neutrino physics steve elliott lanl nuclear physics summer school 2005
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Neutrino Physics
Steve Elliott
LANL
Nuclear Physics Summer School 2005
June 2005 Steve Elliott, NPSS 2005 2
Lecture Outline
• Neutrinos and the weak interaction
• Neutrino oscillations
• Experimental results on neutrinos– Solar-Atmospheric experiments– Reactor-Accelerator experiments
• Double beta decay
• “Direct” neutrino mass studies
June 2005 Steve Elliott, NPSS 2005 3
Outlinefor this lecture
• Neutrinos in the “standard model”
• Sources of neutrinos
• Neutrino detection
• Connections to other physics
June 2005 Steve Elliott, NPSS 2005 4
The Standard Model Particles
uup
ccharm
ttop
gamma
ddown
sstrange
bbottom
ggluon
e WW boson
eelectron
muon
tau
ZZ boson
Fo
rce Carriers
Lep
ton
sQ
uar
ks
The Neutrinos
uup
ccharm
ttop
gamma
ddown
sstrange
bbottom
ggluon
1 WW boson
eelectron
muon
tau
ZZ boson
uup
ccharm
ttop
gamma
ddown
sstrange
bbottom
ggluon
3 WW boson
eelectron
muon
tau
ZZ boson
June 2005 Steve Elliott, NPSS 2005 5
Neutrinos mix, therefore:
• Neutrinos have mass– Might have non-zero magnetic moments– Heavier neutrinos might decay– Might be Majorana or Dirac
• What are the implications for– unification, supersymmetry, and extra
dimensions?– possible existence of additional species?– the possibility that neutrinos have something
to do with the matter-antimatter asymmetry?
June 2005 Steve Elliott, NPSS 2005 6
Why neutrinos are unusual
• Neutrinos might be the ultimate neutral particle– They would not be distinct from their
antiparticles.– If so they would be Majorana particles
• They might also be Dirac particles– Like the charged quarks and leptons
June 2005 Steve Elliott, NPSS 2005 7
Neutrinos and the weak interaction
• The weak interaction violates parity.
• Hence there are no right handed current interactions
• This can be interpreted two ways.– There are no right handed neutrinos– There are RH neutrinos, they just don’t
interact
June 2005 Steve Elliott, NPSS 2005 8
There are 3 active light neutrinos
The width of the Z decay depends on the number of channels available for the decay.
June 2005 Steve Elliott, NPSS 2005 9
Dirac vs. Majorana
(D, D) (D, D)
(M, M)
CPT CPT
CPT
Lorentz
Lorentz
) addresses Dirac/Majorana
nature of .
June 2005 Steve Elliott, NPSS 2005 10
Typical Dirac mass term
Quarks and leptons get their mass by a coupling to the Higgs. Here is an example (the electron): a Dirac particle.
€
−Lmass = fijv
2ij∑ e ie j + h.c.
= Mijij∑ e iLe jR( ) + h.c.
€
Mij =v
2fij
Mij doesn’t have to be diagonal, although it is for the charged leptons.
€
eL =12
1−γ 5( )e
June 2005 Steve Elliott, NPSS 2005 11
For neutrinos:
In the standard model, jR (the RH neutrino) doesn’t exist, therefore neutrinos are massless by construction.
Now that we know that neutrinos have mass, we need to learn how to incorporate that into the model. There are many possibilities.
€
−Lmass = Mijij∑ ν iLν jR( ) + h.c.
June 2005 Steve Elliott, NPSS 2005 12
We could simply put in jR
The coupling fij doesn’t have to be diagonal and in general it isn’t. To find the physical fields, those of definite mass, we need to diagonalize Mij.
€
U+MV = m
ν iL = Uiαα∑ ν αL; ν iR = Viα
α∑ ν αR
€
−Lmass = Mijij∑ ν iLν jR( ) + h.c.
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Such a term leads to mixing
€
−Lmass =α∑ ν αLmα ν αR + h.c.
m is the th diagonal element of the mass matrix
€
Lcc =g2
l Lγ μ
l∑ ν l LWμ
− + h.c.
