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Neutrino oscillation physics
Alberto Gago PUCP
CTEQ-FERMILAB School 2012Lima, Perú - PUCP
Outline
• Introduction • Neutrino oscillation in vacuum • Neutrino oscillation in matter • Review of neutrino oscillation data • Conclusions
Historical introduction
Observed Spectrum – Continuosthree 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
82
2
cmcm
101010
)()(
41
33
eee
e
Z
0082.09840.2 N
Active neutrinos
Neutrinos -SMTherefore 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-hocassumption)
….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
kk
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 kkLLkLkLk
CCSM
e kLLLL
CCSM
WlUWlUg
L
WlWlg
L
analog to the quark mixing case
LkL
LkL
l
l
LkL
LkL
l
l
CKMUL
DLL
lLPMNS 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 themass 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
iiii
ie
iiiii
UxpitEiU
xpitEiUxt
),(
*
,,
*
exp
exp),(
0,0,,
xtUe
kk
i
iiU *
2
*22
exp),(),( iiii
i UxpitEiUxtxtAP
Neutrino oscillation in vacuum
Analyzing:
onscontributi mass neglecting energy neutrino the isLt assumption
E
LE
mpE
LpELpELptE i
ii
iiiiii 2)(
222
222jiij mmm
L
E
miUUUUP ij
jijjii 2exp
2
,
**
We are using L instead of x
Neutrino oscillation in vacuum
L
E
miUUUUUUELP ij
jijjiii
ii 2
expRe2),(2
**22
energy neutrino distance detector - source
:
:
E
L
constant term oscillating term
2
24
22 ij
oscoscij
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
jijjii
jijjii
jijjiii
ii
ij
jijjiii
ii
2sin
2cosRe2Re2),(
Re2
2expRe2),(
22****
**22
2**22
using
LE
mUUUU
LE
mUUUUELP
ij
jijjii
ij
jijjii
2sinIm2
4sinRe4,
2**
22**
Neutrino oscillation in vacuum• For the antineutrino case:
*UUUi
ii
LE
mUUUU
LE
mUUUUELP
ij
jijjii
ij
jijjii
2sinIm2
4sinRe4,
2**
22**
This is the only difference…we will return to this later
Two neutrino oscillation
cossin
sincos)(U
21
21
cossin
sincos
e
LEm
LEm
LEm
iLEm
LEm
i
LEm
iUUUU
ULE
miUP
ee
ii
ii
ee
4sin2sin
2cos12sin
21
2sin
2cos1sincos
2expcossinsincos
2exp
2exp
22122
2212
2221
22122
2221
2221
2*21
*1
222
*
,
Two neutrino oscillation
IIn the two neutrino framework we have:
yprobabilit transition
yprobabilit survival
phase noscillatioamplitude noscillatio
LEm
ELP
LEm
ELP
e
ee
4sin2sin,
4sin2sin1,
22122
22122
ELPELP
ELPELP
,,
,,
Two neutrino oscillation • Introducing units to L and E
)(
)(27.1)(
)(27.1
4
221
221
221 km
GeVeV
ormMeV
eV 22
LEm
LEm
LEm
kmeV
GeVm
eVMeV
22 )()(
47.2)(
)(47.2
4221
221
221 m
EmE
mE
Losc
Oscillation regimes
oscLL
LE
mL
Em
44
221
221
• Oscillation starting
• Ideal case
• Fast oscillations
114
221
oscLL
LEm
21
~)1(4
221
oscLL
LEm
114
221
oscLL
LEm
04
00
02
221
1212221
E
Lm
mmmmm or
sen2
No oscillation
Oscillation regimes
Short distance
Ideal distance
Long distance
2sin21 2
'2
'22212
2
2'
2
2'
27.1
2
dEe
dEeE
Lm
P
E
E
e EE
EE
sinsin2
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
2221
221
2
221
221
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
EL
m
Exclusion plot
allowed
excluded
LPupper limit of the oscillation probabilityPPL
⟨L/E = 18km/GeV ⟩
Positive signal
⟨L/E = 1km/GeV ⟩
0.05 < P < 0.150.001< P < 0.005
The mixing matrix
1
)1(2 22
2
*
UUUU
NNNNN
NU
iiiUU
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 complexangles 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
Li
i
iTYPECKM
i
i
LLL
LkLk
e
e
e
eUe
e
lU
e
100
00
00
100
00
002
1
321
* : within tionrepresenta 33 matrix unitary a written
rephasing by absorbed be can and nosantineutri neutrinos neutrinos Dirac are IF *
invariant are lagrangian theof terms Other
and
: rephasing by absorbed be can and , phases The *
phase) complex 1 & angles rotation
21
)(,
'
3(
s
elel
UU
Li
LLi
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
21
22
m
m
23m
21
22
m
m
23m
Normal Hierarchy Inverted Hierarchy
22 eVeV 5221
3231 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
iDMDM 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
),(
Di
xpitEi
i
Di
iDi
xpitEi
i
iDi
Mi
xpitEi
i
Mi
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 kLkLkkLLkCP
CClCP
e kkLLkLkLk
CCl
WlUWlUg
ULU
WlUWlUg
L
UUCP * needs
CP violation
• What does CP mean in neutrino oscillation ?:
PPCP
RR
P
LL
C
LL
violated)isandifCPPP
UU ii
(
*
CP violation
L
E
mUUUUPPP ij
jijjii 2
sinIm4,2
**
Jarlskog invariant CPjjii JUUUU **Im
Independent of the mixing matrix parameterization =rephasing invariant
ji
ji
,,)(
,,)(
andin nspermutatio anticyclicandin nspermutatio cyclic
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
231
223
212
231
223
212
),(
sinsinsin
sinsinsin
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
2231
2212
21231
232 10~
mm
mmm with
neglect we 221
2221
232 10)1(~
4)1(~
4mL
Em
LEm
out averaged are related terms
2232
221 10)1(
1~
4)1(~
4
L
E
mL
E
m
221
231
232 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
2312
2sin
2
3
2
3
2312*
22*
113*
3
2312*
223*
3
2312*
113*
3
221
232
231
2
and
Similar structure to the two generation formula
Useful approximations
• Case 1: sensitive to the large scale
LEm
cscsP
LE
msP
LEm
cP
LEm
P
u
e
ee
441
42
42
421
2312
13223
213
223
231
13223
231
23413
231
13
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
2212
2sin
22
1
2
2
2
1
2
222
3
4
3
22122
1
2
2
2
3
2
3
2
1
2
3
2
2
2
3
22122
1
2
2
2
Similar structure for the two generation formula
averaged out
21
4sin
232312
L
E
m
Useful approximations• Case 2: sensitive to the small scale
2413
413
3
221
12413
413
3
421
eeee
ee
PcsP
LE
mcsP
22 sensen
ApproximationFull Probability
scale231m
scale221m
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
213
212
213
2122
122
2132
1322
23
2sin2sin2sin~
4sin
44cos~
4sin2sin
4sin2sin
cJ
LEm
Em
LEm
J
LEm
LEm
sPee
c
223
E
Lm
m
m
2,
221
231
221
13
,
leading term –P2 approximation
Now it is appearing and 2
12m