rightarrow n + e^+$}\\$n+Gd\rightarrow \gamma$\\(8~MeV, $20~\mu$s)} &
%\parbox{2cm}{\center{1~Mt.y\\2~yrs}} & 
%$[15-30]$~MeV & (60-150)/65 \\
\parbox{2cm}{\center{0.7~Mt.y\\5~yrs}} & 
$[15-30]$~MeV & (43-109)/47 \\
        %JEC 3/5/06 END
%                       
\multicolumn{4}{c}{LENA at Pyh\"asalmi} \\[-4mm] 
\parbox{3cm}{\center{$\bar{\nu}_e + p \rightarrow n + e^+$}\\$n+p\rightarrow d+ \gamma$ (2~MeV, $200~\mu$s)} &
\parbox{2cm}{\center{0.4~Mt.y\\10~yrs}} & 
%$[9.5-30]$~MeV & (40-260)/20 \\
% M.Wurm 19-06-06 BEGIN
$[9.5-30]$~MeV & (20-230)/8 \\
% M.Wurm 19-06-06 END

%
\multicolumn{4}{c}{GLACIER} \\[-4mm] 
 $\nu_e + {}^{40}Ar \rightarrow e^- + {}^{40}K^*$ &
\parbox{2cm}{\center{0.5~Mt.y\\5~yrs}} &
%A Bueno 19/5/06 gives the 40-60 events
$[16-40]$~MeV & (40-60)/30 \\
\hline \hline
                \end{tabular}
\end{table*}
 
The DSN signal, although weak, is not only ``guaranteed'', but can
also probe physics different from that of a galactic SN, including
processes which occur on cosmological scales in time or space. 

For instance, the DSN signal is sensitive to the evolution of the SN
rate (SNR), which is closely related to the star formation rate
\cite{Fukugita:2002qw,Ando:2004sb}. Additionally, neutrino decay
scenarios with cosmological lifetimes could be analyzed and
constrained \cite{Ando:2003ie} as proposed in \cite{Fogli:2004gy}.

An upper limit on the DSN flux has been set by the SuperKamiokande
experiment \cite{Malek:2002ns}
\begin{equation}
        \phi_{\bar{\nu}_e}^{\mathrm{DSN}} < 1.2 \flux (E_\nu > 19.3~\mathrm{MeV})
\end{equation}
However most of the predictions are below this limit and therefore 
DSN detection appears to be feasible only with the large detector foreseen, through $\bar{\nu}_e$ inverse
beta decay in MEMPHYS and LENA
detectors and through $\nu_e + {}^{40}Ar \rightarrow e^- + {}^{40}K^*$ (and the associated gamma cascade) in GLACIER \cite{Cocco:2004ac}. 
%A Bueno 19/5/06 add the Cocco:2004ac reference

%
\begin{figure}
%JEC 23/10/06 update the figure given by M. Wurm
\includegraphics[width=0.9\columnwidth]{./figures/dsnspec1.eps}
\caption{Diffuse supernova neutrino signal and background in LENA detector in 10 years of exposure. Shaded regions give the uncertainties of all curves. An observational window between $\sim 9.5$ to 25~MeV that is almost free of background can be identified (for the Pyh\"asalmi site)~\cite{Wurm:2006}.}
\label{fig:Phys-SN-LENAsnr}
\end{figure}

\begin{figure}
\includegraphics[width=0.9\columnwidth]{./figures/GdSKtemp-expect-bis.eps}
\caption{Possible 90\% C.L. measurements of the emission parameters
of supernova electron antineutrino emission after 5
years running of a gadolinium-enhanced SK detector or 1 year of one gadolinium-enhanced MEMPHYS shaft
\cite{Yuksel:2005ae}.}
\label{fig:Phys-DSN-sndpar}
\end{figure}
%
Typical estimates for DSN fluxes (see for example \cite{Ando:2004sb})
predict an event rate of the order of $(0.1- 0.5)$ cm${}^{-2}$
{s}${}^{-1}$ MeV$^{-1}$ for energies above 20~MeV.

The DSN signal energy window is constrained from above by the
atmospheric neutrinos and from below by either the nuclear reactor
$\bar{\nu}_e$ (I), the spallation production of unstable radionuclei
by cosmic ray muons (II), the decay of "invisible" muons into
electrons (III), and solar $\nu_e$ neutrinos (IV). The three detectors
are affected differently by these backgrounds.


