arXiv subjects

Franz Gross

Publications and source records attributed to Franz Gross.

At least 19 recordsLinked to original sources

arXiv2026

Quark mass functions in Minkowski space

Using the Covariant Spectator Theory (CST), we calculate the dressed quark mass function and wave-function renormalization for the five quark flavors from up/down to bottom in both the spacelike and timelike regions of Minkowski space. The calculation employs a model dressed-gluon propagator fitted to lattice data in the spacelike region. The remaining free parameters of the quark self-energy are determined by fits to lattice results for the quark mass function including a constraint built into the wave-function renormalization. We perform these fits using lattice data from two different groups and find that the resulting mass predictions are within the range of the typical constituent masses used in quark models.

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arXiv2022

50 Years of Quantum Chromodynamics

This paper presents a comprehensive review of both the theory and experimental successes of Quantum Chromodynamics, starting with its emergence as a well defined theory in 1972-73 and following developments and results up to the present day. Topics include a review of the earliest theoretical and experimental foundations; the fundamental constants of QCD; an introductory discussion of lattice QCD, the only known method for obtaining exact predictions from QCD; methods for approximating QCD, with special focus on effective field theories; QCD under extreme conditions; measurements and predictions of meson and baryon states; a special discussion of the structure of the nucleon; techniques for study of QCD at high energy, including treatment of jets and showers; measurements at colliders; weak decays and quark mixing; and a section on the future, which discusses new experimental facilities or upgrades currently funded. The paper is intended to provide a broad background for Ph.D. students and postdocs starting their career. Some contributions include personal accounts of how the ideas or experiments were developed.

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arXiv2021

Removal of singularities from the covariant spectator theory

A modification of the one boson exchange (OBE) kernel for the covariant spectator theory (CST) is presented and discussed. When applied to the scattering of two identical particles, the previously used kernels either introduced spurious singularities, or removed them in an ad-hoc way. The new modification not only removes these singularities, but also maintains the convergence of the two-body CST equation (sometimes called the Gross equation) when used to describe the scattering of two identical scalar particles.

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arXiv2019

Covariant Spectator Theory of $np$ scattering: Deuteron form factors

The deuteron form factors are calculated using two model wave functions obtained from the 2007 CST high precision fits to $np$ scattering data. Included in the calculation are a new class of isoscalar $np$ interaction currents which are automatically generated by the nuclear force model used in these fits. If the nuclear model WJC2 is used, a precision fit ($χ^2$/datum $\eqsim1$) to the Sick Global Analysis (GA) of all $ed$ elastic scattering data can be obtained by adjusting the unknown off-shell nucleon form factors $F_3(Q^2)$ (discussed before) and $F_4(Q^2)$ (introduced in this paper), and predicting the high $Q^2$ behavior of the neutron charge form factor $G_{En}(Q^2)$ well beyond the region where it has been measured directly. Relativistic corrections, isoscalar interaction currents, and off-shell effects are defined, discussed, and their size displayed. A rationale for extending $ed$ elastic scattering measurements to higher $Q^2$ is presented.

nucl-th↗

arXiv2019

Quark mass function from a OGE-type interaction in Minkowski space

We present results for the quark mass function in Minkowski space calculated from an interaction kernel that consists of an effective one-gluon-exchange and a constant interaction. We analyze the gauge dependence of our results and compare them in the spacelike region to the available lattice QCD data.

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arXiv2018

Quark mass function from a one-gluon-exchange-type interaction in Minkowski space

We present first results for the quark mass function in Minkowski space in both the spacelike and timelike regions calculated from the same quark-antiquark interaction kernel used in the latest meson calculations using the Gross equation. This kernel consists of a Lorentz vector effective one-gluon-exchange-type interaction, a vector constant, and a mixed scalar-pseudoscalar covariant linear confining interaction that does not contribute to the mass function. We analyze the gauge dependence of our results, prove the gauge independence of the constituent quark mass and mass gap equation, and identify the Yennie gauge as the appropriate gauge to be used in CST calculations. We compare our results in the spacelike region to lattice QCD data and find good agreement.

