arXiv subjects

Craig D. Roberts

Publications and source records attributed to Craig D. Roberts.

At least 37 records · Page 2Linked to original sources

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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arXiv2024

Nucleon charge and magnetisation distributions: flavour separation and zeroes

A symmetry-preserving truncation of the quantum field equations describing hadron properties is used to deliver parameter-free predictions for all nucleon elastic electromagnetic form factors and their flavour separation to large values of momentum transfer, $Q^2$. The proton electric form factor, $G_E^p$, possesses a zero, whereas that of the neutron, $G_E^n$, does not. The difference owes to the behaviour of the Pauli form factor of the proton's singly-represented valence $d$-quark. Consequently, $G_E^n>G_E^p$ on a material large-$Q^2$ domain. These predictions can be tested in modern experiments.

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arXiv2024

Impressions of Parton Distribution Functions

Parton distribution functions (DFs) have long been recognised as key measures of hadron structure. Today, theoretical prediction of such DFs is becoming possible using diverse methods for continuum and lattice analyses of strong interaction (QCD) matrix elements. Recent developments include a demonstration that continuum and lattice analyses yield mutually consistent results for all pion DFs, with behaviour on the far valence domain of light-front momentum fraction that matches QCD expectations. Theory is also delivering an understanding of the distributions of proton mass and spin amongst its constituents, which varies, of course, with the resolving scale of the measuring probe. Aspects of the pion DF and proton spin developments are sketched herein, along with some novel perspectives on gluon and quark orbital angular momentum.

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arXiv2024

Sketching pion and proton mass distributions

A light-front holographic model is used to illustrate an algebraic scheme for constructing a representation of a hadron's zero-skewness generalised parton distribution (GPD) from its valence-quark distribution function (DF) and electromagnetic form factor, $F_H$, without reference to deeply virtual Compton scattering data. The hadron's mass distribution gravitational form factor, $A_H$, calculated from this GPD is harder than $F_H$; and, for each hadron, the associated mass-density profile is more compact than the analogous charge profile, with each pion near-core density being larger than that of its proton partner. These features are independent of the scheme employed.

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arXiv2024

Pion Boer-Mulders function using a contact interaction

A symmetry preserving treatment of a vector $\otimes$ vector contact interaction (SCI) is used as the basis for calculations of the two pion transverse momentum dependent parton distribution functions (TMDs); namely, that for unpolarised valence degrees-of-freedom and the analogous Boer-Mulders (BM) function. Amongst other things, the analysis enables the following themes to be addressed: the quark current mass dependence of pion TMDs; the impact of the gauge link model on the positivity constraint that bounds the BM function relative to the unpolarised TMD; the equivalence of direct diagrammatic and light-front wave function TMD calculations; and the size of the BM shift. Interpreted astutely, these SCI results enable one to draw insightful pictures of pion TMDs.

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arXiv2024

$J/ψ$ photoproduction: threshold to very high energy

A reaction model for $γ+ p \to J/ψ+ p$ photoproduction, which exposes the $c \bar c$ content of the photon in making the transition $γ\to c\bar c + \mathbb P \to J/ψ$ and couples the intermediate $c \bar c$ system to the proton's valence quarks via Pomeron ($\mathbb P $) exchange, is used to deliver a description of available data, viz. both differential and total cross sections from near threshold, where data has newly been acquired, to invariant mass $W \approx 300\,$GeV. The study suggests that it is premature to link existing $γ+ p \to J/ψ+ p$ 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 necessary before the validity of any such connections can be assessed.

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arXiv2024

Contact interaction study of proton parton distributions

Using a symmetry-preserving formulation of a vector$\,\times\,$vector contact interaction (SCI) and treating the proton as a quark + interacting-diquark bound state, whose structure is obtained by solving a Poincaré-covariant Faddeev equation, we provide a comprehensive, coherent set of predictions for unpolarised and polarised proton parton distribution functions (DFs): valence, glue, and four-flavour separated sea. The results enable many themes to be addressed, including: the asymmetry of antimatter in the proton; the neutron:proton structure function ratio; helicity retention in hard scattering processes; the charm quark momentum fraction; the sign and size of the polarised gluon DF; and the origin of the proton spin. In all cases where sound analyses of data are available, SCI predictions are semiquantitatively in agreement with the results. Those mismatches which exist are typically attributable to the momentum-independence of the underlying interaction. Judiciously interpreted, the SCI delivers a sound and insightful explanation of proton structure as expressed in DFs.

