arXiv subjects

Sebastian M. Schmidt

Publications and source records attributed to Sebastian M. Schmidt.

At least 19 recordsLinked to original sources

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.

hep-ph↗

arXiv2025

Anisotropic quark propagation and Zeeman effect in an external magnetic field

We investigated the impact of a constant external magnetic field on the dressed propagators of up-, down-, and strange quarks. In the weak field limit, we derive a general momentum-space representation for the propagator and numerically solve the corresponding gap equation. Our analysis reveals that the vector term of the propagator can be decomposed into components parallel and perpendicular to the magnetic field, resulting in anisotropic effective masses, with the transverse mass consistently exceeding the longitudinal mass. This mass disparity exhibits a power law dependence on the magnetic field strength and is less pronounced for the strange quark compared to up and down quarks. Additionally, the magnetic field induces axial-vector and tensor terms, highlighting the Zeeman effect resulting from quark interactions with the magnetic field. These findings have important implications for (inverse) magnetic catalysis, and phenomena such as vector meson and pion condensations.

hep-ph↗

arXiv2025

Relativistic Quantum Kinetic Theory: Higher order contributions in assisted Schwinger pair production

Quantum kinetic theory is an important tool for studying non-equilibrium, non-perturbative and non-linear interactions within an open quantum system, and as such is able to provide an unprecedented view on particle production in the relativistic, ultra-high intensity regime of quantum electrodynamics. By re-organising the relativistic quantum transport equations for Abelian plasmas and integrating them with a perturbative expansion, we significantly expand the scope for kinetic theories to further elucidate the peculiarities of particle production at a spectral level. Keywords: Assisted Schwinger effect, Strong-field quantum electrodynamics, relativistic quantum transport, quantum kinetic theory, non-equilibrium quantum many-body physics.

hep-ph↗

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.

hep-ph↗

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

Emergence of Hadron Mass and Structure

Visible matter is characterised by a single mass scale; namely, the proton mass. The proton's existence and structure are supposed to be described by quantum chromodynamics (QCD); yet, absent Higgs boson couplings, chromodynamics is scale invariant. Thus, if the Standard Model is truly a part of the theory of Nature, then the proton mass is an emergent feature of QCD; and emergent hadron mass (EHM) must provide the basic link between theory and observation. Nonperturbative tools are necessary if such connections are to be made; and in this context, we sketch recent progress in the application of continuum Schwinger function methods to an array of related problems in hadron and particle physics. Special emphasis is given to the three pillars of EHM -- namely, the running gluon mass, process-independent effective charge, and running quark mass; their role in stabilising QCD; and their measurable expressions in a diverse array of observables.

hep-ph↗

arXiv2022

Hadron and light nucleus radii from electron scattering

Conceptually, radii are amongst the simplest Poincaré-invariant properties that can be associated with hadrons and light nuclei. Accurate values of these quantities are necessary so that one may judge the character of putative solutions to the strong interaction problem within the Standard Model. However, limiting their ability to serve in this role, recent measurements and new analyses of older data have revealed uncertainties and imprecisions in the radii of the proton, pion, kaon, and deuteron. In the context of radius measurement using electron + hadron elastic scattering, the past decade has shown that reliable extraction requires complete elimination of bias associated with practitioner-dependent choices of data fitting functions. Different answers to that challenge have been offered; and this perspective describes the statistical Schlessinger point method (SPM), in unifying applications to proton, pion, kaon, and deuteron radii. Grounded in analytic function theory, independent of assumptions about underlying dynamics, free from practitioner-induced bias, and applicable in the same form to diverse systems and observables, the SPM returns an objective expression of the information contained in any data under consideration. Its robust nature and versatility make it suitable for use in many branches of experiment and theory.

hep-ph↗

arXiv2022

Fresh look at experimental evidence for odderon exchange

Theory suggests that in high-energy elastic hadron+hadron scattering, $t$-channel exchange of a family of colourless crossing-odd states -- the odderon -- may generate differences between $p\bar p$ and $pp$ cross-sections in the neighbourhood of the diffractive minimum. Using a mathematical approach based on interpolation via continued fractions enhanced by statistical sampling, we develop robust comparisons between $p\bar p$ elastic differential cross-sections measured at $\surd s=1.96\,$TeV by the D0 Collaboration at the Tevatron and function-form-unbiased extrapolations to this energy of kindred $pp$ measurements at $\surd s /{\rm TeV} = 2.76, 7, 8, 13$ by the TOTEM Collaboration at the LHC and a combination of these data with earlier cross-section measurements at $\surd s/{\rm GeV} = 23.5, 30.7, 44.7, 52.8, 62.5$ made at the internal storage rings. Focusing on a domain that straddles the diffractive minimum in the $p\bar p$ and $pp$ cross-sections, we find that these two cross-sections differ at the $(2.2-2.6)σ$ level; hence, supply evidence with this level of significance for the existence of the odderon. If combined with evidence obtained through different experiment-theory comparisons, whose significance is reported to lie in the range $(3.4-4.6)σ$, one arrives at a $(4.0 - 5.2)σ$ signal for the odderon.