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arXiv2016

Chiral-symmetry breaking and pion structure in the Covariant Spectator Theory

We introduce a covariant approach in Minkowski space for the description of quarks and mesons that exhibits both chiral-symmetry breaking and confinement. In a simple model for the interquark interaction the quark mass function is obtained and used in the calculation of the pion form factor. We study the effects of the mass function and of the different quark pole contributions on the pion form factor.

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arXiv2015

Charge-conjugation symmetric complete impulse approximation for the pion electromagnetic form factor in the Covariant Spectator Theory

The pion form factor is calculated in the framework of the charge-conjugation invariant Covariant Spectator Theory. This formalism is established in Minkowski space and the calculation is set up in momentum space. In a previous calculation we included only the leading pole coming from the spectator quark (referred to as the relativistic impulse approximation). In this paper we also include the contributions from the poles of the quark which interacts with the photon and average over all poles in both the upper and lower half planes in order to preserve charge conjugation invariance (referred to as the $C$-symmetric complete impulse approximation). We find that for small pion mass these contributions are significant at all values of the four-momentum transfer $Q^2$ but, surprisingly, do not alter the shape obtained from the spectator poles alone.

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arXiv2014

Chiral-symmetry breaking and confinement in Minkowski space

We present a model for the quark-antiquark interaction formulated in Minkowski space using the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. By applying the axial-vector Ward-Takahashi identity we show that our model satisfies the Adler-zero constraint imposed by chiral symmetry. For this model, our Minkowski-space results of the dressed quark mass function are compared to lattice QCD data obtained in Euclidean space. The mass function is then used in the calculation of the electromagnetic pion form factor in relativistic impulse approximation, and the results are presented and compared with the experimental data from JLab.

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arXiv2014

Covariant Spectator Theory of np scattering: Deuteron Quadrupole Moment

The deuteron quadrupole moment is calculated using two CST model wave functions obtained from the 2007 high precision fits to $np$ scattering data. Included in the calculation are a new class of isoscalar $np$ interaction currents automatically generated by the nuclear force model used in these fits. The prediction for model WJC-1, with larger relativistic P-state components, is 2.5% smaller that the experimental result, in common with the inability of models prior to 2014 to predict this important quantity. However, model WJC-2, with very small P-state components, gives agreement to better than 1%, similar to the results obtained recently from $χ$EFT predictions to order N$^3$LO.

nucl-th↗

arXiv2014

Chiral symmetry and pi-pi scattering in the Covariant Spectator Theory

The pi-pi scattering amplitude calculated with a model for the quark-antiquark interaction in the framework of the Covariant Spectator Theory (CST) is shown to satisfy the Adler zero constraint imposed by chiral symmetry. The CST formalism is established in Minkowski space and our calculations are performed in momentum space. We prove that the axial-vector Ward-Takahashi identity is satisfied by our model. Then we show that, similar to what happens within the Bethe-Salpeter formalism, application of the axial-vector Ward-Takahashi identity to the CST pi-pi scattering amplitude allows us to sum the intermediate quark-quark interactions to all orders. The Adler self-consistency zero for pi-pi scattering in the chiral limit emerges as the result for this sum.

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arXiv2014

Covariant Spectator Theory of np scattering: Isoscalar interaction currents

Using the Covariant Spectator Theory (CST), one boson exchange (OBE) models have been found that give precision fits to low energy np scattering and the deuteron binding energy. The boson-nucleon vertices used in these models contain a momentum dependence that requires a new class of interaction currents for use with electromagnetic interactions. Current conservation requires that these new interaction currents satisfy a two-body Ward-Takahashi identity, and using principals of simplicity and picture independence, these currents can be uniquely determined. The results lead to general formulae for a two-body current that can be expressed in terms of relativistic np wave functions, Psi, and two convenient truncated wave functions, ${\it Ψ}^{(2)}$ and $\widehat {\it Ψ}$, which contain all of the information needed for the explicit evaluation of the contributions from the interaction current. These three wave functions can be calculated from the CST bound or scattering state equations (and their off-shell extrapolations). A companion paper uses this formalism to evaluate the deuteron magnetic moment.