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arXiv2024

Onset of scaling violation in pion and kaon elastic electromagnetic form factors

Using a symmetry-preserving truncation of the quantum field equations describing hadron properties, parameter-free predictions are delivered for pion and kaon elastic electromagnetic form factors, $F_{P=π,K}$, thereby unifying them with kindred results for nucleon elastic electromagnetic form factors. Regarding positive-charge states, the analysis stresses that the presence of scaling violations in QCD entails that $Q^2 F_P(Q^2)$ should exhibit a single maximum on $Q^2>0$. Locating such a maximum is both necessary and sufficient to establish the existence of scaling violations. The study predicts that, for charged $π$, $K$ mesons, the $Q^2 F_P(Q^2)$ maximum lies in the neighbourhood $Q^2 \simeq 5\,$GeV$^2$. Foreseeable experiments will test these predictions and, providing their $Q^2$ reach meets expectations, potentially also provide details on the momentum dependence of meson form factor scaling violation.

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arXiv2023

Nucleon to $Δ$ axial and pseudoscalar transition form factors

A symmetry-preserving continuum approach to the calculation of baryon properties in relativistic quantum field theory is used to predict all form factors associated with nucleon-to-$Δ$ axial and pseudoscalar transition currents, thereby unifying them with many additional properties of these and other baryons. The new parameter-free predictions can serve as credible benchmarks for use in analysing existing and anticipated data from worldwide efforts focused on elucidation of $ν$ properties.

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arXiv2023

Pion and kaon electromagnetic and gravitational form factors

A unified set of predictions for pion and kaon elastic electromagnetic and gravitational form factors is obtained using a symmetry-preserving truncation of each relevant quantum field equation. A key part of the study is a description of salient aspects of the dressed graviton + quark vertices. The calculations reveal that each meson's mass radius is smaller than its charge radius, matching available empirical inferences; and meson core pressures are commensurate with those in neutron stars. The analysis described herein paves the way for a direct calculation of nucleon gravitational form factors.

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arXiv2023

Pion distribution functions from low-order Mellin moments

Exploiting an evolution scheme for parton distribution functions (DFs) that is all-orders exact, contemporary lattice-QCD (lQCD) results for low-order Mellin moments of the pion valence quark DF are shown to be mutually consistent. The analysis introduces a means by which key odd moments can be obtained from the even moments in circumstances where only the latter are available. Combining these elements, one arrives at parameter-free lQCD-based predictions for the pointwise behaviour of pion valence, glue, and sea DFs, with sound uncertainty estimates. The behaviour of the pion DFs at large light-front momentum fraction, $x> 0.85$, is found to be consistent with QCD expectations and continuum analyses of pion structure functions, i.e., damping like $(1 -x)^{β_{\rm parton}}$, with $β_{\rm valence} \approx 2.4$, $β_{\rm glue} \approx 3.6$, $β_{\rm sea} \approx 4.6$. It may be possible to test these predictions using data from forthcoming experiments.

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arXiv2023

Revealing the Origin of Mass through Studies of Hadron Spectra and Structure

The Higgs boson is responsible for roughly 1% of the visible mass in the Universe. Obviously, therefore, Nature has another, very effective way of generating mass. In working toward identifying the mechanism, contemporary strong interaction theory has arrived at a body of basic predictions, viz. the emergence of a nonzero gluon mass-scale, a process-independent effective charge, and dressed-quarks with constituent-like masses. These three phenomena - the pillars of emergent hadron mass (EHM) - explain the origin of the vast bulk of visible mass in the Universe. Their expressions in hadron observables are manifold. This contribution highlights a few; namely, some of the roles of EHM in building the meson spectrum, producing the leading-twist pion distribution amplitude, and moulding hadron charge and mass distributions.

