arXiv subjects

C. D. Roberts

Publications and source records attributed to C. D. Roberts.

At least 19 recordsLinked to original sources

arXiv2026

Regarding the Rotational Unruh Effect

We study the rotational Unruh effect by identifying the pseudodynamics which emerges when fundamental spacetime symmetries are violated. We show that there is, fundamentally, no rotational Unruh effect, in agreement with the first explicit calculations of the literature, and that, when such an effect has been claimed to exist in later articles, its origin traces back to the derivation of the standard Unruh effect involving linear acceleration. Such a linear Unruh effect intrudes because the chosen reference frames do not respect the cylindrical symmetry of the system, and thus the analyses require Lorentz boosts. Our study also confirms previous findings that the Unruh effect is a consequence of the pseudodynamics which arises because Instant-Form dynamics explicitly breaks a fundamental symmetry of spacetime: Poincar\'e invariance.

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arXiv2026

Distribution amplitudes and functions of ground-state scalar and pseudoscalar charmonia

Charmonia are often supposed to provide simple hydrogen-like ``atomic'' systems that can be used to obtain insights into heavier-quark QCD. We use continuum Schwinger function methods to analyse this hypothesis in connection with ground-state scalar and pseudoscalar charmonia and find that a more complex picture of these states may be necessary. For instance, considering orbital angular momentum, the $\chi_{c0}$ is not a simple $P$-wave system; similarly, the $\eta_c$ wave function contains more than merely $S$-wave contributions. The distribution amplitudes (DAs) and distribution functions (DFs) of these mesons are also nontrivial. For instance, the $\chi_{c0}$ DA is not positive definite: owing to QCD symmetries, it possesses domains of balanced negative and positive support. This feature is also expressed in the $\chi_{c0}$ DF, but differences between $\chi_{c0}$ and $\eta_c$ DFs diminish under scale evolution. Notably, the light-front momentum fraction carried by glue is the same in both states: it is 10\% less than the in-pion glue momentum fraction. Whilst experimental confirmation of the predictions herein is unlikely, our results should serve as benchmarks for complementary theory attempts to understand local and global structural features of heavier-quark hadrons.

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arXiv2026

Frascati 22 GeV Workshop Summary

This document summarizes the outcomes of the "Science at the Luminosity Frontier: Jefferson Lab at 22 GeV" workshop, held at the INFN Laboratori Nazionali di Frascati in December 2024. The primary goal of the workshop was to critically assess and refine the scientific case for a proposed energy upgrade of the Continuous Electron Beam Accelerator Facility (CEBAF) to 22 GeV. This document intends to capture the progress on developing the scientific case since the publication of a lengthy "White Paper" in summer 2024 signed by about 450 authors.

nucl-ex↗

arXiv2025

Orbital angular momentum in the pion and kaon: rest-frame and light-front

Orbital angular momentum (OAM) is not a Poincar\'e invariant quantity; so, its value is observer dependent. Notwithstanding that, in quantum chromodynamics, a Poincar\'e-invariant theory, OAM is part of every hadron wave function. Using continuum Schwinger function methods, we elucidate both the subjective character of in-hadron OAM and expose some of its impacts on pion and kaon structure and observables. For instance, working with light-front projections of their Bethe-Salpeter wave functions, it is found that the pion is a roughly 50/50 mix of light-front OAM zero and one components and the kaon is a 60/40 system. The overall picture is that (near) Nambu-Goldstone modes are complex bound states, each with significant intrinsic OAM, independent of the observer's reference frame. This feature must be accounted for in the calculation of observables. Inductively, the same is true for all hadrons.

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arXiv2025

Hadron Physics Opportunities at FAIR

This White Paper outlines a coordinated, decade-spanning programme of hadron and QCD studies anchored at the GSI/FAIR accelerator complex. Profiting from intense deuteron, proton and pion beams coupled with high-rate capable detectors and an international theory effort, the initiative addresses fundamental questions related to the strong interaction featuring confinement and dynamical mass generation. This includes our understanding of hadron-hadron interactions and the composition of hadrons through mapping the baryon and meson spectra, including exotic states, and quantifying hadron structure. This interdisciplinary research connects topics in the fields of nuclear, heavy-ion, and (nuclear) astro (particle) physics, linking, for example, terrestrial data to constraints on neutron star structure. A phased roadmap with SIS100 accelerator start-up and envisaged detector upgrades will yield precision cross sections, transition form factors, in-medium spectral functions, and validated theory inputs. Synergies with external programmes at international accelerator facilities worldwide are anticipated. The programme is expected to deliver decisive advances in our understanding of non-perturbative (strong) QCD and astrophysics, and high-rate detector and data-science technology.