=g2 α
∑ l Lγ μ
l∑ Ul α ν αLWμ
−
The neutrinos mix.
June 2005 Steve Elliott, NPSS 2005 14
Shortcomings
• fij is completely arbitrary
• Doesn’t explain why neutrinos are so much lighter than their lepton partners.
• We have not included additional possible mass terms…
June 2005 Steve Elliott, NPSS 2005 15
Adding Majorana mass terms
€
−Lmass
Maj = Mijν iL
c ν jL + Mijν iR
c ν jR + h.c.
• Ms are nxn matrices for n generations. R, L are n element column vectors from n
generations.
€
for n = 1
M =M L M D
M D M R
⎛
⎝ ⎜
⎞
⎠ ⎟
€
−Lmass
tot = Mij
Dν iLν jR + Mij
Lν iL
c ν jL + Mij
Rν iR
c ν jR + h.c.
From NC scattering,We know ML is small
June 2005 Steve Elliott, NPSS 2005 16
Diagonalize M
€
M =0 M D
M D M R
⎛
⎝ ⎜
⎞
⎠ ⎟
O =cosθ −sinθ
sinθ cosθ
⎛
⎝ ⎜
⎞
⎠ ⎟, with tan2θ =
2M D
M R
Leads to two eigenvalues m1 ~(MD)2/MR and m2 ~MR
June 2005 Steve Elliott, NPSS 2005 17
Leads to the seesaw mechanism
• If we take MD to be order of lepton mass, and we know that MR is large:
• We have two Majorana neutrinos– One with a mass much less than the
leptons– One which is very heavy.
June 2005 Steve Elliott, NPSS 2005 18
Phases in the mixing matrix
For nxn unitary matrix (U): 2n2 parameters in a complex matrix -n2 unitarity constraints -(2n-1) unphysical phases: that can be absorbed into the fields, and =(n-1)2 parameters (1/2)(n-1)n of these are rotation angles
€
Uiα ν α
Note however, that for Majorana fields, the phases of and are related. Hence there are only n unphysical phases.
June 2005 Steve Elliott, NPSS 2005 19
Sources of neutrinos
Big BangRadioactive decaysStarsSupernovasCosmic raysReactorsAccelerators
June 2005 Steve Elliott, NPSS 2005 20
Big Bang
• Relic neutrinos contribute at least as much mass to the Universe as all the stars.
• There are as many leftover neutrinos as photons.– N ~420/cc
• Photon energy: 2.728 K• Neutrino energy: 2 K
– There are no viable ideas for detecting such low energy neutrinos.
– Note that neutrinos are studied via their particle nature– The microwave background was discovered by the wave
nature of photons.
June 2005 Steve Elliott, NPSS 2005 21
Radioactive Decays
• MCi sources have been made• Mostly for use by solar neutrino radiochemical
experiments for efficiency measurements.• Electron capture isotopes provide a monoenergetic
neutrino.
51Cr37Ar
June 2005 Steve Elliott, NPSS 2005 22
Stars (our Sun)
FeaturesVery long baseline, e disappearance, x appearanceLow energy, spectral shape well knownL/E is large so sensitive to small m2
Large FluxMatter enhancement
DataRates from several experimentsEnergy dependenceDay vs. NightSeasonal
June 2005 Steve Elliott, NPSS 2005 23
SupernovasFeatures
~ Very long baseline~ 's~ Complicated and poorly understood source~ Target cross sections not all well understood
Data~ Not a common phenomenon
once ~30 years in our galaxy~ SN1987A provided little physics data~ SN1987A did give hope for the future
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6
10
4
10
2
10
0
(/Flux cm
)sec MeV
6
4
( )Energy MeV
supernova
@ kpc
My personal prediction is that neutrinos will teach us a lot about supernovae, but the inverse will be much harder.
June 2005 Steve Elliott, NPSS 2005 24
Supernovas
By using various targets with different energy- and flavor-dependent cross sections, one may be able tode-convolute the various fluxes.
