9. Atmospheric neutrinos and
Neutrino oscillations
(Cap. 11-12 book)
Corso “Astrofisica delle particelle”
Prof. Maurizio Spurio
Università di Bologna a.a. 2014/15
Outlook
•
Some history
•
Neutrino Oscillations
•
How do we search for neutrino oscillations
•
•
•
•
Atmospheric neutrinos
10 years of Super-Kamiokande
Upgoing muons and MACRO
Interpretation in terms on neutrino oscillations
–
Appendix: The Cherenkov light
Once upon a time…
• At the beginning of the ’80s, some theories (GUT) predicted the
proton decay with measurable livetime
• The proton was thought to decay in (for instance) pe+p0ne
• Detector size: 103 m3, and mass 1kt (=1031 p)
• The main background for the detection of proton decay were
atmospheric neutrinos interacting inside the experiment



Water Cerenkov Experiments
(IMB, Kamiokande)
Tracking calorimeters
(NUSEX, Frejus, KGF)
Result: NO p decay ! But some
anomalies on the neutrino
measurement!
gg
e
Neutrino Interaction
Proton decay
Neutrino Oscillations
 Idea of neutrinos being massive was first suggested by B. Pontecorvo
 Prediction came from proposal of neutrino oscillations
Neutrinos are created or annihilated as
W.I. eigenstates
|ne , |nm , |nt =Weak Interactions (WI) eigenstats
|n1 , |n2 , |n3 =Mass (Hamiltonian) eigenstats
•Neutrinos propagate as a superposition
of mass eigenstates
 Weak eigenstates (ne, nm, nt) are expressed as a
combinations of the mass eigenstates (n1, n2,n3).
 These propagate with different frequencies due to their
different masses, and different phases develop with distance
travelled. Let us assume two neutrino flavors only.
 The time propagation: |n(t)= (|n1 , |n2 )
i
M = (2x2 matrix)

M ii 



dn
dt
 M n (t )
2
m
p 2  mi2  En  i
2 En
M ij  0
(eq.1)
(eq.2)
Time propagation
eq.1 becames, using eq.2)
dn

mi2
i
  En 
dt
2 En

whose solution is :

 v(t )

(eq.4)
vi (t )  vi (0) ei it
(eq.5)
with

mi2
 i   En 
2 En




During propagation, the phase difference is:
(m22  m12 )  t
 i 
2 En
(eq.6)
Time evolution of the “physical” neutrino states:
• Let us assume two neutrino flavors only (i.e. the electon and the muon
neutrinos).
• They are linear superposition of the n1,n2 eigenstaten:
|ne
= cosq |n1 + sinq |n2
q = mixing angle
|nm = -sinq |n1 + cosq |n2
(eq.3)
• Using eq. 5 in eq. 3, we get:
ve  cos q v1 (0) e  i 1t  sin q v2 (0) e  i 2 i t
vm   sin q v1 (0) e i 1t  cos q v2 (0) e i 2 i t
(eq.7)
•At t=0, eq. 7 becomes:
ve  cos q v1 (0)  sin q v2 (0)
vm
  sin q v1 (0)  cos q v2 (0)
(eq.8)
• By inversion of eq. 8:
v1 (0)  cos q ve (0)  sin q vm (0)
v2 (0)  sin q ve (0)  cos q vm (0)
(eq.9)
• For the experimental point of view (accelerators, reactors), a pure muon
(or electron) state a t=0 can be prepared. For a pure nm beam, eq. 9:
v1 (0)   sin q vm (0)
v2 (0)  cos q vm (0)
(eq.10)
The time evolution of the nm state of eq. 8:
vm  sin 2 q vm (0) e i 1t  cos 2 q vm (0) e i 2 i t
By definition, the probability that
the state at a given time is a nm is:
(eq.11)
Pn mn m  n m n m
0
Pn mn m  n m n m
t
2
 sin q cos q e
2
2
 sin 4 q  cos 4 q 
i ( 1  2 ) t
2
(eq. 12)
•Using eq. 11, the probability:
0
t
e
i ( 1  2 ) t

