Transcript No Slide Title

Neutrino interactions from 100 keV to 100 GeV:
natural/artificial fluxes and modeling
of neutrino cross sections
… a guided tour of NeutrinoLand
Cracow School of Theoretical Physics, XLIII Course, 2003
Flavio Cavanna
Phys. Dept. - University of l’Aquila & INFN - Laboratori Nazionali del Gran Sasso, ITALY
Outlook:
• OUT:
– implications of neutrino non-zero mass
(i.e. oscillations are not discussed … with a couple of exceptions…)
• IN:
– Neutrino spectra of various origin
– Neutrino cross-section
– The interaction target available (present, past and
“future” experiments*) and the expected rate
calculation
(*) .. many neutrino experiments are mentioned.
The choice is driven ONLY by didactical reasons and NOT by importance ranking !!
100 KeV
NeutrinoLand
Neutrino Sources
Natural Sources
Sun
e
Artificial Sources
Atmosphere
(Cosmic Rays)
SupeNovae
Reactors
-bar
e, e-bar
e, e-bar
e-bar
Accelerators
Beam Dump
Short/Long Baseline
-bar
etc...

etc...
E
1 MeV
10 MeV
100 MeV
1 GeV
10 GeV
100 GeV
1 TeV
Most of the energy range covered by neutrino fluxes from various available sources
has been covered by experimental search for neutrino interactions in large
sensitive mass detectors. Even though fluxes are typically very intense, the
interaction rate (so far) was limited due to the very small neutrino interaction
cross-section with matter.
Different theoretical model for cross-section calculation have been developed
For different energy sub-ranges and targets.
A significant reference quantity for easy evaluation of the expected event rate
is the “SNU” (“Solar Neutrino Unit - J. Bahcall). It represents the product of
a calculated neutrino flux [cm-2 s-1]  a theoretical cross section [cm2]:
n SNU [1036 s1]  n of events per target per second
For sake of comparison, we will compute the SNU calculation for all the

neutrino
sources listed above.
Solar Neut rinos
Weak Inter action Theory
Stel lar Model
Neutri no Cros s Sections
Solar Fluxes
pp
Elastic Scattering
e
pe p
Be
Absorption Reaction
Ge
SK
SN O
ka mio ka nde
IC AR US
Galle x/GNO
SAGE
Cl
B
H ome sta ke
he p
D
SN O
Ar
IC AR US
Solar Neutrino Pr oblem
Neut rino Oscillation
from the
“Standard Solar Model”
The Solar Neutrino Spectrum
 1%
 10%
 10%
 1.5%
 20%
 16%
?
BP00: astro-ph/0010346
Flux Properties
Source
Flux
[1010 cm-2 s-1]
Energy
Spectrum
Energy
Energy
Mean Value
[MeV]
End Point
[MeV]
pp
5.95
Cont .
0.2668
0.423
pep
0.014
line
1.445
1.445
hep
0.00000093
Cont .
9.628
18.778
7
0.477
line
0.3855
0.3855
0.8631
0.8631
6.735
~ 15
Be
8
B
0.000505
Cont .
“Low Energy” range
Neutrino Cross Section
Neutrino Cross Sections are as important as Stellar Models in determining the predicted rates
in solar neutrino detectors
(often uncertainties in  cross sections are larger than uncertainties from solar model fluxes)
Three types of reactions have to be considered (in the “Low Energy” range):
 e  AZ  e  AZ 1
 x  AZ   x  AZ
 x  e  x  e
Absorption reaction on nuclei A
(Charged Current - e-flavor)
Elastic scattering on nuclei A
(Charged Current - e-flavor
and Neutral Current - x=e,t flavors
Elastic scattering on electrons
(Charged Current - e-flavor
and Neutral Current - x=e,t flavors)
(1) Absorption Reactions (Inverse b decay)

