% T. Marrodan Undagoitia 12/12/06 START
% Some ortographic corrections
% and some word changes to have coherence in the language
\section{Geoneutrinos}
%T. Marrodan Undagoitia 12/12/06 END
\label{sec:Geo}


%\REDBLA{Version 0 by JEC 2/3/06}
%\REDBLA{updated by L. Oberauer 13/4/06}
%\REDBLA{updated by J.E Campagne to follow L. Oberauer 3/5/06}
%\REDBLA{updated by J.E Campagne 16/10/06: this is a section now}

The total power dissipated from the Earth (heat flow) has been
measured with thermal techniques to be $44.2\pm1.0$~TW. Despite this
small quoted error, a more recent evaluation of the same data
(assuming much lower hydrothermal heat flow near mid-ocean ridges) has
led to a lower figure of $31\pm1$~TW.

%T. Marrodan Undagoitia 12/12/06 START
%\REDBLA{
On the basis of studies of
chondritic meteorites the calculated radiogenic power is thought to be
19~TW (about half of the total power), 84\% of which is produced by
${}^{238}$U and ${}^{232}$Th decay which in turn produce $\bar{\nu}_e$
by $\beta$ decays (geoneutrinos).
%}
%T. Marrodan Undagoitia 12/12/06 END
It is then of prime importance to measure the
$\bar{\nu}_e$ flux coming from the Earth to get geophysical
information, with possible applications in the interpretation of the
geomagnetism.

%T. Marrodan Undagoitia 12/12/06 START
%\REDBLA{
The KamLAND collaboration has recently reported the first observation
of the geoneutrinos \cite{Araki:2005qa}. The events are identified by
the time and distance coincidence between the prompt $e^+$ and the
delayed (200~$\mu$s) neutron capture produced by $\bar{\nu}_e + p
\rightarrow n + e^+$ and emiting a 2.2~MeV gamma. The energy window
to search for the geoneutrino events is $[1.7,3.4]$~MeV: the lower bound
corresponds to the reaction threshold while the upper bound is
constrained by nuclear reactor induced background events.
%} 
%T. Marrodan Undagoitia 12/12/06 END

The measured rate in the 1~kT liquid scintillator detector located at
Kamioka (Japan) is $25^{+19}_{-18}$ for a total background of $127\pm
13$ events. 

%T. Marrodan Undagoitia 12/12/06 START
%\REDBLA{
The background is composed by $2/3$ of $\bar{\nu}_e$ from
the nuclear reactors in Japan and Korea\footnote{These events have
been used by KamLAND to confirm and measure precisely the Solar driven
neutrino oscillation parameters \ref{sec:oscillation}.} and $1/3$ of
events coming from neutrons of 7.3~MeV produced in
${}^{13}$C$(\alpha,n){}^{16}$O reactions and captured as in the
inverse beta decay reaction. The $\alpha$ particles come from the
${}^{210}$Po decays, a ${}^{222}$Rn daughter which is of natural
radioactivity origin.  The measured geoneutrino events can be
converted in a rate of $5.1^{+3.9}_{-3.6}~10^{-31}$ $\bar{\nu}_e$ per
target proton per year corresponding to a mean flux of
$5.7~10^{6}\flux$, or this can be transformed into a $99\%$ CL upper
bound of $1.45~10^{-30}$ $\bar{\nu}_e$ per target proton per year
($1.62~10^{7}\flux$ and 60~TW for the radiogenic power).
%}
%T. Marrodan Undagoitia 12/12/06 END


%JEC 3/5/06 START L. Oberauer ask to remove this paragraph to avoid redondancies
%The KamLAND result is at $\sim 2\sigma$ level and needs to be confirmed by much more and cleaner statistics. It is expected to register $1500$ events per year in the LENA detector if one takes the mean value of the rate measured by KamLAND. But in the same times the background may be reduced. The reactor neutrino background may be lowered by choosing a different location far from nuclear plants as at Pyh\"asalmi mine (Finland), where one expects a factor $\sim 20$ reduction (\REDBLA{To be confirmed by LENA}). The $\alpha$ induced background may also be lowered requiring R\&D to reduce the natural radioactivity of the detector (the present level of U-Th in KamLAND is $10^{-17}$~g/g) as well as the Radon content of the environment. 
%JEC 3/5/06 END