(eq. 13)
i.e. using trigonometry rules:
Pn mn m
 ( 1   2 )t 
 1  sin 2q  sin 

2

2
2
(eq. 14)
Finally, using eq.5:
Pn mn m  1  sin
2

mi2
 i   En 
2 En




 (m22  m12 )t 
2q  sin 

4
E
n


2
(eq. 15)
With the following substitutions in eq.15:
- the neutrino path length L=ct (in Km)
- the mass difference m2 = m22 – m12
(in eV2)
- the neutrino Energy En
(in GeV)
Pn mn m
2


m
 L
2
2
 1  sin 2q  sin 1.27

En 

(eq. 16)
q 0
To see “oscillations” pattern:

m 2  L 
p
1
.
27



E
2


n


How do we
search for
neutrino
oscillations?
..with
atmospheric
neutrinos
• m2, sin22Q  from
Nature;
• En = experimental
parameter (energy
distribution of neutrino
giving a particular
configuration of events)
• L = experimental
parameter (neutrino path
length from production to
interaction)
Pn mn m

m 2  L 
 1  sin 2q  sin 1.27

En 

2
2
Appearance/Disappearance
Pn mn m

m 2  L 
 1  sin 2q  sin 1.27

En 

2
2
Atmospheric neutrinos
The recipes for the evaluation of the
atmospheric neutrino fluxp   m  n m
m   e  n m  n e
\
i) The primary spectrum
E < 1015 eV
Galactic
5. 1019 < E< 3. 1020 eV
E-3
spectrum
1015 < E< 1018 eV
galactic ?
GZK cut
E  5. 1019 eV
Extra-Galactic?
Unexpected?
ii)- CR-air cross section
It needs a model of nucleus-nucleus interactions
pp Cross section versus center of
mass energy.
Average number of charged hadrons
produced in pp (andpp) collisions
versus center of mass energy
iii) Model of the atmosphere
ATMOSPHERIC NEUTRINO PRODUCTION:
•high precision 3D calculations,
•refined geomagnetic cut-off treatment (also geomagnetic field in
atmosphere)
•elevation models of the Earth
•different atmospheric profiles
•geometry of detector effects
Output: the neutrino (ne,nm) flux
See for instance the FLUKA MC:
http://www.mi.infn.it/~battist/ne
utrino.html
iv) The Detector response
n
Fully
Contained
n
Stopping m
Partially
Contained
m
Pn mn m

m 2  L 
 1  sin 2q  sin 1.27

En 

2
2
Through going m
m
n
m
n
Energy spectrum of n for each event category
up-stop m
up-thru m
Energy spectrum (from
Monte Carlo) of
atmospheric neutrinos
seen with different
event topologies
(SuperKamiokande)
Rough estimate: how many ‘Contained events’
in 1 kton detector
nm
ne
1. Flux: n ~ 1 cm-2 s-1
2. Cross section (@ 1GeV):
sn~0.5 10-38 cm2
3. Targets M= 6 1032 (nucleons/kton)
4. Time t= 3.1 107 s/y
Nint = n (cm-2 s-1) x sn (cm2)x M (nuc/kton) x t (s/y) ~
~ 100 interactions/ (kton y)
15 years of Super-Kamiokande
1996.4 Start data taking
1998 Evidence of atmospheric n oscillation (SK)
SK-I
1999.6 K2K started
2001 Evidence of solar n oscillation (SNO+SK)
2001.7 data taking was stopped
for detector upgrade
2001.11 Accident
partial reconstruction
2002.10 data taking was resumed
SK-II
2005 Confirm n oscillation by accelerator n (K2K)
2005.10 data taking stopped for full reconstruction
SK-III
2006.7 data taking was resumed
SK-IV
2009 data taking
Measurement of contained events and
SuperKamiokande (Japan)




