Transcript ppt

Neutrino Radiography
Gennaro Miele
G. Miele - NOW-2010
University of Naples “Federico II”
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Outlook
•
•
•
•
•
•
The Earth internal structure
Why neutrinos?
Which neutrinos?
How neutrinos?
A toy model to test sensitivity
A more detailed analysis a km3 NT
progress)
G. Miele - NOW-2010
(in
2/22
The Earth internal structure
The Earth crust density is
about 2.7 - 2.8 g cm-3
(direct observations till ~ 20
km depth). Information from
samples brought to the
surface by volcanic activity
and by measuring the
propagation
speed
of
earthquake waves.
It is found that:
• the velocity generally increases gradually with depth in Earth, due to
increasing pressure and rigidity of the rocks
• however, there are abrupt velocity changes at certain depths,
indicating layering
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What we learn from earthquakes
As the result of earthquakes, explosions, or some other process (the incessant
pounding of ocean waves, referred to as the microseisms, and the wind),
seismic waves are continuously excited on Earth.
Earthquakes create two types of waves, body waves and surface waves:
• P waves (primary waves) are longitudinal
body waves
• S waves (secondary waves) are transverse body waves
• L and R waves (Love and Raleigh waves) are horizontal and elliptical surface
waves
• free oscillations are surface wave with
wavelength comparable with the circumference of the Earth
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Wave propagation in the Earth
In solids, the P waves generally travel almost twice as fast as S waves
and can travel through any type of material. S waves can travel only
through solids, as fluids (liquids and gases) do not support shear
stresses.
v (km s-1)
bulk
modulus
modulus
of rigidity
depth (km)
CMB
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Preliminary Reference Earth Model (PREM)
A.M. Dziewonski and D.L. Anderson, Phys. Earth Planet. Inter. 25, 297 (1981)
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Mantle
Ten layers
Upper
Lower
Mantle
Outer Core
Inner Core
CMB at R=3450 km
6/22
Limits of seismic
tomography
• Global seismic tomography is limited by the irregularity in
time and space of the source, and by the incomplete
this stations.
information
more source is
coverageAlthough
of recording
The is
primary
earthquakes,
which
arewhat
impossible
to predict
and only occur
precise
than
we can
realistically
at certainexpect
locations
around
the world.
In addition,
from
neutrino
radiography
in the global
coveragethe
of recording
stations
is limited
due global
to economic and
near future,
aspects
of the
political reasons.
thesecan
limitations,
structureBecause
of the of
Earth
require seismologists
an
must workindependent
with data thatconfirmation.
contains crucial gaps.
• Free-oscillation data only reveal 1-dimensional structure.
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Why
Neutrinos
areNeutrinos?
elusive particles!
PRD 66, 021302(R) (2002)

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
Earth radiography by
neutrinos
1
 N  N A
Askaryan, Usp. Fiz. Nauk 144, 523 (1984)
 ~ 2 REarth  E ~ 10 TeV
Phys. Rep. 99, 341 (1983)
First proposal to use neutrino beams for Earth radiography by De
Rujula, Glashow, Wilson, and Charpak in 1983: a neutrino moving in
rock produces a shower which ionizes the medium and generates an
acustic signal. Moreover, the muons accompanying the neutrino
beam can be detected at the point of emergence from the Earth.
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Atmospheric Neutrinos
The “conventional” part comes from pion and kaon decays (low energy),
a “prompt” isotropic contribution comes from short lived charmed hadrons
(high energy). In the energy range of interest, the contribution from kaons
dominates (~80%) and decay of muons can be neglected. Tau neutrinos
are negligible since oscillation are very suppressed.
Averaged over zenith angle
Beacom & Candia, JCAP 11, 009 (2004)
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PREM versus homogeneous
Gonzales-Garcia, Halzen, Maltoni, Tanaka, PRL100 (2008) 061802
up vertical
horizontal
For high Eth the attenuation factor due to the earth density becomes relevant and
theG.number
of detected events gives information on the earth density.
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Miele - NOW-2010
Neutrinos through the Earth
E. Borriello et al. JCAP 0906:030,2009
A simplified parametrization of Earth radial density profile.
Satisfies the mass constraint but not the moment of inertia.
core~11 g cm-3
mantle~4.5 g cm-3
crust
km3
mantle
A
C
B
crust~2.7 g cm-3
core
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NEMO Site
We consider an under sea km3 NT
Etna
Nemo Site
• Site Location
36°21’ N,
16°10’ E
• Average Deep
≈3500 m
(3424 in our
simulation)
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The rate of lepton events in 1 km3

