Topics covered: Neutrino Physics 2009
- Lecture 1 (Feb 2):
- Lecture 2 (Feb 4):
- Allowed weak interactions, weak isospin partners, forbidden FCNC,
lepton number conservation
- Klein-Gordan equation as relativistic generalization of
Schroedinger's equation
- Dirac equation and its solutions in Dirac-Pauli representation
- Positive-negative energy solutions,
antiparticle interpretation, quantum numbers for all four solutions
- Lecture 3 (Feb 9):
- Helicity operator, Goldhaber experiment
to measure neutrino helicity
- Chirality and properties of [gamma5], Interpretation of
[(1+gamma5)/2] and [(1-gamma5)/2] as right and left chirality
projection operators
- Sixteen possible independent products of [gamma] matrices
- Lecture 4 (Feb 11):
- [psi.bar], as opposed to [psi.dagger], as a covariant object
- Bilinears in spinors as Lorentz covariant ``spinor singlet'' objects:
scalar, pseudoscaler, vector, axial vector and tensor operators
- Lorentz invariant interaction terms, V-A interactions of
quarks and leptons with W
- Nuclear beta decay: net phase space for final state particles,
calculation of the matrix element [M] and hence of [|M|^2] using
properties and trace rules of [gamma] matrices
- Lecture 5 (Feb 16) :
- Calculation of the rate of nuclear beta decay as a function of
electron momentum, Kurie plot, effect of neutrino mass on the
``endpoint spectrum''
- Direct limits on neutrino masses: from Tritium decay and
pion decay
- Atmosphetic neutrino problem: anomaly in the muon/electron
ratio, observations from the
zenith angle distribution
- Assignment 1 given (Feb 16)
- Lecture 6 (Feb 17) :
- Effective Hamiltonian for a neutrino mass eigenstate
- Flavour eigenstates as a linear combination of mass eigenstates,
propagation in terms of mass eigenstates
- Survival probability of a flavour eigenstate after travelling
a distance L in vacuum: two flavour oscillations
- Explanation of
features of atmospheric neutrino data: zenith
angle dependence, up-down asymmetry
- Solution of the atmospheric neutrino problem: mass squared
difference, mixing angle
- Decoherence due to wavepacket separation, finite energy resolution
and averaging over many sources: disappearance of the oscillating term
- Lecture 7 (Feb 18) :
- Clarification of how one can forget about spinorial degrees of
freedom during neutrino propagation
- Effective Hamiltonian for a 2-neutrino system in vacuum, mass
basis to flavour basis conversion
- Neutrino interactions with matter: neutral current and charged
current forward scattering
- calculation of charged current forward scattering amplitude
to get an effective potential [V_CC = Sqrt(2) G_F n_e]
- Effective neutral current forward scattering potential
[V_NC = - G_F n_n / Sqrt(2)]
- Lecture 8 (Feb 23) :
- Lecture 9 (Feb 24) :
- Lecture 10 (Mar 2) :
- Review of earlier lectures
- Number of events at the detector in terms of the initial
neutrino flux, neutrino conversion probabilities, neutrino-nucleus
cross sections, energy and angular resolution, and the efficiency of
the detector
- Tutorial by Subhendu Rakshit (Mar 4)
- Lecture 11 (Mar 9) :
- Confirming the atmospheric neutrino solution by a
source-baseline-detector setup. Choosing the appropriate baseline,
K2K and MINOS experiments
- Solar neutrino solution: no VAC from seasonal variation and
energy dependence, all other solutions involve decoherence
- Adiabaticity parameter [gamma] in terms of neutrino mixing
parameters, energy, and the density profile of the Sun
- Eliminating the SMA solution by energy dependence
- Confirming the solar neutrino solution on Earth: KamLAND
experiment with electron antineutrinos from a reactor
- Lecture 12 (Mar 13) :
- Calculation of solar mixing angle from the
SuperKamiokande data:
combination of charged and neutral current events
- Determining the solar mass squared difference from a
terrestrial experiment: KamLAND
- Ruling out the contribution of sterile neutrinos to solar
neutrino anomaly: the SNO experiment
- Older radiochemical experiments consistent with the "LMA MSW"
oscillation solution
- Older short baseline experiments
that did not find any [nue -> numu] conversions.
- Given solutions to solar and atmospheric neutrino anomalies
through 2-neutrino mixings each,
constructing a three-neutrino framework:
neutrino mass orderings
- Lecture 13 (Mar 16) :
- Three-neutrino mixing: unitary matrix U_PMNS
- [P(nu_alpha -> nu_beta)] in vacuum in terms of elements [U_{alpha i}],
no-oscillation term, oscillation terms, CP violating terms
- Parametrization of U_PMNS in terms of three rotations R23, R13, R12
- CHOOZ experiment: theta13 small, consistent with zero
- Atmospheric neutrinos: theta23 = theta_atm (theta13->0)
- Theta13-> 0 limit: [nu_e] mixes with [nu_mutilde], decoupling of
[nu_tautilde = nu3]
- Solar neutrinos: theta12 = theta_solar (theta13->0)
- Assignment 2 given (Mar 16)
- Lecture 14 (Mar 18) :
- Three neutrino mixing:
contribution of the three flavours
to mass eigenstates
- Origin of U_PMNS through the charged current Lagrangian,
[U_PMNS = U^dagger_(l L) U_(nu L)]
- Absorption of "row" phases possible if charged lepton
phases can be changed globally: always possible
- Absorption of "column" phases possible if neutrino
phases can be changed globally: possible only if
neutrinos do NOT have a Majorana mass
- Two families: all phases can be absorbed if neutrinos
are not majorana, one Majorana phase if they are Majorana
- Three families: one Dirac phase left even if neutrinos
are not Majorana. If they are Majorana, two more Majorana phases.
