I have no idea on how to start this.
Based on the color confinement, discuss about if it is possible to
have the following hadron states:
1) |q>
2) |qq>
3) |qqq (bar)>
4) |qq(bar)qq(bar)>
To discuss whether it is possible to have the mentioned hadron states, we need to understand the concept of color confinement in quantum chromodynamics (QCD).
Color confinement is a fundamental property of QCD, the theory describing the strong nuclear force. According to color confinement, quarks and gluons, which are the basic building blocks of hadrons, such as protons and neutrons, cannot exist as isolated particles. They are always combined in a way that the resulting states are color-neutral.
Let's analyze each of the mentioned hadron states:
1) |q>
This state represents a single quark. However, a single quark cannot be observed as an isolated particle. Due to color confinement, a quark needs to be combined with other quarks or antiquarks to form color-neutral hadrons. Therefore, a state consisting of a single quark is not possible to have as a stable hadron.
2) |qq>
This state represents a combination of two quarks. As mentioned earlier, quarks need to combine in a way that the resulting state is color-neutral. In the case of two quarks, they can form either a meson or a diquark. Mesons consist of a quark-antiquark pair, while diquarks are color-neutral pairs of quarks. Both mesons and diquarks are stable hadron states. So, it is possible to have a state consisting of two quarks.
3) |qqq(bar)>
This state represents a combination of three quarks and an antiquark. Just like in the previous case, quarks need to form color-neutral combinations. Three quarks can combine to form either a baryon or a baryonic resonance. Baryons, such as protons and neutrons, consist of three quarks, whereas baryonic resonances involve excited states of baryons. So, it is possible to have a state consisting of three quarks and an antiquark.
4) |qq(bar)qq(bar)>
In this state, there is a combination of two quarks and two antiquarks. Similar to the previous cases, quarks and antiquarks need to form color-neutral combinations. However, the combination mentioned here does not form any known stable hadronic state. Such a combination violates the color confinement principle and is not observed in nature.
In summary, based on the color confinement principle:
1) A single quark cannot exist in isolation as a stable hadron.
2) A combination of two quarks can form either a meson or a diquark, which are stable hadron states.
3) A combination of three quarks and an antiquark can form a baryon or a baryonic resonance, which are stable hadron states.
4) A combination of two quarks and two antiquarks does not form any known stable hadronic state.
To study and understand the properties of hadrons and their allowed combinations, one needs to use the principles and techniques of quantum chromodynamics, such as lattice QCD simulations or theoretical calculations based on QCD.