Hadron structure functions in a chiral quark model: Regularization, scaling and sum rules

Abstract

We provide a consistent regularization procedure for calculating hadron structure functions in a chiral quark model. The structure functions are extracted from the absorptive part of the forward Compton amplitude in the Bjorken limit. Since this amplitude is obtained as a time-ordered correlation function its regularization is consistently determined from the regularization of the bosonized action. We find that the Pauli-Villars regularization scheme is most suitable because it preserves both the anomaly structure of QCD and the leading scaling behavior of hadron structure functions in the Bjorken limit. We show that this procedure yields the correct pion structure function. In order to render the sum rules of the regularized polarized nucleon structure functions consistent with their corresponding axial charges we find it mandatory to further specify the regularization procedure. This specification goes beyond the double subtraction scheme commonly employed when studying static hadron properties in this model. In particular the present approach serves to determine the regularization prescription for structure functions whose leading moments are not given by matrix elements of local operators. In this regard we conclude somewhat surprisingly that in this model the Gottfried sum rule does not undergo regularization.

Hadron structure functions in a chiral quark model

“…The subscript 'p' indicates that the spectral integral is restricted to those values of ω which cause the respective denominators of the spectral functions to vanish. Similar expressions are obtained for f 1 and g 2 [2]. For the polarized structure functions is important to remark that the isoscalar contribution, which is next to leading order in 1/N C does not undergo regularization while the leading order isovector contribution does.…”

“…In ref. [2] we have shown that considerable simplifications arise in the Bjorken limit; in particular the propagator between two insertions of the sources becomes that of a free quark, yielding the action…”

“…Finally from (6) we calculate the bilocal current correlation function and apply Cutkosky's rules to obtain the absorptive part (2).…”

Pion light-cone wave function and pion distribution amplitude in the Nambu–Jona-Lasinio model

“…To a large extent our treatment of PDA parallels the calculation of PDF carried out in previous works [37,38,39]. There, it has been argued that for inclusive processes, such as in deep inelastic scattering, by far the most convenient regularization scheme is the PauliVillars (PV) method.…”

Light-flavor sea-quark distributions in the nucleon in the SU(3) chiral quark soliton model. I. Phenomenological predictions

“…This is in contrast to some authors' claim that the imaginary action should not be regularized [23], [35]. The ground of their assertion is that the imaginary part of the Euclidean action is ultraviolet finite and that the introduction of regularization would destroy conservation laws of some fundamental quantities like the baryon number and/or the quark numbers.…”