You can view simple planar models for proton and meson formed of quarks ( 3 quarks to the proton, a quark and an antiquark in the meson ) . These models are far from reality , but they have the merit of giving an image , which is required to consider this reality. The next step would be to introduce the third dimension, quantum mechanics and relativity.
The attraction force between quarks is » harmonic » attractive and proportional to their distance. It is necessary to limit the range of these harmonic forces , so that they are not infinite at infinity : beyond a certain distance, the force is switched to zero . In two models « classic » distance limiting the range is the distance between quarks for the first, the distance of the quark to the center of gravity of the proton or meson. In a quantum model , the position of quarks changes any time depending on the probability wave function, which we assume uniform here; we’re not going very far in this model.
In all cases , the orbital angular momentum is assumed to be zero . Quarks are » colored » , and forces are symbolized by elastic with two colors. The proton and meson , which are » hadrons » ( particles formed of quarks and detectable by our apparatus) must be of « neutral color »: three different colors for the proton, color and anti- color for the meson .
We propose a very simple model of scattering of two particles (proton on proton, meson on proton ); there, quarks of two different hadrons (proton or meson ) attract when the particles are closer than a distance equal to the range of potential described above. You can follow the reaction both in the frames of center-of- mass and « laboratory » where the target is fixed, and see statistics on the scattering angle of the projectile particle; and one is then in conditions of an experiment.
Finally, we can look at the generation of hadrons from a quark-antiquark pair , the particles belonging initially to two hadrons which collide at very high energy.