Transcript Big World of Small Neutrinos Hitoshi Murayama QuarkNet July 1, 2002

Big World of Small Neutrinos
Hitoshi Murayama
QuarkNet
July 1, 2002
Neutrinos are Everywhere
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“Wimpy and Abundant”
Neutrinos are Everywhere
• They come from the Big Bang:
– When the Universe was hot, neutrinos were created
equally with any other particles
– They are still left over: ~300 neutrinos per cm3
• They come from the Sun:
– Trillions of neutrinos going through your body every
second
• They are shy:
– If you want to stop them, you need to stack up lead
shield up to three light-years
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Outline
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Introduction
Neutrinos in the Standard Model
Evidence for Neutrino Mass
Solar Neutrinos
Implications of Neutrino Mass
Why do we exist?
Conclusions
(LSND)
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Neutrinos in the Standard Model
Puzzle with Beta Spectrum
F. A. Scott, Phys. Rev. 48, 391 (1935)
• Three-types of
radioactivity: a, b, g
• Both a, g discrete
spectrum because
Ea, g = Ei – Ef
• But b spectrum
continuous
Bohr: At the present stage of atomic theory, however, we may say
that we have no argument, either empirical or theoretical, for
upholding the energy principle in the case of b-ray disintegrations
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Desperate Idea of Pauli
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Three Kinds of Neutrinos
• There are three
• And no more
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Neutrinos are Left-handed
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Neutrinos must be Massless
• All neutrinos left-handed  massless
• If they have mass, can’t go at speed of light.
• Now neutrino right-handed??
 contradictionQuarkNet
 can’t be massive
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Anti-Neutrinos are Right-handed
• CPT theorem in
quantum field theory
– C: interchange
particles & antiparticles
– P: parity
– T: time-reversal
• State obtained by CPT
_
from nL must exist: nR
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Other Particles?
• What about other particles? Electron,
muon, up-quark, down-quark, etc
• We say “weak interaction acts only on lefthanded particles” yet they are massive.
Isn’t this also a contradiction?
No, because of the Higgs condensate.
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Universe is filled with Higgs
• Empty looking space is filled with Higgs
• Particles bump on it, but not photon because Higgs neutral.
• Can’t go at speed of light (massive), and right-handed and
left-handed particles mix  no contradiction
0.511 MeV/c2
105 MeV/c2
176,000 MeV/c2
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But neutrinos can’t
bump because there
isn’t a right-handed
one  stays massless
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Standard Model
• Therefore, neutrinos are strictly massless in
the Standard Model of particle physics
Finite mass of neutrinos imply the Standard
Model is incomplete!
• Not just incomplete but probably a lot more
profound
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Lot of effort since ‘60s
Finally convincing
evidence for “neutrino
oscillation”
Neutrinos appear to
have tiny but finite mass
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Evidence for Neutrino Mass
Super-Kamiokande (SuperK)
• Kamioka Mine in
central Japan
• ~1000m
underground
• 50kt water
• Inner Detector
– 11,200 PMTs
• Outer Detector
– 2,000 PMTs
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Michael Smy
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SuperKamiokaNDE
Nucleon Decay Experiment
• pe+p0, K+n, etc
• Cosmic rays isotropic
– So far not seen
– Atmospheric neutrino
main background
– Atmospheric neutrino
up-down symmetric
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A half of nm lost!
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Neutrino’s clock
• Time-dilation: the
clock goes slower
v2
  t 1  2
c
• At speed of light v=c,
clock stops
• But something seems
to happen to neutrinos
on their own
• Neutrinos’ clock is
going
• Neutrinos must be
slower than speed of
light
Neutrinos must have a
mass
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The Hamiltonian
• The Hamiltonian of a freely-propagating
particle is simply
H  c2 p 2  m 2 c 4
• Therefore, time evolution of a momentum
eigenstate is just the phase factor
p,t  e
iHt /
p, 0  e
i c 2 p2 m 2 c 4 t /
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p,0
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Mass Matrix
• But wait! A set of particles can have a mass
matrix if they have the same quantum
numbers.
• In case of (u,c,t) quarks, (d,s,b) quarks, and
(ne,nm,n) neutrinos, their masses are 33
mass matrices.
• Correspondingly, the Hamiltonian is also a
33 matrix:
H  c2 p 2  m 2 c 4
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22 Mass Matrix
• Discuss 22 mass matrix for simplicity
• Without a loss of generality, parameterize:
2
2 
2   cos 2 sin 2 


1

m
m
m
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12
2

m2   2

m



0
2
 1
2  sin 2 cos 2 
 m 21 m 22 
2  cos  


cos

m
2
2
m

(m
)



• Eigenstates:
0 
2  sin  
 sin  
• Eigenvalues:
2  sin  

sin


m
2
m2 

(m
)


0 
 cos  
2  cos  
2

m
E  c | p |2  m02 
 c2
2  QuarkNet

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Two-Neutrino Oscillation
• When produced (e.g., p+m+nm), neutrino is
a particular type
 1
 cos  
 sin  
n m     cos  |
  sin  

 0
  sin  
 cos  
• After time evolution:
 cos   iE t /
n m , t  cos  
e
  sin  
 sin   iE t /
 sin  
e
 cos  
• No longer 100% nm, partly n!
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Survival Probability
• Probability for nm to be still nm after t
P  n m nm ,t
2
2
iE t /
iE
t
/
2
2

e
cos   e
sin 
2 3
m
c
2
2
 1  sin 2 sin
t
4p
2 4
m
c GeV ct
2
2
 1  sin 2 sin 1.27
eV 2 c p km
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Survival Probability
p=1 GeV/c, sin2 2=1
m2=310–3(eV/c2)2
Half of the up-going
ones get lost
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More cross checks
• Multi-ring events can be used to provide useful
cross checks (Hall, HM)
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More to come
250km
818 events if no oscillation
56 events observed
MINOS (IL  MN) 2005
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Public Interest in Neutrinos
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Solar Neutrinos
How the Sun burns
• The Sun emits light because nuclear fusion
produces a lot of energy
2 Lsun
1
10
1
2
n 

