1. Geo-Neutrino: combined analysis of KamLAND and Borexino results
INCONTRO NAZIONALE INIZIATIVE DI FISICA ASTROPARTICELLARE INFN - Laboratori Nazionali di Frascati, June 2010
Geo-Neutrino: combined analysis of
KamLAND and Borexino results
Anna Maria Rotunno
Dip. Di Fisica, Univ. degli Studi di Bari
Based on:
G.L. Fogli, E. Lisi, A. Palazzo, A.M. Rotunno, Combined analysis of
KamLAND and Borexino Signals from Th and U decays in the Earth’s interior;
e-print arXiv:

2. KamLAND (KL) and Borexino (BX) (currently running) experiments
Purpose of this Work
U, Th, K decay chains
KamLAND (KL) and Borexino (BX)
(currently running) experiments
for the first time
Geo-Neutrinos
data and energy spectra
probe
with solar and
l.b.l. reactor
Our approach:
Earth interior
1) free Th, U event rates in KL and BX;
2) common Th/U abundance ratio;
3) common scaling of Th+U event rates;
4) fixed (chondritic) Th/U abund. ratio.
Our results:
- KL  BX reject the null hypothesis (no geo-ν signal) at 5;
indications on the Th+U geo-ν rates and on the Th/U ratio, in agreement with typical Earth model;
the hypothesis of a georeactor in the Earth’s core is disfavored (Pgeo > few TW) .

3. Contents Introduction to Geo-Neutrinos KamLAND and Borexino data
- Analyses with 4, 3, 2 and 1 d.o.f.
- Additional degree of freedom: the georeactor
Results for the above steps
Conclusions and Prospects

4. What do we know about Earth Interior?
- The mantle convects even though it is “solid”.
- Oceanic crust is being renewed at mid-ocean ridges and recycled at trenches.
- Main issue today: Whole or layered mantle convection?
Seismology: based on sound velocity measurement from seismic data
reconstructs density profile throughout the Earth
- infers crust-mantle-core layer structure
GeoChemistry: based
on direct sampling
- gives direct info on chemical composition of crust and upper mantle
- does not reach deep Earth

5. Where are radioactive elements located?
- Earth’s Global Heat:
· ~ 45 TW (~ 30 TW in some unorthodox
models): not well constrained due to scarce
oceanic sampling and model dependence
· probably 40 – 60% has radiogenic origin:
mainly from decays of 238U, 232Th, 40K
(trace elements) inside crust and mantle
Geo-Neutrinos
from radioactive decays of
238U, 232Th, 40K trace elements
in crust and mantle of Earth
bring to surface information about:
the whole planet
its radioactive contents
energetics and thermal history
Where are radioactive elements located?

6. Earth Global Composition in Trace Elements
U, Th, K
volatile
refractory: expect Th/U as in meteorites (Th/U ~ 3.9)
incompatible: prefer liquid phase (= crust during its formation)
lithophile: prefer rock to metals
Abundances:
[Th]crust >> [Th]mantle , [Th]core ~ 0
[U]crust >> [U]mantle , [U]core ~ 0
Constraints:
Direct sampling (crust & upper mantle) & Neutrino Geophysics (in the future)

7. A recent new field in Neutrino Physics: Geo-n detection by
Liquid Scintillator.
Experiments with Liquid Scintillator
observe:
- Geo–ne
- reactor events (mostly at higher energies)
- backgrounds
KamLAND:
huge reactor flux
- large background
Borexino:
small reactor flux
tiny background

8. - geo-n signal pronounced at lower energy
2005: first geo–ne observation at KamLAND
KamLAND Coll., Nature 436, 499 (2005)
2008: next geo–ne KamLAND results
KamLAND Coll., Phys. Rev. Lett. 100, (2008)
2010: first Geo–ne observation at Borexino
Borexino Coll., Phys. Lett. B 687, 299 (2010)
@ KL:
- geo-n signal pronounced at lower energy
- relatively large contribution from Th
decay (Ep ≤ 1.7 MeV)
@ BX:
- leading contribution from U decay

9. Analyses with 4, 3, 2, and 1 degree of freedom
KL and BX statistical analysis (Poisson 2 function): 7-dimensional manifold
reactor
geo-n
Parameters: (dm2, q12, q13 ; R(Th)KL, R(U)KL, R(Th)BX, R(U)BX )
Equivalent parameters:
R(Th+U) = R(Th) + R(U)
(Th/U) = [R(Th)/ R(U)]/ 6.96 ·10-2
3n oscillation parameters:
- constrained by solar-n data
- marginalized away
KamLAND
Borexino
abundance ratio
TABLE I: Summary of adopted degrees of freedom and constraints
ND Constraints R(Th + U)KL (Th/U)KL R(Th + U)BX (Th/U)BX
None free free free free
(Th/U)BX = (Th/U)KL free free free
(Th/U)BX = (Th/U)KL and RBX = 1.15 RKL free free
(Th/U)BX = (Th/U)KL = 3.9 and RBX = 1.15 RKL free
approximate scaling law, coming from comparison of KL and BX event rate estimates for a wide range of admissible Earth models

