7. Atmospheric neutrinos
and Neutrino oscillations
Corso “Astrofisica delle particelle”
particelle”
Prof. Maurizio Spurio
Università di Bologna. A.a. 2011/12
Outlook
Some history
Neutrino Oscillations
How do we search for neutrino oscillations
Atmospheric neutrinos
10 years of SuperSuper-Kamiokande
Upgoing muons and MACRO
Interpretation in terms on neutrino oscillations
Appendix: The Cherenkov light
7.1 Some history
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) pe+π0νe
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!
γγ
e
Neutrino Interaction
Proton decay
7.2 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
|ν
νe> , |ν
νµ> , |ν
ντ> =Weak Interactions (WI) eigenstats
|ν1> , |ν2> , |ν3> =Mass (Hamiltonian) eigenstats
•Neutrinos propagate as a superposition
of mass eigenstates
Weak eigenstates (νe, νµ, ντ) are expressed as a
combinations of the mass eigenstates (ν
ν1, ν2,ν
ν3).
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: |ν
ν(t)>
>= (|ν
|ν1> , |ν2> )
i
M = (2x2 matrix)

M ii =



dν
dt
= M ν (t )
2
m
p 2 + mi2 ≈ Eν + i
2 Eν
M ij = 0
(eq.1)
(eq.2)
Time propagation
eq.1 becames, using eq.2)
dν

mi2
i
=  Eν +
dt
2 Eν

whose solution is :

 v(t )

(eq.4)
vi (t ) = vi (0) e − iϖ it
(eq.5)
with

mi2
ϖ i =  Eν +
2 Eν




During propagation, the phase difference is:
(m22 − m12 ) ⋅ t
∆Φ i =
2 Eν
(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:
|νe>
= cosθ |ν1> + sinθ |ν2>
θ = mixing angle
|νµ> = -sinθ |ν1> + cosθ |ν2>
(eq.3)
• Using eq. 5 in eq. 3, we get:
v e = cos θ v 1 ( 0 ) e − i ϖ 1 t + sin θ v 2 ( 0 ) e − i ϖ 2 i t
vµ
= − sin θ v 1 ( 0 ) e − i ϖ 1 t + cos θ v 2 ( 0 ) e − i ϖ 2 i t
(eq.7)
•At t=0, eq. 7 becomes:
ve
= cos θ v 1 ( 0 ) + sin θ v 2 ( 0 )
vµ
= − sin θ v 1 ( 0 ) + cos θ v 2 ( 0 )
(eq.8)
• By inversion of eq. 8:
v1 (0 )
= cos θ v e ( 0 ) − sin θ v µ ( 0 )
v2 (0 )
= sin θ v e ( 0 ) + cos θ v µ ( 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 νµ beam, eq. 9:
v1 (0 )
= − sin θ v µ ( 0 )
v2 (0 )
= cos θ v µ ( 0 )
(eq.10)
The time evolution of the νµ state of eq. 8:
v µ = sin 2 θ v µ ( 0 ) e − iϖ 1t + cos 2 θ v µ ( 0 ) e − iϖ 2 i t
By definition, the probability that
the state at a given time is a νµ is:
Pν
µν µ
(eq.11)
ν
≡
0
µ
Pν µ ν µ ≡
+ sin
2
ν
ν
µ
θ cos
2
t
µ
2
= sin
θ (e i ( ϖ
2
µ
(eq. 12)
•Using eq. 11, the probability:
0
ν
t
1
−ϖ
2
4
)t
θ + cos
+ e
− i (ϖ
1
4
−ϖ
θ +
2
)t
)
(eq. 13)
i.e. using trigonometry rules:
Pν µ ν µ = 1 − sin
2
 (ϖ 1 − ϖ 2 ) t 
2 θ ⋅ sin 

