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Frank Vera

Publications and source records attributed to Frank Vera.

7 recordsLinked to original sources
arXiv2025

Spinor Representations for Fields with any Spin: Lorentz Tensor Basis for Operators and Covariant Multipole Decomposition

This paper discusses a framework to parametrize and decompose operator matrix elements for particles with higher spin $(j > 1/2)$ using chiral representations of the Lorentz group, i.e. the $(j,0)$ and $(0,j)$ representations and their parity-invariant direct sum. Unlike traditional approaches that require imposing constraints to eliminate spurious degrees of freedom, these chiral representations contain exactly the $2j+1$ components needed to describe a spin-$j$ particle. The central objects in the construction are the $t$-tensors, which are generalizations of the Pauli four-vector $\sigma^\mu$ for higher spin. For the generalized spinors of these representations, we demonstrate how the algebra of the $t$-tensors allows to formulate a generalization of the Dirac matrix basis for any spin. For on-shell bilinears, we show that a set consisting exclusively of covariant multipoles of order $0\leq m \leq 2j$ forms a complete basis. We provide explicit expressions for all bilinears of the generalized Dirac matrix basis, which are valid for any spin value. As a byproduct of our derivations we present an efficient algorithm to compute the $t$-tensor matrix elements. The formalism presented here paves the way to use a more unified approach to analyze the non-perturbative QCD structure of hadrons and nuclei across different spin values, with clear physical interpretation of the resulting distributions as covariant multipoles.

hep-ph↗
arXiv2022

A New Structure in the Deuteron

We demonstrate that a paradigm shift from considering the deuteron as a system of bound proton and neutron to considering it as a pseudo-vector system in which we observe proton and neutron, results in a possibility of probing a new "incomplete" P-state like structure on the light-front (LF), at extremely large internal momenta, which can be achieved in high energy transfer electro-disintegration of the deuteron. Investigating the deuteron on the light-front, where the vacuum-fluctuations are suppressed, we found that this new structure, together with conventional S- and D- states, is a leading order in transferred energy of the reaction, thus it is not suppressed on the light-front.The incompleteness of the observed P-state results in a violation of angular condition which can happen only if deuteron contains non-nucleonic structures such as $Δ$$Δ$, $N^*N$ or hidden color components. We demonstrate that experimentally verifiable signatures of "incomplete" P-states are angular anisotropy of LF momentum distribution of the nucleon in the deuteron as well as an enhancement of the tensor polarization strength beyond the S- and D- wave predictions at large internal momenta in the deuteron.

nucl-th↗
arXiv2021

Probing the Structure of Deuteron at Very Short Distances

We study the electrodisintegration of deuteron at quasi-elastic kinematics and high transferred momentum as a probe for the short distance structure in nuclei. In this reaction, an electron hits a nucleus of deuterium, which breaks up into a proton-neutron pair. We focus our attention on events where fast nucleons emerge, corresponding to nuclear configurations where the bound nucleons have a high relative momentum (exceeding 700 MeV/c). The present research is relevant to physical systems where high-density nuclear matter is present. This condition covers a wide range of physics, from neutron stars to nuclei stability and the repulsive nuclear core. The present work differs from previous studies in two crucial features. One is the definition of the deuteron wave function, which include terms of a relativistic origin that can be ordered based on their relative contribution to the deuteron's internal momentum distribution. These terms, related to the off-shell properties of the nucleon-nucleon bound-state, do not occur in non-relativistic quantum mechanics. However, they become increasingly important in describing configurations with a high nucleon-nucleon relative momentum. The second difference is that we account for the off-shell nature of the bound nucleon that enters on the definition of the (half-off-shell) electromagnetic current. We avoid many of the difficulties inherent to the relativistic nature of the processes involved by adopting a theoretical framework known as Light Front dynamics. Simultaneous simplifications in the definition of the relativistic wave function for the proton-neutron bound state and the treatment of the (half-off-shell) electromagnetic current for the bound nucleon are among the essential advantages resulting from the use of the Light Front dynamics.

nucl-th↗
arXiv2021

A Novel Feature of Valence Quark Distributions in Hadrons

Examining the evolution of the maximum of valence quark distribution weighted by Bjorken x, $h(x,t)\equiv xq_V(x,t)$, we observe that $h(x,t)$ at the peak should become a one parameter function; $h(x_p,t)=Φ(x_p(t))$, where $x_p$ is the position of the peak and $t= \log{Q^2}$. This observation is used to derive a new model independent relation which connects the partial derivative of the valence parton distribution functions (PDFs) in $x_p$ to the QCD evolution equation through the $x_p$-derivative of the logarithm of the function $Φ(x_p(t))$. A numerical analysis of this relation using empirical PDFs results in a observation of the exponential form of the $Φ(x_p(t)) = h(x_p,t) = Ce^{D x_p(t)}$ for leading to next-to-next leading order approximations of PDFs for the all $Q^2$ range covering four orders in magnitude. The exponent, $D$, of the observed "height-position" correlation function converges with the increase of the order of approximation. This result holds for all PDF sets considered. A similar relation is observed also for pion valence quark distribution, indicating that the obtained relation may be universal for any non-singlet partonic distribution. The observed "height - position" correlation is used also to indicate that no finite number exchanges can describe the analytic behavior of the valence quark distribution at the position of the peak at fixed $Q^2$.

hep-ph↗
arXiv2021

The Constituent Counting Rule and Omega Photoproduction

The constituent counting ruling (CCR) has been found to hold for numerous hard, exclusive processes. It predicts the differential cross section at high energies and fixed $\cos θ_{c.m.}$ should follow $\frac{d σ}{dt} \sim \frac{1}{s^{n-2}}$, where $n$ is the minimal number of constituents involved in the reaction. Here we provide an in-depth analysis of the reaction $γp \rightarrow ωp$ at $θ_{c.m.}\sim 90^\circ$ using CLAS data with an energy range of $s = 5 - 8$ GeV$^2$, where the CCR has been shown to work in other reactions. We argue for a stringent method to select data to test the CCR and utilize a Taylor-series expansion to take advantage of data from nearby angle bins in our analysis. Naïvely, this reaction would have $n=9$ (or $n=10$ if the photon is in a $q\bar{q}$ state) and we would expect a scaling of $\sim s^{-7}$ ($s^{-8}$). Instead, a scaling of $s^{-(9.08 \pm 0.11)}$ was observed. Explanations for this apparent failure of the naïve CCR assumptions are examined.

hep-ph↗
arXiv2018

Electron scattering from a deeply bound nucleon on the light-front

We calculate the cross section of the electron scattering from a bound nucleon within light-front approximation. The advantage of this approximation is the possibility of systematic account for the off-shell effects which become essential in high energy electro-nuclear processes aimed at probing the nuclear structure at small distances. We derive a new dynamical parameter which allows to control the extent of the "off-shellness" of electron - bound-nucleon electromagnetic current for different regions of momentum transfer and initial light-cone momenta of the bound nucleon. The derived cross section is compared with the results of other approaches in treating the off-shell effects in electron-nucleon scattering.

nucl-th↗