Structure Functions of the Nucleon in a Soliton Model

Abstract

We study nucleon structure functions in the soliton picture of the bosonized Nambu-Jona-Lasinio model. We focus on their vacuum contributions and examine whether they are outweighed by their valence quark counterparts.

Chiral Soliton Models and Nucleon Structure Functions

“…The results discussed in this section are mostly taken from Refs. [25,26]. There are several steps until we can perform a sensible comparison with experimental data.…”

“…We will refrain from presenting lengthy formulas as, e.g., the extremely bulky expressions involving the Fourier transforms of the radial functions in Ψ α [25,26]. Rather we focus on explaining the treatment of the pole terms without going into too much details.…”

“…A posteriori this justifies the omission of all terms in Equation ( 25) that did not contain a factor q / in the numerator (The full calculation also produces terms involving (k / − p / ± q /) 2 in Equation (25). With Equation (26) it is obvious that they do not contribute to the absorptive part even though they have a finite Bjorken limit.). After taking the traces in color and spinor spaces the structure function can be read off from T 11 + T 22 Bj −→ 2F(x) using, e.g.,…”

“…For this example we will also explain how sum rules are established in the fully regularized formulation. For further details on other structure functions, that are obtained using quite a similar procedure, we refer to to original literature [24][25][26].…”

“…At this stage of the project we will not identify the quark degrees of freedom with those of QCD, which, for example, means that the current quark mass is a free parameter. The theoretical framework has been derived already some time ago [24] while the numerical results arising from costly simulations have only been obtained recently [25,26]. As mentioned above, a major motivation for the soliton picture arises from generalizing QCD to a nonabelian gauge theory with large N C .…”