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Hadronic structure on the light front. VIII. Light scalar and vector mesons

We use the QCD instanton vacuum model to discuss the emergence of the light scalar and vector mesons on the light front. We take into account both the instanton and anti-instanton single and molecular interactions on the light quarks, in the form of nonlocal effective interactions. Although the molecular induced interactions are suppressed by a power of the packing fraction, they are still sufficient to bind the vector mesons, while keeping most of the scalar spectrum relatively unchanged. We explicitly derive the light front distribution amplitudes and partonic functions for the scalar and vector mesons, and compare them after pertinent QCD evolution, to the available empirical and lattice measured counterparts. The Dirac electric form factors for both the pion and ρ meson are derived, and shown to compare well with current data. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

Determination of Pion and Kaon Structure Using the Sullivan Process at Moderate to large Fractional Momentum

Significant progress has been made in describing the structure of hadrons in terms of Quantum ChromoDynamics (QCD) degrees of freedom. The recently developed framework of Generalized Parton Distribtions (GPDs) may provide the path towards three-dimensional imaging of the hadronic structure. Integrating the GPDs over the fractional momentum (x), the form factors are obtained which are integrally related to understanding the emergent hadron mass-generating mechanism (EHM) embedded in QCD and the mass-scale that characterizes the proton [Roberts (2016)]. The Sullivan process, in which one scatters electrons off the proton?s virtual meson cloud and thus creates a meson target, is used to probe this structure. Studies of kaon electroproduction offer unique opportunities in this. The last two decades saw a dramatic improvement in the precision of charged meson form factor data, and new results have become available on the transition form factor. The KaonLT experiment (E12-09-011) carried out in Hall C at Jefferson Lab (Jlab) was designed to measure longitudinal/transverse (L/T) separated kaon cross sections required to access form factors and GPDs [Bosted et al. (2008)]. KaonLT aimed to confirm the exclusive kaon electroproduction mechanism, which is essential for determining the kaon form factor and investigating GPDs. The results obtained from this experiment have provided the highest Q2 for L-T separated kaon electroproduction cross section, and it is the first time that a separated kaon cross-section measurement has been carried out above W = 2:2GeV.

Trotta, Richard↗

Light-front puzzles

Abstract Light-front formulations of quantum field theories have many advantages for computing electroweak matrix elements of strongly interacting systems and other quantities that are used to study hadronic structure. The theory can be formulated in Hamiltonian form so non-perturbative calculations of the strongly interacting initial and final states are in principle reduced to linear algebra. These states are needed for calculating parton distribution functions and other types of distribution amplitudes that are used to understand the structure of hadrons. Light-front boosts are kinematic transformations so the strongly interacting states can be computed in any frame. This is useful for computing current matrix elements involving electroweak probes where the initial and final hadronic states are in different frames related by the momentum transferred by the probe. Finally in many calculations the vacuum is trivial so the calculations can be formulated in Fock space. The advantages of light front-field theory would not be interesting if the light-front formulation was not equivalent to the covariant or canonical formulations of quantum field theory. Many of the distinguishing properties of light-front quantum field theory are difficult to reconcile with canonical or covariant formulations of quantum field theory. This paper discusses the resolution of some of the apparent inconsistencies in canonical, covariant and light-front formulations of quantum field theory. The puzzles that will be discussed are (1) the problem of inequivalent representations (2) the problem of the trivial vacuum (3) the problem of ill-posed initial value problems (4) the problem of rotational covariance (5) the problem of zero modes and (6) the problem of spontaneously broken symmetries.

Physics↗

Observables for scattering on targets with arbitrary spin

Starting from the Weinberg formalism for fields of arbitrary spin, we discuss a method for the decomposition of matrix elements of QCD operators (local currents, quark/gluon bilinears) for targets with arbitrary spin. This procedure is advantageous for the systematic study of the structure of hadrons and nuclei, particularly in the case of spin-dependent observables. As higher spin targets exhibit new features in their hadronic structure, the investigation of these properties can enhance our understanding of the strong force. The construction allows for a unified framework to discuss spin > 1/2 very similar to the spin 1/2 case, without subsidiary conditions for the wave functions. Different types of spinors (canonical, helicity, light-front helicity) can be easily accommodated. Its numerical implementation is simple and can be entirely reduced to objects familiar from the rotation group. A natural sl(2,C) multipole decomposition emerges, enabling a physical interpretation of non-perturbative objects that multiply spinor bilinears as Generalized Form Factors. To demonstrate the efficacy of this method, we apply it to the description of a spin 1 target, such as the deuteron. We discuss extensions of the formalism to hard exclusive processes on the deuteron and beyond.