In MEMPHYS, one expects 10 times more geo-neutrino events but this would imply to decrease the trigger threshold to 2~MeV which seems very challenging with respect to the present SuperKamiokande threshold set to 4.6~MeV due to high level of raw trigger rate 120~Hz and increasing by a factor 10 each times the trigger is lowered by 1~MeV \cite{Fukuda:2002uc}. This trigger rate is driven by a number of factors as dark current of the PMT, $\gamma$s from the rock surrounding the detector, radioactive decay in the PMT glass itself and Radon contamination in the water. 

%L. Oberauer 13/4/06 START

%T. Marrodan Undagoitia 12/12/06 START
%\REDBLA{
In LENA at the underground laboratory at CUPP a geoneutrino rate of
roughly 1000/y~\cite{Hochmuth:2006} from the dominant $ \bar\nu_e+p\to
e^+ + n $ inverse beta-decay reaction is expected. The delayed
coincidence measurement of the positron %%@
and the 2.2 MeV gamma event, following neutron capture on protons in 
the scintillator provides %%@ 
a very efficient tool to reject background events.
The threshold energy of 1.8 MeV allows the measurement of geoneutrinos
from the Uranium and %%@ 
Thorium series, but not from $^{40}$K.
A reactor background rate of about 240
events per year for LENA at CUPP in the relevant energy window from 1.8~MeV to
3.2~MeV has been calculated.
%}
%T. Marrodan Undagoitia 12/12/06 END

This background can be subtracted statistically using the information
on the entire reactor neutrino spectrum up to $\simeq$~8 MeV.  As it
was shown in KamLAND a serious background source may come from radio
impurities. There the correlated background from the isotope
$^{210}$Po is dominating. However, with an enhanced radiopurity of the
scintillator, the background can be significantly reduced. Taking the
radio purity levels of the CTF detector, where a $^{210}$Po activity
of $35\pm12/\rm{m^3d}$ in PXE has been observed, this background would
be reduced by a factor of about 150 compared to KamLAND and would
account to less than 10 events per year in the LENA detector.  An
additional background that imitates the geoneutrino signal is due to
$^9$Li, which is produced by cosmic muons in spallation reactions with
$^{12}$C and decays in a $\beta$-neutron cascade.  
% T. Marrodan Undagoitia 12/12/06 START
%\REDBLA{
Only a small part
of the $^9$Li decays falls into the energy window which is relevant
for geoneutrinos. KamLAND estimates this background to be $0.30 \pm
0.05$ \cite{Araki:2005qa}.
%}
%T. Marrodan Undagoitia 12/12/06 END
 At CUPP the muon reaction rate would be
reduced by a factor $\simeq 10$ due to better shielding and this
background rate should be at the negligible level of $\simeq$~1 event
per year in LENA.
% T. Marrodan Undagoitia 12/12/06 START
%\REDBLA{

From this considerations we follow that LENA would be a very capable
detector for measuring geoneutrinos.  Different Earth's models could
be tested with great significance. The sensitivity of LENA for probing
the unorthodox idea of a geo-reactor in the Earth's core was estimated
too. At the CUPP underground laboratory in Pyh\"asalmi the neutrino
background with energies up to $\simeq 8$~MeV due to nuclear power
plants was calculated to be around 2200 events per year.  At CUPP a
2~TW georeactor in the Earth's core would contribute 420 events per
year and could be identified at a statistical level of better than
$3\sigma$ after only one year of measurement.
%}
% T. Marrodan Undagoitia 12/12/06 END

%L. Oberauer 13/4/06 END

Finally, in GLACIER the $\bar{\nu}_e + {}^{40}Ar \rightarrow e^+ + {}^{40}Cl^*$ has a threshold of $~7.5$~MeV which is too high for geoneutrino detection.