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

2. Spring 2007Steve Elliott, UNM Seminar Series2 Course Format Seminar series on neutrinos Student presentations Hand out enrollment sheet.

3. Spring 2007Steve Elliott, UNM Seminar Series3 Lecture 1 Outline Prerequisites References Discussion regarding course Connections to other physics Neutrinos in the “standard model”

4. Spring 2007Steve Elliott, UNM Seminar Series4 Prerequisite Topics But, 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. Spring 2007Steve Elliott, UNM Seminar Series5 Some References hep-ph/0606054, Strumia/Vissani APS neutrino study and its working groups –https://www.interactions.orghttps://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

6. Spring 2007Steve Elliott, UNM Seminar Series6 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

7. Spring 2007Steve Elliott, UNM Seminar Series7 The Standard Model Particles u up c charm t top  gamma d down s strange b bottom g gluon e   W W boson e electron  muon  tau Z Z boson Force Carriers Leptons Quarks The Neutrinos u up c charm t top  gamma d down s strange b bottom g gluon 1   W W boson e electron  muon  tau Z Z boson u up c charm t top  gamma d down s strange b bottom g gluon 3   W W boson e electron  muon  tau Z Z boson

8. Spring 2007Steve Elliott, UNM Seminar Series8 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. Spring 2007Steve Elliott, UNM Seminar Series9 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. Spring 2007Steve Elliott, UNM Seminar Series10 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

11. Spring 2007Steve Elliott, UNM Seminar Series11 There are 3 active light neutrinos The width of the Z decay depends on the number of channels available for the decay.

12. Spring 2007Steve Elliott, UNM Seminar Series12 Dirac vs. Majorana ( D , D  ) ( M , M  ) CPT Lorentz  ) addresses Dirac/Majorana nature of.

13. Spring 2007Steve Elliott, UNM Seminar Series13 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.

14. Spring 2007Steve Elliott, UNM Seminar Series14 Field Theory Overview - II, QED L Free electron Photon Interaction Term

15. Spring 2007Steve Elliott, UNM Seminar Series15 Field Theory Overview - III diagrams resulting from the QED interaction  e+e+ e±e± e±e±  e-e- e+e+ e±e± e±e± e-e-  

16. Spring 2007Steve Elliott, UNM Seminar Series16 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. M ij doesn’t have to be diagonal, although it is for the charged leptons.

17. Spring 2007Steve Elliott, UNM Seminar Series17 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.

18. Spring 2007Steve Elliott, UNM Seminar Series18 We could simply put in jR The coupling f ij 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 M ij.

19. Spring 2007Steve Elliott, UNM Seminar Series19 Such a term leads to mixing m  is the  th diagonal element of the mass matrix The neutrinos mix.

20. Spring 2007Steve Elliott, UNM Seminar Series20 Shortcomings f ij 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. Spring 2007Steve Elliott, UNM Seminar Series21 Adding Majorana mass terms Ms are nxn matrices for n generations.  R, L are n element column vectors from n generations. From NC scattering, We know M L is small

22. Spring 2007Steve Elliott, UNM Seminar Series22 Diagonalize M Leads to two eigenvalues m 1 ~(M D ) 2 /M R and m 2 ~M R

23. Spring 2007Steve Elliott, UNM Seminar Series23 Leads to the seesaw mechanism If we take M D to be order of lepton mass, and we know that M R is large: We have two Majorana neutrinos –One with a mass much less than the leptons –One which is very heavy.

24. Spring 2007Steve Elliott, UNM Seminar Series24 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

25. Spring 2007Steve Elliott, UNM Seminar Series25 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?