| Date | Reading and Homework Assignment |
|---|---|
| Thu. Aug. 24, 2017 |
Lecture: An introduction to particle physics and particles. This
lecture is meant to be a broad overview of the fundamental particles
(leptons, quarks, force carriers), the hadrons, their discovery, and
the concept of cross-sections. Students are required to read Chapter 1
of Griffiths on their own and ask questions in class on 8/29 if
anything is unclear.
Homework (due 8/31/17): Griffiths 1.1, 1.16. |
| Tue. Aug. 29, 2017 |
Lecture: An introduction to "force carriers", i.e., the bosons that
"communicate" between fermions. Electromagnetic (QED), weak, and
strong (QCD) interactions. The simplest 1-vertex diagrams that are
allowed and how we form more complicated diagrams from them. Some
simple rules: neutrinos always imply weak interactions, and similarly
the presence of photons in reactions always implies an electromagnetic
process. Weak interactions: charged and neutral currents. No
flavor-changing neutral currents (FCNC) allowed in the Standard Model
(SM). The complex CKM matrix and quark
mixing from mass eigenstates to weak eigenstates.
Homework (due 9/7/17): Griffiths 2.1, 2.3. |
| Thu. Aug. 31, 2017 |
Lecture: Masses and lifetimes of leptons, quarks, and gauge
bosons. Decays of the tau. The light hadrons, their masses, lifetimes,
and decay modes. Helicity suppression in decays in charged pion
decays. The Zweig rule. Some problems from the end of Griffiths,
Chapter 2 (2.5a: Cascade decays to Lambda pi vs. n pi). The CKM matrix:
magnitudes of elements and their implications. Branching Fractions,
lifetimes, and survival curves. Problems 2.5b, 2.5c, and 2.6.
Homework: (due 9/7/17): Look up, in the Particle Data Book, the decays of the W-boson and explain the branching fractions given. |
| Tue. Sep. 5, 2017 |
Lecture: Completed solutions to Griffiths's Chapter 2 problems.
Homework: (due 9/14/17): No homework. |
| Thu. Sep. 7, 2017 |
Lecture: Relativity and how the wave equation leads to the Lorentz
transformation. Definitions of β and γ. Frames of
reference. Events. 4-vectors. The coordinate 4-vector. Transforming
4-vector components between frames of reference. Contra- and
co-variant 4-vectors. Lorentz-invariant inner products of 4-vectors.
Time-like, space-like, and light-like 4-vectors.
Decays of cosmic-ray induced pions and muons.
Invariant infinitesimal intervals: ds2, and
dτ2, and the connection between dt and dτ. How
the gradient vector transforms like the inverse Lorentz
transformation and is a covariant vector.
Homework: (due 9/14/17): Griffiths 3.2, 3.6. |
| Tue. Sep. 12, 2017 |
Lecture: 4-velocity and 4-momentum. Interpretation of the
time-component of 4-momentum. Solutions to some standard problems:
the wavelength of Compton scattered light as a function of
scattering angle; energies and momenta of decay products of a
two-body decay in the rest frame of the decaying
particle. Definition of the Mandelstam variables.
Homework: (due 9/21/17): Griffiths 3.20a and 3.21 to be taken together as a single problem. |
| Thu. Sep. 14, 2017 |
Lecture: The Mandelstam variables s, t, u. Meaning and importance of s and how
to obtain sqrt{s} for colliders, and for fixed targets. The
theorist's view of s, t, u: s-channel, t-channel, and u-channel
processes. Luminosity and energy of accelerators. t, and u, and
their connection to scattering angle in the CM frame. The concept of
"phase space". Two-body phase space is proportional to
the magnitude of the momentum of the decay products in the CM
frame. 2-body phase space in purely leptonic decays of charged pions.
Homework: (due 9/21/17): A positron beam impinges on a stationary electron cloud. A purported e+e- resonance at precisely 1.87214 MeV is to be explored. What should the energy of the beam be? [Needs a precise numerical answer.] |
| Mon. Sep. 18, 2017 9:45 AM |
Pre-poned Lecture: Dimensionality of Lorentz Invariant Phase Space
(LIPS), 3-body phase space, and Dalitz plots. 2-body and 3-body
examples of how to "read off" the physics contained in the matrix
element from observed departures from phase space expectations.
