Quark-Hadron Duality and Color Polarizabilities

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Color polarizabilities: response of the color electric Ec→ and magnetic Bc→ fields in the nucleon when the nucleon is polarized in the direction given by the spin vector S.→

Within the theoretical framework of the operator product expansion, the moments, or integrals over Bjorken-x, of structure functions can be expanded in inverse powers of the momentum scale Q2. The leading term in the expansion corresponds to scattering from free quarks and is responsible for the scaling of the structure functions. The higher order terms involve mixed quark-gluon operators and contain information on long-range correlations between partons, which are related to quark confinement. Quark-hadron duality (equivalence of quark and hadron descriptions of structure function moments) occurs when the higher-order interaction terms are small.
An example of a quantity which reflects such quark-gluon interactions that was extracted recently from moments of the spin dependent structure functions of the nucleon is the "color polarizability." This describes how the color electric and magnetic fields respond when the nucleon is polarized. The results indicate small but positive color electric polarizabilities for both the proton and neutron, but a negative magnetic polarizability for the proton, and one consistent with zero for the neutron. The negative value for the proton magnetic polarizability suggests that, on average, the induced color magnetic field in a proton is oriented in a direction opposite to that of its spin.
Also see Quark-Hadron Duality entry.
M. Osipenko et al., Phys. Lett. B 609 (2005) 259
Z. -E. Meziani et al., Phys. Lett. B 613 (2005) 148
W. Melnitchouk, R. Ent and C.E. Keppel, Physics Reports 406 (2005) 127