arXiv subjects

Craig D. Roberts

Publications and source records attributed to Craig D. Roberts.

At least 19 recordsLinked to original sources

arXiv2026

Quest for an Understanding of Pion and Kaon Structure

The emergence of massless (Nambu-Goldstone) bosons in association with a dynamically global broken symmetry is a long known and widespread phenomenon in physics. However, practically nothing is known about the expressions of Nambu--Goldstone boson character on the internal structure of these bound states. Indeed, their structure is often ignored. In strong interactions, pions and kaons are the (would-be) Nambu-Goldstone bosons and experiments underway or planned at existing or anticipated high-energy, high-luminosity facilities will gather data that it is hoped will enable maps to be drawn of their internal structure. Meanwhile, theory and phenomenology find themselves in something of a quagmire. Herein, we provide a snapshot of the current status, highlighting issues under debate and identifying areas that deserve greater attention so that best use can be made of what is likely to be a huge volume of data delivered in the next decade or so.

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arXiv2026

Contact interaction treatment of {\pi} and {\rho} elastic and transition tensor form factors

Predictions for tensor charges and form factors, elastic and transition, involving $\pi$- and $\rho$-mesons and their scalar and axialvector diquark partners, are delivered using a symmetry-preserving treatment of a vector*vector contact interaction (SCI). Two distinct SCI regularisation schemes are employed, with the results showing little sensitivity. Although, as typical in SCI analyses, the form factors are stiff; their infrared behaviour may be considered physically reliable. Notable amongst related quantities are the following: the pion tensor charge is approximately $0.36$ and the associated tensor form factor radius is practically the same as the pion charge radius; the $\rho$-meson tensor charge is roughly 80% of that for the proton; and diquark tensor charges and form factors are semiquantitatively alike with those of their $\pi$, $\rho$ partners. In addition to being interesting in themselves, the SCI predictions can serve as baselines for future studies with a closer connection to QCD.

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arXiv2026

Kaon Boer-Mulders function using a contact interaction

Using a symmetry preserving treatment of a vector*vector contact interaction (SCI), results are delivered for the four kaon transverse momentum dependent parton distribution functions (TMDs), viz. helicity-independent (HI) and Boer-Mulders (BM) TMDs for the kaon's $u$, $s$ valence degrees of freedom. In completing this analysis, we are able to deliver insights into, amongst other things, the role played by emergent hadron mass (EHM) phenomena in producing these TMDs; the EHM modulating effect of the Higgs-boson coupling that produces the strange quark current mass; the impact of gauge link models on whether predictions satisfy the positivity constraint that bounds the BM function relative to the HI TMD; and the size of the BM shift and effects thereupon of off-diagonal terms in the associated scale-evolution kernel.

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arXiv2026

Contact interaction treatment of the nucleon Faddeev equation

Working with a symmetry-preserving treatment of a vector*vector contact interaction (SCI), a largely algebraic three-body Faddeev equation treatment of the nucleon bound state problem is introduced and used to deliver results for all nucleon charge and magnetisation distributions and their flavour separation. A strength of the SCI treatment is that it provides for a transparent understanding of this three-body approach to developing predictions for baryon observables. Comparisons of SCI results with predictions obtained in realistic-interaction Faddeev equation studies reveal the sensitivities of a given observable to the pointwise behaviour of the quark-quark interaction and phenomena associated with the emergence of hadron mass.

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arXiv2026

Insights into Meson and Baryon Structure using Continuum Schwinger Function Methods

The bulk of visible mass is supposed to emerge from nonperturbative dynamics within quantum chromodynamics (QCD). Following years of development and refinement, continuum and lattice Schwinger function methods have recently joined in revealing the three pillars that support this emergent hadron mass (EHM); namely, a nonzero gluon mass-scale, a process-independent effective charge, and dressed-quarks with running masses that take constituent-like values at infrared momenta. One may argue that EHM and confinement are inextricably linked; and theory is now working to expose their manifold expressions in hadron observables and highlight the types of measurements that can be made in order to validate the paradigm. This contribution sketches these ideas via the unified explanation of pion and proton electromagnetic and gravitational form factors.