No homework. |
| Tue. Sep. 19, 2017 |
Lecture: Estimating lifetimes of particles using knowledge of
interaction type /
coupling constants, dimensionality, and phase space only. [Using 1 =
0.2 GeV-fm]. Applications: lifetime of the charged and neutral
pions, and of the muon. Definition of GF. The 3 big
developments in twentieth century physics were Relativity, Quantum
Mechanics, and Gauge Theories. In order to understand the last of
these, and much of particle physics, we need to study symmetries in
greater detail. Why we need to use unitary operators; why we need
group theory. What is a group of operations. Representations of
groups and faithful representations. Griffiths problems 4.1, 4.2:
the triangle group, its multiplication table. Angular momentum and
its importance by itself, as a prototype for isospin, and as a
prototype for other continuous groups we will need. Clebsch-Gordan
coefficients for angular momentum addtion.
Homework: (due 9/28/17): Griffiths 4.14. |
| Thu. Sep. 21, 2017 |
Lecture: Isospin: a property conserved in strong interactions. Using
isospin conservation and tables of Clebsch-Gordan coefficients to find
ratios of strong cross-sections and to find strong branching
fractions.
Homework: (due 9/28/17): Griffiths 4.30. |
| Tue. Sep. 26, 2017 |
Lecture: Basic ideas of Lie groups: rank, multiplets, Lie algebra,
structure constants, commuting generators, Casimir operators.
Homework: (due 10/5/17): Group Theory Homework. |
| Thu. Sep. 28, 2017 |
Lecture: Description of particle detectors, their components, the
general behavior of various particle types, triggers, and some
general comments about the passage of particles through matter (to
be discussed in detail later).
Homework: (due 10/5/17): A freight train of mass 5000 metric tons traveling at 100 mph smashes directly into a fly which is momentarily at rest. If the mass of the fly is 0.23 g, what is the final velocity of the fly which bounces off elastically? What is the change in energy of the train? |
| Tue. Oct. 3, 2017 |
Lecture: Discrete symmetries. The Parity operation (P) and what it does to the
coordinate vector, to momentum, and to angular momentum. Eigenstates of parity,
and its eigenvalues. Violation of parity: decay of polarized Co-60 nuclei, the
tau-theta puzzle, and neutrinos. The charge-conjugation operation (C). Eigenstates
of C-parity and eigenvalues. Extending C-parity to G-parity via a rotation by π
around the Iy-axis. Strong interactions conserve P, C, G. Determining
C-parity by counting the number of photons in a final state with all
photons, and the G-parity by counting the number of pions in an
all-pion final state. Electromagnetic interactions
conserve P, C. Weak interactions do not conserve any of these. Why CP conservation
is enough to guarantee equality of a particle's decay rate to a final state with
the anti-particle's decay rate to the corresponding anti-final
state. T-reversal invariance. There is no T-parity due to the
anti-unitary nature of T-reversal. Implications of CPT conservation:
total decay rates and masses of particles and anti-particles are identical.
Homework: (due 10/12/17): The three charm-anticharm states χc0, χc1, and χc2 have JPC values of 0++, 1++, and 2++ respectively. What can you say about the S, L, and I values for these particles? What electromagnetic decays might they have? |
| Thu. Oct. 5, 2017 | Lecture: The eigenvalues of a
2x2 Hermitian matrix. The semileptonic (self-tagging) decay modes
of neutral kaons. The hadronic decay modes of neutral kaons and the
possibility of neutral kaon mixing. The lifetimes of neutral
kaons. The Hamiltonian matrix for a two-particle system at rest
which can decay, and its eigenvalues. Neutral kaons and their
CP-transformed versions. Time evolution of a two-particle system
without decays, and then with decays. The probability of finding a
K0 as a function of time when we begin with a
K0.
Homework: (due 10/12/17): In the D0D0 system the values of the width difference ΔΓ and the mass difference Δm between the eigenstates are very small compared to the average lifetime Γ. Work out the time evolution of the neutral D system in this approximation, i.e., when x ≡ Δm/Γ and y ≡ ΔΓ/Γ are both very small compared to 1. [Clarification: we are interested in times of order of one or two or at most three lifetimes. Beyond that time essentially all the neutral D-mesons have decayed away.] |
| Tue. Oct. 10, 2017 | Lecture: Preponed to 9/18. |
| Thu. Oct. 12, 2017 |
Lecture: More on Bethe-Bloch curve, the Vavilov distribution, and
electromagnetic showers. Energy resolution of electromagnetic
calorimaters.
Homework: (due 10/19/17): No homework. |
| Tue. Oct. 17, 2017 |
Lecture: More on CP violation in the kaon system: the phenomena of
regeneration and CP violation which result in two-pion decays of
neutral kaons after many KS lifetimes. CP violation in
the semileptonic decays of neutral kaons.