hep-ph↗

arXiv2022

Valence quark ratio in the proton

Beginning with precise data on the ratio of structure functions in deep inelastic scattering (DIS) from $^3$He and $^3$H, collected on the domain $0.19 \leq x_B \leq 0.83$, where $x_B$ is the Bjorken scaling variable, we employ a robust method for extrapolating such data to arrive at a model-independent result for the $x_B=1$ value of the ratio of neutron and proton structure functions. Combining this with information obtained in analyses of DIS from nuclei, corrected for target-structure dependence, we arrive at a prediction for the proton's valence-quark ratio: $\left. d_v/u_v \right|_{x_B\to 1} = 0.230 (57)$. Requiring consistency with this result presents a challenge to many descriptions of proton structure.

hep-ph↗

arXiv2022

A correspondence between the free and interacting field theories

We discover a correspondence between the free field and the interacting states. This correspondence is firstly given from the fact that the free propagator can be converted into a tower of propagators for massive states, when expanded with the Hermite function basis. The equivalence of propagators reveals that in this particular case the duality can naturally be regarded as the equivalence of one theory on the plane wave basis to the other on the Hermite function basis. More generally, the Hermite function basis provides an alternative quantization process with the creation/annihilation operators that correspond directly to the interacting fields. Moreover, the Hermite function basis defines an exact way of dimensional reduction. As an illustration, we apply this basis on 3+1 dimensional Yang-Mills theory with three dimensional space being reduced through the Hermite function basis, and if with only the lowest order Hermite function, the equivalent action becomes the Banks-Fischler-Shenker-Susskind (BFSS) matrix model.

hep-ph↗

arXiv2021

Pauli radius of the proton

Using a procedure based on interpolation via continued fractions supplemented by statistical sampling, we analyse proton magnetic form factor data obtained via electron+proton scattering on $Q^2 \in [0.027,0.55]\,$GeV$^2$ with the goal of determining the proton magnetic radius. The approach avoids assumptions about the function form used for data interpolation and ensuing extrapolation onto $Q^2\simeq 0$ for extraction of the form factor slope. In this way, we find $r_M = 0.817(27)\,$fm. Regarding the difference between proton electric and magnetic radii calculated in this way, extant data are seen to be compatible with the possibility that the slopes of the proton Dirac and Pauli form factors, $F_{1,2}(Q^2)$, are not truly independent observables; to wit, the difference $F_1^\prime(0)-F_2^\prime(0)/κ_p = [1+κ_p]/[4 m_p^2]$, viz. the proton Foldy term.

hep-ph↗

arXiv2021

Pion charge radius from pion+electron elastic scattering data

With the aim of extracting the pion charge radius, we analyse extant precise pion+electron elastic scattering data on $Q^2 \in [0.015,0.144]\,$GeV$^2$ using a method based on interpolation via continued fractions augmented by statistical sampling. The scheme avoids any assumptions on the form of function used for the representation of data and subsequent extrapolation onto $Q^2\simeq 0$. Combining results obtained from the two available data sets, we obtain $r_π= 0.640(7)\,$fm, a value $2.4\,σ$ below today's commonly quoted average. The tension may be relieved by collection and similar analysis of new precise data that densely cover a domain which reaches well below $Q^2 = 0.015\,$GeV$^2$. Considering available kaon+electron elastic scattering data sets, our analysis reveals that they contain insufficient information to extract an objective result for the charged-kaon radius, $r_K$. New data with much improved precision, low-$Q^2$ reach and coverage are necessary before a sound result for $r_K$ can be recorded.

hep-ph↗

arXiv2021

Fresh extraction of the proton charge radius from electron scattering

We present a novel method for extracting the proton radius from elastic electron-proton ($ep$) scattering data. The approach is based on interpolation via continued fractions augmented by statistical sampling and avoids any assumptions on the form of function used for the representation of data and subsequent extrapolation onto $Q^2\simeq 0$. Applying the method to extant modern $e p$ data sets, we find that all results are mutually consistent and, combining them, arrive at $r_p=0.847(8)\,$fm. This result compares favourably with values obtained from contemporary measurements of the Lamb shift in muonic hydrogen, transitions in electronic hydrogen, and muonic deuterium spectroscopy.

hep-ph↗

arXiv2020

Higgs modulation of emergent mass as revealed in kaon and pion parton distributions

