Elements of Modern Physics
372
up of c c (c has charm 1 while c has charm –1). Since each charmed quark
retains its charm these Ψ-mesons cannot decay into particles which do not contain
c or c as constituents which explains their long lifetimes (other particles which
contain charm are too heavy to provide decay channels).
10.3 ELECTROMAGNETIC INTERACTION
All charged particles (leptons, quarks and hadrons) interact electromagnetically.
Even neutral particles have this interaction because of their charge distribution,
for example, the neutron has zero charge but a fairly large magnetic dipole
moment. The electromagnetic interaction between particles is propagated by
the exchange of photons. An emission by a particle, of a photon of energy
E introduces an uncertainty in the energy of the particle. The uncertainty principle
implies that the system can remain in this state for a period of time
∆t ~ /E
(10.14)
During this time the photon can travel a distance
x ~ /
c E
(10.15)
which essentially defines the range of the interaction. Since photons have zero
mass, they can have an indefinitely small energy which means that the
electromagnetic forces are long-range forces. The strength of these forces is
characterized by the fine structure constant α
α ≈ 1/37
(10.16)
which is much smaller than the strength of strong interactions characterised by
α s in Eq. (10.4).
The interaction between hadrons is dominated by the strong interaction,
with electromagnetic interaction providing small corrections. For example, the
proton an the neutron (as also π
+
and π
0
, and other multiplets of a given isospin
multiplet) have slightly different masses which is generally attributed to the
difference in their electromagnetic interactions. Small differences due to
electromagnetic interaction are observed in the so-called mirror nuclei, which
have the same strong interactions but different charges. However, strong
interactions are of short range r 0 ~ 10
–15
m, so that the interaction between
hadrons at large distances is dominated by the electromagnetic forces, e.g.
Rutherford scattering.
The electromagnetic interaction comes into its own domain in the description
of the properties of charged leptons. The dominant interaction of the charged
leptons (which do not have strong interaction) is the electromagnetic interaction.
Fortunately, electromagnetic interactions of charged particles are well-defined
through a generalization of the minimal electromagnetic interaction introduced
by Eqs. (4.89) and (4.90). Furthermore, since the strength of the electromagnetic
372
up of c c (c has charm 1 while c has charm –1). Since each charmed quark
retains its charm these Ψ-mesons cannot decay into particles which do not contain
c or c as constituents which explains their long lifetimes (other particles which
contain charm are too heavy to provide decay channels).
10.3 ELECTROMAGNETIC INTERACTION
All charged particles (leptons, quarks and hadrons) interact electromagnetically.
Even neutral particles have this interaction because of their charge distribution,
for example, the neutron has zero charge but a fairly large magnetic dipole
moment. The electromagnetic interaction between particles is propagated by
the exchange of photons. An emission by a particle, of a photon of energy
E introduces an uncertainty in the energy of the particle. The uncertainty principle
implies that the system can remain in this state for a period of time
∆t ~ /E
(10.14)
During this time the photon can travel a distance
x ~ /
c E
(10.15)
which essentially defines the range of the interaction. Since photons have zero
mass, they can have an indefinitely small energy which means that the
electromagnetic forces are long-range forces. The strength of these forces is
characterized by the fine structure constant α
α ≈ 1/37
(10.16)
which is much smaller than the strength of strong interactions characterised by
α s in Eq. (10.4).
The interaction between hadrons is dominated by the strong interaction,
with electromagnetic interaction providing small corrections. For example, the
proton an the neutron (as also π
+
and π
0
, and other multiplets of a given isospin
multiplet) have slightly different masses which is generally attributed to the
difference in their electromagnetic interactions. Small differences due to
electromagnetic interaction are observed in the so-called mirror nuclei, which
have the same strong interactions but different charges. However, strong
interactions are of short range r 0 ~ 10
–15
m, so that the interaction between
hadrons at large distances is dominated by the electromagnetic forces, e.g.
Rutherford scattering.
The electromagnetic interaction comes into its own domain in the description
of the properties of charged leptons. The dominant interaction of the charged
leptons (which do not have strong interaction) is the electromagnetic interaction.
Fortunately, electromagnetic interactions of charged particles are well-defined
through a generalization of the minimal electromagnetic interaction introduced
by Eqs. (4.89) and (4.90). Furthermore, since the strength of the electromagnetic