%New version JEC 13/4/06 due to material written by M. Wurm (see below) Namely, MEMPHYS filled with pure water is mainly affected by type III due to the fact that the muons may have not enough energy to produce \c{C}erenkov light, while LENA takes benefit from the delayed neutron capture in $\bar{\nu}_e + p \rightarrow n + e^+$, so it is mainly affected by type I which impose to choose an underground site far from nuclear plants, and GLACIER looking at $\nu_e$ is mainly affected by type IV. 

GLACIER looking at $\nu_e$ is mainly affected by type IV. MEMPHYS filled with pure water is mainly affected by type III due to the fact that the muons may have not enough energy to produce \v{C}erenkov light. As pointed out in \cite{Fogli:2004ff} with the addition of Gadolinium \cite{Beacom:2003nk} the detection of the captured neutron releasing 8~MeV gamma after $\sim20~\mu$s (10 times faster than in pure water) would give the possibility to reject  the "invisible"  muon (type III) as well as spallation background (type II). 
%JEC 10/4/06 Then, MEMPHYS (Gd loaded) would be in the same position with respect to the location as for LENA.
% BEGIN LENA M. Wurm 12-04-06
LENA taking benefit from the delayed neutron capture in $\bar{\nu}_e +
p \rightarrow n + e^+$, is mainly affected by reactor neutrinos
(I) which impose to choose an underground site far from nuclear
plants:
% M.Wurm 19-06-06 BEGIN
if LENA is deployed at the Center for Underground Physics in Pyh\"asalmi (CUPP, Finland),
% M.Wurm 19-06-06 END
% M.Wurm 23-08-06 BEGIN
there will be an observational window from $\sim 9.7$ to 25~MeV that is almost free of background. The expected rates of signal and background are presented in \refTab{tab:Phys-SN-DiffuseRates}.


%According to DSN models \cite{Ando:2004sb} that are using different SN simulations
%from the LL \cite{Totani:1997vj}, TBP \cite{Thompson:2002mw} and KRJ \cite{Keil:2002in} groups for the
%prediction of the DSN energy spectrum and flux, a detection of the DSN
%in this energy regime with LENA seems all but certain. Within ten
%years, 20 to 230 events are expected, the exact number mainly
%depending on the uncertainties of the Star Formation Rate (SFR) in the
%near universe. Signal rates corresponding to three different DSN
%models and the background rates due to the reactor (I) and atmospheric
%neutrinos are shown in \refFig{fig:Phys-SN-LENAsnr} for 10 years of measurement
%with LENA in CUPP.

According to current DSN models \cite{Ando:2004sb} that are using
different SN simulations from the LL \cite{Totani:1997vj}, TBP
\cite{Thompson:2002mw} and KRJ \cite{Keil:2002in} groups for the
prediction of the DSN energy spectrum and flux, a detection of
$\sim$10 DSN events per year is expected in LENA. Signal rates
corresponding to three different DSN models and the background rates
due to the reactor (I) and atmospheric neutrinos are shown in
\refFig{fig:Phys-SN-LENAsnr} for 10 years of measurement with LENA in
CUPP.

Apart from mere detection, spectroscopy of the DNS events in LENA will
constrain the parameter space of core-collapse models. If the SNR
signal is known at a sufficient precision, the spectral slope of the
DSN can be used to determine the hardness of the initial SN neutrino
spectrum. For the currently favoured value of the SNR, the
discrimination between the discussed LL and TBP core-collapse models
will be possible at 2.6$\sigma$ after 10 years of measuring
time~\cite{Wurm:2006}.

In addition, by an analysis of the flux in the energy region from 10
to 14~MeV the SNR for $z<2$ could be constrained at high significance
levels, as in this energy regime the DSN flux is only weakly dependent
on the assumed SN model. This could be used to cross-check FIR and UV
measurements.

%Moreover, assuming the most likely rates of 2.8 to 5.5 DSN events per
%year, after a decade of measurement statistics in LENA might already
%be good enough to distinguish between the LL and the TBP model that
%give the most different predictions on the DSN's spectral slope and
%therefore event rates. This will give valuable constraints on the SN
%neutrino spectrum and explosion mechanism.


