Flux tube model

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## Flux tube model

The flux tube model is a method for deciding which quarks are to interact by the exchange of gluon(s).

Quantum Chromo-Dynamics (QCD) adds a new quantum number to quarks. This allows all three quarks of a baryon to have otherwise similar quantum numbers. (The Pauli exclusion principle would apply otherwise) Quarks therefore come in three colours: red, green and blue. The combination of the three colours in a baryon results in a colourless particle. QCD suggests that the reason quarks are not observed in isolation is because only colourless assemblies can be observed. three-quark4Possible flux tube arrangements for three quarks

In the case of mesons, (pions, kaons, etc.) there are two quarks involved: a quark and an anti-quark. The anti-quark of a red quark is anti-red, so mesons are also colourless. (Similarly for blue and green quarks, but colour is degenerate in mesons)

Properly, the gluons that carry the strong force are also carriers of colour. This allows gluons to actually form complex arrangements not possible in quantum electrodynamics (QED). In the context of this experiment, an important aspect of the colour carrying nature of the gluons is that they can result in colour exchanges between the quarks. This mode of interaction has not been included.

In the flux tube model, the gluons become tubes connecting two or three quarks. In a system of many quarks, the selection of which pairs or triplets to connect is done in a way to minimize the total distance involved. The longer the flux tube, the further that the gluon particles are must travel. Since they travel at a finite velocity, a longer distance requires a longer time. (See figure ) two-quark-optimum5Optimal arrangement for three pairs By the uncertainty equation, , the longer the virtual particle exists, the lower the energy available to be borrowed to make the virtual particle.

mcr@ccs.carleton.ca