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Register a new userNucleon quasi-Parton Distributions in the large N$_c$ limit
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In this letter, we investigate the nucleon quasi-parton distribution functions in the chiral quark soliton model. We derive a set of sum-rules depending on the velocity of the nucleon and on the Dirac matrix defining the distribution functions. We present numerical results for the isosinglet unpolarized distribution, in which we find that the anti-quark distribution breaks the positivity condition at nucleon velocities $vapprox 0.99;(P_Napprox 7.0 M_N)$ and smaller. We found that, for the isosinglet unpolarized case, a large nucleon momentum is required for the quasi-parton distribution to get close enough to the usual parton distribution function.
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Recently the concept of quasi parton distributions (quasi-PDFs) for hadrons has been proposed. Quasi-PDFs are defined through spatial correlation functions and as such can be computed numerically using quantum chromodynamics on a four-dimensional lattice. As the hadron momentum is increased, the quasi-PDFs converge to the corresponding standard PDFs that appear in factorization theorems for many high-energy scattering processes. Here we investigate this new concept in the case of generalized parton distributions (GPDs) by calculating the twist-2 vector GPDs in the scalar diquark spectator model. For infinite hadron momentum, the analytical results of the quasi-GPDs agree with those of the standard GPDs. Our main focus is to examine how well the quasi-GPDs agree with the standard GPDs for finite hadron momenta. We also study the sensitivity of the results on the parameters of the model. In general, our model calculation suggests that quasi-GPDs could be a viable tool for getting information about standard GPDs.
We discuss the structure of the parton quasi-distributions (quasi-PDFs) $Q(y, P_3)$ outside the canonical $-1 leq y leq 1$ support region of the usual parton distribution functions (PDFs). Writing the $y^n$ moments of $Q(y, P_3)$ in terms of the combined $x^{n-2l} k_perp^{2l}$-moments of the transverse momentum distribution (TMD) ${cal F} (x,k_perp^2)$, we establish a connection between the large-$|y|$ behavior of $Q(y,P_3)$ and large-$k_perp^2$ behavior of ${cal F} (x,k_perp^2)$. In particular, we show that the $1/k_perp^2$ hard tail of TMDs in QCD results in a slowly decreasing $sim 1/|y|$ behavior of quasi-PDFs for large $|y|$ that produces infinite $y^n$ moments of $Q(y,P_3)$. We also relate the $sim 1/|y|$ terms with the $ln z_3^2$-singulariies of the Ioffe-time pseudo-distributions $mathfrak{M} ( u, z_3^2)$. Converting the operator product expansion for $mathfrak{M} ( u, z_3^2)$ into a matching relation between the quasi-PDF $Q(y,P_3)$ and the light-cone PDF $f(x, mu^2)$, we demonstrate that there is no contradiction between the infinite values of the $y^n$ moments of $Q(y,P_3)$ and finite values of the $x^n$ moments of $f(x, mu^2)$.
I review the current status of lattice calculations for two selected observables related to nucleon structure: the second moment of the unpolarized parton distribution, <x> (u-d), and the first moment of the polarized parton distribution, the non-singlet axial coupling gA. The major challenge is the requirement to extract them sufficiently close to the chiral limit. In the former case, there still remains a puzzling disagreement between lattice data and experiment. For the latter quantity, however, we may be close to obtaining its value from the lattice in the immediate future.
We derive one-loop matching relations for the Ioffe-time distributions related to the pion distribution amplitude (DA) and generalized parton distributions (GPDs). They are obtained from a universal expression for the one-loop correction in an operator form, and will be used in the ongoing lattice calculations of the pion DA and GPDs based on the parton pseudo-distributions approach.
We propose a revised definition of quasi-distributions within the framework of large-momentum effective theory (LaMET) that improves convergence towards the large-momentum limit. Since the definition of quasi-distributions is not unique, each choice goes along with a specific matching function, we can use this freedom to optimize convergence towards the large-momentum limit. As an illustration, we study quasi-distributions with a Gaussian weighting factor that naturally suppresses long-range correlations, which are plagued by artifacts. This choice has the advantage that the matching functions can be trivially obtained from the known ones. We apply the Gaussian weighting to the previously published results for the nonperturbatively renormalized unpolarized quark distribution, and find that the unphysical oscillatory behavior is significantly reduced.
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