The detection of the redshifted DSN from $z>1$ is limited by the flux
of the reactor $\bar\nu_e$ background. In Pyhasalmi, a lower threshold
of 9.5~MeV resuls in a spectral contribution of 25\% DSN from $z>1$.

% Start - Supressed & replaced by T. Marrodan Undagoitia 10/12/06
%Finally, if one achieves a threshold below 10~MeV for the DSN
%detection it might be possible to get a glimpse at the low-energetic
%part of the spectrum that is dominated by neutrinos emitted by SN at
%redshifts $z>1$. About $25\%$ of the DSN events in the observational
%window will be caused by these high-$z$ neutrinos. This might provide
%a new way of measuring the SFR at high redshifts. At these distances,
%conventional astronomy looking for Star Formation Regions is strongly
%impeded by dust extinction of the UV light that is emitted by young
%stars. The $z$-sensitivity of the detector could be further improved
%by choosing a location far away from the nuclear power plants of the
%northern hemisphere. For instance, a near to optimum DSN detection
%threshold of 8.4~MeV could be realized by deploying LENA in
%Hawaii. This would also lower the background due to atmospheric
%$\bar\nu_e$.
% End - Supressed & replaced by T. Marrodan Undagoitia 10/12/06

% END M. Wurm 23-08-2006
%JEC 18/4/06 to be more general: LENA would for instance, 
%This might provide a new way of measuring the SFR
%at high redshifts. At these distances, conventional astronomy looking
%for Star Formation Regions is strongly impeded by dust extinction of
%the UV light that is emitted by young stars. The $z$-sensitivity of the
%detector could be further improved by choosing a location far away
%from the nuclear power plants of the northern hemisphere. For
%instance, a near to optimum DSN detection threshold of 8.4~MeV could
%be realized by deploying LENA in New Zealand.
% END M. Wurm

%JEC + A. Tonazo 9/5/06 START: eplace the paragraphe describing the figure snrelic.eps 
An analysis of the expected DSN spectrum that would be observed
with a gadolinium-loaded \WC\ detector has been carried out in \cite{Yuksel:2005ae}. 
The possible measurements of the parameters (integrated luminosity and average energy) of
supernova $\bar\nu_e$ emission have been computed for 5 years running of
a Gd-enhanced SuperKamiokande detector, which would correspond to 1 year
of one Gd-enhanced MEMPHYS shaft. The results are shown in \refFig{fig:Phys-DSN-sndpar}.
Even if detailed studies on characterization of the background are needed, the DSN events
may be as powerful as the measurement made by Kamioka and IMB with the SN1987A $\bar\nu_e$ events. 
%}
 %T. Marrodan Undagoitia 10/12/06 END 
% Some corrections and some paragraphs replaced


%As an example of energy spectra, for the MEMPHYS detector, the results are shown in \refFig{fig:snr}: the signal could be observed with a statistical significance of about 2 standard deviations after 10 years. The spectra of the two backgrounds were taken from the 
%Super-Kamiokande estimates
%and rescaled to a fiducial mass of 440~kton of water, while the
%expected signal was computed according to the model called LL
%in \cite{Ando:2004sb}. 
%%
%\begin{figure}
%\begin{center}
%\epsfig{figure=./figures/snrelic.eps,width=13cm}
%\caption{Diffuse supernova neutrino signal and backgrounds (left)
%and subtracted signal with statistical errors (right) in MEMPHYS
%in 10 years exposure. The selection efficiencies of SK were assumed; 
%the efficiency change at 34~MeV is due to the spallation cut.}
%\label{fig:snr}
%\end{center}
%\end{figure}
%JEC + A. Tonazo 9/5/06 END
%