Vera, Frank↗

Transverse Spin and Momentum Structure of Hadrons in QCD (Final Technical Report)

This final technical report summarizes the work on the award DE-FG02-07ER41460, Transverse Spin and Momentum Structure of Hadrons in QCD. During the performance period, we addressed fundamental questions in nuclear physics, focusing on how hadrons—and, by extension, light nuclei—emerge from quark and gluon interactions within Quantum Chromodynamics (QCD).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Investigating the Transverse Structure of Hadrons Using Parton Pseudodistributions

Within the pseudo-PDF framework, we investigate the perturbative contributions to correlators that are used to study transverse momentum dependent parton distributions (TMDs) on the lattice. Our results contain the full perturbative corrections which arise as artifacts from performing the calculation for a Euclidean separation between the parton fields, as well as the corrections which yield the evolution equations for the TMDs. This gives a path to extraction of the genuine non-perturbative features of the three-dimensional structure of the hadrons from lattice calculations.

Santiago, Melvin Gabriel [Old Dominion Univ., Norf↗

CLAS Database for Studies of the Structure of Hadrons in Electromagnetic Processes

The CLAS Physics Database (CLAS DB) has been developed in collaboration between SINP at MSU and Hall B at Jefferson Lab. CLAS DB contains most experimental results on inclusive, semi-inclusive, and exclusive reactions on proton and nuclei obtained with the CLAS detector. The substantial part of these experimental results represents the only data sets available in the world. The results and analysis tools provided by the CLAS DB are of particular importance for studies of the structure of the ground and excited hadron states, offering insight into strong nonperturbative QCD dynamics, which underlie the generation of hadrons from quarks and gluons.

Chesnokov, V. V.↗

Machine-learning prediction for quasiparton distribution function matrix elements

There have been rapid developments in the direct calculation in lattice QCD (LQCD) of the Bjorken-x dependence of hadron structure through large-momentum effective theory (LaMET). LaMET overcomes the previous limitation of LQCD to moments (that is, integrals over Bjorken x) of hadron structure, allowing LQCD to directly provide the kinematic regions where the experimental values are least known. LaMET requires large-momentum hadron states to minimize its systematics and allow us to reach small- x reliably. This means that very fine lattice spacing to minimize lattice artifacts at order $(P_za)^n$ will become crucial for next-generation LaMET-like structure calculations. Furthermore, such calculations require operators with long Wilson-link displacements, especially in finer lattice units, increasing the communication costs relative to that of the propagator inversion. In this work, we explore whether machine-learning algorithms can make predictions of correlators to reduce the computational cost of these LQCD calculations. We consider two algorithms, gradient-boosting decision tree and linear models, applied to LaMET data, the matrix elements needed to determine the kaon and $η_s$ unpolarized parton distribution functions (PDFs), meson distribution amplitude (DA), and the nucleon gluon PDF. We find that both algorithms can reliably predict the target observables with different prediction accuracy and systematic errors. The predictions from smaller displacement z to larger ones work better than those for momentum p due to the higher correlation among the data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Simple relativistic quark models

A class of phenomenological relativistic models of hadronic systems motivated by quantum chromodynamics that have dual representations as models of mesons and nucleons or quarks and gluons is investigated. These models are designed to provided qualitative insight into the role of sea quarks in hadronic structure and reactions. The model assumption is that the Hamiltonian can be divided into two parts: one that involves degrees of freedom in the same connected local and global color singlet and the remaining interactions that allow the connected local and global color singlets to interact. The first class of interactions results in infinite towers of bare “particles” with hadronic quantum numbers. All but a finite number of these remain stable when the second class of interactions is included. The model interactions are expressed in terms of subhadronic degrees of freedom, which determine the bare hadronic spectrum and the interactions involving the bare hadrons in terms of a small number of subhadronic model parameters. As a first test, this paper considers the simplest case of mesons that interact via a string-breaking interaction. One virtue of this model is that all of the bare meson masses and eigenfunctions can be computed analytically. In addition, the string-breaking interaction leads to production vertices that can also be computed analytically. The relativistic wave functions have a light-front kinematic symmetry. The goal is to find a simple relativistic quantum mechanical model based on subhadronic degrees of freedom that can provide an efficient, qualitatively consistent description of hadronic masses, lifetimes, cross sections, sea quark effects, and electromagnetic properties. The simplicity of the model makes it a potentially useful tool to study the impact of sea quarks on hadronic structure and reactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