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arXiv2026

Helicity Dependent Distribution Functions of the Proton and $\Lambda$ and $\Sigma^0$ Baryons

Using continuum Schwinger function methods, a coherent set of predictions for proton, $\Lambda$ and $\Sigma^0$ distribution functions (DFs) has been made available -- both helicity dependent and unpolarised. The results and comparisons between them reveal impacts of diquark correlations and SU$(3)$-flavour symmetry breaking, some of which are highlighted in this contribution. For instance: in-proton ratios of helicity-dependent/unpolarised valence-quark DFs are presented; it is highlighted that, were it not for the presence of axialvector diquarks in the $\Sigma^0$, the valence strange quark would carry none of the $\Sigma^0$ spin; and the sign and size of polarised gluon DFs is discussed -- at a scale typical of modern measurements, gluon partons carry roughly 40% of each octet baryon's spin.

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arXiv2025

Symmetry-preserving calculation of pion light-front wave functions

Poincar\'e-covariant Bethe-Salpeter wave functions are used to calculate light-front wave functions (LFWFs) of the pion, $\pi$, and an analogue state, $\pi_{s\bar s}$. The current masses of the degenerate valence constituents in the $\pi_{s\bar s}$ are around $25$-times larger than those of the pion's valence constituents. Both valence spin-antialigned ($\mathcal L=0$) and valence spin-aligned ($\mathcal L=1$) components are obtained and combined to produce the complete LFWF for each system. Comparing predictions delivered by two distinct Bethe-Salpeter kernels, the impact of nonperturbative dynamical effects contained in the more sophisticated (bRL) kernel are seen to be significant; and contrasts between $\pi$, $\pi_{s \bar s}$ results reveal the interplay between emergent hadron mass and mass effects owing to Higgs-boson couplings. Amongst the results, one finds that for $\pi$, $\pi_{s\bar s}$, the LFWFs can be approximated by a separable form, with that representation being pointwise reliable in the bRL cases. Moreover, the $\mathcal L=1$ component is important; so a LFWF obtained after omission of this piece is typically a poor representation of the system. These features are naturally expressed in $\pi$, $\pi_{s\bar s}$ transverse momentum dependent parton distribution functions (TMDs). In this connection, it is found that a Gaussian \textit{Ansatz} can only provide a rough guide to TMD pointwise behaviour: magnitude deviations between \textit{Ansatz} and prediction exceed a factor of two on $k_\perp^2 \gtrsim 0.55\,$GeV$^2$. One should therefore be cautious in interpreting conclusions drawn from phenomenological analyses based upon Gaussian \textit{Ans\"atze}.

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arXiv2025

Insights into Nucleon Resonances via Continuum Schwinger Function Methods

The first baryon resonance was discovered in the early 1950s. The Roper resonance joined the collection ten years later. Today, many baryon resonances are known and more are being discovered. As baryons, these states are the most fundamental three-body systems in Nature. They must all be understood, not just the isolated ground state nucleon. This contribution sketches applications of continuum Schwinger function methods to the baryon resonance problem. Whilst spectroscopy is of value, particular emphasis is placed on resonance electroproduction because transition form factors extracted from electroproduction data provide a keen tool for revealing resonance structure.

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arXiv2025

Symmetry Constraints on Pion Valence Structure

The profile of the pion valence quark distribution function (DF) remains controversial. Working from the concepts of QCD effective charges and generalised parton distributions, we show that since the pion elastic electromagnetic form factor is well approximated by a monopole, then, at large light-front momentum fraction, the pion valence quark DF is a convex function described by a large-$x$ power law that is practically consistent with expectations based on quantum chromodynamics.

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arXiv2025

Kaon and Pion Fragmentation Functions

The Drell-Levy-Yan relation is employed to obtain pion and kaon elementary fragmentation functions (EFFs) from the hadron-scale parton distribution functions (DFs) of these mesons. Two different DF sets are used: that calculated using a symmetry-preserving treatment of a vector $\times$ vector contact interaction (SCI) and the other expressing results obtained using continuum Schwinger function methods (CSMs). Thus determined, the EFFs serve as driving terms in a coupled set of hadron cascade equations, whose solution yields the complete array of hadron-scale fragmentation functions (FFs) for pion and kaon production in high energy reactions. After evolution to scales typical of experiments, the SCI and CSM FF predictions are seen to be in semiquantitative agreement. Importantly, they conform with a range of physical expectations for FF behaviour on the endpoint domains $z\simeq 0, 1$, e.g., nonsinglet FFs vanish at $z=0$ and singlet FFs diverge faster than $1/z$. Predictions for hadron multiplicities in jets are also delivered. They reveal SU$(3)$ symmetry breaking in the charged-kaon/neutral-kaon multiplicity ratio, whose size diminishes with increasing reaction energy, and show that, with increasing energy, the pion/kaon ratio in $e^+ e^- \to h X$ diminishes to a value that is independent of hadron masses.