e  AZ  e  AZ 1
Absorption Reactions: the incoming  is absorbed, an electron is created, and a neutron in the
target Nucleus (A) is transformed into a proton. (with detection of electron and/or of AZ+1)
Dominant transitions are ALLOWED transitions:
Nuclear spin change
 J = 0 (Fermi Trans.),  1 (Gamo w - Teller Trans.)
Nuclear parity (no change)
 = 0
In particular, SUPER-ALLOWED transitions:
I = 0 (Isot op ic An alo g ue State Tran s.)
Absorption Cross Section can be written in terms of atomic and kinematic factors
times the nuclear matrix element (representing the n-p transformation):
   o  pe We FZ,We 
 o  k Mi  f
2
M 2  BF  + BGT 
F:
where
Fermi fun ction
 o 1046 cm2 :
tr ansition m a tr ix ele m ent
B(F) : Fermi Matrix Elements
B(GT ) : Gamow - Teller Matrix Elements
B(F) and B(GT) ( o) can be evaluated with shell-model calculations (high precision
for B(F)) and comparedwith experimental data from half-life measurements of inverse
nuclear processes (e.g. Electron Capture) by symmetry relations.
(FORBIDDEN reactions provide small corrections in the “Low energy” range)
• The emitted electron energy We is given by:
We  E  E nucl
with Enucl being the nuclear mass difference
• The Fermi function F(Z, We) takes into account corrections due to finite nuclear size
and electron screening (important effect for high Z materials)
3/2-
Target Nuclei in some present (past & “future”) experiments
0.500 MeV
•
71Ga
1/2-
: GALLEX (now GNO) and SAGE
71Ge
3/2-
0.233 MeV
71Ga
3/2+
IAS
37Ar
• 37Cl : HOMESTAKE
0.814 MeV
3/2+
37Cl
• 2H
: SNO

p
D
+e
p
0+
40K*
• 40Ar : ICARUS
IAS
4.384 MeV
4+
0+
40Ar
40K
1.505 MeV
Expected rates calculations
 Absorption cross-section “averaged” over single flux component energy spectrum
f 
Ema x
7
8

E

E
dE
;
f

pp,
Be,
B, ...
    f   
mi n
E
f 
n ormalized en erg y sp ectrum
Emin  Enucl  me  Ethr 
SNU 10 s
-36 1
   f 10 cm
-46
2
Nevt  SNU  Ntarg  t ;


30 evt
2 evt
of Ga target, 
of Ar target
e.g. 
t  yr
t  yr


   f 10 cm s
2 1
10
Ntarg 

 10


A
N Av
1
g
6
 MDe t t 
Reference Numbers useful for Event Rate Calculations
Experiment
GALLEX/GNO
SAGE
HOMESTAKE
SNO
ICARUS
o
Reaction
Nuclear Target
[10-46cm2]
Enucl
Flux
SNU
[MeV]
[10-36 s-1]
(no det. Thres.)
Main
Components
pp + 7Be+8B
128.0
ve  Ga  e  Ge
8.611  0.4%
(GT)
0.2327
ve 37Cl  e 37 Ar
1.725
(F)
0.814
H1
ve 2H  e   p  p
(GT)
1.442
Ar18
ve  Ar  e  K
71
Ga33
37
Cl 17
2
40
71
40


71
40

148.58 (F)
…
44.367 (GT2)
…
41.567 (GT6)
…
8
4. 384
…
1.505 +
3. 798
…
2. 730
B + 7Be
7.6
8
B
6.8
8
B
4.6
+
6.5
Important Experimental Observable
Radio-chemical experiments (Ge, Cl target):  rate
 time variation of the rate
Real-time experiments (D, Ar target):  rate
 electron Energy Spectrum
 (D target) - recoil proton Energy Spectrum
 (Ar target) - calorimetric measurement of
de-excitation energy (K*K+g)
 electron Energy Spectrum:
d
  E   f E  ;
dWe
Det
E = We + Enucl +Ethr