%%%%%%%%%%%%%
%A.Mirizzi 9/4/06 END




%% Text replaced by contribution by A. Mirizzi 9/4/06 who started with this material and elarged the sections.
%\subsubsection{Core-collapse}
%The core collapse of a Supernova (SN) occurs during the terminal phase of a massive star $M\gtrsim 8M_\odot$ which becomes instable at the end of its life. It collapses and ejects its outer mantle in a shock wave driven explosion. In more or less 10~sec, 99\% of the released energy ($\approx 10^{53}$~erg) is emitted by $\nu$ and $\bar{\nu}$ of all flavors. It is expected to see $1-3$ SN per century in our Galaxy ($d \approx O(10~\mathrm{kpc})$).
%
%The event rate observed by a detector is a convolution of the initial spectrum of a given neutrino flavor $\phi(\nu_\alpha)$, the oscillation probability $P(\nu_\alpha \rightarrow \nu_\beta)$, the cross-section $\sigma(\nu_\beta)$ and finally the detector detection efficiency $\epsilon(\nu_\beta)$. The initial flux is the result of the SN explosion simulation (see for instance \cite{LIVERMOREsn}), and the oscillation probability depends from the intrinsic neutrino properties (mixing angles and mass spectrum) as well as the matter density profile which comes from the SN simulation too. The cross section and the detector efficiency are expected to be under control.
%
%The neutrinos are produced in three time scales well separated: first the neutronization burst $\approx 25$~ms after the explosion produces $\nu_e$ neutrinos with $1\%$ of the total energy, then the thermal burst during the accretion phase ($\approx 0.5$~s) and the cooling phase ($\approx 10$~s) produce via $Z^0$ all the $\nu_x \bar{\nu}_x$ pairs. 
%
%The initial neutrino spectra are well described by thermal spectra with an energy hierarchy as: $<E_{\nu_e}> \approx [9-12]$~MeV, $<E_{\bar{\nu}_e}> \approx [14-17]$~MeV and $<E_{\nu_x}> \approx [18-22]$~MeV. As a result, the $\nu_e$ spectrum is suppressed at high energy.
%
%To transport the initial spectra from the SN to Earth, one should used the matter density profile inside the SN and the oscillation parameters, in particular: the unknown $\mathrm{sign}(\Delta m^2_{31})$ ($>0$ means Normal Hierarchy, $<0$ means Inverted Hierarchy) and  $\theta_{13}$ mixing angle as well as the solar mixing angle $\sin^2\theta_{12}\cong 0.31$. As a good approximation one uses:
%\begin{eqnarray}
%       F_{\nu_e} & = & p F^0_{\nu_e} + (1-p) F^0_{\nu_x} \nonumber \\
%       F_{\bar{\nu}_e} & = & \bar{p} F^0_{\bar{\nu}_e} + (1-\bar{p}) F^0_{\nu_x}\nonumber \\
%       4 F_{\nu_x} &=& (1-p)F^0_{\nu_e} + (1-\bar{p})F^0_{\bar{\nu}_e} + (2+p+\bar{p})F^0_{\nu_x}
%       \label{eq:Phys-SN-Flux}
%\end{eqnarray}
%with $F_i$ ($F^0_i$) the Earth (initial SN) flux of the $i$ neutrino flavor, and $\nu_x$ stands for neutrino flavor different from $\nu_e$ and $\bar{\nu}_e$. The $p$ and $\bar{p}$ parameters (Eqs.~\ref{eq:Phys-SN-Flux}) are given in Tab.~\ref{tab:Phys-SN-Flux}.
%\begin{table}[htb]
%       \centering
%               \begin{tabular}{cccc} \hline\hline
%               Mass Hierarchy        & $\sin^2(\theta_{13})$ & $p$     & $\bar{p}$ \\ \hline
%               Normal                & $\gtrsim 10^{-3}$              & 0        & $\cos^2(\theta_{12})$ \\ 
%               Inverted                          & $\gtrsim 10^{-3}$              & $\sin^2(\theta_{12})$ & 0 \\
%               Any                   &  $\lesssim 10^{-5}$             & $\sin^2(\theta_{12})$ & $\cos^2(\theta_{12})$ \\ \hline\hline
%               \end{tabular}
%               \caption{\label{tab:Phys-SN-Flux}Values of the $p$ and $\bar{p}$ parameters used in Eqs.~\ref{eq:Phys-SN-Flux} in different scenario of Mass Hierarchy and  $sin^2(\theta_{13})$.}
