Post on 23-Mar-2021
Neutrino oscillation physics
Alberto Gago PUCP
CTEQ-FERMILAB School 2012 Lima, Perú - PUCP
Outline
• Introduction
• Neutrino oscillation in vacuum
• Neutrino oscillation in matter
• Review of neutrino oscillation data
• Conclusions
Historical introduction
Observed Spectrum – Continuos three body decay
(1930) W. Pauli propose a new particle for saving the incompatibility between the observed electron energy spectrum and the expected.
XeZAZA )1,(),(
Expected Spectrum-Monoenergetic two body decay
eZAZA )1,(),(
1,, ZAMZAMQEe
XeEZAMZAMQE 1,,
Historical introduction
(1956)- F. Reines y C.Cowan detected for the first time a neutrino through the reaction
This search was called as poltergeist project.
First reactor neutrino experiment
(1962)-Lederman-Schwartz-Steinberger, discovered in Brookhaven the muon antineutrino through the reaction:
they did not observe:
Confirming that
e
First neutrino experiment that used
Historical introduction
(2000) In Fermilab the DONUT collaboration observed for the first time events of . They detected four events.
X
SD
Neutrinos
8
2
2
cm
cm10
10
10
)(
)(41
33
e
ee
e
Z
0082.09840.2 N
Active neutrinos
Neutrinos -SM
Therefore in the Standard Model (SM) we have:
Neutrinos are fermions and neutrals
LLL
e
e
Left-handed doublet
Only neutrinos of two kinds have been seen in nature: left-handed –neutrino right-handed- antineutrinos
Neutrino –SM
In the SM the neutrinos are consider massless (ad-hoc assumption) ….BUT we know that they have non-zero masses because they can change flavour or oscillate …
Neutrino oscillations -history
).( to analogy
in of idea the time first the
for suggested Pontecorvo Bruno
0000 KKKK
)1957(
(1962) Maki, Nakagawa and Sakata proposed the mixing
Neutrino oscillation in vacuum
.
.
.
.
2
1
e
Flavour conversion
k
k
kU *
,,e seigenstate flavour 3,2,1k seigenstate mass
ikki
The flavour (weak) eigenstates are coherent superposition of the mass eigenstates
Non-diagonal
332211 UUU
Neutrino mixing
• The mixing matrix is appearing in the charged current interaction of the SM :
,,
*
,,
2
2
e k
kLLkLkLk
CC
SM
e k
LLLL
CC
SM
WlUWlUg
L
WlWlg
L
analog to the quark mixing case
LkL
LkL
l
l
LkL
LkL
l
l
CKM
U
L
D
LL
l
LPMNS UVVVVU
PMNS=Pontecorvo-Maki-Nakagawa-Sakata
D= down quarks U= up quarks
Neutrino oscillation in vacuum the scheme
Detector
Propagation
k
Source
Flavour states Flavour states
v v
Mass eigenstates
*
kU
kU
Coherent superposition of the mass eigenstates The flavour conversion happens
at long distances!
Neutrino oscillation in vacuum
• Starting point :
• Evolving the mass eigenstates in time and position (Plane wave approximation):
seigenstateflavourseigenstatemass α,βi,k
amplitudeyprobabilitxtA
iii
i
i
e
i
iiii
UxpitEiU
xpitEiUxt
),(
*
,,
*
exp
exp),(
0,0,,
xtUe
kk
i
iiU
*
2
*22
exp),(),( iii
i
i UxpitEiUxtxtAP
Neutrino oscillation in vacuum
Analyzing:
onscontributi mass neglecting energy neutrino the is
Lt assumption
E
LE
m
pE
LpELpELptE i
ii
iiiiii
2)(
222
222
jiij mmm
L
E
miUUUUP
ij
ji
jjii2
exp
2
,
**
We are using L instead of x
Neutrino oscillation in vacuum
LE
miUUUUUUELP
ij
ji
jjiii
i
i2
expRe2),(
2
**22
energy neutrino
distance detector - source
:
:
E
L
constant term oscillating term
2
24
22 ij
oscosc
ij
m
ELL
E
m
Oscillation wavelength
