Valence QCD: Connecting QCD to the quark model

Abstract

A valence QCD theory is developed to study the valence quark properties of hadrons. To keep only the valence degrees of freedom, the pair creation through the Z graphs is deleted in the connected insertions; whereas, the sea quarks are eliminated in the disconnected insertions. This is achieved with a new "valence QCD" lagrangian where the action in the time direction is modified so that the particle and antiparticle decouple. It is shown in this valence version of QCD that the ratios of isovector to isoscalar matrix elements (e.g. F A /D A and F S /D S ratios) in the nucleon reproduce the SU (6) quark model predictions in a lattice QCD calculation. We also consider how the hadron masses are affected on the lattice and discover new insights into the origin of dynamical mass generation. It is found that, within statistical errors, the nucleon and the ∆ become degenerate for the quark masses we have studied (ranging from one to four times the strange mass). The π and ρ become nearly degenerate in this range. It is shown that valence QCD has the C, P, T symmetries. The lattice version is reflection positive. It also has the vector and axial symmetries, the latter leads to a modified partially conserved axial Ward identity. As a result, the theory has a U (2N F ) symmetry in the particle-antiparticle space. Through lattice simulation, it appears that this is dynamically broken down to U q (N F ) × U q(N F ). Furthermore, the lattice simulation reveals spin degeneracy in the hadron masses and various matrix elements. This leads to an approximate U q (2N F ) × U q(2N F ) symmetry which is the basis for the valence quark model. In addition, we find that the masses of N, ∆, ρ, π, a 1 , and a 0 all drop precipitously compared to their counterparts in the quenched QCD calculation. This is interpreted as due to the disapperance of the 'constituent' quark mass which is dynamically generated through tadpole diagrams. The origin of the hyper-fine splitting in the baryon is largely attibuted to the Goldstone boson exchanges between the quarks. Both of these are the consequences of lacking chiral symmetry in valence QCD. We discuss its implication on the models of hadrons.

Pion distribution amplitude from lattice QCD

“…One can then convert the quasi observable to the light cone one through a factorization or matching formula [23] (there exist also other approaches to extract light cone quantities from Euclidean ones, see e.g. [24][25][26][27][28]). There have been many studies on factorization [29] and determinations of the one-loop corrections needed to connect finite-momentum quasidistributions to light cone distributions for nonsinglet leading-twist PDFs [30], generalized parton distributions (GPDs) [31], transversity GPDs [32] and pion DA [31] in the continuum.…”

Parton Distribution Function from Hadronic Tensor

“…It has been shown [1,2,3,4,5] that the hadronic tensor W µν (q 2 , ν) can be obtained from the Euclidean path-integral formalism. In this case, one considers the ratio of the four-point function χ N ( p,t)…”

“…In addressing the origin of the Gottfried sum rule violation, it is shown [1,2,3] that the contributions to the four-point function of the Euclidean path-integral formulation of the hadronic tensor W µν ( q 2 , τ) in Eq. (1.6) can be classified according to different topologies of the quark paths between the source and the sink of the proton.…”

“…Recently, there is an improved MEM which can lead to more stable fit [22]. The improved probability to maximize is 2) where N τ is the number of τ i and S is modified to…”

Quark and glue momenta and angular momentum in the nucleon

“…The three-point functions for quarks have two topologically distinct contributions in the pathintegral diagrams -one from connected (CI) and the other from disconnected insertions (DI) [10,11,12]. For DI, we sum over the current insertion time, t 1 , between the source and the sink time, i.e.…”