Download Neutrinos Theory


Neutrinos Theory
~
Carlos Pena Garay
IAS, Princeton
March 11, 2005
Benasque

References
Neutrino Unbound
http://www.nu.to.infn.it/
Massive Neutrinos : Dirac
n(p,h)
n(p,-h)
CPT
Boost,
if m ≠ 0
Boost,
if m ≠ 0
n(p,-h)
n(p,h)
CPT
Standard Model + right handed
g
 0
Ln  in i  n i 
n i Z n i
2 cos W

g


li U ijW n i  h.c.
2 cos W
 m in in i  h.c.  ...
yv
mn n 
(v R v L  v L v R )
2
1
PR , L  (1   5 )
2
Standard Model + right handed
g
 0
Ln  in i  n i 
n i Z n i
2 cos W

g


li U ijW n i  h.c.
2 cos W
 m in in i  h.c.  ...
yv
m in in i 
(v R v L  v L v R )
2
1
PR , L  (1   5 )
2
Parameters : Dirac
mi
0   c13
0 s13e iδ   c12 s12 0 
 U e1 U e 2 U e3   1 0

 





U i  U μ1 U μ 2 U μ 3    0 c23 s23  
0
1
0
   s12 c12 0 

 U U U   0  s c    s e iδ 0

c
0
0
1

τ2
τ3  
23
23 
13
 τ1

 13

Exercise
m0
Δm  0
2

ΔM  0 0   ij 
2
2
0  
Wave packets : Neutrino osc.
 i ( x, t )  
dp
2 p

( p   pi  ) 2
e
4 2p
e
i ( px  Ei t )
Relativistic neutrinos :
Pv  n   ~  U *iU iU *jU j e
4 E
If losc 
2
m
 lcoh
2 2
L2 ( m ji )
i
L 
2
2
32

E
x
2E
m 2ji
e
E2
 4 2 x
 Osc.
2
m
if losc  L  average oscillatio ns


 Same result
if lcoh  L  Incoherent propagatio n 
Size of the wave packet
Coherent neutrino emission in plasma :
Interrupted by e.m interactions of the source particles
(pressure broadening)
x ~
l
~
v

1  3T
 2 2 2 
N  2Z1 Z 2 e 
3T
m
2
3/ 2
~ 1.4 1017
 T 
m

MeV

 Km  10 12  10 11 Km (Sun)
 N 
Z12 Z 22  3 
 cm 
Reactor : e.m. interactions of produced e 10 9 Km (Reactor)
Accelerator : time scale of weak interactions
~ c  10 3 Km (Accelerat or)
Matter effects
Only the difference of potential is relevant
Net effect :
H int
GF

ve  (1   5 )ve  d 3 pe f(E e , T) e   (1   5 )e  2GF N e
2
l matt
2

2GF N e
 e 0 e  N e
 e i e  N e v i
Some Neutrino Sources
4 E
l osc 
2
m
Solar
10 - 103 Km
Snova 10-11 - 10 7 Km
React
1, 10 2 Km
l coh
E2
 4 2 x
2
m
l
e
matt
2

2GF N e
105  107 Km
10 2 Km
10-8  10  4 Km
10 10 Km
106 , 108 Km
10 4 Km
Atmos 10 - 105 Km
1014 - 10 22 Km
103 - 10 4 Km
Accel 10 2 - 103 Km
1016 - 1018 Km
10 4 Km
ne
Neutrino spectrum
 1%
Solar
 10%
 10%
 1.5%
P(n e  νa )  P(Δ
2
msol
 20%
 16%
?
, sol )
Atmospheric
P(n   ν )  P(Δ
2
M ATM
, ATM )
Reactor : …,Chooz/Palo Verde,…
P( νe  νe )  P( Δ
2
M atm
,chooz )
R  1.01  2.8%  2.7%
Reactor : …,KamLAND
P( νe  νe )  P( Δ
2
msun
, sun )
Accelerator : K2K
2
P(n   ν )  P(ΔM ATM
, ATM )
LSND, Miniboone
n  ne
Proton beam producing


