5 Strong Interactions
5.1 Strong interactions
The strong interaction binds the constituents of nucleons and other hadrons. Its properties can
be summarised as follows:
• It acts only on quarks.
• It is strong, overcoming the Coulomb repulsion in the nucleus
• It binds quarks in only two configurations: 𝑞𝑞𝑞𝑞𝑞𝑞 for baryons (and 𝑞𝑞�𝑞𝑞�𝑞𝑞� for antibaryons)
and 𝑞𝑞𝑞𝑞� for mesons.
[Note: The discovery of states known as “pentaquarks” was recently announced. These states
are made of 4 quarks and one anti-quark. ]
In this section, we discuss the properties of the strong interaction, while we will cover the
classification of hadrons in a later chapter.
The quarks in baryons can be described by a wavefunction with a spin and a spatial part.
However, it appears that the quarks violate the Pauli exclusion principle, in that there are
cases where the total wave function is symmetric under the interchange of two identical
quarks – indeed, in some cases three identical quarks have identical spin and orbital quantum
numbers! For example the Δ++ particle is made of 3 identical u-quarks in the same quantum
state, appearing to violate the Pauli exclusion principle.
The explanation of this is that the quarks also carry an additional quantum number, which is
different for all three quarks in a baryon. This quantum number also corresponds to the
source or “charge” of the strong interaction. The fact that the sum of three equivalent but
different “strong charges” are required to produce a neutral state has led to this charge being
known as colour, in analogy with the addition of three primary colours, red, green and blue,
making white light. Each quark is labelled as red, green or blue, while antiquarks carry the
equivalent “anticolours”. All hadrons, whether 𝑞𝑞𝑞𝑞𝑞𝑞 or 𝑞𝑞�𝑞𝑞 , are therefore seen to be colour-
neutral states.
The strong interaction is a gauge interaction mediated by a massless, spin 1 gluon, g, which is
electrically neutral but carries a composite colour such as red- ������
blue (where ������
blue means “anti-
blue”). The coupling constant is known as 𝛼𝛼𝑠𝑠 (alpha-strong) and the theory is known as
Quantum Chromodynamics or QCD in analogy with QED. Fig. 5.1 (a) shows the interaction
between two quarks of different colour (red and blue in this example) by exchanging a gluon
������.
carrying red- blue
Unlike in QED, the gluon e.g. the exchange quantum is also a source of the field, so processes
such as the branching of one gluon into two can occur, with the vertex in Fig 5.1 (b) also
possible along with the vertex in Fig 5.1 (c) which is similar to the basic QED vertex.
37
, (a) (b) (c)
Fig 5.1. (a) QCD interaction between two quarks with an exchange in colour. (b) the three-
gluon vertex (x) the qqg vertex
A consequence of the additional gluon interaction vertex is a different expression for the
static QCD potential, which takes the form:
4 𝛼𝛼𝑠𝑠 ℏ𝑐𝑐
𝑈𝑈𝑠𝑠 = − + 𝑘𝑘𝑘𝑘
3 𝑟𝑟
The first term has a 1/r dependency, which is similar to what we would have in QED
𝑒𝑒 2 1 𝛼𝛼𝑒𝑒𝑒𝑒 ℏ𝑐𝑐
𝑈𝑈𝑒𝑒𝑒𝑒 = − =−
4𝜋𝜋𝜖𝜖0 𝑟𝑟 𝑟𝑟
(note the 𝛼𝛼𝑠𝑠 constant to replace the 𝛼𝛼𝑒𝑒𝑒𝑒 constant in QED).
The second term has an interesting dependency in r, which means that the potential energy
gets larger as the distance increases. In QED the potential energy goes to zero if the distance
goes to infinity. In QCD if a quark-antiquark pair is pulled apart their potential energy will
increase with the distance.
The behaviour of a quark-antiquark pair is shown in Fig 5.2 (which is not a Feynman diagram,
but just a drawing of how a quark-antiquark pair behaves). As the distance increases from
picture (1) to picture (2), the potential energy increases. If we keep pulling, there is enough
potential energy to create a new quark-antiquark pair as in picture (3).
Hence quarks cannot be isolated and studied individually, unlike electromagnetic charged
particles. This property is called quark confinement, and is a specific feature of QCD derived
by the presence of additional interaction vertexes as the one in Fig 5.1 (b).
Fig 5.2. Picture of a 𝑄𝑄�𝑄𝑄 pair being pulled apart until a new pair is created
If a quark is ejected from a hadron, the colour field builds up until it becomes energetically
favourable to create a quark-antiquark pair and reduce the field. The new 𝑞𝑞 and 𝑞𝑞� are
attracted to the original particles, and produce a colourless meson and baryon. When many
pairs are produced, this results in a jet of particles following the original quark direction.
These can be observed both in inelastic scattering of a lepton from a hadron (where the struck
quark in the hadron is ejected) and in 𝑒𝑒 + 𝑒𝑒 − annihilation, where a rapidly separating 𝑞𝑞𝑞𝑞� pair
is produced.