NB: spectrum distortion introduced by neutrino oscillation !!
Elastic Scattering on Electrons

 x  e  x  e

CC+NC (purely leptonic F. Diagrams)
Main characteristic (vs Absorption reactions):
(neglecting atomic binding) there is no
threshold on the  minimal energy in producing
Electron (i.e. Emin=0.)
Important Diagnostic Features:
• angular distribution, strongly peaked in the forward direction of the Earth-Sun axis
• electron energy spectrum, reflecting the solar neutrino spectrum
• cross-section magnitude, sensitive to neutrino flavor
• time information, sensitive to flux modulation.
The actual  energy defines the max value of the electron kinetic energy:
2
2E

Temax 
me  2E
The total cross-section, calculated at specific  energy, parametrically depends
on the minimal kinetic energy of the emitted electron
 E S   e f E ;T
min
e
 ; where : f E ;T
min
e
1
 0.
E
kMeV ]
The differential cross-section for producing a recoil electron with kinetic energy Te
by scattering with a neutrino of initial energy E is:
2



d E S
Te 
m
T
2
2 
  e  gL  gR 1    gL gR e 2 e 
dTe
 E 
E 

where : gL   1 2  sin 2  W  ; gR  sin 2  W
   e ;     ,t
and :
 e  cost 10-46 cm2 
Target material in present (past & “future”) experiments
• H2O : SuperKamiokande (SK)
(Kamiokande)
• 2H2O : SNO
•
40Ar
18 :
ICARUS
ZH2O  2  8  10 ; ESK
thr  5MeV
ZH2O  2  8  10 ; ESNO
thr  5MeV
ZAr  18 ;
EICARUS
 5  7MeV
thr
Expected rates calculations
 Elastic Scattering cross-section “averaged” over single flux component energy spectrum
f 
Ema x
  E   f E  dE ; f 

7
Be , 8 B, hep
mi n
E
f 
n ormalized energ y s pectrum
Emin  E Dete ctor
th r
SNU   f
10
-46
cm   f 10 cm s
2
Nevt  SNU  Ne-ta rg  t ;


12 evt
1 evt
thr
reducing to 
for Ee  5MeV 
e.g. 
t  yr
t  yr


10
N e -targ  Z
2 1



A
N Av
1
g
 10  MDe t t 
6
Reference Numbers useful for Event Rate Calculations
Experiment
Nuclear Target
E.S. Reaction
Det. Thres.
Ethr
[MeV]
[10-36 s-1]
5.0


5.0
8
B
0.9


5.0 (-7.0)
8
B
1.6
ve  e  v e  e
SNO
H2O
ve  e  v e  e
Ar18
Main
Components

H2O
40
SNUxZ

SK/Kami okande
ICARUS
Flux
ve  e  v e  e
8
B + (hep)
0.9
Important Experimental Observable
Real-time experiments (H2O, Ar target):  rate
 directionality
 electron Energy Spectrum
 directionality (of emitted electron)
Ema x
d
d cos

Tmi n

0
 d 
 f E  dE
d cos 
TT
 electron Energy Spectrum:
Ema x
d
d
 
 f E  dE
dT
dT
E mi n

mi m
7 Experiments; 35 years of activity!!!;
Reactor
are emitted in the same (“Low”)energy range of Solar-:
the interaction cross-sections with matter are established by the
theoretical models discussed in the Solar neutrino section
The average energy distribution for the energy released per fission with a thermal neutron in uranium-235
The tremendous anti-neutrino flux produced by
nuclear reactors
(
per second for a 2800 MW reactor)
already led to the neutrino experimental discovery.
R
Energy Spectrum
~2 < E < 9 MeV
Source
Flux
[1010 cm-2 s-1]
Energy
Spectrum
Energy
Energy
Mean Value
(E>2MeV)
End Point
[MeV]
- 3
- 9
[MeV]
235
U
Pu
Fission
239
- 2000
Cont.
The detection technique is generally very similar to that pioneered
by Reines and Cowan experiment:
a large tank of liquid scintillator
(CnH2n+2 hydrocarbon molecule rich in H, n >20)
doped with an element (Cd) adequate for neutron capture is
exposed to the neutrino flux.
Anti-neutrinos interact with protons in the target through the inverse beta decay reaction:

