Neutrino Physics - Lecture 1 Steve Elliott LANL Staff Member UNM Adjunct Professor 505-665-0068,...

Neutrino Physics - Lecture 1

Steve Elliott

LANL Staff Member

UNM Adjunct Professor

505-665-0068, [email protected]

Spring 2007 Steve Elliott, UNM Seminar Series

2

Course Format

• Seminar series on neutrinos

• Student presentations

• Hand out enrollment sheet.


3

Lecture 1 Outline

• Prerequisites

• References

• Discussion regarding course

• Connections to other physics

• Neutrinos in the “standard model”


4

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


5

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

https://www.interactions.org/


6

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


8

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?


9

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


10

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.


12

Dirac vs. Majorana

(D, D) (D, D)

(M, M)

CPT CPT

CPT

Lorentz

Lorentz

) addresses Dirac/Majorana

nature of .


13

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


15

Field Theory Overview - IIIdiagrams resulting from the QED interaction

e+

e±

e±

e-

e+

e±

e±

e-


16

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


17

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.


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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.


20

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…


21

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


22

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?

Neutrino Physics - Lecture 1 Steve Elliott LANL Staff Member UNM Adjunct Professor 505-665-0068,...

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