Nuclear Physics : Origin of elements But the Hoyle resonance hints at fine tuning. “You are all stardust. You couldn’t be here if stars hadn’t exploded, because the elements - the carbon, nitrogen, oxygen, iron, all the things that matter for evolution and for life - weren’t created at the beginning of time. They were created in the nuclear furnaces of stars, and the only way for them to get into your body is if those stars were kind enough to explode. So, forget Jesus. The stars died so that you could be here today.” – Lawrence Krauss

Today’s Plan G-parity review Gauge symmetry Review: QED and Feynman diagram examples Quiz 4 (QED, Feynman diagrams, atomic energy levels) on Monday.

G parity basics Thus the charged pion is not an eigenstate of C but is an eigenstate of G. Example: a ρ has I=1, C=-1 so G=+1 so it cannot decay to two pions but not three. Non-strange (non-charm, non-bottom) mesons are eigenstates of G. G is -1 for a single pion and for n pions, A φ, ω, ψ all have I=0, C=-1 so G=-1 and hence can decay to three pions but not two

Intro to Gauge Symmetry Electromagnetism can be expressed in terms of the two vector E and B or in terms of the vector potential A and the scalar potential ϕ. In classical mechanics, change the zero of the gravitational potential energy by any constant, the physics is unchanged. In electrostatics, pick the zero of the electric potential at any fixed point, the physics is unchanged. Gauge symmetry for Maxwell’s equations

Introduction to Gauge Symmetry Note that gauge symmetries are “local” symmetries not “global” and are continuous not discrete. EM can only be gauge invariant if the wavefunction obeys the following symmetry: This gauge symmetry corresponds to a one-parameter phase rotation or the Lie Group U(1). The Standard Model of Particle Physics has a SU(3) X SU(2) X U(1) symmetry. In later chapters, we will discover that the QED has a U(1) gauge symmetry, the electro-weak interaction has a SU(2) x U(1) symmetry and the strong interaction has a SU(3) gauge symmetry.

Antiparticles This is a fermion in an x vs t Feynman diagram. Question: How do we represent an anti-fermion line in a Feynman diagram ? Ans: a anti-particle is a particle traveling backwards in time ! Note the same is true for bosons and anti-bosons.

Connection between Feynman and Dirac Anti-particles have positive energies.

Griffiths writes down the Feynman rules for QED after the warm-up with a toy model.

Griffiths: QED Feynman rules

Griffiths: QED Feynman rules. Apologies: The Particle Physics graduate course, PHYS777, does most of these QED calculations in detail.

Review and examples

Fine structure in hydrogen and hydrogen-like atoms Review example: Fine structure in hydrogen and hydrogen-like atoms Calculate the energy difference due to the spin-orbit coupling between 3P3/2 and 3P1/2 states From the Dirac equation, notice the alpha2 dependence So how do we use this ?

Question: How does the fine structure splitting compare to the hyperfine splitting ?

Estimate the Bohr radius and energies for a K- p system. Example problem: Estimate the Bohr radius and energies for a K- p system. Hence μ=323 MeV, compared to 0.511 MeV for hydrogen Since the Bohr radius is 53 pm, this gives 83 fm for the kaonic-proton bound state. Could you do the case when an anti-deuteron (1875.6 MeV) is bound to a Si nucleus (A=28) as in the GAPS experiment ? (Also calculate x-ray energies for n=9876)

(Also calculate x-ray energies for n=9876) Could you do the case when an anti-deuteron (1875.6 MeV) is bound to a Si nucleus (A=28) as in the GAPS experiment ? (Also calculate x-ray energies for n=9876) Note that following the emission of x-rays, the anti-deuteron encounters matter. What happens next ? Is this a strong, weak or EM interaction ?

3) 2) 1) Compare the rates of these three processes ? 2) Amplitude~ α2 Rate~α4 3) Amplitude~ α3Rate~α6 2) and 3) are sometimes called radiative corrections.

Question: Is the decay π0γγ an electromagnetic, strong or weak decay ? Question: Draw the Feynman diagram for this process.

Question: Is light by light scattering possible ? (Yes, No) If no, explain why If yes, draw the Feynman diagram to produce new particles. What kinds of quarks can come out ? Two-photon physics is an important branch of high energy physics. Only q, qbar pairs. What are other possible final states ?

Draw the Feynman diagram (hint K0=sbar d) Question: Is the decay K0- π-e+ ν strong, weak, or EM ? Why ? Draw the Feynman diagram (hint K0=sbar d)

Consider the decay Δ++p π+. Is this a strong, weak or EM process ? Draw the Feynman diagram (Hint the Δ++ is a u u u bound state). Another hint.

Question: What is the Feynman diagram for muon decay ? (Hint: what are the decay products ? How many neutrinos are produced ?) Second hint: an electron and two neutrinos ?

Griffith’s catalogue of basic QED processes