hep-ex↗

arXiv2025

Light-Front Transverse Nucleon Charge and Magnetisation Densities

Nucleon elastic electromagnetic form factors obtained using both the three-body and quark + fully-interacting-diquark pictures of nucleon structure are employed to calculate an array of light-front transverse densities for the proton and neutron and their dressed valence-quark constituents, viz. flavour separations of the proton and neutron results. These two complementary descriptions of nucleon structure deliver mutually compatible predictions, which match expectations based on modern parametrisations of available data, where such are available. Amongst other things, it is found that transverse-plane valence $u$- and $d$-quark Dirac radii are practically indistinguishable; but regarding kindred Pauli radii, the $d$ quark value is roughly 10% greater than that of the $u$-quark. Moreover, magnetically, the valence $d$ quark is far more active than the valence $u$ quark, probably because it has much greater orbital angular momentum. Both pictures of nucleon structure agree in predicting that, in a polarised nucleon, the transverse-plane charge densities are no longer rotationally invariant. Instead, for a $+\hat x$ polarised nucleon, positive charge is displaced in the $+\hat y$ direction, with the opposite effect for negative charge.

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arXiv2025

Distribution Functions of a Radially Excited Pion

A nonperturbatively-improved, symmetry-preserving approximation to the quantum field equations relevant in calculations of meson masses and interactions is used to deliver predictions for all distribution functions (DFs) of the ground state pion, $\pi_0$, and its first radial excitation, $\pi_1$, viz. valence, glue, and sea. Regarding Mellin moments of the valence DFs, the $m=0,1$ moments in both states are identical; but for each $m\geq 2$, that in the $\pi_0$ is greater than its partner in the $\pi_1$. Working with such information, pointwise reconstructions of the hadron-scale $\pi_{0,1}$ valence DFs are developed. The predicted $\pi_0$ valence DF is consistent with extant results. The $\pi_1$ valence DF is novel: it possesses three-peaks, with the central maximum partnered by secondary peaks on either side, each separated from the centre by a zero: the zeroes lie at $x\approx 0.2,0.8$ and the secondary peaks at $x\approx 0.1,0.9$. Evolution to $\zeta =3.2\,$GeV, a typical scale for nonperturbative calculations, is accomplished using an evolution scheme for parton DFs that is all-orders exact. At this higher scale, differences between the $\pi_{0,1}$ valence DFs remain significant, but analogous differences between glue and sea DFs are far smaller. This analysis shows that, owing to constraints imposed by chiral symmetry and the pattern by which it is broken in Nature, there are noticeable differences between the structural properties of the pion ground state and its radial excitations.

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arXiv2024

Nucleon Gravitational Form Factors

A symmetry-preserving analysis of strong interaction quantum field equations is used to complete a unified treatment of pion, kaon, nucleon electromagnetic and gravitational form factors. Findings include a demonstration that the pion near-core pressure is roughly twice that in the proton, so both are significantly greater than that of a neutron star; parton species separations of the nucleon's three gravitational form factors, in which, inter alia, the glue-to-quark ratio for each form factor is seen to take the same constant value, independent of momentum transfer; and a determination of proton radii orderings, with the mechanical (normal force) radius being less than the mass-energy radius, which is less than the proton charge radius. This body of predictions should prove useful in an era of anticipated experiments that will enable them to be tested.

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arXiv2024

Pseudoscalar Mesons and Emergent Mass

Despite its role in the continuing evolution of the Universe, only a small fraction of the mass of visible material can be attributed to the Higgs boson alone. The overwhelmingly dominant share may/should arise from the strong interactions that act in the heart of nuclear matter; namely, those described by quantum chromodynamics. This contribution describes how studying and explaining the attributes of pseudoscalar mesons can open an insightful window onto understanding the origin of mass in the Standard Model and how these insights inform our knowledge of hadron structure. The survey ranges over distribution amplitudes and functions, electromagnetic and gravitational form factors, light-front wave functions, and generalized parton distributions. Advances made using continuum Schwinger function methods and their relevance for experimental efforts are highlighted.