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arXiv2025

Exclusive photoproduction of light and heavy vector mesons: thresholds to very high energies

A reaction model for $\gamma + p \to V + p$, $V=\rho^0, \phi, J/\psi, \Upsilon$, which exposes the quark-antiquark content of the photon in making the transition $\gamma\to {q} \bar{q} + \mathbb P \to V$, where ${q}$ depends on $V$, and couples the intermediate ${q} \bar{q}$ system to the proton's valence quarks via Pomeron ($\mathbb P$) exchange, is used to deliver a unified description of available data -- both differential and total cross sections -- from near threshold to very high energies, $W$, for all the $V$-mesons. For the $\Upsilon$, this means $10\lesssim W/{\rm GeV} \lesssim 2\,000$. Also provided are predictions for the power-law exponents that are empirically used to characterise the large-$W$ behaviour of the total cross sections and slope parameters characterising the near-threshold differential cross sections. Appealing to notions of vector meson dominance, the latter have been interpreted as vector-meson--proton scattering lengths. The body of results indicate that it is premature to link any $\gamma + p \to V + p$ data with, for instance, in-proton gluon distributions, the quantum chromodynamics trace anomaly, or pentaquark production. Further developments in reaction theory and higher precision data are required before the validity of any such links can be assessed.

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arXiv2025

Distribution Functions of $Λ$ and $Σ^0$ Baryons

Treating baryons as quark + interacting-diquark bound states, a symmetry-preserving formulation of a vector$\,\times\,$vector contact interaction (SCI) is used to deliver an extensive, coherent set of predictions for $Λ, Σ^0$ baryon unpolarised and polarised distribution functions (DFs) -- valence, glue, and four-flavour separated sea -- and compare them with those of a like-structured nucleon. $Λ, Σ^0$ baryons are strangeness negative-one isospin partners within the SU$(3)$-flavour baryon octet. This makes such structural comparisons significant. The study reveals impacts of diquark correlations and SU$(3)$-flavour symmetry breaking on $Λ$, $Σ^0$ structure functions, some of which are significant. For instance, were it not for the presence of axialvector diquarks in the $Σ^0$ at the hadron scale, the $s$ quark could carry none of the $Σ^0$ spin. The discussion canvasses issues that include helicity retention in hard scattering processes; the sign and size of polarised gluon DFs; and the origin and decomposition of baryon spins. Interpreted judiciously, the SCI analysis delivers an insightful explanation of baryon structure as expressed in DFs.

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arXiv2025

Quark + Diquark Description of Nucleon Elastic Electromagnetic Form Factors

Working with a Poincaré-covariant quark + diquark, $q(qq)$, Faddeev equation approach to nucleon structure, a refined symmetry preserving current for electron + nucleon elastic scattering is developed. The parameters in the interaction current are chosen to ensure that the $q(qq)$ picture reproduces selected results from contemporary $3$-body analyses of nucleon elastic electromagnetic form factors. Although the subset of fitted results is small, the $q(qq)$ picture reproduces almost all the $3$-body predictions and often results in better agreement with available data. Notably, the $q(qq)$ framework predicts a zero in $G_E^p/G_M^p$, the absence of such a zero in $G_E^n/G_M^n$, and a zero in the proton's $d$-quark Dirac form factor. Derived $q(qq)$ results for proton flavour-separated light-front-transverse number and anomalous magnetisation densities are also discussed. With the $q(qq)$ framework thus newly benchmarked, one may proceed to comparisons with a broader array of $3$-body results. This may enable new steps to be made toward answering an important question, viz. is the quark + fully-interacting diquark picture of baryon structure only a useful phenomenology or does it come close to expressing robust features of baryon structure?

