Neutrino oscillations: status and plans
Enrique Fernández
Univ. Autónoma Barcelona/IFAE
Trobada de Nadal, Univ. Barcelona, Dec 21-22, 2005
1
Neutrino properties
Neutrinos are somewhat special particles. This is mainly
due to the fact that they only interact weakly.
At low energies (MeV’s), the cross-section for interacting
with 1 nucleon is very small, ~ 10-40 cm2. This implies that
they are “invisible” in most cases.
The charged current weak interaction is also very peculiar:
it only acts on the left-handed chiral projection of particle
spinors (right-handed, for antiparticles). It does not
conserve P (nor CP). Spin effect are thus very strong.
They also have a very small mass, compared with
that of the other elementary particles.
2
Neutrino properties
Quark and Lepton masses in units of MeV/c2
Quarks
Leptones
mu= 400
md= 400
me= 0.5
mne< 0.0000022
mc= 1,600
ms= 500
mm= 106
mnm< 0.000170
mt=175,000
mb=4,300
mt= 1,776
mnt< 15.5
From CMB anisotropies:
Smi<0.00000071
3
Neutrinos in the SM
In the SM there are 3 lepton families, each containing a
charged lepton and a neutrino.
Neutrinos are massless particles and each family lepton
number (as well as global lepton number) is conserved.
The neutrino has three states (weak eigenstates): ne, nm, nt.
By definition these are the states that couple to the W
together with the corresponding charged leptons.
These assumptions, in particular the massless assumption,
were built up from experiments.
4
Massive neutrinos and neutrino oscillations
In 1998 there was a turning point in neutrino physics. Data
from atmospheric neutrinos collected by the Superkamiokande
detector showed that there were neutrino oscillations.
As we will see neutrino oscillations requires that neutrinos
have mass and that there is lepton mixing.
The SK results were preceded by many experiments on solar
neutrinos that showed a deficit, with respect to solar models,
on the number of neutrinos coming from the Sun.
New solar neutrino experiments, in particular SNO (Sudbury
Neutrino Observatory) have now shown unequivocally that the
deficit of solar neutrinos is also due to oscillations.
5
What do we mean by oscillations?
(ref.: B. Kaiser, hep-ph/0506165).
Let’s assume that a neutrino of flavor a, na, is produced
at the source. When it interacts at the target it does so
as a neutrino of a different flavor, nb.
6
Neutrino Oscillations:
Oscillation requires both mixing between the leptons
and massive neutrinos.
Suppose that there are several neutrino mass states ni. Mixing
means that the state produced together with charged lepton
la is a superposition of different ni:
U*ai= amplitude of W+ decay to la ni
The set of all U*ai (for 3 ni) form a unitary matrix. Inverting it:
n e 
n 1 
n   PMNS n 
 m
n 2 
 3
n t 
Pontecorvo-Maki-Nakagawa-Sakata matrix
7
Neutrino Oscillations:
The oscillation probability is given by the square of the amplitude:
8
Neutrino Oscillations:
In the n rest frame:
In terms of laboratory variables:
To interfere coherently, the different
ni have to have the same E.
 
(if they had the same p the phase would be exp (-i(Ei-Ej)t) which,
averaged over t, would be zero, unless Ei=Ej).
The momentum is given by (for mi2<<E2):
Therefore the phase is:
(constant for all ni, thus not contributing to the probability)
9
Neutrino oscillations. Squaring the amplitude:
The oscillation implies that lepton family number is no longer
conserved.
10
Neutrino Oscillations:
This is entirely similar to what happens in the case of the quarks,
where favor is not conserved in weak decays, e.g
L (uds) p (uud)+ p- (du)
The reason for the non-conservation of “quark family number” or
“flavor” is quark mixing, the fact that weak and mass eigenstates are
different.
u
d’
c
s’
t
b’
 d '
d 
 s'   CKM  s 
 b' 
b 
 