%\end{table}
%   
%One of the unsolved problems in astrophysics is the mechanism of supernova
%core-collapse. 
%Inverse beta decay events from the silicon burning phase preceding 
%the supernova explosion have very low (sub-threshold) positron 
%energies, and could only be detected through neutron capture by adding
%Gadolinium \cite{Beacom:2003nk}, 
%provided that they can be statistically distinguished from background
%fluctuations. 
%The silicon burning signal should then be seen with a statistical
%significance of $2\div8$ standard deviations at a reference distance of 1
%kpc. Unfortunately, at the 
%galactic center ($\sim 10$~kpc) the estimated silicon burning signal would
%be 100 times smaller and thus unobservable.
%
%More promising are the expected event rates in the three proposed detectors after the SN explosion. The numbers are listed in Tab.~\ref{tab:Phys-SN-DetectorRates} and  
%are to be compared with the 19 (11 for Kamiokande and 8 for IMB)
%events ($\bar{\nu}_e$ I$\beta$D) coming from the SN1987A in the Large Magellanic Cloud (50~kpc).  One can also appreciate that $\bar{\nu}_e$ detection by Inverse $\beta$ Decay is the golden channel for MEMPHYS and LENA, while GLACIER has a unique opportunity to see the  $\nu_e$ flavor by charged current on ${}^{40}Ar$ with a very low threshold. 
%\begin{table}[htb]
%       \centering
%               \begin{tabular}{cccccc} \hline\hline
%               \multicolumn{2}{c}{MEMPHYS} & \multicolumn{2}{c}{LENA} & \multicolumn{2}{c}{GLACIER} \\
%               Interaction    & Rates  & Interaction    & Rates  & Interaction    & Rates  \\ \hline
%               $\bar{\nu}_e$ I$\beta$D & $2~10^{5}$ &
%               $\bar{\nu}_e$ I$\beta$D & $9~10^{3}$ &
%               $\nu_e^{CC}({}^{40}Ar,{}^{40}K^*)$ & $2.5~10^{4}$ \\
%%              
%               $\nunubar{e}{}^{CC} ({}^{16}O,X) $ & $10^{4}$ &
%               $\nu_x$ pES  & $7~10^{3}$ &
%               $\nu_x^{NC}({}^{40}Ar^{*})$ & $3.0~10^{4}$ \\            
%%              
%               $\nu_x$ $e$ES  & $10^{3}$ &
%               $\nu_x^{NC} ({}^{12}C^{*})$ & $3~10^{3}$ &
%               $\nu_x$ $e$ES & $10^{3}$ \\
%%
%               & & 
%               $\nu_x$ $e$ES & $600$ &
%               $\bar{\nu}_e^{CC}({}^{40}Ar,{}^{40}Cl^*)$ & $540$ \\
%%              
%         &             &
%               $\bar{\nu}_e^{CC} ({}^{12}C,{}^{12}B^{\beta^+})$ & $500$ & &\\
%%              
%               & &
%               $\nu_e^{CC} ({}^{12}C,{}^{12}N^{\beta^-})$ & $85$  & & \\
%%
%               \hline\hline
%               \multicolumn{6}{l}{Neutronization Burst rates}\\
%                 MEMPHYS & 15 & ${\nu}_e$ eES & & & \\
%                   LENA & \REDBLA{$~10$ ???} & $\nu_e^{CC} ({}^{12}C,{}^{12}N^{\beta^-})$ & &  & \\
%                   GLACIER & 380 & $\nu_x^{NC}({}^{40}Ar^{*})$ & & & \\
%               \hline\hline
%               \end{tabular}
%               \caption{\label{tab:Phys-SN-DetectorRates}Summary of the expected neutrino interaction rates in the different detectors for a $8 M_\odot$ SN located at 10~kpc (Galactic center). The following notations have been used: I$\beta$D, $e$ES and pES stands for Inverse $\beta$ Decay, electron and proton Elastic Scattering, respectively. The final state nuclei are generally unstable and decay either radiatively (notattion ${}^*$), or by $\beta^-/\beta^+$ weak interaction (notation ${}^{\beta^{-,+}}$). The event rates during the neutronization phase (see text) has been emphasized as if detected it will constitute a discovery compared to the historical SN1987A explosion detection by Kamioka and IMB.}
%\end{table}