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arXiv2014

Covariant Spectator Theory of np scattering: Deuteron magnetic moment and form factors

The deuteron magnetic moment is calculated using two model wave functions obtained from 2007 high precision fits to $np$ scattering data. Included in the calculation are a new class of isoscalar $np$ interaction currents which are automatically generated by the nuclear force model used in these fits. After normalizing the wave functions, nearly identical predictions are obtained: model WJC-1, with larger relativistic P-state components, gives 0.863(2), while model WJC-2 with very small P-state components gives 0.864(2) These are about 1\% larger than the measured value of the moment, 0.857 n.m., giving a new prediction for the size of the $ρπγ$ exchange, and other purely transverse interaction currents that are largely unconstrained by the nuclear dynamics. The physical significance of these results is discussed, and general formulae for the deuteron form factors, expressed in terms of deuteron wave functions and a new class of interaction current wave functions, are given.

nucl-th↗

arXiv2014

Quark mass functions and pion structure in Minkowski space

We present a study of the dressed quark mass function and the pion structure in Minkowski space using the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. We use an interaction kernel in momentum space that is a relativistic generalization of the linear confining q-qbar potential and a constant potential shift that defines the energy scale. The confining interaction has a Lorentz scalar part that is not chirally invariant by itself but decouples from the equations in the chiral limit and therefore allows the Nambu-Jona-Lasinio mechanism to work. We adjust the parameters of our quark mass function calculated in Minkowski-space to agree with Lattice QCD data obtained in Euclidean space. Results of a calculation of the pion electromagnetic form factor in the relativistic impulse approximation using the same mass function are presented and compared with experimental data.

hep-ph↗

arXiv2014

Confinement, quark mass functions, and spontaneous chiral symmetry breaking in Minkowski space

We formulate the covariant equations for quark-antiquark bound states in Minkowski space in the framework of the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. We show that these equations are charge-conjugation invariant, and that in the chiral limit of vanishing bare quark mass, a massless pseudoscalar bound state is produced in a Nambu-Jona-Lasinio (NJL) mechanism, which is associated with the Goldstone boson of spontaneous chiral symmetry breaking. In this introductory paper, we test the formalism by using a simplified kernel consisting of a momentum-space delta-function with a vector Lorentz structure, to which one adds a mixed scalar and vector confining interaction. The scalar part of the confining interaction is not chirally invariant by itself, but decouples from the equations in the chiral limit and therefore allows the NJL mechanism to work. With this model we calculate the quark mass function, and we compare our Minkowski-space results to lattice QCD data obtained in Euclidean space. In a companion paper, we apply this formalism to a calculation of the pion form factor.

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arXiv2014

Pion electromagnetic form factor in the Covariant Spectator Theory

The pion electromagnetic form factor at spacelike momentum transfer is calculated in relativistic impulse approximation using the Covariant Spectator Theory. The same dressed quark mass function and the equation for the pion bound-state vertex function as discussed in the companion paper are used for the calculation, together with a dressed quark current that satisfies the Ward-Takahashi identity. The results obtained for the pion form factor are in agreement with experimental data, they exhibit the typical monopole behavior at high-momentum transfer, and they satisfy some remarkable scaling relations.

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arXiv2012

Scalar-particle self-energy amplitudes and confinement in Minkowski space

We analyze the analytic structure of the Covariant Spectator Theory (CST) contribution to the self-energy amplitude for a scalar particle in a ϕ^2 χ-theory. To this end we derive dispersion relations in 1+1 and in 3+1 dimensional Minkowski space. The divergent loop integrals in 3+1 dimensions are regularized using dimensional regularization. We find that the CST dispersion relations exhibit, in addition to the usual right-hand branch cut, also a left-hand cut. The origin of this "spectator" left-hand cut can be understood in the context of scattering for a scalar ϕ^2 χ^2-type theory. If the interaction kernel contains a linear confining component, its contribution to the self-energy vanishes exactly.

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arXiv2012

Covariant nucleon wave function with S, D, and P-state components

Expressions for the nucleon wave functions in the covariant spectator theory (CST) are derived. The nucleon is described as a system with a off-mass-shell constituent quark, free to interact with an external probe, and two spectator constituent quarks on their mass shell. Integrating over the internal momentum of the on-mass-shell quark pair allows us to derive an effective nucleon wave function that can be written only in terms of the quark and diquark (quark-pair) variables. The derived nucleon wave function includes contributions from S, P and D-waves.

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