March 11, 2005 Benasque
Neutrinos Theory Neutrinos Theory
Carlos Pena Garay
IAS, Princeton
~
References References
Neutrino Unboundhttp://www.nu.to.infn.it/
Massive Neutrinos : Dirac Massive Neutrinos : Dirac
(p,h) (p,-h)CPT
(p,h)(p,-h)CPT
Boost, if m ≠ 0
Boost, if m ≠ 0
Standard Model + right handed Standard Model + right handed
... h.c. m
h.c. cos2
-
cos2i
i
0
ii
iijiW
iiW
ii
WUlg
Zg
L
)1(2
1
)(2
vm
5,
LR
RLLR
P
vvvvy
Standard Model + right handed Standard Model + right handed
... h.c. m
h.c. cos2
-
cos2i
i
0
ii
iijiW
iiW
ii
WUlg
Zg
L
)1(2
1
)(2
vm
5,
i
LR
RLLRii
P
vvvvy
Parameters : Dirac Parameters : Dirac
100
0
0
0
010
0
0
0
001
1212
1212
1313
1313
2323
2323
321
321
321
cs
sc
ciδes
iδesc
cs
sc
UUU
UUU
UUU
U
τττ
μμμ
eee
i
im
20
ij 002 mΔ 02 MΔ0m
Exercise
2
22
2
22
2
2
)(
322**
)(4
)(
~
2
),(
E
mLL
E
mi
jjii
tEpxi
pp
pi
ji
x
ji
ip
i
eeUUUUvP
eedp
tx
Osc. 24l 4
l If2
2
coh2osc
m
E
m
Ex
Wave packets : Neutrino osc. Wave packets : Neutrino osc.
Relativistic neutrinos :
Same result
npropagatio Incoherent Ll if
nsoscillatio average Ll if
coh
osc
Coherent neutrino emission in plasma : Interrupted by e.m interactions of the source particles (pressure broadening)
Reactor : e.m. interactions of produced e-
Accelerator : time scale of weak interactions
(Sun) 1010 Km 104.1~3
231
~v
l~ 1112
322
21
2/3
17
2
222
21 Km
cmN
ZZ
MeVT
m
mT
eZZT
Nx
or)(Accelerat Km 10~
(Reactor) Km 10
3
9
c
Size of the wave packet Size of the wave packet
Only the difference of potential is relevant
Net effect :
i
0
vei
e
Nee
Nee
eF NG2
2lmatt
eFeeeF NGeepdvv
GH 2 )1( T),f(E )1(
25e
35int
Matter effects Matter effects
Some Neutrino SourcesSome Neutrino Sources
Km 10 Km 10-10 Km 10-10 Accel
Km 10-10 Km 10-10 Km 10-10 Atmos
Km 10 Km 10 ,10 Km 10 1, React
Km 10 Km 1010 Km 10-10 Snova
Km 10 Km 1010 Km 10-10Solar
2
2l 24l
4l
4181632
4322145
4862
1048-711-
2753
ematt2
2
coh2osc
eF
xNGm
E
m
E
SolarSolar
),2solsolae mP(Δ)νP(
Neutrino spectrum%1
%10%10
%5.1
%16%20
?
e
AtmosphericAtmospheric
),2ATMATMMP(Δ)νP(
Reactor : …,Chooz/Palo Verde,…Reactor : …,Chooz/Palo Verde,…),( 2
choozatmee MΔP)ννP(
%7.2%8.201.1 R
Reactor : …,KamLANDReactor : …,KamLAND),( 2
sunsunee mΔP)ννP(
Accelerator : K2KAccelerator : K2K),2
ATMATMMP(Δ)νP(
LSND, MinibooneLSND, Miniboone
e
8GeVBooster
magnetic hornand target
decay pipe25 or 50 m
LMC
450 m dirt detectorabsorber
e
0.64.229.87
Proton beam producing
)( eN
MeVEMeV 6020 md 30
GeVEGeV 15.0 md 500
The Neutrino Matrix :SM + The Neutrino Matrix :SM + massmassALL oscillation neutrino data BUT LSND
)2.8( 3.9eV10
3.725
2m
Δ
)2.2( 6.3eV10
M6.1
23
2
Δ
3 ranges
81.056.074.044.053.020.0
82.058.073.042.052.019.0
20.000.061.047.088.079.0
||||||
||||||
||||||
||
321
321
321
τττ
μμμ
eee
i
UUU
UUU
UUU
U
(0.39) 60.0tan0.28 122
(1.0) 1.2tan0.51 232
(0.005) 041.0sin 132
The Neutrino Matrix : SM + The Neutrino Matrix : SM + massmass
ALL oscillation neutrino data BUT LSND
)1(2
1)cos1(
2
1)cos1(
2
1
)1(2
1)cos1(
2
1)cos1(
2
1
)1(2
1)1(
2
1
~||
iU
04.023.0 06.000.0
12.01cos1
1 ranges
SM + SM + massmass
0001.00009.0
Neutrinos: Cosmological dark matter to be discovered
eV) 1( 03.0~
