122 Thermal History of the Universe
Protons and anti-protons have electromagnetic interactions similar to positrons
and electrons. They can also annihilate into photons, or for instance into an electron–
positron pair via the mediation of a virtual photon,
p+p→훾virtual→e−+e+. (6.33)The reverse reaction is also possible, provided the electron and positron possess
enough kinetic energy to create a proton, or 938.3MeV.
Conservation laws. Note that the total electric charge is conserved throughout the
reactions in Equations (6.29)–(6.32). Electric charge can never disappear nor arise
out of neutral vacuum, but it can easily move from a charged particle to a neutral one
as long as that does not violate the conservation of total charge in the reaction. In
the annihilation of an e−e+pair into photons, all charges do indeed vanish, but only
because the sum of the charges was zero to start with.
There are two further conservation laws governing the behavior of baryons and
leptons.
(i)퐵orbaryon numberis conserved. This forbids the total number of baryons
minus anti-baryons from changing in particle reactions. To help the bookkeep-
ing in particle reactions one assigns the value퐵=1 to baryons and퐵=−1to
anti-baryons in a way analogous to the assignment of electric charges. Photons
and leptons have퐵=0.
(ii)퐿푙orl-lepton numberis conserved for each of the lepton flavours푙=e,휇,휏.
This forbids the total number of푙-leptons minus푙-anti-leptons from changing
in particle reactions. We assign퐿e=1toe−and휈e,퐿e=−1toe+and휈e,and
correspondingly to the members of the휇and휏families. Photons and baryons
have no lepton numbers.However, there is an amendment to this rule, caused by the complications in the
physics of neutrinos. Although the flavour state푙is conserved in neutrino reac-
tions, it is not conserved in free flight. To observe the flavour state푙of neutrinos is
not the same as observing the neutrino mass states. There are three neutrino mass
states called휈 1 ,휈 2 ,휈 3 , which are not identical to the flavour states; rather, they are
quantum-mechanical superpositions of them. The states are entangled in such a way
that a pure mass state is a mixture of flavour states, and vice versa. Roughly, the휈휇is
the mixture of^14 휈 1 ,^14 휈 2 and^12 휈 3.
All leptons participate in the weak interactions mediated by the heavy virtual vector
bosons W±and Z^0 and the scalarHiggs bosonH^0 .TheZ^0 is just like a photon except
that it is very massive, about 91GeV, and the two W±are its 10GeV lighter charged
partners. The mass of the H^0 is 125GeV. All these bosons freeze out of thermal equi-
librium at퐸≈100GeV.
There is no difference between weak and electromagnetic interactions: there are
charged-current electroweak interactions mediated by the W±, and neutral-current
interactions mediated by the Z^0 ,theH^0 and the훾. However, the electroweak symmetry
is imperfect because of the very different masses.