Strangeness was discovered roughly seventy years ago, lodged in a particle now known as the kaon, $K$. Kindred to the pion, $π$; both states are massless in the absence of Higgs-boson couplings. Kaons and pions are Nature's most fundamental Nambu-Goldstone modes. Their properties are largely determined by the mechanisms responsible for emergent mass in the standard model, but modulations applied by the Higgs are crucial to Universe evolution. Despite their importance, little is known empirically about $K$ and $π$ structure. This study delivers the first parameter-free predictions for all $K$ distribution functions (DFs) and comparisons with the analogous $π$ distributions, i.e. the one-dimensional maps that reveal how the light-front momentum of these states is shared amongst the gluons and quarks from which they are formed. The results should stimulate improved analyses of existing data and motivate new experiments sensitive to all $K$ and $π$ DFs.

hep-ph↗

arXiv2020

Reflections upon the Emergence of Hadronic Mass

With discovery of the Higgs boson, science has located the source for $\lesssim 2$% of the mass of visible matter. The focus of attention can now shift to the search for the origin of the remaining $\gtrsim 98$%. The instruments at work here must be capable of simultaneously generating the 1 GeV mass-scale associated with the nucleon and ensuring that this mass-scale is completely hidden in the chiral-limit pion. This hunt for an understanding of the emergence of hadronic mass (EHM) has actually been underway for many years. What is changing are the impacts of QCD-related theory, through the elucidation of clear signals for EHM in hadron observables, and the ability of modern and planned experimental facilities to access these observables. These developments are exemplified in a discussion of the evolving understanding of pion and kaon parton distributions.

hep-ph↗

arXiv2020

Nucleon elastic form factors at accessible large spacelike momenta

A Poincaré-covariant quark+diquark Faddeev equation is used to compute nucleon elastic form factors on $0\leq Q^2\leq 18 \,m_N^2$ ($m_N$ is the nucleon mass) and elucidate their role as probes of emergent hadronic mass in the Standard Model. The calculations expose features of the form factors that can be tested in new generation experiments at existing facilities, e.g. a zero in $G_E^p/G_M^p$; a maximum in $G_E^n/G_M^n$; and a zero in the proton's $d$-quark Dirac form factor, $F_1^d$. Additionally, examination of the associated light-front-transverse number and anomalous magnetisation densities reveals, inter alia: a marked excess of valence $u$-quarks in the neighbourhood of the proton's centre of transverse momentum; and that the valence $d$-quark is markedly more active magnetically than either of the valence $u$-quarks. The calculations and analysis also reveal other aspects of nucleon structure that could be tested with a high-luminosity accelerator capable of delivering higher beam energies than are currently available.

hep-ph↗

arXiv2019

Drawing insights from pion parton distributions

A symmetry-preserving continuum approach to the two valence-body bound-state problem is used to calculate the valence, glue and sea distributions within the pion; unifying them with, inter alia, electromagnetic pion elastic and transition form factors. The analysis reveals the following momentum fractions at the scale $ζ_2:=2\,$GeV: $\langle x_{\rm valence} \rangle = 0.48(3)$, $\langle x_{\rm glue} \rangle = 0.41(2)$, $\langle x_{\rm sea} \rangle = 0.11(2)$; and despite hardening induced by the emergent phenomenon of dynamical chiral symmetry breaking, the valence-quark distribution function, ${q}^π(x)$, exhibits the $x\simeq 1$ behaviour predicted by quantum chromodynamics (QCD). After evolution to $ζ=5.2\,$GeV, the prediction for ${q}^π(x)$ matches that obtained using lattice-regularised QCD. This confluence should both stimulate improved analyses of existing data and aid in planning efforts to obtain new data on the pion distribution functions.

hep-ph↗

arXiv2019

Pion and Kaon Structure at the Electron-Ion Collider

Understanding the origin and dynamics of hadron structure and in turn that of atomic nuclei is a central goal of nuclear physics. This challenge entails the questions of how does the roughly 1 GeV mass-scale that characterizes atomic nuclei appear; why does it have the observed value; and, enigmatically, why are the composite Nambu-Goldstone (NG) bosons in quantum chromodynamics (QCD) abnormally light in comparison? In this perspective, we provide an analysis of the mass budget of the pion and proton in QCD; discuss the special role of the kaon, which lies near the boundary between dominance of strong and Higgs mass-generation mechanisms; and explain the need for a coherent effort in QCD phenomenology and continuum calculations, in exa-scale computing as provided by lattice QCD, and in experiments to make progress in understanding the origins of hadron masses and the distribution of that mass within them. We compare the unique capabilities foreseen at the electron-ion collider (EIC) with those at the hadron-electron ring accelerator (HERA), the only previous electron-proton collider; and describe five key experimental measurements, enabled by the EIC and aimed at delivering fundamental insights that will generate concrete answers to the questions of how mass and structure arise in the pion and kaon, the Standard Model's NG modes, whose surprisingly low mass is critical to the evolution of our Universe.

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