Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMultiplicative renormalizability of quasi-parton operators
101
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Extracting parton distribution functions (PDFs) from lattice QCD calculation of quasi-PDFs has been actively pursued in recent years. We extend our proof of the multiplicative renormalizability of quasi-quark operators in Ref. [1] to quasi-gluon operators, and demonstrated that quasi-gluon operators could be multiplicatively renormalized to all orders in perturbation theory, without mixing with other operators. We find that using a gauge-invariant UV regulator is essential for achieving this proof. With the multiplicative renormalizability of both quasi-quark and quasi-gluon operators, and QCD collinear factorization of hadronic matrix elements of there operators into PDFs, extracting PDFs from lattice QCD calculated hadronic matrix elements of quasi-parton operators could have a solid theoretical foundation.
rate research
Read More
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.
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 $f(x, mu^2)$.
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.
Two-loop anomalous dimensions and one-loop renormalization scheme matching factors are calculated for six-quark operators responsible for neutron-antineutron transitions. When combined with lattice QCD determinations of the matrix elements of these operators, our results can be used to reliably predict the neutron-antineutron vacuum transition time, $tau_{nbar{n}}$, in terms of basic parameters of baryon-number violating beyond-the-Standard-Model theories. The operators are classified by their chiral transformation properties, and a basis in which there is no operator mixing due to strong interactions is identified. Operator projectors that are required for non-perturbative renormalization of the corresponding lattice QCD six-quark operator matrix elements are constructed. A complete calculation of $delta m = 1/tau_{nbar{n}}$ in a particular beyond-the-Standard-Model theory is presented as an example to demonstrate how operator renormalization and results from lattice QCD are combined with experimental bounds on $delta m$ to constrain the scale of new baryon-number violating physics. At the present computationally accessible lattice QCD matching scale of $sim$ 2 GeV, the next-to-next-to-leading-order effects calculated in this work correct the leading-order plus next-to-leading-order $delta m$ predictions of beyond-the-Standard-Model theories by $< 26%$. Next-to-next-to-next-to-leading-order effects provide additional unknown corrections to predictions of $delta m$ that are estimated to be $< 7%$.
We present the first Monte Carlo based global QCD analysis of spin-averaged and spin-dependent parton distribution functions (PDFs) that includes nucleon isovector matrix elements in coordinate space from lattice QCD. We investigate the degree of universality of the extracted PDFs when the lattice and experimental data are treated under the same conditions within the Bayesian likelihood analysis. For the unpolarized sector, we find rather weak constraints from the current lattice data on the phenomenological PDFs, and difficulties in describing the lattice matrix elements at large spatial distances. In contrast, for the polarized PDFs we find good agreement between experiment and lattice data, with the latter providing significant constraints on the spin-dependent isovector quark and antiquark distributions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