1000 m Deep Underground
50.000 ton of Ultra-Pure Water
11000 +2000 PMTs
Working since 1996
Cherenkov Radiation
 As a charged particle travels, it disrupts the
local electromagnetic field (EM) in a medium.
Electrons in the atoms of the medium will be
displaced and polarized by the passing EM field
of a charged particle.
 Photons are emitted as an insulator's electrons
restore themselves to equilibrium after the
disruption has passed.
 In a conductor, the EM disruption can be
restored without emitting a photon.
 In normal circumstances, these photons
destructively interfere with each other and no
radiation is detected.
 However, when the disruption travels faster
than light is propagating through the medium,
the photons constructively interfere and intensify
the observed Cerenkov radiation.
Effetto Cerenkov
Per una trattazione classica dell’effetto Cerenkov:
Jackson : Classical Electrodynamics, cap 13 e par. 13.4 e 13.5
La radiazione Cerenkov e’ emessa ogniqualvolta una particella carica
attraversa un mezzo (dielettrico) con velocita’ bc=v>c/n, dove v e’
la velocita’ della particella e n l’indice di rifrazione del mezzo.
Intuitivamente: la particella incidente polarizza il dielettrico  gli
atomi diventano dei dipoli. Se b>1/n  momento di dipolo
elettrico  emissione di radiazione.
b<1/n
b1/n
L’ angolo di emissione qc puo’ essere interpretato qualitativamente
come un’onda d’urto come succede per una barca od un aereo
supersonico.
llight=(c/n)t
wav
e fro
nt
q
lpart=bct
1
cosq C 
nb
with n  n(l )  1
qC
Esiste una velocità di soglia bs = 1/n  qc ~ 0
Esiste un angolo massimo qmax= arcos(1/n)
La cos(q) =1/bn e’ valida solo per un radiatore infinito, e’ comunque
una buona approssimazione ogniqualvolta il radiatore e’ lungo L>>l
essendo l la lunghezza d’onda della luce emessa
Numero di fotoni emessi per unità di
percorso e intervallo di lunghezza d’onda.
Osserviamo che decresce al crescere della l
dN/dl
l
d 2 N 2pz 2 
1  2pz 2
2



1


sin
qC
2
2 2 
2

dxdl
l  b n 
l
d 2N
1
 2
dxdl l
c
hc
with l  
n E
d 2N
 const .
dxdE
dN/dE
Il numero di fotoni emessi per unita’ di
percorso non dipende dalla frequenza


dE
 
1
2

 z    1  2 2
d
dx
c
 b n   
L’ energia persa per radiazione Cerenkov cresce con b. Comunque
anche con b  1 e’ molto piccola.
Molto piu’ piccola di quella persa per eccitazione/ionizzazione
(Bethe Block), al massimo 1% .
qmax (b=1)
air
1.000283 1.36
isobutane 1.00127 2.89
water
1.33
41.2
quartz
1.46
46.7
medium
n
Nph (eV-1 cm-1)
0.208
0.941
160.8
196.4
1)
Esiste una soglia per emissione di luce Cerenkov
2)
La luce e’ emessa ad un angolo particolare
Facile utilizzare l’effetto Cerenkov per identificare le particelle.
Con 1) posso sfruttare la soglia  Cerenkov a soglia.
Con 2) misurare l’angolo  DISC, RICH etc.
La luce emessa e rivelabile e’ poca.
Consideriamo un radiatore spesso 1 cm un angolo qc = 30o ed un
E = 1 eV ed una particella di carica 1.
 N ph
dN
z 2