1,,,,
ee
PP
Valid if there is no sterile neutrinos
Neutrino oscillation in vacuum
LE
miL
E
mUUUUUUUUELP
UUUUUU
LE
miUUUUUUELP
ijij
ji
jjii
ji
jjii
ji
jjiii
i
i
ij
ji
jjiii
i
i
2sin
2cosRe2Re2),(
Re2
2expRe2),(
22
****
**22
2
**22
us ing
LE
mUUUU
LE
mUUUUELP
ij
ji
jjii
ij
ji
jjii
2sinIm2
4sinRe4,
2
**
2
2**
Neutrino oscillation in vacuum
• For the antineutrino case:
*UUUi
ii
LE
mUUUU
LE
mUUUUELP
ij
ji
jjii
ij
ji
jjii
2sinIm2
4sinRe4,
2
**
2
2**
This is the only difference…we will return to this later
Two neutrino oscillation
cossin
sincos)(U
21
21
cossin
sincos
e
LE
m
LE
m
LE
miL
E
m
LE
mi
LE
miUUUU
ULE
miUP
ee
ii
i
i
ee
4sin2sin
2cos12sin
2
1
2sin
2cos1sincos
2expcossinsincos
2exp
2exp
2
2122
2
212
22
21
2
2122
22
21
2
2
212
*
21
*
1
222
*
,
Two neutrino oscillation
I
In the two neutrino framework we have:
yprobabi l i t trans ition
yprobabi l i t survival
phase noscillatioamplitude noscillatio
LE
mELP
LE
mELP
e
ee
4sin2sin,
4sin2sin1,
2
2122
2
2122
ELPELP
ELPELP
,,
,,
Two neutrino oscillation
• Introducing units to L and E
)(
)(27.1)(
)(27.1
4
2
21
2
21
2
21 kmGeV
eVorm
MeV
eV 22
LE
mL
E
mL
E
m
kmeV
GeVm
eV
MeV22 )(
)(47.2
)(
)(47.2
42
21
2
21
2
21 m
E
m
E
m
ELosc
Oscillation regimes
oscL
LL
E
mL
E
m
44
2
21
2
21
• Oscillation starting
• Ideal case
• Fast oscillations
114
2
21
oscL
LL
E
m
2
1~)1(
4
2
21
oscL
LL
E
m
114
2
21
oscL
LL
E
m
04
00
02
2
21
1212
2
21
E
Lm
mmmmm or
sen2
No oscillation
Oscillation regimes
Short distance
Ideal distance
Long distance
2sin2
1 2
'2
'22
212
2
2'
2
2'
27.1
2
dEe
dEeE
Lm
P
E
E
e EE
EE
s in
s in2
Fixed E
Sensitivity plot
c
a
b
Not sensitivity
sensitivity
L
LL
L
L
PL
Em
PL
Em
E
LmP
E
LmP
P
27.1log2log2
1)(log
27.12
127.12
27.12
22
1
22
21
2
21
2
2
21
2
21
sin
sinsinc)
sinsinb)
sina)
2
22
2
LP lower probability limit for having a positive signal in a detector
ysensitivit maximum b @
2~27.1 2
E
Lm
Exclusion plot
allowed
excluded
LPupper limit of the oscillation probability PPL
⟨L/E⟩ = 18km/GeV
Positive signal
⟨L/E⟩ = 1km/GeV
0.05 < P < 0.15 0.001< P < 0.005
The mixing matrix
1
)1(2 22
2
*
UUUU
NNNNN
NU
i
iiUU
NN
condition the satisfies and unitary is matrix ng mixi the
parameters 2 has matrix complex general A
from
rows different between ityorthogonalrow eachof length unitarity
phases complex
angles rotation has matrix mixing unitary
phases complexangles rotation
2
)1(2
)1(
2
)1(
2
)1(2
NN
NN
NNNNN
phases complex )(
angles rotation )(
:scheme 3 In
62
133
32
133
-
The mixing matrix
L
L
L
i
i
i
TYPECKM
i
i
LLL
LkLk
e
e
e
eUe
e
lU
e
100
00
00
100
00
00
2
1
321
* : within tionrepresenta 33 matrix unitary a written
rephas ing by absorbed be can and
nosantineutri neutrinos neutrinos Dirac are IF *
invariant are lagrangian theof terms Other
and
: rephas ing by absorbed be can and , phases The *
phase) complex 1 & angles rotation
21
)(
,
'
3(
s
elel
UU
L
i
LL
i
elL
e
CKM
l
The mixing matrix
• If neutrinos are equal than antineutrinos
condition Majorana
noantineutrineutrino
TC C
2
12
phases physical
2
2
angles mixing
Neutrinos Majorana Neutrinos Dirac
:scheme 3 the In
3)1()2)(1(
3)1(
3)1(
NNNN
NNNN
Charge conjugation operator
fixed are phases neutrino the since absorbed be not can and 21
CiCiii vevevevevv 2if instance, For zero be to has
3-mass scheme
2
1
2
2
m
m