e  p  e  n
The gold-plated reaction!!
leaving as signature a prompt light pulse corresponding to the positron annihilation
followed by a delayed light pulse from the de-excitation after neutron capture.
The reaction has a threshold on neutrino energy:
E  Mn  Mp  me  1.805 MeV
Thr
•Precise cross-section calculation
•Low threshold
•Unambiguous signature
•Target availability
Cross Section
n
In 1933 E. Fermi assumed that an electron and an
antineutrino are produced in the process

Fermi Theory:
e
and calculated the n-decay matrix element.
p
If the interaction responsible for the decay of the neutron is known, one can connect the cross section of the
process, at the small reactor energies, with the lifetime of the neutron.

Neglecting small corrections due to neutron recoil, the total cross section of the process e  p  e  n
is given by:
   0  pe We ; where  0 10-42 cm 2 : trans. matrix element
and
We  E - (M n - Mp )
 R    E   R E  dE  2  10 45 cm2
averaged over Reactor -flux
"SNU" 1036 s1 R  R  4 104
N evt
Evt. Rate:
 3  4 for a det ect or Mass of 0.2 t
h
p-beam
p

e

H2O Cu Block



Detector
e
Neutrino fluxes from decay of Pion and Muon at rest (“beam dump neutrinos”)
have well defined energy spectra (and angular distributions). The neutrino energy
range encompasses the solar & reactor range and extends up to about 50 MeV
(the “Moderate Energy” range).
The interaction cross-sections with matter can be established by the theoretical models
discussed in the Solar&Reactor neutrino sections…. but need some further deepening.
Weak Processes: leptonic decay

u
d

    
;
  e  e   
      
;
   e    e  





-
e-
We
Dominant
Channel:
• N(+) > N (- )
• - and - are captured
Shape of the
Neutrino Flux
Range of
investigation
p-beam: (LAMPF) 800 MeV p-energy, 1 mA p-intensity (6x1015 pot/s)
Flux Properties
Source
Type
<Flux>
@ detector
[106 cm-2 s-1]
Energy
Spectrum
Energy
Mean Value
[MeV]
Energy
End Point
[MeV]
 

- 5.
Line
29.8
29.8
 

- 5.
Cont.
~ 45.
 
e
- 5.
Cont.
~ 36.
 

- 2.5x10-3
Line
29.8
 

- 2.5x10-3
Cont.
~ 45.
 
e
- 2.5x10-3
Cont.
~ 36.
 