7
10
sec
cm
25MeV 4p (1AU) 2
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We don’t get enough
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Neutrino oscillation?
LMA
• Can explain the data
• Two major solutions:
– LMA
– LOW/Quasi-Vacuum
(Friedland)
• Biggest systematics is
the solar neutrino flux
calculations
• Problem with the solar
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LOW
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Josh Klein, Lepton Photon 2001
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SNO comes to the rescue
• Charged Current:ne
CC  1.76  0.05  0.09 106 cm2 sec 1
• Neutral Current: ne+nm+n
 NC  5.09
0.44 0.46
0.43 0.43
106 cm2 sec 1
• 5.3s difference
 nm, are coming from the Sun!
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Wrong Neutrinos
• Only ne produced in the
Sun
• Wrong Neutrinos nm, are
coming from the Sun!
• Somehow some of ne were
converted to nm, on their
way from the Sun’s core
to the detector
 neutrino oscillation!
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Dark Side of Neutrino Oscillation
• Traditional parameterization of neutrino
oscillation in terms of (m2, sin22) covers
only a half of the parameter space
(de Gouvêa, Friedland, HM)
• Convention: n2 heavier than n1
– Vary  from 0˚ to 90˚ n1  n e cos   n m sin 
– sin22 covers 0˚ to 45˚ n2  n e sin   n m cos 
– Light side (0 to 45˚) and Dark Side (45˚ to 90˚ )
• To cover 0   90 use tan2 
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March 2002
April 2002
with SNO
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What Next?
• Can we convincingly
verify oscillation with
man-made neutrinos?
Psurv
KamLAND

m 2 c 4 GeV L 

 1  sin 2 sin  1.27
eV 2 En km 

2
2
• Hard for low m2
• To probe LMA, need
L~100km, 1kt
• Need low En, high n
• Use neutrinos from
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nuclear reactors
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Location, Location, Location
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KamLAND sensitivity on LMA
• First terrestrial expt
relevant to solar
neutrino problem
• KamLAND will
exclude or verify
LMA definitively
• Data taking since Nov
2001
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KamLAND first neutrino event
n e p  e n
49.2ms later
np  dg
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Measurements at KamLAND
• Can see the dip when
m2>210–5eV2
• Can measure mass &
mixing parameters
(Pierce, HM)
Data/theory
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Implications of Neutrino Mass
Mass Spectrum
What do we do now?
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Two ways to go
(1) Dirac Neutrinos:
– There are new
particles, right-handed
neutrinos, after all
– Why haven’t we seen
them?
– Right-handed neutrino
must be very very
weakly coupled
– Why?
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Extra Dimensions
• All charged particles are on a 3-brane
• Right-handed neutrinos SM gauge singlet
 Can propagate in the “bulk”
• Makes neutrino mass small
(Arkani-Hamed, Dimopoulos, Dvali, March-Russell;
Dienes, Dudas, Gherghetta; Grossman, Neubert)
• mn ~ 1/R if one extra dim  R~10mm
• An infinite tower of sterile neutrinos
• Or anomaly mediated SUSY breaking
4
1
(Arkani-Hamed, Kaplan, HM, Nomura)
d
 (LH u N )
M 
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Pl
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Two ways to go
(2) Majorana Neutrinos:
– There are no new light
particles
– What if I pass a
neutrino and look
back?
– Must be right-handed
anti-neutrinos
– No fundamental
distinction between
neutrinos and antineutrinos!
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Seesaw Mechanism
• Why is neutrino mass so small?
• Need right-handed neutrinos to generate
neutrino mass , but nR SM neutral
n L

n R 
 mD
mD   n L 
 
M  n R
2
mD
mn 
 mD
M
To obtain m3~(m2atm)1/2, mD~mt, M3~1015GeV (GUT!)
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Grand Unification
• electromagnetic, weak,
and strong forces have
very different strengths
• But their strengths
become the same at 1016
GeV if supersymmetry
• To obtain
m3~(m2atm)1/2, mD~mt
 M3~1015GeV!
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M3
Neutrino mass may be
probing unification:
Einstein’s dream
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Why do we exist?
Matter Anti-matter Asymmetry
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Matter and Anti-Matter
Early Universe
10,000,000,001
10,000,000,000
Matter
Anti-matter
They basically have all annihilated away
except a tiny difference between them
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Matter and Anti-Matter
Current Universe
us
1
Matter
Anti-matter
They basically have all annihilated away
except a tiny difference between them
The Great Annihilation
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Sakharov’s Conditions
for Creating Matter Excess
• Necessary requirements for creating excess matter
to survive The Great Annihilation:
– Non-conservation of Matter
(matter conversion to anti-matter etc)
– CP violation
(subtle fundamental difference between matter and antimatter)
– Non-equilibrium
 G(M>0) > G(M<0)
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Majorana Neutrino
To The Rescue
• Majorana neutrino: no fundamental
distinction between matter and anti-matter
 There are processes that can change the balance
between matter and anti-matter
• Produce nR in the Early Universe
• Their decay can preferentially produce
matter over anti-matter
Leptogenesis
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Conclusions
• Neutrinos are weird
• Strong evidence for neutrino mass
• Small but finite neutrino mass:
– Need drastic ideas to understand it
• If Majorana, neutrino mass may be
responsible for our existence
• A lot more to learn in the next few years
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