sin 2 c
dEdx c
 370  sin 2 c  L  E  370  0.25  92.5
Considerando inoltre che l’efficienza quantica di un fotomoltiplicatore
e’ ~20%  Npe=18  fluttuazioni alla Poisson
Cherenkov Radiation
One of the 13000
PMTs of SK
How to tell a nm from a ne :
Pattern recognition
nm
ne
Contained event in SuperKamiokande
Fully Contained (FC)
Partially Contained (PC)
m
e or m
No hit in Outer Detector
Reduction
One cluster in Outer Detector
Automatic ring fitter
Particle ID
Energy reconstruction
Fiducial volume (>2m from wall, 22 ktons)
Evis > 30 MeV (FC), > 3000 p.e. (~350 MeV) (PC)
Fully Contained
8.2 events/day
Evis<1.33 GeV : Sub-GeV
Evis>1.33 GeV : Multi-GeV
Partially Contained
0.58 events/day
Contained events. The
up/down symmetry in
SK and nm/ne ratio.
Up/Down asymmetry interpreted as
neutrino oscillations
En=0.5GeV
Expectations:
events inside the
detector.
For En > a few
GeV,
Upward /
downward = 1
En=3 GeV
En=20 GeV
Zenith angle
distribution
SK:1289 days (79.3 kty)
• Electron neutrinos =
DATA and MC
(almost) OK!
• Muon neutrinos =
Large deficit of DATA
w.r.t. MC !
DATA
m /e
m /e
Zenith angle distributions for e-like and µ-like contained atmospheric
neutrino events in SK. The lines show the best fits with (red) and without (blue)
oscillations; the best-fit is m2 = 2.0 × 10−3 eV2 and sin2 2θ = 1.00.
Data
MC
= 0.638 
0.017  0.050
Zenith Angle Distributions (SK-I + SK-II)
nm–nt oscillation (best fit)
null oscillation
P<400MeV/c
P<400MeV/c
P>400MeV/c
P>400MeV/c
Livetime
•SK-I
1489d (FCPC)
1646d (Upmu)
•SK-II
804d (FCPC)
828d(Upmu)
m-like
e-like
NOTE: All topologies, last results (September 2007)
Upgoing muons and MACRO (Italy)
R.I.P December 2000
The Gran Sasso National Labs
http://www.lngs.infn.it/
Neutrino event topologies in MACRO
Up throughgoing
In up
Absorber
Streamer
Scintillator
Up stop
1)
In down
4)
3)
2)
• Liquid scintillator counters, (3
planes) for the measurement of
time and dE/dx.
• Streamer tubes (14 planes), for
the measurement of the track
position;
• Detector mass: 5.3 kton
• Atmospheric muon neutrinos
produce upward going muons
• Downward going muons ~ 106
upward going muons
• Different neutrino topologies
Energy spectra of nm events in MACRO
• <E>~ 50 GeV
throughgoing m
• <E>~ 5 GeV, Internal
Upgoing (IU) m;
• <E>~ 4 GeV , internal
downgoing (ID) m and
for upgoing stopping
(UGS) m;
Neutrino induced events are upward throughgoing
muons, Identified by the time-of-flight method
T2
1
Streamer tube track
b

T1  T2   c
T1
m from n: upgoing
1
b

T1  T2   c
L

L

+1 m
-1 m
Atmospheric m:
downgoing
MACRO Results: event deficit and distortion
of the angular distribution
- - - - No oscillations
____ Best fit m2= 2.2x10-3 eV2
sin22q=1.00
Observed= 809 events
Expected= 1122 events (Bartol)
Observed/Expected
= 0.721±0.050(stat+sys)±0.12(th)
MACRO Partially contained events
IU
Obs. 154 events
Exp. 285 events
Obs./Exp. = 0.54±0.15
MC with oscillations
ID+UGS
Obs. 262 events
Exp. 375 events
Obs./Exp. = 0.70±0.19)
consistent with up
throughgoing muon results
Effects of nm oscillations on upgoing events
• If q is the zenith angle and D= Earth
n
diameter L=Dcosq
m
underground
• For throughgoing neutrino-induced muons
q detector
in MACRO, En = 50 GeV (from MC)
Earth
Pn mn m

m 2  L 
 1  sin 2q  sin 1.27

E
n


2
2
1,00
0,002
q
0
-10
-20
-30
-40
-50
-60
-70
50
cos(q) m2=0.0002 m2=0.0001
-1,000
0,62
0,89
-0,985
0,63
0,90
-0,940
0,66
0,91
-0,866
0,71
0,92
-0,766
0,77
0,94
-0,643
0,83
0,96
-0,500
0,89
0,97
-0,342
0,95
0,99
0,90
0,80
Pn mn m
0,70
0,60
0,50
0,40
0,30
0,20
0,10
0,00
-1,00
-0,80
-0,60
-0,40
-0,20
cosq
0,00
Oscillation Parameters
• The value of the “oscillation parameters” sin2q and m2
correspond to the values which provide the best fit to the data
• Different experiments  different values of sin2q and m2
• The experimental data have an associated error. All the values of
(sin2q, m2) which are compatible with the experimental data are
“allowed”.
• The “allowed” values span a region in the parameter space of (sin2q,
m2)
Pn mn m
2