52.8 

52.8
m
2
m
2
29.8
 
52.8 

52.8
m
2
m
2
“Moderate Energy” range
In the 36 < E < 52.8 MeV energy range, the e rate relative to  in even lower
so that the observation of a significant e rate would be evidence for   e oscillations.
The signature for a e interaction in a liquid scintillator detector is the reaction:
e  p  e  n
followed by n + p
d + g (2.2 MeV)
… the same signature exploited with reactor neutrinos at lower  energy.
The reaction has a threshold on neutrino energy:
E  Mn  Mp  me  1.805 MeV
Thr
LSND Experiment
@ Los Alamos Meson Physic Facility:
• 200 m3 of Liq.Scint. (r=0.85)
Cross Section
(Fermi Theory):
See formulas from “Reactor Neutrino” section
   0  pe We ; where  0 10-42 cm 2 : trans. matrix element
and
We  E - (M n - Mp )
NB:  increases ≈ quadratically with  energy. Compared to the Reactor experiments,
at the higher energies (>36 MeV) investigated at beam dump experiments,
larger cross section compensate lower flux
(… but cross-section calculation with Fermi Theory not fully adequate).
 BD    E   R E  dE  4  10 41 cm2
averaged over BeamDump -flux
"SNU" 1036 s1 BD  BD  0.1
N ev t
Evt. Rate :
 45
yr
(!!!) for a detector Mass of 180 t
The negligible e expected rate makes the search for   e oscillation
very effective due to the much larger  flux (22 events have been detected !! by LSND).
• SN-type II: temperature hierarchy among  flavors (Te < T)
• Te = 3.5 MeV  <E> = 11 MeV
• T = 8.0 MeV  <E> = 25 MeV
• Energy spectra: Fermi-Dirac distribution
• SN @ 10kpc (53% of stars in the galactic disk), E=3X1053 erg
Supernova Neutrinos in the SN “electron neutrino heating “ hypothesis
• SN signal is usually dominated by e on free proton
• Detector based on e reactions may contribute significantly
in case of “e MSW oscillation mechanism”:
 SuperK: e + 16O  e + 16F (Q=15.4 MeV)
 LVD, Borexino, KamLand, Baksan :
e + 12C  e + 12B (Q=17.4 MeV)
 SNO: e + D  e + p + p (Q=1.4 MeV)
Among SN detectors, only ICARUS has a signal dominated by e flux !!!
 ICARUS:
e + 42Ar  e + 40K (F + GT)
(Q = 5.9 - 4.2÷7.9 MeV)
 Cross-Sections:
• El. Scattering on el. [linear increase with Eall flavors]
• Absorption on Ar nuclei (F + GT transitions)
[˜ quadratic increase with ECC-e only
•Statistics (no threshold): ES - 13 evt/kTon
Abs (F+GT) - 50 evt/kTon
Supernova Neutrinos
Oscillated e
No oscill. e
Spectra include Eethr = 5 MeV and Abs Q value
F. Vissani,
e



Cosmic Rays (p, A-nuclei) after entering the atmosphere collide with nuclei in the air
(NB: Primary C.R. Fluxes suffer large uncertainties and
Hadronic Interaction cross-section at extremely high energies are poorly known).
Pions and Kaons in the hadronic cascades decay in flight producing ’s and ’s.
Muons can in turn decay into ’s.






    
;
  e  e   
 u
Wd

      
;
   e    e  
e-
W
e
   
2
The -flavor Ratio at Earth surface is approximately constant R 
 e  e
.. however for E≈ 1 GeV, the parent muon reaches the surface of the Earth
before it decays  the e-neutrino fluxes decreases and R becomes larger
Downward-going 
Earth
Underground
Detector
(atmosphere around)
Upward-going 
Precise calculation of the atmospheric -flux required a tremendous effort
of many different groups (it took about 20 yr of re-iterated discussions and checks)
[e.g. 1D vs 3D models]
The energy spectrum covers many
orders of magnitude. The largest
fraction is concentrated below 1 GeV.
The explored range (present & past
experiments) is:
 400 MeV  E   10 GeV
… but future experiment(s) will
cover soon the lower energy
part of the atm. -spectrum
The “Intermediate Energy”
range
Differential -flux energy distributions at fixed zenith angles
(1D model - Bartol Group, Honda et al., Volkova)
The shape of the -fluxes depends on the location of the experimental site
(due to the different Geo-magnetic cut-off, relevant at low -energies)
Example:
GranSasso Site
Effect of Geo-magnetic cut-off:
clearly visible in the zenith angle differential -flux distributions at fixed energies
(1D model - Bartol Group, Honda et al., Volkova)
Differential -flux distributions
(integrated over zenith angle)
from recent 3D model calculation
(FLUKA-MonteCarlo Battistoni, Ferrari, Lipari, Sala)
FLUKA-MonteCarlo
Source
Type
Flux
@ detector
[cm-2 s-1]
Energy Sp ectrum
Energy
Mean Value
[GeV]
 ;  
   