2

2
(eq. 14)

mi2
ϖ i =  Eν +
2 Eν

Finally, using eq.5:
Pν
µν µ
= 1 − sin
2
2 θ ⋅ sin
2



 ( m 22 − m 12 ) t 


4 Eν


(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 Eν
ν
(in GeV)
Pν µν µ
2

∆m ⋅ L 
2
2
= 1 − sin 2θ ⋅ sin 1.27

Eν 

(eq. 16)
θ ≠ 0
To see “oscillations” pattern:

∆m 2 ⋅L 
π
 ≈
 1 . 27
Eν
2


7.3 How do
we search
for neutrino
oscillations?
..with
atmospheric
neutrinos
• ∆m2, sin22Θ from
Nature;
• Eν = experimental
parameter (energy
distribution of neutrino
giving a particular
configuration of events)
• L = experimental
parameter (neutrino path
length from production to
interaction)
Pν µν µ

∆m 2 ⋅ L 
= 1 − sin 2θ ⋅ sin 1.27

Eν 

2
2
Appearance/Disappearance
Pν µν µ

∆m 2 ⋅ L 
= 1 − sin 2θ ⋅ sin 1.27

Eν 

2
2
7.4- Atmospheric neutrinos
The recipes for the evaluation of the
atmospheric neutrino fluxfluxπ + → µ + +ν µ
µ + → e+ + ν µ + ν 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
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 (ν
νe,ν
νµ) flux
See for instance the FLUKA MC:
http://www.mi.infn.it/~battist/ne
utrino.html
iv) The Detector response
ν
Fully
Contained
ν
Stopping µ
Partially
Contained
µ
µ
Pν µν µ