%The detection complementarity is of great interest and would afford a unique way to probe SN explosion mechanism as well as neutrino intrinsic properties. The huge statistics would allow spectral studies in time and in energy, and using different channels during the three phases: the neutronization burst, the shock wave dynamics, and finally the passing through the Earth matter. 
%
%For the SN explosion mechanism topic, an examples is given in \cite{Fogli:2004ff} in the context of shock-wave 
%effects, based on the comparison of arrival times in different energy bins.
%And by using LENA elastic scattering on proton events at low threshold would provide an unique way to separate the non-electron-like neutrino contribution to the binding energy from the electron-like neutrino contribution.  
%
%Concerning the spectral properties which depend on neutrino oscillation parameters, it has been shown in \cite{Minakata:2001cd} that a detector
%like MEMPHYS, considering the Inverse $\beta$ Decay channel alone with
%the current best values of solar neutrino oscillation parameters,
%would allow the determination of the parameter $\tau_E$, defined as
%the ratio of the average energy of time-integrated neutrino spectra
%$\tau_E=\langle E_{\bar\nu_\mu}\rangle /\langle E_{\bar\nu_e}\rangle$,
%with a precision at the level of few percent, to be compared with a
%$\sim$20\% error possible at Super-Kamiokande. This would make it possible to
%distinguish normal from inverted mass hierarchy, if
%$\sin^2\theta_{13}>10^{-3}$ \cite{Lunardini:2003eh}. 
%In the region $\sin^2\theta_{13}\sim (3\times 10^{-6}-3\times
%10^{-4})$, measurements of $\sin^2\theta_{13}$ are possible with a
%sensitivity at least an order of magnitude better than planned
%terrestrial experiments \cite{Lunardini:2003eh}. However, using the unique GLACIER features to look at $\nu_e$ CC it is possible to probe oscillation physics during the early stage of the SN explosion, and also using the NC it is possible to decouple the SN mechanism from the 
%%Antonio Bueno 23/03/06 START
%oscillation physics~\cite{Gil-Botella:2004bv,Gil-Botella:2003sz}. 
%%Antonio Bueno 23/03/06 END
%The Earth matter effects can be revealed by wiggles in energy spectra and LENA benefit from a better energy resolution than MEMPHYS in this respect which may be partially compensated by 10 times more statistics. A qualitative summary of what can be done to probe neutrino properties is shown in Tab.~\ref{tab:Phys-SN-SummaryOscNeut}
%\begin{table}[htb]
%       \centering
%               \begin{tabular}{ccccc}\hline\hline
%               \parbox[b]{2cm}{\center{Mass\\ Hierarchy}}   & $\sin^2\theta_{13}$ & \parbox[b]{3cm}{\center{$\nu_e$ neutronization\\peak}} & Shock wave & Earth effect \\[2mm] \hline
%               Normal    & $\gtrsim 10^{-3}$ & Absent  & $\nu_e$   & \parbox[b]{3cm}{\center{$\bar{\nu}_e$\\$\nu_e$ (delayed)}} \\
%               Inverted    & $\gtrsim 10^{-3}$ & Present  & $\bar{\nu}_e$   & \parbox[b]{4cm}{\center{$\nu_e$\\$\bar{\nu}_e$ (delayed)}} \\
%               Any    & $\lesssim 10^{-5}$ & Present  & -   & \parbox[b]{3cm}{\center{both $\bar{\nu}_e$ $\nu_e$}} \\[2mm]
%\hline\hline
%               \end{tabular}
%               \caption{\label{tab:Phys-SN-SummaryOscNeut}Summary of the neutrino properties effect on $\nu_e$ and $\bar{\nu}_e$ signals.}
%\end{table}
%
%Up to now, we have investigated SN in our Galaxy, but the calculated rate of supernova explosions within a distance of 
%10~Mpc is about 1 per year. Although the number of events from
%a single explosion at such large distances would be small, the signal
%could be separated from the background with the
