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Gerald A. Miller

Publications and source records attributed to Gerald A. Miller.

At least 19 recordsLinked to original sources
arXiv2026

Three-dimensional, boost-invariant formalism for systems of relativistically moving constituents

Light front quantum mechanics in three dimensions can be used to construct boost-invariant wave functions for the internal structure of relativistic systems. The Miller-Brodsky variable $\tilde{z}$ -- which is canonically conjugate to the momentum fraction $x$ -- allows a spatial description of the longitudinal degree of freedom. We show how $\tilde{z}$ can be constructed as an operator and prove its boost invariance. A relativistic harmonic oscillator potential from Li, Maris, Zhao and Vary [Phys Lett B 758 (2016) 118] is used as an example of a two-body interaction that can be constructed using $\tilde{z}$ and for which closed-form analytic solutions can be found. We systematically explore the conditions in which the non-relativistic harmonic oscillator solutions are reproduced and the conditions in which relativistic corrections are significant. Harmonic oscillator states are commonly used as a basis for nuclear many-body calculations. The present effort may provide a basis for providing light-front wave functions of nuclei.

nucl-th↗
arXiv2026

Evidence for Quark Confinement in the Proton

The strong interaction is the fundamental force that holds quarks and the gluon force carriers together to form protons and neutrons and also binds the atomic nucleus. The theory governing quark-gluon interactions is Quantum Chromodynamics (QCD). A wide variety of experimental data teaches us that quarks and gluons cannot be observed in isolation, a phenomenon known as confinement that is unique to QCD. But no one has used QCD to mathematically prove confinement. Here we show how to define and measure the force on quarks in the proton using available experimental data. Direct evidence for confinement is obtained because the force is found to be attractive and constant for a wide range of quark positions. This work guides future experimental efforts at future Electron-Ion Colliders aimed at obtaining a rigorous quantitative understanding of confinement and the origin of nuclear mass.

hep-ph↗
arXiv2026

The Proton Radius Puzzle

Pohl et al. measured the energy difference between the 2P and 2S states of muonic hydrogen and used it to determine a precise value of the proton radius. The result disagreed significantly from values extracted from electronic hydrogen and elastic electron-proton scattering. This discrepancy was exciting because it indicated a breakdown of Coulomb's law. In more technical terms, the discrepancy indicated that a fundamental property of the Standard Model, known as lepton universality, could be violated. This chapter explains the origins, meaning and significance of the puzzle. A resolution, based on very recent experiments, is stated. The proton radius puzzle is no more.

nucl-ex↗
arXiv2026

Imaging baryon number density within the proton

The spatial extent of the proton is a key factor in nuclear physics. Different measurement techniques probe different aspects of the proton, yielding different radii. The mass and charge radii depend on the parton and quark distributions respectively, while the mechanical radius depends on the mass/energy distribution. Here, we probe the spatial distribution of a new proton characteristic, studying the distribution of baryon number within the proton. We investigate the baryon number distribution by studying four exclusive meson production channels arising from photon-proton collisions ($γp \rightarrow p ρ^0$, $γp \rightarrow p ω$, $γp \rightarrow n π^+$, and $γp \rightarrow p π^0$). The two-dimensional transverse sizes of the interacting systems are extracted by analyzing the transverse momentum, $p_T$, dependence of the meson production cross section, using Fourier-Bessel transformations. We find that baryon number is confined to a transverse radius of $0.33 - 0.53$~fm. In comparison, the transverse radius of the proton charge and mass distributions are considerably larger, at least 0.67~fm. The baryon number is concentrated in the center of the proton.

hep-ex↗
arXiv2026

Proton-Size Resolution of the Hyperfine Puzzle in Hydrogen

Baym and Farrar (arXiv:2601.02300v1) have recently pointed out a puzzle in understanding the role of the hyperfine interaction in the ground state of a hydrogen atom. If one uses a variational wave function in which the Bohr radius, $a_0$ is replaced by a variational radius parameter, $R$, first-order perturbation theory can give a contribution to the energy proportional to $-1/R^3$. This raises the question of why the hyperfine interaction does not lead to collapse of hydrogen. I show that including the effects of the non-zero size of the proton leads to a resolution of the puzzle such that the variational procedure yields a value of $R$ that is indistinguishable from $a_0$.

physics.atom-ph↗
arXiv2025

Seeing Through the Nucleus: A Review of Color Transparency Phenomena

We review the current status of the phenomenon of Color Transparency (CT), a fundamental consequence of the description of hadrons from Quantum Chromo Dynamics. CT refers to the vanishing of final (and/or initial) state interactions with the nuclear medium for exclusive process at sufficiently high enough momentum transfers. We discuss the current experimental observations relating to CT and their theoretical implications for other high energy processes. Future CT experiments and facilities are also described.

nucl-ex↗
arXiv2025

On the Impossibility of Obtaining Time-Independent, Three-Dimensional, Spherically-Symmetric Densities of Confined Systems of Relativistically Moving Constituents