∆m 2 ⋅ L 
= 1 − sin 2θ ⋅ sin 1.27

Eν 

2
Through going µ
2
ν
µ
ν
Energy spectrum of ν for each event category
1000
FC ν µ
FC ν e
PC ν µ
750
500
up-stop µ
up-thru µ
250
0 −2
−1
10
10
1
10
10
E ν (GeV)
2
10
3
10
4
10
5
Energy spectrum (from
Monte Carlo) of
atmospheric neutrinos
seen with different
event topologies
(SuperKamiokande)
Rough estimate: how many ‘Contained
events’ in 1 kton detector
νµ
νe
1. Flux: Φν ~ 1 cm-2 s-1
2. Cross section (@ 1GeV):
σν~0.5 10-38 cm2
3. Targets M= 6 1032 (nucleons/kton)
4. Time t= 3.1 107 s/y
Nint = Φν (cm-2 s-1) x σν (cm2)x M (nuc/kton) x t (s/y) ~
~ 100 interactions/ (kton y)
7.5 10 years of Super-Kamiokande
1996.4 Start data taking
1998 Evidence of atmospheric ν oscillation (SK)
SK-I
1999.6 K2K started
2001 Evidence of solar ν 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 ν oscillation by accelerator ν (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 UltraUltra-Pure Water
11000 +2000 PMTs
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.
Cherenkov Radiation
One of the 13000
PMTs of SK
How to tell a νµ from a νe :
Pattern recognition
νµ
νe
Contained event in SuperKamiokande
Fully Contained (FC)
Partially Contained (PC)
µ
e or µ
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
νµ/νe ratio.
Up/Down asymmetry interpreted as
neutrino oscillations
Eν
ν=0.5GeV
Expectations:
events inside the
detector.
For Eν > a few
GeV,
Upward /
downward = 1
Eν
ν=3 GeV
Eν
ν=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
µ /e
µ /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(SK-I + SK
SK--II)
νµ–ντ oscillation (best fit)
SK-I + SK-II
null oscillation
SK-I + SK-II
400
400
Sub-GeV µ-like
P < 400 MeV/c
P<400MeV/c
200
300
300
150
200
200
100
100
100
50
0
-1
Number of Events
Sub-GeV e-like
P < 400 MeV/c
P<400MeV/c
400
-0.5
0
0.5
1
Sub-GeV e-like
P > 400 MeV/c
P>400MeV/c
300
0
-1
600
-0.5
0
0.5
1
0
-1
300
multi-ring e-like
100
-0.5
0
0.5
1
PC stop
300
20
200
100
0
0.5
1
0
-1
200
200
150
150
100
100
50
50
0
-1
-0.5
0
cosΘ
0.5
-0.5
0
0.5
1
0
-1
Multi-GeV µ-like
Multi-GeV e-like
1
0
-1
0
-1
-0.5
0
0.5
1
PC through
40
400
-0.5
multi-ring µ-like
200
Sub-GeV µ-like
P > 400 MeV/c
P>400MeV/c
200
0
-1
Livetime
SK-I + SK-II
•SK-I
1489d (FCPC)
1646d (Upmu)
•SK-II
804d (FCPC)
828d(Upmu)
-0.5
0
0.5
1
Upward stopping µ
200
µ-like
100
e-like
0
-1
600
150
-0.5
0
0.5
Upward through-going
non-showering µ
1
150
400
100
200
50
Upward through-going
showering µ
100
50
-0.5
0
cosΘ
0.5
1
0
-1 -0.8 -0.6 -0.4 -0.2 0
cosΘ
0
-1 -0.8 -0.6 -0.4 -0.2 0
0
-1 -0.8 -0.6 -0.4 -0.2 0
cosΘ
NOTE: All topologies, last results (September 2007)
cosΘ
Atmospheric Neutrino Anomaly
Summary results since the mid-1980's:
R’=
µ /e
µ /e
D a ta
MC
Double ratio between the number of
detected and expected νµ and νe
Calorimetric
Water
Cherenkov
7.6 Upgoing muons and MACRO
(Italy)
• Large acceptance
(~10000 m 2 sr for an isotropic
flux)
• Low downgoing
µ rate (~10 -6 of the surface rate )
• ~600 tons of liquid scintillator to measure
(time resolution ~500psec)
• ~20000 m 2 of streamer tubes (3cm cells) for
tracking (angular resolution < 1° )
T.O.F.
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
In down
1)
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 νµ events in MACRO
• <E>~ 50 GeV
throughgoing µ
• <E>~ 5 GeV, Internal
Upgoing (IU) µ;
• <E>~ 4 GeV , internal
downgoing (ID) µ and
for upgoing stopping
(UGS) µ;
Neutrino induced events are upward throughgoing
muons,, Identified by the timemuons
time-ofof-flight method
1
T2
Streamer tube track
β
=
(T 1
T1
µ from ν: upgoing
1
β
=
(T 1
− T
L
2
)⋅ c
=
− T
L
2
)⋅ c
=
+1 µ
-1 µ
Atmospheric µ:
downgoing
MACRO Results: event deficit and
distortion of the angular distribution
- - - - No oscillations
____ Best fit ∆m2= 2.2x10-3 eV2
sin22θ
θ=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 νµ oscillations on upgoing events
• If θ is the zenith angle and D= Earth diameter
ν
L=Dcosθ
µ
underground
θ detector • For throughgoing neutrino-induced muons in
MACRO, Eν = 50 GeV (from Monte Carlo)
Earth
Pν µν µ
θ
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
cos(θ ) ∆ 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
-0,174
0,99
1,00
0,000
1,00
1,00

∆m2 ⋅ L 
= 1 − sin 2θ ⋅ sin 1.27

E
ν


2
2
1,00
0,90
0,80
Pν µν µ
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
cosθ
0,00
Oscillation Parameters
• The value of the “oscillation parameters” sin2θ and ∆m2
correspond to the values which provide the best fit to the data
• Different experiments different values of sin2θ and ∆m2
• The experimental data have an associated error. All the values of
(sin2θ, ∆m2) which are compatible with the experimental data are
“allowed”.
• The “allowed” values span a region in the parameter space of (sin2θ,
∆m2)
Pν µν µ
2

