1. The Physics of Neutrinos
Pervez Hoodbhoy
Physics Department
Forman Christian College
Lahore

2. Outline What is a neutrino? Detecting neutrinos
Pre-Standard Model Neutrino Physics
Neutrinos in the Standard Model
Giving neutrinos a mass
Neutrino oscillations
Double beta decay
Cosmological neutrinos

3. What is a neutrino?

4. Neutron decay – momentum balanced

5. Neutron decay – momentum not balanced
Pauli (1930) guessed
existence of a third
particle. Antineutrino
found in 1956.
On theoretical grounds every
neutrino has to have its own
anti-neutrino.

6. How to detect a neutrino?

7. Sources of neutrinos Sun, nuclear reactors,
supernovae (exploding stars)
2. Cosmic rays
3. Remnants from Big Bang

8. CROSS-SECTIONS quark gluon photon quark W quark proton electron proton
neutrino
proton
quark W

10. Anti-Neutrino Detector

11. Neutrino Physics before the Standard Model

13. Parity
A definition:

14. Parity was once thought to be a perfect fundamental symmetry
Parity was once thought to be a perfect fundamental symmetry. But it’s not!
Madame Wu’s
Co experiment
(1957)
Left-handed neutrinos exist in nature (1958). Right-handed ones do not.
Right-handed anti-neutrinos exist in nature. Left-handed ones do not.

15. Two-Component Neutrino Theory
“sterile”

16. The 4-fermions-at-a-point theory worked beautifully but it had
to be fundamentally wrong/insufficient.

17. Fermions of the Standard Model

19. Quark Mixing in the Standard Model
Quarks and leptons participating
in strong interactions have well
defined masses.
u c t
d s b
Leptons participating in weak
interactions do not have well
defined masses. They are mixtures
of mass eigenstates.
u c t
d’ s’ b’

20. Only if neutrinos have mass! No neutrino mass means no neutrino mixing
Can neutrinos also mix?
Only if neutrinos have mass! No neutrino mass means no neutrino mixing

21. Easy way to find neutrino masses (doesn’t work well)
Just observe a supernova
emitting photons and
neutrinos and look to
see which arrives first!
Particles with mass move
slower than light.
Surprise! Neutrinos from
SN 1987A arrived first!
Explanation: the velocity of
light in matter is smaller
than the velocity in vacuum.
In spite of a rather low density of matter (about 5/cm3), light is slowed down more than neutrinos.

22. Bad way of finding
neutrino mass but
still establishes that
it is in O(eV) range.
m<1.8 eV (2)
(Mainz-Troisk)

23. Neutrinos are much lighter than all other fermions !

24. Theoretical Issues Why neutrino mass? Why so little?
The Standard Model does have an answer but a terrible one !
To understand masses, we’ll first need understand the role of basic symmetries.

25. Charge conjugation C changes particle to anti-particle
Charge conjugation C changes particle to anti-particle. (Badly violated in weak interactions)
Ettore Majorana ?
9 papers
No Ph.D!!!!!!

26. Charge-Parity CP operation (almost completely respected in weak interactions)
CP-VIOLATION

27. Dirac Masses for Neutrinos

28. Majorana Masses for Neutrinos

29. Seesaw Mechanism

30. mD

31. Mixing in a 2-state system (toy model for oscillations)

32. 3-neutrino case is only a little more complicated

33. Neutrino Oscillations

34. Neutrino Oscillation Channels

35. Disappearance of Reactor Neutrinos

36. Neutrino Parameters

37. Parametrizing the Neutrino Mixing Matrix

38. Main Results From Neutrino Oscillation Experiments

40. Neutrino physics generally respects CP (violation being sought with great eagerness)
Mass eigenstates
Complex phases (at least requiring 3x3 mixing) leads for both cases to CP violation

41. Can Neutrinos Actually Be Majorana Particles?
DOUBLE BETA DECAY
Can Neutrinos Actually Be Majorana Particles?

42. Neutrinoless Double Beta Decay [0]
Nucleus Z
Nucleus Z+2
This tests if neutrinos are their own antiparticles. Why?

43.  i W– e– Nuclear Process Nucleus Z Nucleus Z+2 SM vertex Uei
Mixing matrix

44. the i is emitted [RH + O{mi/E}LH]. Thus, Amp [i contribution]  mi
Assume double beta decay is dominated by the simplest possible diagram
the i is emitted [RH + O{mi/E}LH].
Thus, Amp [i contribution]  mi
Amp[0]   miUei2 m i i W– e–
Nuclear Process
Nucleus Z
Nucleus Z+2
Uei
SM vertex 
Mixing matrix
Mass (i)

45. But we also need non-conservation of lepton number
Nucleus Z
Nucleus Z+2
Majorana neutrinos do not conserve L.
But the Standard Model (SM) weak interactions do conserve L. So the L = 2 of 0 can only come from Majorana neutrino masses, such as, mL X L
()R
mL( Lc L + LLc)

46. Assuming Standard Model vertices, 0 is —mL X W– W–
Nucleus Z
Nuclear Process
Nucleus Z+2
The Majorana neutrino mass term plays two roles:
Violate L
Flip handedness
It will be needed for (1) even when not needed for (2).

47. Neutrinos in the Cosmos

48. Thermal History of the Universe

49. Standard Cosmology Einstein equation with cosmological constant
Matter in universe flows
like an ideal fluid

50. Photons and Neutrinos in the Early Universe
Energy density for type i depends only on temperature, gi is the number of type i particles.

51. Photons and Neutrinos in the Early Universe

52. Question: There are so many neutrinos
Question: There are so many neutrinos. Can they be made to account for all the dark matter we know is there?

53. m = 0 eV
m = 1 eV
Ma ’96
m = 7 eV
m = 4 eV

54. END