 
The difference is that we produce weak-interaction quarks (in the
weak decay of the L) but observe them as mass states (in the p or p).
11
Neutrino oscillations. Squaring the amplitude:
From this expression we see that:
1)
as required by CPT invariance.
2) In general (if U complex):
CP violation.
3) The sin2[..L/E] gives “oscillatory” pattern.
The above formula is very complicated but nature has been kind
enough as to make it simple in certain cases of interest.
12
Neutrino oscillation:
To gain some understanding of the above formula write:
Lc3 
Lkm 

2
2
2
sin 2  mij2

  sin 1.27mij eV


4
E

E
GeV




 
For a given term to be relevant the argument of sin2() should not
be much smaller than p/2, otherwise sin2( ) is too small.
It can also be that for a given experiment only one mixing angle is
relevant.
The bottom line is that in some cases the oscillation can be
treated as a two-family mixing.
U PMNS   cos 
 - sin 
sin  
cos 
13
Neutrino oscillation:
Oscillation probabilities (2 neutrino case; relevant
for CNGS beam):
14
The first clear signature of oscillations came from
the SuperKamiokande experiment in 1998
15
SuperKamiokande detector principle
Detect Cherenkov light produced by charged lepton l  from
reacction n+N l  +X (l =e,m), or e- from n+e-n+e- . Detector
operates in real time and has directional information.
16
SuperKamiokande events (fairly typical)
muon
electron
17
Evidence for neutrino oscillations
SK atmospheric n
18
The evidence for oscillations: solar neutrinos
The flux of solar neutrinos is
very large but their detection
is very difficult.
The pioneer experiment of
R.Davies took place at the
Homestake Mine in S. Dakota
(at 1350m depth).
Large (600 tons) of
Perchloroethylene (C2Cl4).
The detection method is
radiochemical.
37
37
n 17
Cl  e - 18
Ar *
En  0.814 MeV
About 2 radioactive atoms/day!
22
The evidence for oscillations: solar neutrinos
The measurement was repeated by other experiments
using Galium instead of Clorine. All of them saw less
neutrinos than expected.
This was known as the “solar neutrino problem”.
Kamiokande, and later SK, measured the “elasticscattering” reaction
e- ne
ne
n x + e- → n x + ewhere nx is mostly ne.
W
e-
Z
ne
nm,t
ne
e-
e-
nm,t
Z
e-
e-
23
The evidence for oscillations: solar neutrinos
24
The evidence for oscillations: solar neutrinos
25
Definive solution of the Solar neutrino puzzle
The Sudbury Neutrino
Observatory (SNO)
SNO: 1 kT of D2O (heavy
water) surrounded by
7.8kT of ultra pure H2O.
Located at 2000m depth at
the INCO mine in Sudbury,
Ontario, Canada.
26
Definive solution of the Solar neutrino puzzle
SNO
A neutrino of En>2.2 MeV can disociate the Deuterium
nucleous, into proton and neutron. This NC process
takes place for any neutrino species.
SNO detects 3 reactions:
ne + D  p + p + e-
(CC)
nx + e- → nx + e-
(ES; like SK)
nl + D  nl + p + n
(NC; l = e,m,t)
The neutron is captured producing 6.25 MeV.
But detecting a single neutron is difficult...
27
Definive solution of the Solar neutrino puzzle
SNO Results
28
Oscillation signatures
Atmospheric neutrino disappear, but, is it due to oscillations?
A controlled accelerator experiment: K2K (KEK to Kamioka).
29
K2K (KEK to Kamioka)
~1 event/2days
~1011 nm/2.2sec
(/10m10m)
1º tilt downwards
12GeV protons
p+
~106 nm/2.2sec
nm (/40m40m)
SK nt
m
Target+Horn
p monitor
200m
decay pipe
m monitor
100m
~250km
Near n detectors
(ND)
(monitor the beam center)
Signal of n oscillation at K2K
Reduction of nm events
 Distortion of nm energy spectrum