m
∆
⋅ L
2
2
= 1− sin 2θ ⋅ sin 1.27

Eν 

1.9 x 10-3 eV2 < ∆m2 < 3.1 x 10-3 eV2
sin2 2θ
θ > 0.93
(90% CL)
“Allowed” parameters region
90% C. L. allowed regions for νµ → ντ oscillations of atmospheric
neutrinos for Kamiokande, SuperK, Soudan-2 and MACRO.
Why not νµ→νe ?
Apollonio et al., CHOOZ Coll.,
Phys.Lett.B466,415
νµ disappearance: History
Anomaly in R=(µ
R=(µ/e)observed/(
/(µ
µ/e)predicted
Kamiokande: ZenithZenith-angle distribution
Super-Kamiokande: PRL 1998
SuperMACRO, PRL 1998
K2K: First acceleratoraccelerator-based long
baseline experiment: 1999 – 2004
Confirmed atmospheric neutrino results
Kamiokande: PLB 1994
Super-Kamiokande/MACRO:
SuperDiscovery of νµ oscillation in 1998
Kamiokande: PLB 1988, 1992
Discrepancies in various experiments
Final result 4.3σ
4.3σ: PRL 2005, PRD 2006
MINOS: Precision measurement: 2005 First result: PRL2006
See for review:
The “Neutrino Industry”
Janet Conrad web pages:
http://projects.fnal.gov/nuss/
Torino web Pages:
http://www.nevis.columbia.edu/~conrad/nupage.html
Fermilab and KEK “Neutrino Summer School”
http://www.hep.anl.gov/ndk/hypertext/
http://www.nu.to.infn.it/Neutrino_Lectures/
Progress in the physics of massive neutrinos, hepph/0308123
Appendice:
La radiazione Cerenkov
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’ βc=v>c/n
c=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 β>1/n momento di dipolo elettrico emissione di radiazione.
β<1/n
β>1/n
β>
L’ angolo di emissione θc 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
θ
lpart=βc
β ∆t
1
cosθ C =
nβ
with n = n(λ ) ≥ 1
θC
Esiste una velocita’ di soglia βs = 1/n θc ~ 0
Esiste un angolo massimo θmax= arcos(1/n)
La cos(θ
cos(θ) =1/β
=1/βn e’ valida solo per un radiatore infinito, e’ comunque
una buona approssimazione ogniqualvolta il radiatore e’ lungo L>>λ
L>>λ
essendo λ la lunghezza d’onda della luce emessa
Numero di fotoni emessi per unita’ di
percorso e intervallo unitario di
lunghezza d’onda. Osserviamo che
decresce al crescere della λ
dN/dλ
λ
d N 2πz α 
1  2πz α
2


=
1
−
=
sin
θC
2
2 2 
2

dxdλ
λ  β n 
λ
2
2
d 2N
1
∝ 2
dxdλ λ
2
c
hc
with λ = =
ν E
d 2N
= const.
dxdE
dN/dE
Il numero di fotoni emessi per unita’ di
percorso non dipende dalla frequenza
Ε


dE
1
2 h
dω
−
= z α ∫ ω 1 − 2 2
dx
c  β n (ω ) 
L’ energia persa per radiazione Cerenkov cresce con β. Comunque
anche con β 1 e’ molto piccola.
Molto piu’ piccola di quella persa per collisione (Bethe Block), al
massimo 1% .
θmax (β=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.
particelle.
Con 1) posso sfruttare la soglia Cerenkov a soglia
soglia..
Con 2) misurare l’angolo DISC, RICH etc.
La luce emessa e rivelabile e’ poca
poca..
Consideriamo un radiatore spesso 1 cm un angolo θc = 30o ed un
∆E = 1 eV ed una particella di carica 1.
⇒ N ph
dN
z 2α
sin 2 ϑc
=
dEdx hc
= 370 ⋅ sin 2 ϑc ⋅ L ⋅ ∆E = 370 × 0.25 = 92.5
Considerando inoltre che l’efficienza quantica di un fotomoltiplicatore e’
~20% Npe=18 fluttuazioni alla Poisson