Quarks, Leptons, and the Big Bang
In this chapter we introduce two topics that are the
core of modern physics research:
•Cosmology: What is the universe made of?
•Particle Physics: How did the universe come to
be the way it is?
1 General Properties of Elementary
1.1 Elementary Particles
Just by the time that quantum physics seemed to ex-
plain most questions about the atomic world, a new
wave of particle discoveries started.
Most of these particles (muon, pion, kaon, sigma) ex-
ist only for a few moments before transforming into
other particles following the same laws that govern
Consider that the number of any one type of particle
present in a sample is N0at time t= 0. Then the re-
maining number of particles in the sample Nat time
and the rate of decay Ris
for an initial rate of decay R0.
In the same way, the half-life of the particle is
Some of these particles have life spans so short - in
the 10−23 to 10−6seconds - that is impossible to ob-
serve them directly.
So, how do physicists generate the conditions for
creating these particles? They use particle accelera-
tors, like the Fermilab (in Chicago) or the CERN in
The number of these type of fundamental particles is
in the hundreds by the time this document was pre-
Is not our goal to account for all of them, but instead
we are going to use the classiﬁcation known as Stan-
dard Model to classify different types of fundamen-
1.2 Fermions or Bosons
Remember that all particles have an intrinsic angular
momentum called spin ~
In general, we are interested in its magnitude, and
the projection along the z-axis:
Sz=ms~for ms=s, s −1,...,−s, (4)
•msis the spin magnetic quantum number,
•sis the spin quantum number.
The spin quantum number is always of the form
2,for n= 1,2,3,.... (5)
An electron has s= 1/2, so it is called a spin-1
Afermion -named after Enrico Fermi - is any particle
with an spin quantum number of the form
2, . . .
i.e., its numerator is always an odd number.
Electrons, protons and neutrons are all fermions.
Aboson - named after Satyendra Nath Bose, is a par-
ticle with an integer spin quantum number.
For example, photons have s= 1 are bosons.
Why is so important to make a distinction between
these two groups of particles? For a simple but good
reason: fermions obey the Pauli exclusion principle,
while bosons are not bound by it.
Therefore, bosons can pile up in the quantum state
with lowest energy.