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

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

What is a neutrino?

Neutron decay – momentum balanced

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.

How to detect a neutrino?

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

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

Anti-Neutrino Detector

Neutrino Physics before the Standard Model

Parity A definition:

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.

Two-Component Neutrino Theory “sterile”

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

Fermions of the Standard Model

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’

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

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.

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

Neutrinos are much lighter than all other fermions !

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.

Charge conjugation C changes particle to anti-particle Charge conjugation C changes particle to anti-particle. (Badly violated in weak interactions) Ettore Majorana 1906 - ? 9 papers No Ph.D!!!!!!

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

Dirac Masses for Neutrinos

Majorana Masses for Neutrinos

Seesaw Mechanism

mD

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

3-neutrino case is only a little more complicated

Neutrino Oscillations

Neutrino Oscillation Channels

Disappearance of Reactor Neutrinos

Neutrino Parameters

Parametrizing the Neutrino Mixing Matrix

Main Results From Neutrino Oscillation Experiments

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

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

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

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

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)

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)

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).

Neutrinos in the Cosmos

Thermal History of the Universe

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

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

Photons and Neutrinos in the Early Universe

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?

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

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