arXiv subjects

Wolfgang Bentz

Publications and source records attributed to Wolfgang Bentz.

At least 19 recordsLinked to original sources

arXiv2025

Relations between three-particle interactions in nuclear matter to observable quantities

In the first part of this paper, we use the framework of the Fermi liquid theory to derive model-independent relations between the slope parameters of the symmetry energy and of the incompressibility in nuclear matter to three-particle interaction parameters. Based on these relations, we present simple estimates and compare with the empirical information. In the second part, we discuss the general structure of the three-particle scattering amplitude in nuclear matter, and use methods similar to the Bethe-Brueckner-Goldstone theory to show how three-particle cluster diagrams emerge naturally in the Fermi liquid theory.

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arXiv2025

Effects of quark core sizes of baryons in neutron star matter

We describe the quark substructure of hadrons and the equation of state of high density neutron star matter by using the Nambu$-$Jona-Lasinio (NJL) model, which is an effective quark theory based on QCD. The interaction between quarks fully respects the chiral and flavor symmetries. Guided by the success of various low energy theorems, we assume that the explicit breaking of these symmetries occurs only via the current quark masses, and all other symmetry breakings are of dynamical nature. In order to take into account the effects of the finite quark core sizes of the baryons on the equation of state, we make use of an excluded volume framework which respects thermodynamic consistency. The effects generated by the swelling quark cores generally act repulsively and lead to an increase of the pressure with increasing baryon density. On the other hand, in neutron star matter they also lead to a decrease of the density window where hyperons appear, because it becomes energetically more favorable to convert the faster moving nucleons into hyperons. Our quantitative analysis shows that the net effect of the excluded volume is too small to solve the long standing "hyperon puzzle," which is posed by the large observed masses of neutron stars. Thus the puzzle persists in a relativistic effective quark theory which takes into account the short range repulsion between baryons caused by their finite and swelling quark core sizes in a phenomenological way.

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arXiv2023

Composite octet baryons in a relativistic mean field description of nuclear and neutron star matter

We examine the properties of composite octet baryons in the nuclear medium and neutron star matter. The internal quark-diquark structure of the octet baryons and the equations of state of nuclear matter and neutron star matter in the mean field approximation are described by using the three-flavor Nambu--Jona-Lasinio (NJL) model as an effective quark theory of QCD. After introducing our model, we first discuss the properties of single baryons and their effective meson exchange interactions in symmetric nuclear matter by using concepts of Fermi liquid theory. Several model independent implications of this description are derived, and illustrated by numerical results obtained in our model. Second, we extend the model description to high baryon densities, and investigate the equation of state of neutron star matter and the resulting star masses. We find that the so called hyperon puzzle persists also for the case of composite hadrons. To get more information on this point, we also investigate the role of 6-fermi and 8-fermi interactions, in addition to the standard 4-fermi interactions. The strengths of those higher order fermi interactions is determined so as not to spoil the saturation properties of nuclear matter. Among them, an interaction characterized by a product of four quark current operators plays a special role to stabilize the stars over a large region of central baryon densities, although it has little effect on the maximum star masses.

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arXiv2022

Gluon EMC effects in nuclear matter

We investigate the gluonic structure of nuclei within a mean-field model of nuclear structure based upon the modification of the structure of a bound nucleon, with the nucleon described by the Nambu--Jona-Lasinio model. This approach has been shown to reproduce the European Muon Collaboration (EMC) effect, involving the ratio of the spin-independent structure functions of a heavier nucleus to that of the deuteron. It also predicts a significant nuclear modification for the spin structure functions, known as the polarized EMC effect. Here we report sizeable nuclear modifications of the gluon distributions (a "gluon EMC effect") for the ratios of both the unpolarized and polarized gluon distributions in nuclear matter to those of a free nucleon.

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arXiv2022

Slope parameter of the symmetry energy and the structure of three-particle interactions in nuclear matter

In the first part of this paper, we present a study of the symmetry energy ($a_s$) and its slope parameter ($L$) for nuclear matter in the framework of the Fermi liquid theory of Landau and Migdal. We derive an exact relation between $a_s$ and $L$, which involves the nucleon effective masses and three-particle Landau-Migdal parameters. We present simple estimates which suggest that there are two main mechanisms to explain the empirical values of $L$: The proton-neutron effective mass difference in isospin asymmetric matter and the $\ell=0$ moment of the isovector in-medium three-particle scattering amplitude. In the second part of this paper, we discuss the general structure of three-particle interactions in nuclear matter in the framework of the Fermi liquid theory. The connections to the Bethe-Brueckner-Goldstone theory and other approaches are also discussed. We show explicitly how the first few terms in the Faddeev series, together with medium induced three-particle interactions, emerge naturally in the Fermi liquid theory.

