arXiv subjects

G. Eichmann

Publications and source records attributed to G. Eichmann.

18 recordsLinked to original sources

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

The anomalous magnetic moment of the muon in the Standard Model: an update

We present the current Standard Model (SM) prediction for the muon anomalous magnetic moment, $a_\mu$, updating the first White Paper (WP20) [1]. The pure QED and electroweak contributions have been further consolidated, while hadronic contributions continue to be responsible for the bulk of the uncertainty of the SM prediction. Significant progress has been achieved in the hadronic light-by-light scattering contribution using both the data-driven dispersive approach as well as lattice-QCD calculations, leading to a reduction of the uncertainty by almost a factor of two. The most important development since WP20 is the change in the estimate of the leading-order hadronic-vacuum-polarization (LO HVP) contribution. A new measurement of the $e^+e^-\to\pi^+\pi^-$ cross section by CMD-3 has increased the tensions among data-driven dispersive evaluations of the LO HVP contribution to a level that makes it impossible to combine the results in a meaningful way. At the same time, the attainable precision of lattice-QCD calculations has increased substantially and allows for a consolidated lattice-QCD average of the LO HVP contribution with a precision of about 0.9%. Adopting the latter in this update has resulted in a major upward shift of the total SM prediction, which now reads $a_\mu^\text{SM} = 116\,592\,033(62)\times 10^{-11}$ (530 ppb). When compared against the current experimental average based on the E821 experiment and runs 1-6 of E989 at Fermilab, one finds $a_\mu^\text{exp} - a_\mu^\text{SM} =38(63)\times 10^{-11}$, which implies that there is no tension between the SM and experiment at the current level of precision. The final precision of E989 (127 ppb) is the target of future efforts by the Theory Initiative. The resolution of the tensions among data-driven dispersive evaluations of the LO HVP contribution will be a key element in this endeavor.

hep-ph↗

arXiv2023

Heavy baryon spectroscopy in a quark-diquark approach

We report progress on calculations of the heavy-light baryons $\Sigma_c$ and $\Lambda_c$ and their excitations with $J^P = 1/2^+$ using functional methods. We employ a covariant quark-diquark approach, where the interaction amounts to a quark exchange between quarks and diquarks and the ingredients are determined from the quark level. A partial-wave analysis reveals the presence of orbital angular momentum components in terms of p waves, which are non-relativistically suppressed.

hep-ph↗

arXiv2022

Prospects for precise predictions of $a_\mu$ in the Standard Model

We discuss the prospects for improving the precision on the hadronic corrections to the anomalous magnetic moment of the muon, and the plans of the Muon $g-2$ Theory Initiative to update the Standard Model prediction.

hep-ph↗

arXiv2020

The anomalous magnetic moment of the muon in the Standard Model

We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant $α$ and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including $\mathcal{O}(α^5)$ with negligible numerical uncertainty. The electroweak contribution is suppressed by $(m_μ/M_W)^2$ and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at $\mathcal{O}(α^2)$ and is due to hadronic vacuum polarization, whereas at $\mathcal{O}(α^3)$ the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads $a_μ^\text{SM}=116\,591\,810(43)\times 10^{-11}$ and is smaller than the Brookhaven measurement by 3.7$σ$. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future-which are also discussed here-make this quantity one of the most promising places to look for evidence of new physics.

hep-ph↗

arXiv2020

Diquark Correlations in Hadron Physics: Origin, Impact and Evidence

The last decade has seen a marked shift in how the internal structure of hadrons is understood. Modern experimental facilities, new theoretical techniques for the continuum bound-state problem and progress with lattice-regularised QCD have provided strong indications that soft quark+quark (diquark) correlations play a crucial role in hadron physics. For example, theory indicates that the appearance of such correlations is a necessary consequence of dynamical chiral symmetry breaking, viz. a corollary of emergent hadronic mass that is responsible for almost all visible mass in the universe; experiment has uncovered signals for such correlations in the flavour-separation of the proton's electromagnetic form factors; and phenomenology suggests that diquark correlations might be critical to the formation of exotic tetra- and penta-quark hadrons. A broad spectrum of such information is evaluated herein, with a view to consolidating the facts and therefrom moving toward a coherent, unified picture of hadron structure and the role that diquark correlations might play.

hep-ph↗

arXiv2014

MesonNet 2014 International Workshop. Mini-proceedings

The MesonNet International Workshop was held in the Laboratori Nazionali di Frascati from September the 29th to October the 1st, 2014, being the concluding meeting of the MesonNet research network within EU HadronPhysics3 project. MesonNet is a research network focused on light meson physics gathering experimentalist and theoreticians from Europe and abroad. An overview of the research projects related to the scope of the network is presented in these mini-proceedings.

nucl-ex↗

arXiv2010

Baryons in and beyond the quark-diquark model

We examine the nucleon's electromagnetic form factors in a Poincare-covariant Faddeev framework. The three-quark core contributions to the form factors are obtained by employing a quark-diquark approximation. We implement the self-consistent solution for the quark-photon vertex from its inhomogeneous Bethe-Salpeter equation. We find that the resulting transverse parts which add to the Ball-Chiu vertex have no significant impact on nucleon magnetic moments. The current-quark mass evolution of the form factors agrees with results from lattice QCD.