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arXiv2023

Developing predictions for pion fragmentation functions

Exploiting crossing symmetry, the hadron scale pion valence quark distribution function is used to predict the kindred elementary valence quark fragmentation function (FF). This function defines the kernel of a quark jet fragmentation equation, which is solved to obtain the full pion FFs. After evolution to a scale typical of FF fits to data, the results for quark FFs are seen to compare favourably with such fits. However, the gluon FF is markedly different. Notably, although FF evolution equations do not themselves guarantee momentum conservation, inclusion of a gluon FF which, for four quark flavours, distributes roughly 11% of the total light-front momentum fraction, is sufficient to restore momentum conservation under evolution. Overall, significant uncertainty is attached to FFs determined via fits to data; hence, the features of the predictions described herein could potentially provide useful guidance for future such studies.

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arXiv2023

QCD Running Couplings and Effective Charges

We discuss our present knowledge of $α_s$, the fundamental running coupling or effective charge of Quantum Chromodynamics (QCD). A precise understanding of the running of $α_s(Q^2) $ at high momentum transfer, $Q$, is necessary for any perturbative QCD calculation. Equally important, the behavior of $α_s$ at low $Q^2$ in the nonperturbative QCD domain is critical for understanding strong interaction phenomena, including the emergence of mass and quark confinement. The behavior of $α_s(Q^2)$ at all momentum transfers also provides a connection between perturbative and nonperturbative QCD phenomena, such as hadron spectroscopy and dynamics. We first sketch the origin of the QCD coupling, the reason why its magnitude depends on the scale at which hadronic phenomena are probed, and the resulting consequences for QCD phenomenology. We then summarize latest measurements in both the perturbative and nonperturbative domains. New theory developments include the derivation of the universal nonperturbative behavior of $α_s(Q^2)$ from both the Dyson-Schwinger equations and light-front holography. We also describe theory advances for the calculation of gluon and quark Schwinger functions in the nonperturbative domain and the relation of these quantities to $α_s$. We conclude by highlighting how the nonperturbative knowledge of $α_s$ is now providing a parameter-free determination of hadron spectroscopy and structure, a central and long-sought goal of QCD studies.

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arXiv2023

Constraining the pion distribution amplitude using Drell-Yan reactions on a proton

Using a reaction model that incorporates pion bound state effects and continuum results for proton parton distributions and the pion distribution amplitude, $φ_π$, we deliver parameter-free predictions for the $μ^+$ angular distributions in $πN \to μ^+ μ^- X$ reactions on both unpolarised and polarised targets. The analysis indicates that such angular distributions are sensitive to the pointwise form of $φ_π$ and suggests that unpolarised targets are practically more favourable. The precision of extant data is insufficient for use in charting $φ_π$; hence, practical tests of this approach to charting $φ_π$ must await data with improved precision from new-generation experiments. The reaction model yields a nonzero single-spin azimuthal asymmetry, without reference to $T$-odd parton distribution functions (DFs). This may necessitate additional care when attempting to extract such $T$-odd DFs from data.

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arXiv2022

Schwinger mechanism for gluons from lattice QCD

Continuum and lattice analyses have revealed the existence of a mass-scale in the gluon two-point Schwinger function. It has long been conjectured that this expresses the action of a Schwinger mechanism for gauge boson mass generation in quantum chromodynamics (QCD). For such to be true, it is necessary and sufficient that a dynamically-generated, massless, colour-carrying, scalar gluon+gluon correlation emerge as a feature of the dressed three-gluon vertex. Working with results on elementary Schwinger functions obtained via the numerical simulation of lattice-regularised QCD, we establish with an extremely high level of confidence that just such a feature appears; hence, confirm the conjectured origin of the gluon mass scale.