If lowest mass is negligible, and normal hierarchy
If highest mass is 1 eV
PlanPlan
I. Neutrinos as Dirac Particles
II. Making Neutrinos
III. Neutrinos as Majorana Particles
Neutrino SourcesNeutrino Sources
Reactor
Accelerator
Cosmic Neutrino BackgroundCosmic Neutrino Background
56 cm-3 at 1.9K (0.17 meV)
Possible mechanical effect : torque of order GF if target and neutrino background are polarized (Stodolsky effect) and net neutrino-antineutrino asymmetry
Still far from observability, awaiting for future technology
Neutrinos from Thermal PlasmaNeutrinos from Thermal Plasma
BremsstrahlungBremsstrahlung
Photo (Compton)Photo (Compton) Plasmon decayPlasmon decay Pair annihilationPair annihilation
Solar (thermonuclear) NeutrinosSolar (thermonuclear) Neutrinos
SK, SNOClGa
Thermonuclear NeutrinosThermonuclear Neutrinos
GeoneutrinosGeoneutrinos
Site U
(106 cm-2s-1)
Th
(106 cm-2s-1)
Kamioka 3.7 3.2
GS 4.2 3.7
Sanduleak Sanduleak 69 69 202202
Large Magellanic Cloud Large Magellanic Cloud Distance 50 kpcDistance 50 kpc (160.000 light years)(160.000 light years)
Tarantula NebulaTarantula Nebula
Supernova 1987ASupernova 1987A 23 February 198723 February 1987
Stellar Collapse and Supernova ExplosionStellar Collapse and Supernova ExplosionCollapse (implosion)Collapse (implosion)ExplosionExplosionNewborn Neutron StarNewborn Neutron Star
~ 50 km~ 50 km
Proto-Neutron StarProto-Neutron Star
nucnuc 3 3 10101414 g cm g cm33
T T 30 MeV 30 MeV
NeutrinoNeutrinoCoolingCooling
Neutrino Signal of Supernova 1987ANeutrino Signal of Supernova 1987A
Within clock uncertainties,Within clock uncertainties,signals are contemporaneoussignals are contemporaneous
Kamiokande (Japan)Kamiokande (Japan)Water Cherenkov detectorWater Cherenkov detectorClock uncertainty Clock uncertainty 1 min1 min
Irvine-Michigan-Brookhaven (US)Irvine-Michigan-Brookhaven (US)Water Cherenkov detectorWater Cherenkov detectorClock uncertainty Clock uncertainty 50 ms50 ms
Baksan Scintillator TelescopeBaksan Scintillator Telescope(Soviet Union)(Soviet Union)Clock uncertainty +2/-54 sClock uncertainty +2/-54 s
Limits on Supernova Relic NeutrinosLimits on Supernova Relic Neutrinos
Super-Kamiokande
MeV 19.3 (90%CL) scm 1.2 -1-2 e
Ando et al (2004)
Atmospheric NeutrinosAtmospheric Neutrinos
+
Undiscovered neutrino sourcesUndiscovered neutrino sources
Neutrinos fromthe Sun
Neutrinos fromthe Earth
GRBs?
by Eli Waxman
Sources above 10GeV Sources above 10GeV
Sources above 10GeV Sources above 10GeV
90% CL upper limits in 10-8 cm-2s-1 for E-2 spectrum
from AMANDA II (2000-2002)
E-2.7
E-3.0
Flavor ratio for far Flavor ratio for far sources sources
basisflavor in 1:1:1 with end We
10%) ~precision (present basis massin 1:1:1 with end We
) 1 ,cossin ,sincos ( 0,2
||2||)(
separate packets wave: eDecoherenc
0:2:1 start with We
122
122
122
122
1323
22
ieii
i
UU
Man-made Neutrino Sources : ReactorsMan-made Neutrino Sources : Reactors
E
Lm27.1sin2sincos
E
Lm27.1sin2sin1P
212
122
134
213
132
ee
Goal : Measure
Man-made Neutrino Sources : AcceleratorMan-made Neutrino Sources : Accelerator
• conventional beams / superbeams
• -beams• neutrino factories