hep-ph↗

arXiv2010

Delta properties in the rainbow-ladder truncation of Dyson-Schwinger equations

We present a calculation of the three-quark core contribution to nucleon and Delta-baryon masses and Delta electromagnetic form factors in a Poincare-covariant Faddeev approach. A consistent setup for the dressed-quark propagator, the quark-quark, quark-'diquark' and quark-photon interactions is employed, where all ingredients are solutions of their respective Dyson-Schwinger or Bethe-Salpeter equations in a rainbow-ladder truncation. The resulting Delta electromagnetic form factors concur with present experimental and lattice data.

hep-ph↗

arXiv2009

Covariant solution of the three-quark problem in quantum field theory: the nucleon

We provide details on a recent solution of the nucleon's covariant Faddeev equation in an explicit three-quark approach. The full Poincare-covariant structure of the three-quark amplitude is implemented through an orthogonal basis obtained from a partial-wave decomposition. We employ a rainbow-ladder gluon exchange kernel which allows for a comparison with meson Bethe-Salpeter and baryon quark-diquark studies. We describe the construction of the three-quark amplitude in full detail and compare it to a notation widespread in recent publications. Finally, we discuss first numerical results for the nucleon's amplitude.

hep-ph↗

arXiv2009

Nucleon mass from a covariant three-quark Faddeev equation

We report the first study of the nucleon where the full Poincare-covariant structure of the three-quark amplitude is implemented in the Faddeev equation. We employ an interaction kernel which is consistent with contemporary studies of meson properties and aspects of chiral symmetry and its dynamical breaking, thus yielding a comprehensive approach to hadron physics. The resulting current-mass evolution of the nucleon mass compares well with lattice data and deviates only by ~5% from the quark-diquark result obtained in previous studies.

hep-ph↗

arXiv2008

Faddeev equations: a view of baryon properties

We present a calculation of the three-quark core contribution to the mass of the Delta-baryon in a Poincare-covariant Faddeev framework. A consistent setup for the dressed-quark propagator, the quark-quark and quark-diquark interactions is used, where all the ingredients are solutions of their respective Dyson-Schwinger or Bethe-Salpeter equations in rainbow-ladder truncation. We discuss the evolution of the Delta mass with the current-quark mass and compare to the previously obtained mass of the nucleon.

hep-ph↗

arXiv2008

Delta-baryon mass in a covariant Faddeev approach

hep-ph↗

arXiv2008

Survey of nucleon electromagnetic form factors

A dressed-quark core contribution to nucleon electromagnetic form factors is calculated. It is defined by the solution of a Poincare' covariant Faddeev equation in which dressed-quarks provide the elementary degree of freedom and correlations between them are expressed via diquarks. The nucleon-photon vertex involves a single parameter; i.e., a diquark charge radius. It is argued to be commensurate with the pion's charge radius. A comprehensive analysis and explanation of the form factors is built upon this foundation. A particular feature of the study is a separation of form factor contributions into those from different diagram types and correlation sectors, and subsequently a flavour separation for each of these. Amongst the extensive body of results that one could highlight are: r_1^{n,u}>r_1^{n,d}, owing to the presence of axial-vector quark-quark correlations; and for both the neutron and proton the ratio of Sachs electric and magnetic form factors possesses a zero.

nucl-th↗

arXiv2008

On unifying the description of meson and baryon properties

A Poincare' covariant Faddeev equation is presented, which enables the simultaneous prediction of meson and baryon observables using the leading-order in a truncation of the Dyson-Schwinger equations that can systematically be improved. The solution describes a nucleon's dressed-quark core. The evolution of the nucleon mass with current-quark mass is discussed. A nucleon-photon current, which can produce nucleon form factors with realistic Q^2-evolution, is described. Axial-vector diquark correlations lead to a neutron Dirac form factor that is negative, with r_1^{nu}>r_1^{nd}. The proton electric-magnetic form factor ratio falls with increasing Q^2.

nucl-th↗

arXiv2008

Current quark mass dependence of nucleon magnetic moments and radii

A calculation of the current-quark-mass-dependence of nucleon static electromagnetic properties is necessary in order to use observational data as a means to place constraints on the variation of Nature's fundamental parameters. A Poincare' covariant Faddeev equation, which describes baryons as composites of confined-quarks and -nonpointlike-diquarks, is used to calculate this dependence The results indicate that, like observables dependent on the nucleons' magnetic moments, quantities sensitive to their magnetic and charge radii, such as the energy levels and transition frequencies in Hydrogen and Deuterium, might also provide a tool with which to place limits on the allowed variation in Nature's constants.

nucl-th↗

arXiv2008

Perspective on rainbow-ladder truncation

Prima facie the systematic implementation of corrections to the rainbow-ladder truncation of QCD's Dyson-Schwinger equations will uniformly reduce in magnitude those calculated mass-dimensioned results for pseudoscalar and vector meson properties that are not tightly constrained by symmetries. The aim and interpretation of studies employing rainbow-ladder truncation are reconsidered in this light.

nucl-th↗

arXiv2007

A covariant view on the nucleons' quark core

Established results for the quark propagator in Landau gauge QCD, together with a detailed comparison to lattice data, are used to formulate a Poincare covariant Faddeev approach to the nucleon. The resultant three-quark amplitudes describe the quark core of the nucleon. The nucleon's mass and its electromagnetic form factors are calculated as functions of the current quark mass. The corresponding results together with charge radii and magnetic moments are discussed in connection with the contributions from various ingredients in a consistent calculation of nucleon properties, as well as the role of the pion cloud in such an approach.

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