- 2.
Cont.
0.1
 
 e  e
- 1.
Cont.
0.1
Cross Section
In the “Intermediate Energy” range (100 MeV <E<2-3 GeV) the -projectile “sees”
the nucleon N - possibly bound inside the Nucleus AZ (above this energies - in the
Deep Inelastic Region - the quark structure inside the nucleon starts to be “visible”).
Neutrino Cross-Section in the “Intermediate” Energy range can be decomposed
according to the final state multiplicity:
 CC   QEL   RES   DIS
where :
 QEL   n 

 RES   N 

 DIS   N 

 e,  ,t
 p and  QEL   p 
 

 N  1
 N  X n ,

,
 n

 and    N 
RES

and DIS   N 
N  p,n
NC reaction are obtained replacing



 
 N   Xn  ,

 N  1

,

For atmospheric neutrinos
•QEL (“quasi-elastic” scattering) channel is dominant (65% of the rate)
•RES (“resonance excitation” production) channel is sub-dominant (30%)
•DIS (Deep Inelastic Scattering) is almost negligible (5%)
 only QEL will be discussed in details
Dynamics of QEL interaction is described by “current-current” Lagrangian
(valid in the limit of Q2<<M2W)
Leptonic V-A Current
l

The Hadronic Current is defined
through the
W
G
N

Vector (FV1,FV2) and Axial (FA1)
N’
Weak Form Factors of the Nucleon
Hadronic Current
The Weak f.f. (dipole form) are defined with a free parameter (MV and MA) to be
fixed by experimental fits (or by non-perturbative QCD, but results are controversial !!).
The large error (≈15%) on MA introduce a large uncertainty on the QEL cross section
(new precise data are required to establish correct Cross section estimate).
From Q.F. Theory:
d 
2  
2 dp
1
1
2
1
 Pf  Pi 
M fi FV , FV ,FA 
2E 2mN
2E
4
1
2
where :
G
M fi 
u g  (1 g 5 ) u  cos c u p  un

2
 funct ion of t he Nucleon Weak Form Factors

After integration over final
state kinematics:
QEL E  10-38cm2 
CC-QEL thresholds:
 e : Ethr  0.
  : Ethr  110. MeV
 t : Ethr  3.45 GeV

dpN 
2EN 
In atmospheric  experiments however nucleon targets are bound in Nuclei AZ
Therefore QEL interactions are:
  AZ 

 p  A 1Z and   AZ 

 n   A 1Z 1
This introduces some constraints on both initial and final state kinematics
due to Nuclear Effects (i.e. cross-section is reduced):
• Fermi Motion of the nucleon N in AZ
• Binding Energy of the Nucleus
• Pauli blocking
Different types of nuclear target (O, Fe, Ar,…) introduce second order
corrections to the QEL cross section (and additional uncertainty).
Several theoretical models are available to describe nucleonic states inside Nuclei.
The easiest (i.e. the most commonly used) is the “modified- Fermi Gas Model”:
• incoherent impulse approximation (hit nucleon off-shell + spectator (A-1) on-shell)
• Fermi momentum distribution flat up to kF, and modified with high momentum tail (N-N correlation)
Best suited techniques for cross-section calculation are MonteCarlo calculations
(a big effort is being produced by the “neutrino community” to reach a common
framework to define cross sections … but new dedicated measurements are indeed
necessary).
Cross section plots
Difference between QEL cross
Section for  scattering on
free nucleon (n) or bound nucleon
in AZ Nuclei
Quasi-Elastic Cross Section on n , p bound in 40Ar18 Nuclei
Electron Neutrino
Electron AntiNeutrino
Muon Neutrino
Muon AntiNeutrino
Atmospheric neutrino event rate in present (“future”) experiments
Nuclear targets in use in present experiments:
• O (Oxygen in H2O)  SupeKamiokande (Kamiokande and IMB)
• Fe  SOUDAN
• Ar  ICARUS
• [O(50%) + Si(30%) + … (Rock)  MACRO
in high en range]
For the event rate calculation, Z/A ratio is more important
than differences from nuclear effects (kF, EB).
38
 Atm    CC
cm2
QEL E   Atm E ,cos  Z  dE d cos  Z  1.2  10
"SNU" 1036 s1 Atm  Atm  0.033
Evt. Rate:
N ev t
 300
yr
for a det ect or Mass of 1 kt!!);
(!
thr
e Det  1, EDet
 0. (ideal case)
Summing up contributions of QEL (CC only) reactions from   47%,  15%,  e 30%, 8%
Oscillation (50% suppression of  rate) effect ARE NOT included!!
MonteCarlo Event (atmospheric , QE interaction) in an ideal LAr detector
e