dN l
d 2  ( E , a )
l



 D   d a  dS a  dE
dE

(
E
)
cos

k
E
,
E
;
r
l
l
a
a

l a , a 

dt
dE d a
a
Same calculation for Auger
in PLB634:137-142 (2006)
PRD 77:045019 (2008)
Probability that an incoming , with
energy E and direction a, crossing
the Earth, produces a lepton l which
enters the fiducial volume with energy
Ell through the lateral surface dSa at
the position ra.
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A km3 Neutrino Telescope at Nemo site
An energy threshold of 1 TeV is considered in counting the muons detected
in the fiducial volume and the condition of a minimal track length of 300 m
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in the apparatus defines detectable events.
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Likelihood analysis
4  m/(g cm-3)  5
9  c/(g cm-3)  12
We consider 5 angular bins for the interval cosθ = 1 (upgoing) to cosθ =
0 (horizontal) and make the analysis integrating the muons at different
energies for Eth = 1 TeV (optimized value).
Observables N i produced for a grid of 20 theoretical models of densities. Then, likelihood analysis with likelihood function
  2 2 and
Le
Δ=0.25
overall uncertainty on  and 
5
2 ( m , c , ,)  
N (
i
0 2
,

)(1

)(1


cos

)

N
m
c
i
i 
i1
uncertainty on  due to ang. distr.
G. Miele - NOW-2010
N i0
  2   2
     
   
Δ =0.05
expected counts for the sPREM
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Likelihood analysis
Eth=1 TeV
2% (5%) uncertainty
on m (c) at 2
10 years of observations
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Taking into account the Moment of
Inertia of the Earth
I=0.330695 ME RE2
K. E. Bullen 1930’
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A more realistic Earth model
To be tested at IceCube or Mediterranean sea NT
(by G. Mangano, G.M., S. Pastor, O. Pisanti & M.A.
Tortola)
In progress
Known quantities: Rc1, Rc2, Rm, ρ(r≥Rm)
Model parameters: ρ0, ∆1, ρ1, ∆2. Constraints: Earth mass and
moment of inertia.
ρ0
∆1
PREM
This
work
ρ1
∆2
Outer
core
The constraints give:
Mantle
Inner core
ρ2
Input parameters: ρ0,
ρ1.
Rc1
Rc2
1  28.8  1.2  0  1.4 1
 2  6.5  0.0099  0  1.1 1
Rm
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New Monte Carlo for a km3 NT
• e and  (anti)neutrinos injected according to the
atmospheric  flux in the range 1102 TeV (Honda et
al., 2007).
• CC neutrino interaction and neutrino regeneration by
NC processes
•  energy loss in matter (ionization, bremsstrahlung,
pair production, nuclear interaction)
• maximum stepsize in each layer given from adiabatic
variation of density: ∆ρ/ρ«1.
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Conclusions
• Study of the sensitivity of a NT to Earth interior
for a simplified Earth model (sPREM)
• 2% (5%) uncertainties (at 2 level) on m (c)
for 10 years of observations and Eth=1 TeV with
no details of the experimental apparatus
• Low number of model parameters  good level
of sensitivity in their determination  By using
all geological inputs one can perform a more
realistic study expecting a good resolution on the
free parameters
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