38
5.1 Strong interactions
The strong interaction binds the constituents of nucleons and other hadrons. Its properties can
be summarised as follows:
• It acts only on quarks.
• It is strong, overcoming the Coulomb repulsion in the nucleus
• It binds quarks in only two configurations: 𝑞𝑞𝑞𝑞𝑞𝑞 for baryons (and 𝑞𝑞�𝑞𝑞�𝑞𝑞� for antibaryons)
and 𝑞𝑞𝑞𝑞� for mesons.
[Note: The discovery of states known as “pentaquarks” was recently announced. These states
are made of 4 quarks and one anti-quark. ]
In this section, we discuss the properties of the strong interaction, while we will cover the
classification of hadrons in a later chapter.
The quarks in baryons can be described by a wavefunction with a spin and a spatial part.
However, it appears that the quarks violate the Pauli exclusion principle, in that there are
cases where the total wave function is symmetric under the interchange of two identical
quarks – indeed, in some cases three identical quarks have identical spin and orbital quantum
numbers! For example the Δ++ particle is made of 3 identical u-quarks in the same quantum
state, appearing to violate the Pauli exclusion principle.
The explanation of this is that the quarks also carry an additional quantum number, which is
different for all three quarks in a baryon. This quantum number also corresponds to the
source or “charge” of the strong interaction. The fact that the sum of three equivalent but
different “strong charges” are required to produce a neutral state has led to this charge being
known as colour, in analogy with the addition of three primary colours, red, green and blue,
making white light. Each quark is labelled as red, green or blue, while antiquarks carry the
equivalent “anticolours”. All hadrons, whether 𝑞𝑞𝑞𝑞𝑞𝑞 or 𝑞𝑞�𝑞𝑞 , are therefore seen to be colour-
neutral states.
The strong interaction is a gauge interaction mediated by a massless, spin 1 gluon, g, which is
electrically neutral but carries a composite colour such as red- ������
blue (where ������
blue means “anti-
blue”). The coupling constant is known as 𝛼𝛼𝑠𝑠 (alpha-strong) and the theory is known as
Quantum Chromodynamics or QCD in analogy with QED. Fig. 5.1 (a) shows the interaction
between two quarks of different colour (red and blue in this example) by exchanging a gluon
������.
carrying red- blue
Unlike in QED, the gluon e.g. the exchange quantum is also a source of the field, so processes
such as the branching of one gluon into two can occur, with the vertex in Fig 5.1 (b) also
possible along with the vertex in Fig 5.1 (c) which is similar to the basic QED vertex.
37
, (a) (b) (c)
Fig 5.1. (a) QCD interaction between two quarks with an exchange in colour. (b) the three-
gluon vertex (x) the qqg vertex
A consequence of the additional gluon interaction vertex is a different expression for the
static QCD potential, which takes the form:
4 𝛼𝛼𝑠𝑠 ℏ𝑐𝑐
𝑈𝑈𝑠𝑠 = − + 𝑘𝑘𝑘𝑘
3 𝑟𝑟
The first term has a 1/r dependency, which is similar to what we would have in QED
𝑒𝑒 2 1 𝛼𝛼𝑒𝑒𝑒𝑒 ℏ𝑐𝑐
𝑈𝑈𝑒𝑒𝑒𝑒 = − =−
4𝜋𝜋𝜖𝜖0 𝑟𝑟 𝑟𝑟
(note the 𝛼𝛼𝑠𝑠 constant to replace the 𝛼𝛼𝑒𝑒𝑒𝑒 constant in QED).
The second term has an interesting dependency in r, which means that the potential energy
gets larger as the distance increases. In QED the potential energy goes to zero if the distance
goes to infinity. In QCD if a quark-antiquark pair is pulled apart their potential energy will
increase with the distance.
The behaviour of a quark-antiquark pair is shown in Fig 5.2 (which is not a Feynman diagram,
but just a drawing of how a quark-antiquark pair behaves). As the distance increases from
picture (1) to picture (2), the potential energy increases. If we keep pulling, there is enough
potential energy to create a new quark-antiquark pair as in picture (3).
Hence quarks cannot be isolated and studied individually, unlike electromagnetic charged
particles. This property is called quark confinement, and is a specific feature of QCD derived
by the presence of additional interaction vertexes as the one in Fig 5.1 (b).
Fig 5.2. Picture of a 𝑄𝑄�𝑄𝑄 pair being pulled apart until a new pair is created
If a quark is ejected from a hadron, the colour field builds up until it becomes energetically
favourable to create a quark-antiquark pair and reduce the field. The new 𝑞𝑞 and 𝑞𝑞� are
attracted to the original particles, and produce a colourless meson and baryon. When many
pairs are produced, this results in a jet of particles following the original quark direction.
These can be observed both in inelastic scattering of a lepton from a hadron (where the struck
quark in the hadron is ejected) and in 𝑒𝑒 + 𝑒𝑒 − annihilation, where a rapidly separating 𝑞𝑞𝑞𝑞� pair
is produced.
38
