- #26

tom.stoer

Science Advisor

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In a sense you DO detect quarks experimentally.If you cannot detect quarks by themselves, what logic is used to experimentally detect an amount of spin or a magnetic moment to the quarks?

In deep inelastic scattering a

*single electron*interacts via a

*single photon exchange*with a

*single quark*. This interactions itself can be described perturbatively and reveals some information regarding the nucleon structure in terms of quarks (and gluons). The structure of the nucleon is encoded in so-called structure functions f

_{n}(x,Q²) saying that a certain particle species n (up-, down, strange, ..., anti-up, ..., gluon, ...) carries a certain fraction x of the total nucleon momentum when probed at a certain energy Q (carried by the exchanged photon).

You can find the kinematics of DIS and the detailed definiton of the structure functions in http://arxiv.org/abs/0812.3535v2

In DIS the logic is that the nuceon structure is intrinsically non-perturbative and that the quarks and gluons are confined in a highly non-trivial manner, but that the interaction with the electron via the exchanged photon is well-described perturbatively. This last assumption is based on the so-called

*asymptotic freedom*which says that a large momentum transfer quarks (and gluons) behave like free particles. This assumption can be cast in a mathematical expression and is proven to be valid as in the so-called scaling limit the above mentioned structure functions are Q-independent, i.e. F(x,Q²) → F(x). Small Q-dependence enters via so-called scaling violations still treated perturbatively. In this regime where the quarks behave like free particles their individual spin and magnetic moment is that of free spin 1/2 particles.

What we are discussing here is more complex than this simple explanation b/c we talk about so-called polarized or spin structure functions; the description can again be found in the article. The basic ideas regarding perturbative interaction of single electrons with asymptotic free quarks in the scaling limit is similar.