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arXiv2025

Electroexcitation of Nucleon Resonances and the Emergence of Hadron Mass

Developing an understanding of phenomena driven by the emergence of hadron mass (EHM) is one of the most challenging problems in the Standard Model. This discussion focuses on the impact of results on nucleon resonance ($N^\ast$) electroexcitation amplitudes (or $γ_vpN^\ast$ electrocouplings) obtained from experiments during the 6-GeV era in Hall~B at Jefferson Lab on understanding EHM. Analyzed using continuum Schwinger function methods (CSMs), these results have revealed new pathways for the elucidation of EHM. A good description of the $Δ(1232)3/2^+$, $N(1440)1/2^+$, and $Δ(1600)3/2^+$ electrocouplings, achieved by CSM analyses that express a realistic dressed quark mass function, sheds light on the strong interaction dynamics that underlies EHM. Extensions to nucleon resonance studies for higher-mass states are outlined, as well as experimental results anticipated in the 12-GeV era at Jefferson Lab and those that would be enabled by a further increase of the beam energy to 22~GeV.

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arXiv2025

Pion, Kaon and nucleon gravitational form factors

A unified set of predictions for pion, kaon and nucleon gravitational form factors is obtained using a symmetry-preserving truncation of each relevant quantum field equation. A crucial aspect of the study is the self-consistent characterization of the dressed quark-graviton vertices, applied when probing each quark flavor inside mesons or nucleons. The calculations reveal that each hadron's mass radius is smaller than its charge radius, matching available empirical inferences; moreover, core pressures are significantly greater than those in neutron stars. This set of predictions is expected to be instrumental as forthcoming experiments provide opportunities for validation.

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arXiv2025

Hadron Structure: Perspective and Insights

The bulk of visible mass is supposed to emerge from nonperturbative dynamics within quantum chromodynamics (QCD) -- the strong interaction sector of the Standard Model. Following years of development and refinement, continuum and lattice Schwinger function methods have recently joined in revealing the three pillars that support this emergent hadron mass (EHM); namely, a nonzero gluon mass-scale, a process-independent effective charge, and dressed-quarks with constituent-like masses. One may argue that EHM and confinement are inextricably linked; and theory is now working to expose their manifold expressions in hadron observables and highlight the types of measurements that can be made in order to validate the paradigm. This contribution sketches the role played by EHM in shaping hadron electromagnetic and gravitational form factors, exciting nucleon resonances, and moulding hadron parton distributions.

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arXiv2024

Likelihood of a zero in the proton elastic electric form factor

Working with the $29$ available data on the ratio of proton electric and magnetic form factors, $μ_p G_E^p(Q^2)/ G_M^p(Q^2)$, and independent of any model or theory of strong interactions, we use the Schlessinger point method to objectively address the question of whether the ratio possesses a zero and, if so, its location. Our analysis predicts that, with 50% confidence, the data are consistent with the existence of a zero in the ratio on $Q^2 \leq 10.37\,$GeV$^2$. The level of confidence increases to $99.9$\% on $Q^2 \leq 13.06\,$GeV$^2$. Significantly, the likelihood that existing data are consistent with the absence of a zero in the ratio on $Q^2 \leq 14.49\,$GeV$^2$ is $1/1$-million.

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arXiv2024

Kaon Distribution Functions from Empirical Information

Using available information from Drell-Yan data on pion and kaon structure functions, an approach is described which enables the development of pointwise profiles for all pion and kaon parton distribution functions (DFs) without reference to theories of hadron structure. The key steps are construction of structure-function-constrained probability-weighted ensembles of valence DF replicas and use of an evolution scheme for parton DFs that is all-orders exact. The DFs obtained express qualitatively sound features of light-meson structure, e.g., the effects of Higgs boson couplings into QCD and the size of heavy-quark momentum fractions in light hadrons. In order to improve the results, additional and more precise data on the $u$-quark-in-kaon, $u^K$, to $u$-quark-in-pion, $u^π$, DF ratio would be necessary. Of greater value would be extraction of $u^K$ alone, thereby avoiding inference from the ratio: currently, the data-based form of $u^K$ is materially influenced by results for $u^π$.

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