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arXiv2020

Massive Neutron Stars with a Color Superconducting Quark Matter Core

We construct the equation of state for high density neutron star matter at zero temperature using the two-flavor Nambu--Jona-Lasinio (NJL) model as an effective theory of QCD. We build nuclear matter, quark matter, and the mixed phases from the same NJL Lagrangian, which has been used to model free and in-medium hadrons as well as nuclear systems. A focus here is to determine if the same coupling constants in the scalar diquark and vector meson channels, which give a good description of nucleon structure and nuclear matter, can also be used for the color superconducting high density quark matter phase. We find that this is possible for the scalar diquark (pairing) interaction, but the vector meson interaction has to be reduced so that superconducting quark matter becomes the stable phase at high densities. We compare our equation of state with recent phenomenological parametrizations based on generic stability conditions for neutron stars. We find that the maximum mass of a neutron star, with a color superconducting quark matter core, exceeds $2.01 \pm 0.04\,M_\odot$ which is the value of the recently observed massive neutron star PSR J0348+0432. The mass-radius relation is also consistent with gravitational wave observations (GW170817).

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arXiv2019

Effects of charge symmetry breaking on form factors of the pion and kaon

Effects of charge symmetry breaking associated with the $u$ and $d$ quark mass difference in the elastic form factors of the pion and kaon are presented. We use a confining version of the Nambu--Jona-Lasinio model. The pion and kaon are described as a dressed quark and antiquark bound states governed by the Bethe-Salpeter equation, and exhibit the properties of Goldstone bosons, with the pion mass difference given by $m_{π^{+}}^2 - m_{π^{0}}^2 \propto (m_u -m_d)^2$ as demanded by dynamical chiral symmetry breaking. We found significant charge symmetry breaking effects for realistic current quark mass ratios ($m_u/m_d \sim 0.5$) in the quark electromagnetic form factors of the pion and kaon. We also report the effects of charge symmetry breaking on the parton distribution functions, which are rather smaller than those found in the electromagnetic form factors.

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arXiv2019

Skewness of nuclear matter and three-particle correlations

We present a study of the skewness of nuclear matter, which is proportional to the third derivative of the energy per nucleon with respect to the baryon density at the saturation point, in the framework of the Landau-Migdal theory. We derive an exact relation between the skewness, the nucleon effective mass, and two-particle and three-particle interaction parameters. We also present qualitative estimates, which indicate that three-particle correlations play an important role for the skewness.

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arXiv2018

Charge Symmetry Breaking Effects in Pion and Kaon Structure

Charge symmetry breaking (CSB) effects associated with the $u$ and $d$ quark mass difference are investigated in the quark distribution functions and spacelike electromagnetic form factors of the pion and kaon. We use a confining version of the Nambu--Jona-Lasinio model, where CSB effects at the infrared scale associated with the model are driven by the dressed $u$ and $d$ quark mass ratio, which because of dynamical chiral symmetry breaking is much closer to unity than the associated current quark mass ratio. The pion and kaon are given as bound states of a dressed quark and a dressed antiquark governed by the Bethe-Salpeter equation, and exhibit the properties of Goldstone bosons, with a pion mass difference given by $m_{π^+}^2 - m_{π^0}^2 \propto (m_u - m_d)^2$ as demanded by dynamical chiral symmetry breaking. We find significant CSB effects for realistic current quark mass ratios ($m_u/m_d \sim 0.5$) in the quark flavor-sector electromagnetic form factors of both the pion and kaon. For example, the difference between the $u$ and $d$ quark contributions to the $π^+$ electromagnetic form factors is about 8\% at a momentum transfer of $Q^2 \simeq 10\,$GeV$^2$, while the analogous effect for the light quark sector form factors in the $K^+$ and $K^0$ is about twice as large. For the Parton distribution functions, we find CSB effects which are considerably smaller than those found in the electromagnetic form factors.

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arXiv2017

TMDs of Spin-one Targets: Formalism and Covariant Calculations

We present a covariant formulation and model calculations of transverse momentum-dependent quark distribution functions (TMDs) for spin-one hadrons. Emphasis is placed on a description of these 3-dimensional distribution functions which is independent of any constraints on the spin quantization axis. We apply our covariant spin description to all nine leading-twist time-reversal even $ρ$ meson TMDs in the framework provided by the Nambu--Jona-Lasinio model, incorporating important aspects of quark confinement via the infrared cut-off in the proper-time regularization scheme. In particular, the behavior of the 3-dimensional TMDs in a tensor polarized spin-one hadron are illustrated. Sum rules and positivity constraints are discussed in detail. Results of particular interest include the finding that the tensor polarized TMDs -- associated with spin-one hadrons -- are very sensitive to quark orbital angular momentum, and that the TMDs associated with the quark operator $γ^+\boldsymbolγ_Tγ_5$ would vanish were it not for dynamical chiral symmetry breaking. In addition, we find that 44% of the $ρ$ meson's spin is carried by the orbital angular momentum of the quarks, and that the magnitude of the tensor polarized quark distribution function is about 30% of the unpolarized quark distribution. A qualitative comparison between our results for the tensor structure of a quark-antiquark bound state is made to previous experimental and theoretical results for the two-nucleon (deuteron) bound state.