10. Th/U vs R(Th+U) joint 1s (Dc2 = 1) regions
4 dof: both KL and BX
- place upper and lower bounds on R(Th+U)
- consistency with typical Earth model expectations:
29-41 TNU for KL TNU for BX at 1s
- can not currently determine Th and U separately. In fact:
KL compatible with all events from Th (Th/U → ∞)
BX compatible with all events from U (Th/U → 0)
A broad range compatible with KL and BX results at 1s: we impose the same Th/U ratio
3 dof:
- total rate estimates not significantly altered with respect to 4 dof case
- KL  BX data sensitive to the global Th/U ratio of Earth (although only at ~ 1s level)
1 TNU = 1032 events/proton yr

11. - approximate scaling law: RBX = 1.15 RKL
1 TNU = 1032 events/proton yr
2 dof:
- approximate scaling law: RBX = 1.15 RKL
- KL parameters free, BX derived (dotted curve)
- Th/U best fit not significantly altered with respect to 3 dof case
1 dof:
- chondritic assumption: Th/U = KL, BX
- preference for Earth models with relatively high expectations in Th and U contents
2 dof
1 dof

12. Bounds on Th/U ratio 4 dof: - KL data place lower 1s limit on Th/U
- BX data place upper 1s limit on Th/U
- no significant sensitivity in opposite directions
- weak bounds: they vanish at ~ 1.3s in KL and at ~ 1.6s in BX
3 dof, 2dof:
- joint limit on Th/U at the 1s level, with no significant variation between 3dof and 2dof cases
1 dof:
- Dirac delta at Th/U = 3.9

13. Bounds on R(Th+U) 4 dof, 3 dof:
- the null hypothesis (no geo-n) rejected at:
2.9s in KamLAND and s in Borexino
- independently of the Th/U constraint
2 dof, 1dof:
- significant error reduction, induced by scaling law assumption
- null hypothesis rejection at 5s
- the chondritic assumpion (Th/U= 3.9) has a minor impact on combined rate constraints

14. Additional degree of freedom: the georeactor
Georeactor hypothesis:
enough uranium in the Earth’s core to naturally start a nuclear fission chain over geological timescale
typical power (at current epoch) Pgeo ≈ 3-10 TW
independent probe
disfavored by geochemical & geophysical arguments
Particle Physics
confirms
6 dof: s upper limit: Pgeo ≤ 4.1 TW BX Pgeo ≤ 6.7 TW KL
< 6 dof: joint KL + BX limit: Pgeo ≤ 3.9 TW at 2s (Pgeo ≤ 5.2 TW at 3s )
- independent of the chosen geo-n degree of freedom

15. Conclusions
We have performed a detailed analysis of current geoneutrino events from Th and U decay chains as detected in KamLAND and Borexino
The relevant parameter space is spanned by the total Th+U event rates and the Th/U ratio in the two experiments, while te oscillation parameters (dm2, q12, q13 ) are marginalized away
- constrained analyses with fewer dof are obtained by successively assuming for both KL and BX a common Th/U ratio, a common scaling of Th+U event rates, and a fixed (chondritic) Th/U ratio
we have also considered the case of an hypothetical georeactor
Results:
agreement with typical Earth model expectations, although within still large uncertainties
global Th+U signal emerges at 2.9s in KL and at 4.1s in BX, reaching 5s in combination
preferred Th/U values in broad agreement with chondritic expectations
slight preference for relatively high Th and U contents in the Earth
data disfavor the hypothesis of a georeactor, and limit its power to Pgeo ≤ 3.9 TW at 2s (Pgeo ≤ 5.2 TW at 3s )

16. Prospects
Significantly higher statistics, possibly from new large volume detector, with some directional sensitivity will be needed to improve our understanding of the Earth’s interior.
Even a minimal directional information would help the source discrimination:
reactor & crust anti-n → horizontal
mantle anti-n → vertical
NEW EXPERIMENTS in sites with both
LOWER FLUX (mantle) &
HIGHER FLUX (thick crust)
- LENA
- Sudbury
- Hawaii
- Baksan

17. Backup

18. Radiogenic Heat A correlation is expected between:
H = radiogenic heat production rate
R = geo-n event rate
from the same Th + U sources.
The results for KL can be approximated as:
H(Th+U)~ (1.11±0.14) · R(Th+U)
TW TNU
KL, 6 TW ≤ H ≤ 40 TW
fully radiogenic limit
provides a total KL signal in excess of the “garanteed” min contribution from Earth’s crust R(Th+U) ≥ 24 TNU.
From: G. Fiorentini, M. Lissia and F. Mantovani, Phys. Rept. 453, 117 (2007)

19. Implications of our results
From: G. Fiorentini, M. Lissia and F. Mantovani, Phys. Rept. 453, 117 (2007)
In the most constrained case (ND=1):
at fixed R(Th+U)KL = 47.7 TNU
(central value) we obtain the allowed range
H(Th+U) ~ 21 – 35 TW
somewhat above typical expectation TW.
Including the 1s rate, the allowed range is enlarged:
H(Th+U) ~ 10 – 49 TW
Lower value exceeds the “guaranteed” contribution from Th and U in the crust ~ 6 TW and suggest (indirectly) the presence of an additional contribution from a different reservoir – which can be naturally identified with the mantle.