%request to observe at least two events within a time window 
%comparable to the neutrino emission time-scale ($\sim10$~sec),
%together with the full energy and time distribution of the 
%events \cite{Ando:2005ka}.
%In a MEMPHYS-type detector,
%with at least two neutrinos observed, a supernova could be identified 
%without optical confirmation, so that the start of the light curve 
%could be forecasted by a few hours, along with a short list of probable
%host galaxies. This would also allow the detection of supernovae
%which are either heavily obscured by dust  or are optically
%dark due to prompt black hole formation.
%%\begin{table}[htb]
%%      \centering
%%              \begin{tabular}{cc} \hline\hline
%%              Interaction    & Rates \\
%%              \multicolumn{2}{c}{MEMPHYS} \\
%%              $\bar{\nu}_e + p \rightarrow n + e^+$ & $2~10^{5}$ \\
%%              $\bar{\nu}_e/\nu_e + O \rightarrow X + e^{+/-}$ & $10^{4}$ \\
%%              $\nu_x + e^- \rightarrow \nu_x + e^-$ & $10^{3}$ \\
%%              \multicolumn{2}{c}{LENA} \\
%%              $\bar{\nu}_e + p \rightarrow n + e^+$ & $9~10^{3}$ \\
%%              $\nu_x + p \rightarrow \nu_x + p$ & $7~10^{3}$ \\
%%              $\nu_x + {}^{12}C \rightarrow \nu_x + {}^{12}C^*$ & $3~10^{3}$ \\
%%              $\nu_x + e^- \rightarrow \nu_x + e^-$ & $600$ \\
%%              $\bar{\nu}_e + {}^{12}C \rightarrow e^+ + {}^{12}B$ & $500$ \\
%%              $\nu_e + {}^{12}C \rightarrow e^- + {}^{12}N$ & $85$ \\
%%\multicolumn{2}{c}{GLACIER} \\
%%              $\nu_e + {}^{40}Ar \rightarrow e^- + {}^{40}K^*$ & $2.5~10^{4}$ \\
%%              $\nu_x + {}^{40}Ar \rightarrow \nu_x + {}^{40}Ar^*$ & $3.0~10^{4}$ \\            
%%              $\nu_x + e^- \rightarrow \nu_x + e^-$ & $10^{3}$ \\
%%              $\bar{\nu}_e + {}^{40}Ar \rightarrow e^+ + {}^{40}Cl^*$ & $540$ \\
%%              \hline\hline
%%              \end{tabular}
%%              \caption{\label{tab:Phys-SN-DetectorRates}}
%%\end{table}
%
%
%\begin{figure}
%\begin{center}
%\epsfig{figure=./figures/snburst.eps,width=8cm,height=8cm}
%\caption{\it % Figure to be redone for 440 kt! 
%The number of events in a 400 kt water \v{C}erenkov detector (left scale)
%and in SK (right scale) in all channels and in the individual
%detection channels as a function of distance for a supernova
%explosion \cite{Fogli:2004ff}.}
%\label{fig:SN}
%\end{center}
%\end{figure}
%
%Finally, one may note that electron elastic scattering events would provide in MEMPHYS and GLACIER a pointing accuracy of 
%the SN explosion of about $1\degree$, while in LENA the proton elastic scatering events would provide a $9\degree$ pointing resolution.
%%
%\subsubsection{Diffuse Supernova neutrinos}
%%
%An upper limit on the flux of
%neutrinos coming from all past core-collapse supernovae 
%(the Diffuse Supernova Neutrinos\footnote{We prefer the "Diffuse" rather the "Relic" word to not confuse with the primordial neutrinos produced one second after the Big Bang.}, DSN) has been set by the
%Super-Kamiokande experiment \cite{Malek:2002ns} 
%\begin{equation}
%       \phi_{\bar{\nu}_e}^{DSN} < 1.2~\flux  \hspace{2cm} (E_\nu > 19.3~\mathrm{MeV})
%\end{equation}
%However, most of the estimates are below this limit and therefore 
%DSN detection appears to be feasible only with the large detector foreseen, through $\bar{\nu}_e$ Inverse
%$\beta$ Decay in MEMPHYS and LENA
%detectors and through $\nu_e + {}^{40}Ar \rightarrow e^- + {}^{40}K^*$ (and the associated gamma cascade) 
%in GLACIER~\cite{Cocco:2004ac}.
%
%Typical estimates for DSN fluxes 
%(see for example \cite{Ando:2004sb}) predict an event
%rate of the order of $(0.1\div0.5)$\flux MeV$^{-1}$ 