2
3m2
1
2
2
m
m
23m
Normal Hierarchy Inverted Hierarchy
22 eVeV 52
21
32
31 1010 mm
2m
M
D
D
i
i
U
i
i
M
e
e
cs
sc
ces
esc
cs
scU
100
00
00
100
0
0
0
010
0
0
0
001
2
1
1212
1212
1313
1313
2323
2323
The mixing matrix in 3 scheme
03
withii
i
DMDM eUDUU
Dirac CP phase
Majorana phases
…Tomorrow we will see the current measurements of these angles done by the experiments
:Notation ijijijij sc sincos
Majorana phases and neutrino oscillations
2
*
2
*
2
*2
),(
D
i
xpitEi
i
D
i
iD
i
xpitEi
i
iD
i
M
i
xpitEi
i
M
i
UeU
eUeeUUeUxtA
ii
i
ii
i
ii
Only the dirac phase is observable in neutrino oscillation
CP violation
,, 3,2,1
*1
,, 3,2,1
*
2
2
e k
LkLkkLLkCP
CC
lCP
e k
kLLkLkLk
CC
l
WlUWlUg
ULU
WlUWlUg
L
UUCP * needs
CP violation
• What does CP mean in neutrino oscillation ?:
PPCP
RR
P
LL
C
LL
violated)is
andif
CPPP
UU ii
(
*
CP violation
LE
mUUUUPPP
ij
ji
jjii2
sinIm4,
2
**
Jarlskog invariant CPjjii JUUUU **Im
Independent of the mixing matrix parameterization =rephasing invariant
ji
ji
,,)(
,,)(
andin nspermutatio anticycl ic
andin nspermutatio cycl ic
CP violation
sen sencossencossencos 2323121213132CPJ
CP violation phase All the mixing angles have to be
non-zero to have CP violated.
013
CPS
CP
CP
LE
mL
E
mL
E
mJ
LE
mL
E
mL
E
mJP
44416
2224
2
31
2
23
2
12
2
31
2
23
2
12),(
s ins ins in
s ins ins in
In particular we just found out that
CP violation
• It is interesting to note that :
• Checking for CPT
conserved is CPT
PPCPT
LL
T
LL
P
RR
C
RR
,, ODDTCP PPPPPP
ODDTCP PP
Useful approximations
• In the three neutrino framework we have:
• Case 1 : sensitive to the large scale :
• Case 2: sensitive to the small scale
2
2
31
2
212
21
2
31
2
32 10~
m
mmmm with
neglect we 2
21
22
21
2
32 10)1(~4
)1(~4
mLE
mL
E
m
out averaged are related terms
22
32
2
21 10)1(1
~4
)1(~4
LE
mL
E
m
2
21
2
31
2
32 mmm
Useful approximations
• Case 1: sensitive to the large scale
LE
mUU
LE
mUUUUUU
LE
mUUUUL
E
mUUUUP
Smmm
eff
CP
4sin4
4sinRe4
4sinRe
4sinRe4
)0(0
2
312
2sin
2
3
2
3
2
312*
22
*
113
*
3
2
312*
223
*
3
2
312*
113
*
3
2
21
2
32
2
31
2
and
Similar structure to the two generation formula
Useful approximations
• Case 1: sensitive to the large scale
LE
mcscsP
LE
msP
LE
mcP
LE
mP
u
e
ee
441
42
42
421
2
312
13
2
23
2
13
2
23
2
3113
2
23
2
3123
4
13
2
3113
2
22
22
22
sen-1
sensen
sensen
sensen
Explicit formulas
Useful approximations
• Case 2: sensitive to the small scale
LE
m
UU
UUUU
LE
mUUUU
UUUULE
mUUP
eff
4sin411
4sin4121
2
1
2
14
4sin41
2
212
2sin
22
1
2
2
2
1
2
222
3
4
3
2
2122
1
2
2
2
3
2
3
2
1
2
3
2
2
2
3
2
2122
1
2
2
2
Similar structure for the two generation formula
averaged out
2
1
4sin
2
32312
L
E
m
Useful approximations
• Case 2: sensitive to the small scale
24
13
4
13
3
2
2112
4
13
4
13
3
421
eeee
ee
PcsP
LE
mcsP
22 sensen
Approximation
Full Probability
scale2
31m
scale2
21m
Useful approximations
• We can get a better approximation for the oscillation formula when we expand this in small parameters up to second order. We are in the case of
sensitivity of the large scale.
• These small parameters are :
23121313
2
13
2
12
2
13
2
122
12
2
2
132
13
22
23
2sin2sin2sin~
4sin
44cos
~
4sin2sin
4sin2sin
cJ
LE
m
E
mL
E
mJ
LE
m
LE
msP
ee
c
223
E
Lm
m
m
2,
2
21
2
31
2
2113
,
leading term –P2 approximation
Now it is appearing and 2
12m