Lecture 9

Recall from last lecture:

The Dirac Equation

(ig_m d/dx_m - m)y = 0

where y is four-component spinor, each component being a wave function.

Lepton Flavors, Quark Flavors, and Interactions

Not all particles interact via all the forces. It is useful to state explicitly which forces act on which particles.

All of the fundamental particles are subject to gravitational interactions, even those with no mass (photons).
All of the quarks and leptons are subject to weak interactions.
Only the charged quarks and leptons are subject to electromagnetic interactions -- the neutrinos do not interact electromagnetically.
Only the quarks are subject to strong interactions -- the leptons do not interact strongly.

We do not see free quarks in our experiments -- we call this phenomenon confinement. An individually produced quark will dress into a hadron on a time scale of 10^-25 sec, as either a 3-quark combination called a baryon, or a quark-antiquark combination called a meson. For now, I list some of the hadrons and their constituent quark combinations. Also listed for each is its mass, and a quantity called strangeness that is discussed in the section on conservation laws.

Meson	Composition	Mass (MeV)	Strangeness
p⁺	u dbar	139.57018	0
K⁰	d sbar	497.672	+1
K^-	ubar s	493.677	-1
r^-	ubar d	771.1	0
w⁰	u ubar	782.57	0

Baryon	Composition	Mass	Strangeness
p	uud	938.27200	0
L	uds	1115.683	-1
X⁰	uss	1314.83	-2
S⁺	uus	1197.449	-1
W^-	sss	1672.45	-3

All of these particles have antiparticles, even the neutral particles, K⁰, L, and X⁰

Conservation Laws

Conserved quantities play an important role in physics, especially particle physics. I want to remind you of quantities that are conserved generally as well as the particular ones introduced for leptons and quarks. The table below lists the quantities with some examples of their application and some comments. Note that some quantities are conserved only in certain types of interactions.

Quantity	Forbidden Reaction	Comment
Charge	pp –> p‾p	Charge conservation rules out reactions such as the above.
Energy / Momentum	g –> e⁺e^-	This is called pair creation and can only happen in the presence of other matter; energy and momentum cannot both be conserved in this reaction.
Angular Momentum	r⁰ –> gg
Lepton Number	m^- –> e^-g	Lepton number conservation forbids this decay; neutrino oscillation indicates that lepton number can be violated in weak interactions.
Baryon Number	p –> p⁰e⁺	Baryon number conservation means that the lightest baryon, the proton, is absolutely stable; some GUT's predict proton decay, but with a lifetime of >10³¹ years.
Quark Flavor	L –> pp^-	Strangeness is conserved in strong and EM interactions; this is weak decay, explaining the long lifetime of the lambda.

The Cosmic Connection

I encourage you to read this section. Particle physics is important in the theory of the big bang, the processes in stars, and the collapse of stars into white dwarfs, neutron stars, and black holes. I will discuss these topics later as time permits.