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arXiv2022

Emergence of pion parton distributions

Supposing only that there is an effective charge which defines an evolution scheme for parton distribution functions (DFs) that is all-orders exact, strict lower and upper bounds on all Mellin moments of the valence-quark DFs of pion-like systems are derived. Exploiting contemporary results from numerical simulations of lattice-regularised quantum chromodynamics (QCD) that are consistent with these bounds, parameter-free predictions for pion valence, glue, and sea DFs are obtained. The form of the valence-quark DF at large values of the light-front momentum fraction is consistent with predictions derived using the QCD-prescribed behaviour of the pion wave function.

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arXiv2022

Symplectic Effective Field Theory for Nuclear Structure Studies

A Symplectic Effective Field Theory that unveils the observed emergence of symplectic symmetry in atomic nuclei is advanced. Specifically, starting from a simple extension of the harmonic-oscillator Lagrangian, an effective field theory applied against symplectic basis states is shown to yield a Hamiltonian system with one fitted parameter. The scale of the system can be determined self consistently as the ratio of the average volume of a nucleus assumed to be spherical to its volume as determined by the average number of oscillator quanta, which is stretched by the fact that the plane-wave solution satisfies the equations of motion at every order without the need for perturbative corrections. As an application of the theory, results for 20Ne, 22Ne and 22Mg are presented that yield energy spectra, B(E2) values, and matter radii in good agreement with experimentally measured results.

nucl-th↗

arXiv2022

Artificial Dynamical Effects in Quantum Field Theory

In Newtonian mechanics, inertial pseudoforces - or fictitious forces - appear in systems studied in non-Galilean reference frames; e.g., a centrifugal force seems to arise if the dynamics is analyzed in a rotating reference frame. The equivalent of Galilean invariance for relativistic kinematics is Poincaré invariance; analogous artificial effects may arise in relativistic quantum field theory (QFT) if a system is studied in a framework violating Poincaré invariance. We highlight how such issues complicate the traditional canonical quantization of QFTs and can lead to a subjective description of natural phenomena. In fact, if the system involves the strong interaction, obtaining objective results can become an intractable problem using canonical quantization because the pseudoforces are essentially nonperturbative. In contrast, the treatment of the same problem using light-front (LF) quantization is free of spurious pseudoeffects because Poincaré invariance is manifest; thus the treatment of strong interaction problems becomes simpler. These statements are illustrated using several examples: the Gerasimov-Drell-Hearn (GDH) relation, a fundamental feature of QFT; the absence of any measurable impact of Lorentz contraction in high-energy collisions; and the fictitious character of vacuum fluctuation contributions to the cosmological constant.

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arXiv2021

Concerning pion parton distributions

Analyses of the pion valence-quark distribution function (DF), ${u}^π(x;ζ)$, which explicitly incorporate the behaviour of the pion wave function prescribed by quantum chromodynamics (QCD), predict ${u}^π(x\simeq 1;ζ) \sim (1-x)^{β(ζ)}$, $β(ζ\gtrsim m_p)>2$, where $m_p$ is the proton mass. Nevertheless, more than forty years after the first experiment to collect data suitable for extracting the $x\simeq 1$ behaviour of ${u}^π$, the empirical status remains uncertain because some methods used to fit existing data return a result for ${u}^π$ that violates this constraint. Such disagreement entails one of the following conclusions: the analysis concerned is incomplete; not all data being considered are a true expression of qualities intrinsic to the pion; or QCD, as it is currently understood, is not the theory of strong interactions. New, precise data are necessary before a final conclusion is possible. In developing these positions, we exploit a single proposition, viz. there is an effective charge which defines an evolution scheme for parton DFs that is all-orders exact. This proposition has numerous corollaries, which can be used to test the character of any DF, whether fitted or calculated.

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arXiv2020

Spectrum of fully-heavy tetraquarks from a diquark+antidiquark perspective

Using a relativized diquark model Hamiltonian, we calculate the masses of $J^{PC}=0^{++}$ ground-state tetraquarks in the following systems: $b s \bar b \bar s$, $bb \bar n \bar n$ ($n=u, d$), $bb \bar s \bar s$, $cc\bar c \bar c$, $b b \bar b \bar b$, $b c\bar b \bar c$ and $b b \bar c \bar c$. We also compute extensive spectra for the fully-heavy quark flavour combinations. Finally, as a test of the diquark model approach, we compute the masses of fully-heavy baryons in the diquark model. Our results may be compared soon to the forthcoming experimental data for fully-heavy three-quark systems.

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