m
 L
2
2
 1  sin 2q  sin 1.27

En 

1.9 x 10-3 eV2 < m2 < 3.1 x 10-3 eV2
sin2 2q > 0.93
(90% CL)
“Allowed” parameters region
90% C. L. allowed regions for νm → νt oscillations of atmospheric
neutrinos for Kamiokande, SuperK, Soudan-2 and MACRO.
Why not νμνe ?
Apollonio et al., CHOOZ Coll.,
Phys.Lett.B466,415
nm disappearance: History
• Anomaly in R=(m/e)observed/(m/e)predicted
– Kamiokande: PLB 1988, 1992
– Discrepancies in various experiments
• Kamiokande: Zenith-angle distribution
– Kamiokande: PLB 1994
• Super-Kamiokande/MACRO: Discovery of
nm oscillation in 1998
– Super-Kamiokande: PRL 1998
– MACRO, PRL 1998
• K2K: First accelerator-based long baseline
experiment: 1999 – 2004 Confirmed
atmospheric neutrino results
– Final result 4.3s: PRL 2005, PRD 2006
• MINOS: Precision measurement: 2005 – First result: PRL2006
See for review:
• The “Neutrino Industry”
– http://www.hep.anl.gov/ndk/hypertext/
• Janet Conrad web pages:
– http://www.nevis.columbia.edu/~conrad/nupage.html
• Fermilab and KEK “Neutrino Summer School”
– http://projects.fnal.gov/nuss/
• Torino web Pages:
– http://www.nu.to.infn.it/Neutrino_Lectures/
• Progress in the physics of massive neutrinos, hepph/0308123
Oscillations with neutrino telescopes
• Oscillations occur for
En < 100 GeV
• Low energy muons
• dE/dx  2 MeV/cm . Not
dependent from Em
• Muon energy estimated
from the muon range
ER  S  0.2 GeV/m
S  (z max  z min ) / cos q
ANTARES
How oscillations are seend
• Distribution of Eν /cosΘ
for the selected events of
the atmospheric neutrino
simulation.
• Solid lines are without
oscillations, the dashed
lines include oscillations
assuming the best fit values
reported in PDG.
• The red histograms
indicate the contribution of
the single-line sample, in
blue the multi-line events.
ANTARES:
Range of a 50 GeVmuon= 100 m
Distance between storeys = 14.5 m
Distance between strings  60 m
The role of muon reconstruction
• Normalised fit quality of the final multi-line (left) and single-line (right)
samples. Data with statistical errors (black) are compared to simulations
from atmospheric n with oscillations assuming parameters from PDG (red)
and without oscillations (green) and atmospheric muons (blue).
• For a fit quality larger than 1.6 (multi-line) or 1.3 (single-line) the
misreconstructed atmospheric muons dominate. The arrows indicate the
chosen regions.
Results
• Left: Distribution of ER /cosΘR for selected events. Black crosses are
data, the blue histogram shows simulations of atmospheric n without
neutrino oscillations (scaled down by a factor 0.86) plus the residual
background from atmospheric muons. The red histogram shows the result
of the fit assuming oscillations.
• Right: The fraction of events with respect to the non-oscillation
hypothesis.
Oscillation parameters
 68% and 90% C.L.
contours (solid and
dashed red lines) of the
n oscillation parameters
as derived from the fit
of the of ER /cosΘR
distribution.
The best fit point is indicated by the triangle. The solid filled regions
show results at 68% C.L. from K2K (green), MINOS (blue) and
Super-Kamiokande (magenta) for comparison.