Parton densities in the modified chiral quark model

Abstract

The feature of parton densities inside the nucleon at low Q 2 plays an essential role in particle physics. To calculate these densities there are different types of models, among which the chiral quark model (χ QM) is the famous one. In this model, baryons are made from the ground states of constituent quarks, which are initially bare and finally surrounded by pseudo-scalar mesonic clouds. Here, in addition to mesonic clouds, we also take into account the gluonic clouds. The required bare quarks are obtained using the solution of the Dirac equation under a squared radial potential. The wavefunctions which are primarily in momentum space can be converted to a distribution in the x-Bjorken space by two different methods. Using the modified χ QM, we extract the parton distributions inside the proton at low Q 2 values and compare them with some experimental and phenomenological groups. The distributions can be evolved to high-energy scales, using the DGLAP evolution equations. The results are in good agreement with available experimental data and some phenomenological groups.

Unpolarized transverse momentum-dependent densities based on the modified chiral quark model

“…In Eq. (13) we use the relations which exist between the components of four vector momentum in standard coordinates and light cone coordinates so we can write [10,21]: dp 0 dp 3 d 2 p T = 1 2 M t dp − dxd 2 p T .…”

“…In these scales, the light quark masses are not ignorable in comparison with the nucleon mass and chiral symmetry is broken. In the χQM , the bare quarks inside the nucleon are surrounded by the clouds of Goldstone (GS) bosons and gluons [9,10]. Considering the interactions which occur in this bounded system at the first approximation and also the relations between the transverse momentum of the bare quarks and GS bosons(gluons) in these interactions, we can obtain the TMD quark and gluon distributions inside the proton.…”

Unpolarized TMD Quark Distribution Functions at Low $Q^2$ Scales

“…In this model, proton is considered as a bounded system of bare u and d quarks (u 0 , d 0 ). In this system, the clouds of Goldstone (GS) bosons and gluons surround the bare quarks [12,13,14]. At the first approximation, two basic interactions are occurred in the χQM which are represented…”

“…[7] in Fig.1. For the interaction of Fig.1(a), the distribution of j quark is written as [12,13,14]:…”

“…jB denotes the squared invariant mass of the final quark-GS boson state [12,13,14]. On the other hand, the interaction of Fig.1(b) is formulated as follows [14]:…”