# A naive quark model

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.

## Publié par

### Benoît Delcourt

Ex-professeur d'Université à Paris XI, centre d'Orsay. Spécialité de recherche: la physique expérimentale des particules élémentaires. Après une thèse sur la photoproduction du méson éta, j'ai participé aux expériences sur les anneaux de collision ACO et DCI, puis sur une expérience d'annihilation p-pbar au CERN, enfin à l'epérience H1 à Hambourg. Je tiens à rendre hommage à mes maîtres, aujourd'hui disparus: Jean Pérez-Y-Jorba et Jean-Claude Bizot.