%for energies above 20~MeV. 
%
%The DSN signal energy window is constrained from above by the atmospheric neutrinos and from below by either the nuclear reactor $\bar{\nu}_e$ (I), the spallation production unstable radionuclei by cosmic ray muons (II),  the decay of "invisible" muon into electron (III), and solar $\nu_e$ neutrinos (IV).     
%
%The three detectors are affected differently by the above backgrounds. Namely, MEMPHYS filled with pure water is mainly affected by type III due to the fact that the muons may have not enough energy to produce \v{C}erenkov light; while LENA takes benefit from the delayed neutron capture in $\bar{\nu}_e + p \rightarrow n + e^+$, so it is mainly affected by type I which impose to choose an underground site far from nuclear plants; and GLACIER looking at $\nu_e$ is mainly affected by type IV. As pointed out in \cite{Fogli:2004ff}, with addition of Gadolinium \cite{Beacom:2003nk} 
%the detection of the captured neutron, releasing 8~MeV gamma after  of the order of $20~\mu$s (10 times faster than in pure water), 
%would give the possibility to reject neutrinos other than $\bar\nu_e$ that is to say not only the "invisible"  muon (type III) but also the spallation background (type II). 
%
%The expected rates of signal and background are presented in Tab.~\ref{tab:Phys-SN-DiffuseRates}.
%\begin{table}[htb]
%       \centering
%               \begin{tabular}{cccc}\hline \hline
%       Interaction & Exposure     &  Energy Window &  Signal/Bkgd \\ \hline \\[-2mm]
%\multicolumn{4}{c}{MEMPHYS + 0.2\% Gd (at Kamioka)} \\[-5mm]
%\parbox{3cm}{\center{$\bar{\nu}_e + p \rightarrow n + e^+$}\\$n+Gd\rightarrow \gamma$ (8~MeV, $20~\mu$s)} &
%\parbox{2cm}{\center{1~Mt.y\\2~yrs}} & 
%$[15-30]$~MeV & (60-150)/65 \\
%%                      
%\multicolumn{4}{c}{LENA at Pyh\"asalmi} \\[-5mm] 
%\parbox{3cm}{\center{$\bar{\nu}_e + p \rightarrow n + e^+$}\\$n+p\rightarrow d+ \gamma$ (2~MeV, $200~\mu$s)} &
%\parbox{2cm}{\center{0.4~Mt.y\\10~yrs}} & 
%$[9.5-30]$~MeV & (40-260)/20 \\
%%
%\multicolumn{4}{c}{GLACIER} \\[-5mm] 
% $\nu_e + {}^{40}Ar \rightarrow e^- + {}^{40}K^*$ &
%\parbox{2cm}{\center{0.5~Mt.y\\5~yrs}} & 
%$[16-40]$~MeV & (40-60)/30 \\
%\hline \hline
%               \end{tabular}
%       \caption{\label{tab:Phys-SN-DiffuseRates}DSN expected rates. The larger numbers are computed with the present limit on the flux by SuperKamiokande collaboration. The lower numbers are computed for typical models. The background coming from reator plants have been computed for specific locations for MEMPHYS and LENA. For MEMPHYS one has been using the SuperKamiokande background scaled by the exposure. More studies are needed to estimate the background at the new Fréjus laboratory.}
%       
%\end{table}
%As an example of energy spectra, for the MEMPHYS detector, the results are shown in Fig.~\ref{fig:snr}: the signal could be observed with a statistical significance of about 2 standard deviations after 10 years. The spectra of the two backgrounds were taken from the 
%Super-Kamiokande estimates
%and rescaled to a fiducial mass of 440~kton of water, while the
%expected signal was computed according to the model called LL
%in \cite{Ando:2004sb}. 
%%
%\begin{figure}
%\begin{center}
%\epsfig{figure=./figures/snrelic.eps,width=13cm}
%\caption{\it Supernova relic neutrino signal and backgrounds (left)
%and subtracted signal with statistical errors (right) in a 440 kt
%water cherenkov detector with a 10 years exposure. 
%The selection efficiencies of SK were assumed; 
%the efficiency change at 34 MeV is due to the spallation cut.}
%\label{fig:snr}
%\end{center}
%\end{figure}
%
%
%