Real Event (cosmic muon) from the ICARUS T600 test run
Best controlled fluxes of artificial neutrinos can be generated from beams of
accelerated protons: after hitting a dense material target, secondary pions (after
the target) are focused in a long tunnel where decay-in-flight occurs.
A collimated, high energy  beam is thus generated, pointing to the target (the
experiment sensitive mass) located at near or far distance (short/long baseline).
Many neutrino beams have been built (CERN, US, Russia, Japan, ..) in a >30 yrs long history.
We use as an example the NuMI long baseline beam at FERMILAB, presently under construction
NuM I Beam Characteristics
p beam energy
120 GeV
P beam cycle
1.87 s
p beam intensity
4x1013 PoT/cycle
proton on Target (PoT)
3.8 x 1020 PoT/yr
 decay tunnel
670 m
NuMI Beam Flux
“Low Energy Option”
"Low Neutrino Energy Option"
 fluence
1.6 x 1013 /cm2
Average Flux
5 x 105  cm2s
Energy Mean Value
- 3 GeV
NB: “Low Energy
Option”
corresponds to the
“High-Intermediate”
range in
NeutrinoLand
Cross Section
Neutrino Cross-Section in the “High-Intermediate” Energy range can be decomposed in:
 CC  QEL   RES   DIS

QEL cross section
RES cross section
DIS cross section
(dominant channel)
Huge unprecedented Rate is expected at the close station
38
2
 Beam    CC
E

E
dE

2.2
10
cm




DIS

Beam



DIS
4
"SNU" 1036 s1  Beam
 NuMI
1.1410
Beam
Evt. Rate:

N evt
 8.5 107
yr
for a det ector Mass of 1 kt!!);
(!
thr
eDet  1, E Det
 0. (ideal case)

With the “High Energy option” of NuMI Beam a much larger rate can be
obtained (… but it is less attractive for present oscillation studies).
Obviously the Flux at far distance (730 Km) is MUCH smaller due to the
divergence of the neutrino beam.
Summary
Source
SNU [10-36 s-1]
Solar – pp (Ge absorpt ion channel)
128
Solar – 8B (Ar absorption channel)
11.1
Solar – 8B (elast ic e-channel)
1
Reactor (reaction of free p)
4 x 104
Beam Dump (reaction of free p)
0.1
Atmospheric (quas i-elastic on N )
0.033
Long Baseline Beam (Deep Inelast ic)
1.14 x 10
•
•
•
•
•
•
4
•
Guided tour of NeutrinoLand
Artificial/Natural  sources
Cross-section from various model
calculations
 interaction counting rate
New physics beyond Standard
Model? YES ( oscillations is now
a well established effect  m0)
New generation experiments are
now in preparation … but a very
accurate control of cross-section
(and fluxes)is a mandatory request.
… we still need to further probe
standard neutrino properties!!!
from both the experimental and the
theoretical sides
Elastic Scattering on Nuclei A
 x  AZ   x  AZ
… to be completed….