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GPS
SK Events
Tspill
SK
TOF=0.83msec
TSK
Decay electron cut.
500msec
20MeV Deposited Energy
No Activity in Outer Detector
Event Vertex in Fiducial Volume
More than 30MeV Deposited Energy
107 events
5msec Analysis Time Window
for 0.89x1020 p.o.t.
-0.2<TSK-Tspill-TOF<1.3msec
(BG: 1.6 events within 500ms
2.4×10-3 events in 1.5ms)
TDIFF. (ms)
31
K2K near-detector complex
•
•
•
•
•
1KT Water Cherenkov Detector (1KT)
Scintillating-fiber/Water sandwich Detector (SciFi)
Lead Glass calorimeter (LG) before 2002
Scintillator Bar Detector (SciBar) after 2003
Muon Range Detector (MRD)
32
Oscillation signatures
E. Aliu et al., Phys. Rev. Letters 94:081802, 2005.
35
KAMLAND Reactor Experiment
“Solar” neutrino oscillations in a controlled reactor-experiment
36
Evidence for neutrino oscillations
SK atmospheric n
K2K
Solar experiments
KAMLAND reactor exp.
37
Neutrino oscillations:
In addition to the Solar (+Kamland) and Atmospheric (+K2K),
there are two other very relevant experiments:

Chooz reactor experiment. Sees no oscillation of
reactor ne over a baseline of 1 Km.

LSND accelerator experiment. Sees positive signal of
oscillations of nm → ne over 30 m baseline
conveniently ignored
Excess of 87.9±22.4±6.0 events!
38
Results of the analysis of the oscillation data
39
Results of the analysis of the oscillation data
40
Oscillation parameters
m2atm≡ m232=m23-m22 = [(2.40.3)x10-3 eV2]
dm2sol≡ m221=m22-m21 = (0.80.3)x10-5 eV2
n12/3 ne
ne
n21/3 ne
n30%
Mixing angles:
12  sol  34º2º
23  atm  45º3º
13 < 12º (at 3s)
sin213≡|Ue3|2 < 0.04
41
Parameterization of the PMNS matrix
In view of the results it is convenient to parameterize the PMNS
matrix as:
atmospheric
1
U  0

0
CP violation phase
0
c23
-s23
0   c13
s23   0

c23   -s13eid
solar
0
1
0
s13eid   c12
0   -s12

c13   0
s12
c12
0
0
0

1
Links atmospheric & solar sectors
cij≡cosij sij≡sinij
42
Solar Oscillations and the MSW effect
The solar neutrinos pass through the very dense Sun core.
Electron neutrinos can interact forward with the solar matter
in two ways, while mu or tau neutrinos only do so through NC.
ne,m,t
ne,m,t
Z
e
e
ne
W
e
e
ne
Forward interactions cannot be distinguished from no-interaction
at all  coherent scattering, which affects propagation through
matter. The extra term for ne gives an extra phase to mass
eigenstates which interplays with that which gives rise to
oscillations. The effect has the opposite sign for neutrinos and
antineutrinos (has nothing to do with CP violation).
43
Solar Oscillations and the MSW effect
Formulae are similar to those in vacuum with the replacement:
m 
sin 2 
2
mM2  m 2 sin 2 2  (cos 2 - x) 2
sin 2 2
sin 2 M 
sin 2 2  (cos 2 - x)
2
2 2GF N e En
x
m 2

-
+ for neutrinos
- for antineutrinos
x < cos212
sign of x depends on
sign of m2
x>1
Pee
E 1 MeV
44
Accelerator experiments and their primary goals:
MiniBoone (FNAL):
prove or disprove LSND
K2K (KEK-Kamioka):
check SK, improve m
Near
MINOS (FNAL-Soudan)
check SK, improve m, 13?
Term
OPERA (CERN-LNGS)
see nt appearance in nm beam
T2K (KEK-Kamioka)
try to measure 13 . . .
Longer
Nona (FNAL-Nth Minn.)
try to measure 13 . . .
Many ideas for future
13, CP-violation, ...
Term
45
Conclusions
• Neutrinos played a crucial role in establishing the Standard
Model.
• Neutrinos have mass and mix. This is physics beyond the Standard
Model.
• The masses and pattern of mixing is quite different from that of
quarks. This may be a hint to the physics beyond the SM.
• Accelerator experiments permit the control of E, L and the initial
neutrino state. They will have a role in elucidating fully the
pattern of masses and mixings.
• Progress will require a variety of experiments at different
energies and baselines.
46