neutrino physics - lecture 1 steve elliott lanl staff member unm adjunct professor 505-665-0068,...
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Neutrino Physics - Lecture 1
Steve Elliott
LANL Staff Member
UNM Adjunct Professor
505-665-0068, elliotts@lanl.gov
Spring 2007 Steve Elliott, UNM Seminar Series
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Course Format
• Seminar series on neutrinos
• Student presentations
• Hand out enrollment sheet.
Spring 2007 Steve Elliott, UNM Seminar Series
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Lecture 1 Outline
• Prerequisites
• References
• Discussion regarding course
• Connections to other physics
• Neutrinos in the “standard model”
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Prerequisite TopicsBut, I can cover topics on request
• Schrodinger level quantum mechanics– We will make reference to quantum field theory
on occasion
• Kinematics/Relativity• Particle Reactions• Cross Sections• Radioactivity ()• Energy Loss• Symmetries (P,C,T, CP, CPT)• Linear Algebra Basics
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Some References
• hep-ph/0606054, Strumia/Vissani• APS neutrino study and its working groups
– https://www.interactions.org
• “Neutrino Astrophysics” - John Bahcall• “The Physics of Massive Neutrinos” - Boris
Kayser• “Massive Neutrinos in Physics and
Astrophysics” Mohapatra/Pal• “Physics of Massive Neutrinos”
Boehm/Vogel
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Why are neutrinos relevant?
• Basic Particle Physics– We know little about the neutrino’s properties
• Beyond the Standard Model– The neutrino is an important ingrediant to understanding the
inclusion of mass and the various energy scales
• Nuclear Physics– Key to understanding symmetries and interactions
• Astrophysics– Supernovae
• Cosmology– Dark matter– Large scale structure– Particle, anti-particle asymmetry
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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
Spring 2007 Steve Elliott, UNM Seminar Series
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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?
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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
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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
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There are 3 active light neutrinos
The width of the Z decay depends on the number of channels available for the decay.
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Dirac vs. Majorana
(D, D) (D, D)
(M, M)
CPT CPT
CPT
Lorentz
Lorentz
) addresses Dirac/Majorana
nature of .
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Field Theory Overview - I
• Field operators obey equations of motion derived from a Lagrangian (L) via a variational principle.
• If the interaction term in L is small (small coupling constant), a perturbative approach is used.
• Represent successive terms as Feynman diagrams.
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Field Theory Overview - II, QED L
€
LQED = ψ (iγ μ∂ μ − m)ψ + eψ γ μ Aμψ −14
(∂μ Aν −∂ν Aμ )(∂ μ Aν −∂ ν Aμ )
Free electron PhotonInteraction
Term
€
ψ creates electron, annihilates positron
ψ creates positron, annihilates electron
A creates or annihilates photon
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Field Theory Overview - IIIdiagrams resulting from the QED interaction
e+
e±
e±
e-
e+
e±
e±
e-
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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
€
mψ ψ
Spring 2007 Steve Elliott, UNM Seminar Series
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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.
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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.
Spring 2007 Steve Elliott, UNM Seminar Series
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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.
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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…
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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
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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
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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.
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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
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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?
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