The quantum mechanical definition of probability, the uncertainty principle and Poincare invariance provide strong basic restrictions on the ability to define spatial densities associated with form factors describing the properties of confined systems of relativistically moving constituents. Despite this, many papers ignore one or more of these restrictions. Here I show how to obtain time-independent, two-dimensional densities that are consistent with the stated restrictions. This is done using the light-front, infinite momentum frame formalism. Two-dimensional density interpretations of the axial-vector form factor and all three gravitational form factors are obtained. Additionally, an expression of a two-dimensional mass density related to the trace of the energy momentum tensor is obtained. I also show that all known methods for finding three-dimensional densities: using the Breit frame, Abel transformations, Wigner distributions and spherically-symmetric wave packets with vanishing spatial extent violate the basic restrictions in different manners. Furthermore, the use of the latter leads to densities that vanish almost everywhere in space as time increases from an initial value.

hep-ph↗
arXiv2025

Quark Phase Space Distributions in Nuclei

In [PRC 110, 025201], the authors construct a model for nuclear matter which features a quarkyonic phase. A main feature in this model is that the nucleon occupation is strongly reduced at small momenta. Somewhat surprisingly, this result is supported by data for electron scattering from nuclear matter, where a reduction of the cross section consistent with suppression of nucleons with small momenta is seen. Since nuclear matter data are obtained by extrapolation of electron scattering data on increasingly heavier systems, this feature should manifest at least to some degree in heavy nuclei. To check if this is plausible we extend the approach of [PRC 110, 025201] to finite nuclei by considering the nuclear Wigner distribution. We use non-relativistic and relativistic independent particle models to determine the nuclear Wigner distribution, in addition to the local-density approximation (LDA). Phase-space distributions of quarks are obtained as a convolution of the Wigner distribution with a quark momentum distribution. We highlight some properties of the Wigner distribution in spherical systems, which can spoil the interpretation of the quark phase-space distribution as occupation numbers in the Fermi sea. On the other hand, we show that large systems behave essentially like infinite nuclear matter in their interior, and that LDA and full results are quantitatively similar for large A. We then compute the fraction of baryons that would be in a quarkyonic phase in the same sense as in [PRC 110, 025201] for a set of nuclei with mass $12 \leq A \leq 238$. We find that this fraction systematically tends to a constant at large $A$. It is hence plausible that the suppression seen in the nuclear matter data is a genuine feature, present in large finite nuclei. This result is counter-intuitive and we discuss possible electron scattering measurements that could rule out this model.

nucl-th↗
arXiv2024

The Quark Pauli Principle and the Transmutation of Nuclear Matter

The phase space density, $ρ^Q$, of quarks in nuclei is studied using realistic models of unintegrated quark distributions, known as transverse momentum densities (TMDs). If this density exceeds unity for matter at normal nuclear densities, the effects of the quark Pauli principle must play a role in nuclei, and models in which the nucleon density at low momentum is small (Quarkyonic matter) may become a starting point for an entirely new description of nuclei. We denote the nuclear density for which $ρ^Q=1$ to be a transmutation density, $n_T$, because quark degrees of freedom must be relevant at that density. Including the TMDs of [G. de Teramond et. al, \href{DOI:https://doi.org/10.1103/PhysRevLett.120.182001} Phys. Rev. Lett. {\bf 120}, 182002, (2018)] for the valence quarks and phenomenological TMDs for the sea quarks we find that $n_T=0.17 \pm 0.04\,\rm fm^{-3}$, the density of normal nuclear matter. Some of fhe implications of this finding are discussed.

nucl-th↗
arXiv2024

Electromagnetic Form Factors for Nucleons in Short-Range Correlations and the EMC effect

The relationship between medium modifications of nucleon electromagnetic form factors and nucleon structure functions is examined using a model motivated by Light-Front Holographic QCD (LFHQCD). These modifications are closely connected with the influence of short-ranged correlations. The size of the modifications to nucleon form factors is shown to be about the same as the modifications to the structure functions. Thus, small limits on form factors modifications do not rule out an explanation of the EMC effect motivated by the influence of short range correlations, as claimed by a recent paper.

nucl-th↗
arXiv2024

Might Normal Nuclear Matter be Quarkyonic?

The possibility that nuclear matter might be Quarkyonic is considered. Quarkyonic matter is high baryon density matter that is confined but can be approximately thought of as a filled Fermi sea of quarks surrounded by a shell of nucleons. Here, nuclear matter is described by the IdylliQ sigma model for Quarkyonic matter, generalizing the non-interacting IdylliQ model [Y. Fujimoto et al., Phys. Rev. Lett. 132, 112701 (2024) [arXiv:2306.04304]] to include interactions with a sigma meson and a pion. When such interactions are included, we find that isospin-symmetric nuclear matter binds, with acceptable values of the compressibility and other parameters for nuclear matter at saturation. The energy per nucleon and sound velocity of such matter is computed, and the isospin dependence is determined. Nuclear matter is formed at a density close to but slightly above the density at which Quarkyonic matter forms. Quarkyonic matter predicts a strong depletion of nucleons in normal nuclear matter at low momentum. Such a depletion for nucleon momenta $k \lesssim 120$ MeV is shown to be consistent with electron scattering data.