N (n e )  87.9  22.4  6.0
d  30m 20MeV  E  60MeV
LMC
n  n e
8GeV
Booster
magnetic horn decay pipe
25 or 50 m
and target
0.5GeV  E  1GeV
450 m dirt
d  500m
detector
The Neutrino Matrix :SM + n mass
ALL oscillation neutrino data BUT LSND
3  ranges:
 | U e1 | | U e 2 | | U e3 |   0.79  0.88 0.47  0.61 0.00  0.20 

 

| U i |   | U μ1 | | U μ 2 | | U μ 3 |    0.19  0.52 0.42  0.73 0.58  0.82 
 | U | | U | | U |   0.20  0.53 0.44  0.74 0.56  0.81
τ2
τ3  
 τ1

Δm 2
7.3  5 2  9.3 (8.2)
10 eV
ΔM 2
1.6  3 2  3.6 (2.2)
10 eV
0.28  tan 212  0.60 (0.39)
0.51  tan 2 23  2.1 (1.0)
sin 2 13  0.041 (0.005)
The Neutrino Matrix : SM + n mass
ALL oscillation neutrino data BUT LSND
1

(1   )

2

1
| U  i | ~  (1       cos  )
2
1
 (1       cos  )
2
1  ranges:
1
(1   )
2
1
(1       cos  )
2
1
(1       cos  )
2
  0.23  0.04
  0.00  0.06
  0.12
1  cos   1



1

(1  ) 
2

1
(1  ) 
2


SM + n mass
Neutrinos: Cosmological dark matter to be discovered
If lowest mass is negligible, and normal hierarchy
n  0.0009  0.0001
If highest mass is 1 eV
n ~ 0.03 (1 eV)
Plan
I.
Neutrinos as Dirac Particles
II.
Making Neutrinos
III. Neutrinos as Majorana Particles
Neutrino Sources
Reactor
Accelerator
Cosmic 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 Plasma
Photo (Compton)
Bremsstrahlung
Plasmon decay
Pair annihilation
Solar (thermonuclear) Neutrinos
Ga
Cl
SK, SNO
Thermonuclear Neutrinos
Geoneutrinos
Site
U
(106 cm-2s-1)
Th
(106 cm-2s-1)
Kamioka
3.7
3.2
GS
4.2
3.7
Sanduleak 69 202
Supernova 1987A
23 February 1987
Tarantula Nebula
Large Magellanic Cloud
Distance 50 kpc
(160.000 light years)
Stellar Collapse and Supernova Explosion
Newborn Neutron Star
~ 50 km
Neutrino
Cooling
Proto-Neutron Star
r  rnuc  3 1014 g cm3
T  30 MeV
Collapse
Explosion
(implosion)
Neutrino Signal of Supernova 1987A
Kamiokande (Japan)
Water Cherenkov detector
Clock uncertainty 1 min
Irvine-Michigan-Brookhaven (US)
Water Cherenkov detector
Clock uncertainty 50 ms
Baksan Scintillator Telescope
(Soviet Union)
Clock uncertainty +2/-54 s
Within clock uncertainties,
signals are contemporaneous
Limits on Supernova Relic Neutrinos
Super-Kamiokande :
n e  1.2 cm-2s-1 (90%CL)  19.3 MeV
Ando et al (2004)
Atmospheric Neutrinos
Undiscovered neutrino sources

n

n
+
Sources above 10GeV
GRBs?
by Eli Waxman
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  sources
We start with 1 : 2 : 0
Decoherenc e : wave packets separate n i
 (n i ) | U ei |2 2 | U i |2



 23  2 , 13  0 
 ( cos 2 12  sin 2 12 , sin 2 12  cos 2 12 , 1 )
We end with 1 : 1 : 1 in mass basis (present precision ~ 10%)
 We end with 1 : 1 : 1 in flavor basis
Man-made Neutrino Sources : Reactors
Goal : Measure 13
2
2
1
.
27

m
L
1
.
27

m
2
4
2
13
12 L
Pee 1  sin 213 sin
 cos 13 sin 212 sin
En
En
Man-made Neutrino Sources : Accelerator
• conventional beams / superbeams
• -beams
• neutrino factories