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Quarks: The quarks are charged so besides the color force there is an electromagnetic force as well. This is true for the sea quarks and valence quarks. The Up quark has a charge of +2/3, and the Down quark is -1/3. This is important in the physics of their dynamics because when charges move, they make magnetic fields. The force from the electromagnetic charge scales as 1/r^2, where r is the distance between the quarks (charges). The color force on the other hand does not diminish as fast over distance, it is the same between quarks but will normally only act between two (sea-quarks) or three (valence quarks). The strength of the color force is roughly 137 times that of the electromagnetic force. When the proton is polarized the orbital motion is correlated to the proton's spin when the proton is not polarized the spin direction is chaotic. The up quark and the down quark rotate in opposite directions. The up quark has a mass of about 2 MeV while the down quark has a mass of about 4.8 MeV so the up quark is about 2.4 times faster than the down quark. The momentum of the quarks is faster when the quarks are closer together in the center of the proton and slow when they are farther apart. The valence quarks orbit the center of the proton with Up and Down going in different directions but also following chaotic and wild paths when unpolarized. Polarized protons have much more order with the valence quarks always orbiting the central axis. The sea quarks can also orbit the central axis and follow and interact with the valence quarks. There are sum-rules that govern the exchange between orbital angular momentum, and partonic spin, and how all of this is shared between all the pieces.
Models of Dynamics:
Spin Sum Rule: All of the components of parton spin and dynamics must lead to a total proton spin of 1/2. Its not possible to make this work without imposing some model dependence so its very important that all the above aspects are addressed first. Since the famous EMC experiments revealed that only a small fraction of the nucleon spin is due to quark spins, there has been a great interest in ‘solving the spin puzzle’, i.e. in decomposing the nucleon spin into contributions from quark/gluon spin and orbital degrees of freedom. In this effort, the Ji decomposition:
not only the quark spin contributions ?q but also the quark total angular momenta. Charged particles in a magnetic field are governed by a velocity EXB an orbital angular momentum L=rXEXB where r is the position vector [ref]. This means that the charges will orbit the center of the proton in opposite directions. This however is a very classical picture. The terms in the above equation are defined as quantum mechanical expectation values of the corresponding terms in the angular momentum tensor. A representation of this decomposition should start with the valence quarks and include the intrinsic spin of the quarks that hold the know spin percentage (randomly oriented otherwise). Then the OAM is represented classically as rotating charges in a B-field.
Meson Cloud Model: At any given instant, the proton might really be a neutron (ddu) plus a positively charged pion (ud- ud-)—or another proton (uud) plus a neutral pion. This violates energy conservation but it is allowed, for a fleeting moment, by the Heisenberg uncertainty principle. By adding up the contributions from all the possible channels, the theorists can model the composition of the sea.
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