nucl-th↗
arXiv2024

Quark Counting, Drell-Yan West, and the Pion Wave Function

The relation between the pion's quark distribution function, $q(x)$, its light-front wave function, and the elastic charge form factor, $F(Δ^2)$ is explored. The square of the leading-twist pion wave function at a special probe scale, $ζ_H$, is determined using models and Poincare covariance from realistic results for $q(x)$. This wave function is then used to compute form factors with the result that the Drell-Yan-West and quark counting relationships are not satisfied. A new relationship between $q(x)$ and $F(Δ^2)$ is proposed.

hep-ph↗
arXiv2023

Quark mass difference effects in hadronic Fermi matrix elements from first principles

It was recently estimated that the strong isospin-symmetry breaking (ISB) corrections to the Fermi matrix element in free neutron decay could be of the order $10^{-4}$, one order of magnitude larger than the na\"ıve estimate based on the Behrends-Sirlin-Ademollo-Gatto theorem. To investigate this claim, we derive a general expression of the leading ISB correction to hadronic Fermi matrix elements, which takes the form of a four-point correlation function in lattice gauge theory and is straightforward to compute from first principles. Our formalism paves the way for the first determination of such correction in the neutron sector with fully-controlled theory uncertainties.

hep-ph↗
arXiv2023

Synchronization effects on rest frame energy and momentum densities in the proton

We obtain two-dimensional relativistic densities and currents of energy and momentum in a proton at rest. These densities are obtained at surfaces of fixed light front time, which physically corresponds to using an alternative synchronization convention. Mathematically, this is done using tilted light front coordinates, which consist of light front time and ordinary spatial coordinates. In this coordinate system, all sixteen components of the energy-momentum tensor obtain clear physical interpretations, and the nine Galilean components reproduce results from standard light front coordinates. We find angular modulations in several densities that are absent in the corresponding instant form results, which are explained as optical effects arising from using fixed light front time when motion is present within the target. Additionally, transversely-polarized spin-half targets exhibit an energy dipole moment -- which evaluates to $-1/4$ for all targets if the Belinfante EMT is used, but which is target dependent and vanishes for pointlike fermions if the asymmetric EMT is instead used.

hep-ph↗
arXiv2023

Superfast Quarks in Deuterium

An extension to our previous study on Nuclear Parton Distribution Functions (nPDFs) using Light-Front Holographic Quantum Chromodynamics (LFHQCD) is presented. We focus on applying the effects of nucleon motion inside the nucleus (Fermi motion/smearing) to deuterium, extending our nPDFs (and hence the DIS $F_2$ structure function for deuterium, $F_2^D$) to the superfast, $x > 1$, region. We utilize four different deuteron wavefunctions (AV18, NijmI, NijmII, Nijm93) in this study. We find that our model, with no additional new parameters, is in excellent agreement with deuterium EMC ratio data obtained from the BONuS experiment. Looking beyond conventional nuclear physics, and in anticipation of ongoing 12 GeV experiments at Jefferson Lab, we use a LFHQCD ansatz to predict the contributions of an exotic six-quark state to $F_2^D$ in the superfast region. Our results are that the effects of using other potentials are about the same magnitude as six-quark effects - both have small effects in $x < 1$, but have significant contributions at $x > 1$.

hep-ph↗
arXiv2023

Light front synchronization and rest frame densities of the proton: Electromagnetic densities

We clarify the physical origin and meaning of the two-dimensional relativistic densities of the light front formalism. The densities are shown to originate entirely from the use of light front time instead of instant form time, which physically corresponds to using an alternative synchronization convention. This is shown by using tilted light front coordinates, which consist of light front time and ordinary spatial coordinates, and which are also used to show that the obtained densities describe a system at rest rather than at infinite momentum. These coordinates allow all four components of the electromagnetic current density to be given clear physical meanings. We explicate the formalism for spin-half targets, obtaining charge and current densities of the proton and neutron using empirical form factor parametrizations, as well as up and down quark densities and currents. Angular modulations in the densities of transversely-polarized states are explained as originating from redshifts and blueshifts due to quarks moving in different longitudinal directions.

hep-ph↗
arXiv2023

A convolution formalism for defining spatial densities of hadrons

We clarify the meaning of spatial densities of hadrons. A physical density is given by the expectation value of a local operator for a physical state, and depends on both internal structure and the hadron's wave packet. In some particular cases, the physical density can be written as a convolution between a density function that depends on internal structure but not wave packet, and a smearing function that depends on wave packet but not internal structure. We show that the light front densities often encountered in the literature have this property but that instant form densities do not. For hadrons prepared in broad wave packets, physical instant form densities approximately obey such a convolution relation, with Breit frame densities as the apparent internal densities. However, there is an infinite series of relativistic corrections to this convolution formula.

hep-ph↗