- Most general parametrization of U_PMNS as
[R23 . U13 . R12 . Phi]
- Lecture 15 (Mar 23) :
- ``Plaquette'' in U_PMNS: rephase invariant. Im(Plaquette) as
the Jarlskog invariant parameterizing (Dirac) CP violation
- Majorana phases do not play a role in oscillation experiments
- Antiparticles: Plackette -> Plackette*, V_CC -> -V_CC,
V_NC -> -V_NC
- Expansion of P(e mu)
in terms of two small parameters [theta13] and
[alpha = ratio of solar and atmospheric mass squared differences],
A=0 limit, changes with antiparticles, Magic baseline, limits
of validity of the expansion, theta13 resonance
- Lecture 16 (Mar 25) :
- Two-neutrino limit of P(e mu), short baseline experiments,
the universal shape of constraints with 2-neutrino oscillations
- LSND experiment :
positive oscillation signature, but needs
at least one sterile neutrino
- Possible neutrino mass spectra (3+1, 2+2) if LSND is valid.
- Challenging LSND with MiniBOONE ,
almost ruling it out completely
- Other phenomena where sterile neutrinos find a use: as hot
dark matter, r-process nucleosynthesis inside a supernova,
pulsar kicks
- Lecture 17 (Mar 30) :
- Possible Majorana nature of neutrinos: heuristic arguments
- Particles vs. antiparticles: solutions of Dirac equations
in Pauli-Dirac representation and Chiral representation
- Antiparticles as ``CP'' conjugate particles: argument through
a Gauge group under which the particle is ``charged''
- Lecture 18 (Apr 1) :
- [Particle -> antiparticle] corresponds to [U_PMNS -> U^*_PMNS],
[V_CC -> -V_CC], [V_NC -> -V_NC]
- Neutrino Majorana mass term in the Largangian
- Neutrinoless double beta decay: examples, relevant mass matrix
element [m_ee] in terms of mixing angles, Dirac phase, Majorana phases
- Guest Lectures during ``Aspects of Neutrinos'':
- Lecture 19 (Apr 27) :
- Revising the course contents of the last nine lectures
- Assignment 3 given (Apr 28)
- Lecture 20 (Apr 29) :
- Standard model Lagrangian: free fermions before gauge interactions
- [U(1)_Y] and [SU(2)_L] Gauge symmetries: gauge bosons,
covariant derivatives, kinetic energy terms
- Forbidden mass terms for fermions and gauge bosons
- Higgs terms with gauge interactions
- Feynman diagrams before electroweak symmetry breaking
- Lecture 21 (May 4) :
- Electroweak symmetry breaking: Higgs mechanism
- Mass generation for W and Z, prediction of [rho] parameter
- [SU(2)_L x U(1)_Y] breaking to [U(1)_Q], relation between
Y, Q, and [SU(2)_L] isospin I_3.
- New Feynman rules after electroweak symmetry breaking
- Mass generation for fermions (except neutrinos)
- Neutrino mass from beyond the Standard model: right handed
[nuR] and Dirac mass
- If L is not conserved, [nuR] Majorana mass mandatory
- Lecture 22 (May 7) :
- Seesaw mechanism with one [nuL], and one [nu_R] with
heavy Majorana mass [M_M], interacting via the Dirac mass [m_D]
- Effective neutrino mass matrix in the basis
[(nuL, nuR^C)]: eigenvalues, eigenvectors, small mixing angle,
seesaw of mass eigenvalues
- Lecture 23 (May 11) :
- Principles of extending Standard model to get neutrino
mass terms: introducing new particles with specific gauge
charges, and gauge-invariant interactions
- Type-I seesaw as the addition of a gauge singlet
- Type-II sessaw by introduction of a [SU(2)_L] triplet Higgs
in addition to [nuR]
- Radiative mechanisms for neutrino masses: Zee model, Babu model
- Lecture 24 (May 13) :
- Majorana mass matrix for 3 generations: complex symmetric,
diagonalizable via [U^T M U]
- Seesaw mechanism with three left handed neutrinos and an
arbitrary number [n] of right handed neutrinos: approximate
block diagonalization
- Natural mechanism for leptogenesis through CP violation
in decays of heavy [nuR]
- Roles of neutrinos during the evolution of the universe:
leptogenesis, big bang nucleosynthesis (light element abundance),
structure formation (dark matter), nucleosynthesis inside stars,
supernova explosions
- Lecture 25 (May 18) :
- Lecture 26 (May 20) :
- Comments on solutions of assignments 1, 2 and 3
- Assignment 4 given (May 20)
- Project presentations (May 23)
- Lecture 27 (May 25) :
- Final Examination (May 27)