Homework: (due 10/26/17): No homework. |
| Thu. Oct. 19, 2017 | Fall Break. |
| Tue. Oct. 24, 2017 |
Lecture: Describing mesons: we begin with a reminder of the hydrogen
atom energy levels (with fine structure, hyperfine corrections, and
the Lamb shift). This is then extended to positronium and charmonium
and bottomonium. We worked out Griffiths problems 5.1 and 5.5 in
class.
Homework: (due 11/2/17): Griffiths 5.8. |
| Thu. Oct. 26, 2017 |
A linear model for the qqbar potential and its consequences for
meson masses using the WKB approximation, and using the Cornell
potential with a relativistic radial equation. Mass splittings in
this model and in a simple hyperfine-splitting model. Weight
diagrams in SU(2) and SU(3). The fundamental anti-quark isospin
doublet. Forming the flavor state vectors for pions in SU(2) and
SU(3). Also for other low-lying mesons.
Homework: (due 11/2/17): Griffiths 5.12. |
| Tue. Oct. 31, 2017 |
Reminder of S=0 and S=1 mesons. Baryon wavefunctions and why the
Δ++ and the Ω- require color: to
preserve antisymmetry under exchange of quarks. Spin and flavor
wavefunctions of the proton (Griffiths). Magnetic moments of the
baryons, masses, and vector meson couplings to e+e- as indicators of
quark model success. Homework: (due 11/9/17): Griffiths 5.16. |
| Thu. Nov. 2, 2017 |
A summary of Griffiths's Chapter 6: cross-sections, decay rates,
amplitudes, phase space, relativistic Golden rule, Feynman Rules.
Homework: (due 11/9/17): Griffiths 6.6. |
| Tue. Nov. 7, 2017 |
The Dirac Equation: extending the Schrodinger equation to the
relativistic case, which leads to the Klein-Gordon equation. Probability densities
in the Schrodinger and Klein-Gordon cases. The Schrodinger equation
is unsatisfactory because it's not relativistically covariant; the
K-G equation is also unsatisfactory for a different reason: it gives
negative probability densities. Eventually we find (in field theory)
that the latter problem is solved. However, the K-G equation remains
unsatisfactory as a description of electrons because it does not
account for spin. The Dirac equation is
linear in all spacetime components and thus treats them all
equally. Requiring that the Klein-Gordon equation is nevertheless
satisfied leads to the Clifford algebra. A particular representation
for the γ-matrices that result is the Pauli-Dirac
representation. Griffiths problems 7.1, 7.2.
Homework: (due 11/16/17): Show that a 2x2 matrix representation that satisfies the Clifford algebra is not possible. |
| Thu. Nov. 9, 2017 |
Lecture: The Dirac equation, continued. α & β matrix
form. The adjoint equation, and the conserved current. Brief class
due to Fire Alarm interruption.
Homework: (due 11/16/17): No homework. |
| Tue. Nov. 14, 2017 |
Lecture: Solutions of the Dirac equation for the free particle
case. Normalization and spin of the resulting spinors. Griffiths
problems 7.4, 7.6.
Homework: (due 11/30/17): Griffiths 7.7. |
| Thu. Nov. 16, 2017 | Class postponed. |
| Tue. Nov. 21, 2017 | Class postponed. |
| Thu. Nov. 23, 2017 |
Thanksgiving Break - No classes |
| Mon. Nov. 27, 2017 |
Lecture (10:00 AM): Obtaining the two-component Pauli equation (a
version of the Schrodinger equation that accomodates spin) from the
Dirac equation; followed by manipulation to a form in which g=2 is
manifest.
Homework: (due 12/7/17): No homework. |
| Tue. Nov. 28, 2017 |
Lecture: Finding the Hamiltonian H for the Dirac equation and the
commutator of H with L, S, and J = L + S. Also,
the commutators of H with S2, and p ·
S. Lorentz covariance of the Dirac equation, and bilinear
covariants.
Homework: (due 12/7/17): Griffiths 7.13, 7.14. |
| Thu. Nov. 30, 2017 |
Lecture: Calculation of matrix element for e+e- → μ+μ-.
Homework: (due 12/7/17): Griffiths 7.36. |
| Mon. Dec. 4, 2017 |
Lecture (10:00 AM): Presentations by Luis & David & Krishna.
Homework: No homework. |
| Tue. Dec. 5, 2017 |
Lecture: Presentations by Vincent & Rick.
Homework: No homework. |
| Thu. Dec. 7, 2017 |
Lecture: Presentations by Chris & Chatura.
Homework: No homework. |