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arXiv2023

All-Orders Evolution of Parton Distributions: Principle, Practice, and Predictions

Parton distribution functions (DFs) are defining expressions of hadron structure. Exploiting the role of effective charges in quantum chromodynamics, an algebraic scheme is described which, given any hadron's valence parton DFs at the hadron scale, delivers predictions for all its DFs -- unpolarised and polarised -- at any higher scale. The scheme delivers results that are largely independent of both the value of the hadron scale and the pointwise form of the charge; and, inter alia, enables derivation of a model-independent identity that relates the strength of the proton's gluon helicity DF, $ΔG_p^ζ$, to that of the analogous singlet polarised quark DF and valence quark momentum fraction. Using available data fits and theory predictions, the identity yields $ΔG_p(ζ_{\rm C}=\surd 3{\rm GeV})=1.48(10)$. It furthermore entails that the measurable quark helicity contribution to the proton spin is $\tilde a_{0p}^{ζ_{\rm C}}=0.32(3)$, thereby reconciling contemporary experiment and theory.

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arXiv2023

$Δ$-baryon axialvector and pseudoscalar form factors, and associated PCAC relations

A quark+diquark Faddeev equation treatment of the baryon bound state problem in Poincaré-invariant quantum field theory is used to deliver parameter-free predictions for all six $Δ$-baryon elastic weak form factors. Amongst the results, it is worth highlighting that there are two distinct classes of such $Δ$-baryon form factors, $(g_1, g_3, G_{πΔΔ})$, $(h_1, h_3, H_{πΔΔ})$, the functions within each of which are separately linked via partial conservation of axial current (PCAC) and Goldberger-Treiman (GT) relations. Respectively within each class, the listed form factors possess qualitatively the same structural features as the nucleon axial, induced pseudoscalar, and pion-nucleon coupling form factors. For instance, the $Δ$-baryon $g_1$ axial form factor can reliably be approximated by a dipole function, characterised by an axial charge $g_A^{Δ^+}=0.71(9)$ and mass-scale $m_A^Δ=0.95(2)m_Δ$. Moreover, the two distinct $Δ$-baryon PCAC form factor relations are satisfied to a high degree of accuracy on a large range of $Q^2$; the associated GT relations present good approximations only on $Q^2/m_Δ^2 \simeq 0$; and pion pole dominance approximations are reliable within both classes. There are two $πΔΔ$ couplings: $g_{πΔΔ} = 10.46(1.88)$; $h_{πΔΔ}= 35.73(3.75)$; and the associated form factors are soft. Such couplings commonly arise in phenomenology, which may therefore benefit from our analyses. A flavour decomposition of the axial charges reveals that quarks carry $71$\% of the $Δ$-baryon spin. The analogous result for the proton is $\approx 65$\%.

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arXiv2023

Polarised parton distribution functions and proton spin

Supposing there exists an effective charge which defines an evolution scheme for both unpolarised and polarised parton distribution functions (DFs) that is all-orders exact and using Ansätze for hadron-scale proton polarised valence quark DFs, constrained by flavour-separated axial charges and insights from perturbative quantum chromodynamics, predictions are delivered for all proton polarised DFs at the scale $ζ_{\rm C}^2 = 3\,$GeV$^2$. The pointwise behaviour of the predicted DFs and, consequently, their moments, compare favourably with results inferred from data. Notably, flavour-separated singlet polarised DFs are small. On the other hand, the polarised gluon DF, $ΔG(x;ζ_{\rm C})$, is large and positive. Using our result, we predict $\int_{0.05}^1\,dx\,ΔG(x;ζ_{\rm C}) = 0.214(4)$ and that experimental measurements of the proton flavour-singlet axial charge should return $a_0^{\rm E}(ζ_{\rm C}) = 0.35(2)$.

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