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0
(/Flux cm
)sec MeV
6
4
( )Energy MeV
supernova
@ kpc
Some Estimated Rates (Burrows, Klein, Gandhi PR D45, 3361 (1992) Expt.
e p → e
+
n NC on deuterium CC on oxygen
K -II 55 5.5MACRO 9 Super-K 5 8.5SNO 7 4
June 2005 Steve Elliott, NPSS 2005 25
Cosmic Rays
atmosphere
Detector
Primary
Cosmic Ray
~20 km
~10000 km
€
Expect Rμ / e =ν μ + ν μ
ν e + ν e≈ 2
Meas.Rμ / edata
Rμ / e MC
≈ 0.6 − 0.7
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15
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5
10
0
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-5
10
-10
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-15
(/Flux cm
)sec MeV
6
4
( )Energy MeV
supernova
@ kpc
π
+
DAR
LSNDatmos
CERN SPS
CHORUS
June 2005 Steve Elliott, NPSS 2005 26
Reactors
FeaturesComplicated but well-understood source.Low energyShort, medium, long baselines disappearance experiments
DataSeveral at short baselines; 10-250 mCHOOZ/Palo Verde at ~1 kmKamLAND at ~250 km
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10
0
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-5
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-10
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-15
Anti-
e
(/Flux cm
)sec MeV
6
4
( )Energy MeV
Reactors
CHOOZ
supernova
@ kpc
atmos
June 2005 Steve Elliott, NPSS 2005 27
Accelerators
FeaturesUsually appearanceVarious baselines and wide energy rangeControlled experimental conditions
DataOscillation limits for many speciesLots of experimental results
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0
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-5
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-10
10
-15
(/Flux cm
)sec MeV
6
4
( )Energy MeV
supernova
@ kpc
π
+
DAR
LSNDatmos
CERN SPS
CHORUS
June 2005 Steve Elliott, NPSS 2005 28
Neutrino detectionTargets
• H2O
• D2O
• Scintillator• Ga• Cl• Emulsion• Ice• Iron• Rock
ES on e-: x + e--> x + e-
CC on Nucleus: l + A-> A’+ l
NC on Nucleus: x + A-> A’+ x
June 2005 Steve Elliott, NPSS 2005 29
Cross sections
• 10,000 light years of Pb to stop half of solar neutrinos
• Beta decay provides estimate of strength
€
n → p + e− + ν e
Γ =GF
2
2π 3
mc2
hMif
2f Z, E( )
or : const.
Mif2 = fτ
€
e + p → n + e+
σ 0 =2π 2h3
me5c7 fτ
pe Ee
= 0.0952Ee pe
1MeV2
⎛ ⎝ ⎜
⎞ ⎠ ⎟×10−42 cm2
Neutron beta decay Anti-neutrino absorption
June 2005 Steve Elliott, NPSS 2005 30
Cross Sections
The small size of these cross sections is what led early researchers to believe they had postulated an undetectable particle.
June 2005 Steve Elliott, NPSS 2005 31
Hard experiments
• Rates are very low– Big detectors
• Background difficulties– Signal may not be very distinct– Other more common processes can mimic
signal– Rare variations of common phenomena…
June 2005 Steve Elliott, NPSS 2005 32
Connections to other physics
• Cosmology• Large scale structure• Baryon asymmetry
• Nuclear and Particle physics• Incorporating mass into the standard model
• Astrophysics• Nucleosynthesis• Supernova dynamics
Neutrinos are very practical
June 2005 Steve Elliott, NPSS 2005 33
A summary of the questions
• Are neutrinos Majorana or Dirac?• What is the absolute mass scale?• How small is 13?• How maximal is 23?• Is there CP violation in the neutrino
sector?• Is the mass hierarchy inverted or normal?• Is the LSND evidence for oscillation true?
Are there sterile neutrinos?
June 2005 Steve Elliott, NPSS 2005 34
References
• Mohapatra/Pal book
• Kayser book
• Bahcall book
• Boehm/Vogel book