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arXiv2016

Baryon Octet Electromagnetic Form Factors in a confining NJL model

Electromagnetic form factors of the baryon octet are studied using a Nambu--Jona-Lasinio model which utilizes the proper-time regularization scheme to simulate aspects of colour confinement. In addition, the model also incorporates corrections to the dressed quarks from vector meson correlations in the t-channel and the pion cloud. Comparison with recent chiral extrapolations of lattice QCD results shows a remarkable level of consistency. For the charge radii we find the surprising result $r_{E}^p < r_{E}^{Σ^+}$ and $|r_{E}^n| < |r_{E}^{Ξ^0}|$, whereas the magnetic radii have a pattern largely consistent with a naive expectation based on the dressed quark masses.

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arXiv2015

Relativistic and Nuclear Medium Effects on the Coulomb Sum Rule

In light of the forthcoming high precision quasielastic electron scattering data from Jefferson Lab, it is timely for the various approaches to nuclear structure to make robust predictions for the associated response functions. With this in mind, we focus here on the longitudinal response function and the corresponding Coulomb sum rule for isospin-symmetric nuclear matter at various baryon densities. Using a quantum field-theoretic quark-level approach which preserves the symmetries of quantum chromodynamics, as well as exhibiting dynamical chiral symmetry breaking and quark confinement, we find a dramatic quenching of the Coulomb sum rule for momentum transfers $\left|\mathbf{q}\right| \gtrsim 0.5\,$GeV. The main driver of this effect lies in changes to the proton Dirac form factor induced by the nuclear medium. Such a dramatic quenching of the Coulomb sum rule was not seen in a recent quantum Monte Carlo calculation for carbon, suggesting that the Jefferson Lab data may well shed new light on the explicit role of QCD in nuclei.

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arXiv2015

Rho meson form factors in a confining Nambu--Jona-Lasinio model

Elastic electromagnetic form factors for the $ρ^+$ meson are calculated in a Nambu--Jona-Lasinio model which incorporates quark confinement through the use of the proper-time regularization scheme. A comparison is made with recent lattice QCD results and previous quark model calculations for static quantities and the Sachs form factors. The results are qualitatively in good agreement with the lattice QCD calculations, with the exception of the quadrupole moment and corresponding form factor, which may be related to a lack of spherical symmetry on the lattice.

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arXiv2014

Role of diquark correlations and the pion cloud in nucleon elastic form factors

Electromagnetic form factors of the nucleon in the space-like region are investigated within the framework of a covariant and confining Nambu-Jona-Lasinio model. The bound state amplitude of the nucleon is obtained as the solution of a relativistic Faddeev equation, where diquark correlations appear naturally as a consequence of the strong coupling in the colour $\bar{3}$ $qq$ channel. Pion degrees of freedom are included as a perturbation to the "quark-core" contribution obtained using the Poincaré covariant Faddeev amplitude. While no model parameters are fit to form factor data, excellent agreement is obtained with the empirical nucleon form factors (including the magnetic moments and radii) where pion loop corrections play a critical role for $Q^2 \lesssim 1\,$GeV$^2$. Using charge symmetry, the nucleon form factors can be expressed as proton quark sector form factors. The latter are studied in detail, leading, for example, to the conclusion that the $d$-quark sector of the Dirac form factor is much softer than the $u$-quark sector, a consequence of the dominance of scalar diquark correlations in the proton wave function. On the other hand, for the proton quark sector Pauli form factors we find that the effect of the pion cloud and axialvector diquark correlations overcomes the effect of scalar diquark dominance, leading to a larger $d$-quark anomalous magnetic moment and a form factor in the $u$-quark sector that is slightly softer than in the $d$-quark sector.

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arXiv2013

Dihadron Fragmentation Functions within the NJL-jet Model

Dihadron Fragmentation Functions (DFF) provide a vast amount of information on the intricate details of the parton hadronization process. Moreover, they provide a unique access to the "clean" extraction of nucleon transversity parton distribution functions in semi inclusive deep inelastic two hadron production process with a transversely polarised target. The NJL-jet model has been extended for calculations of light and strange quark unpolarised DFFs to pions, kaons and several vector mesons. This is accomplished by using the probabilistic interpretation of the DFFs, and employing the NJL-jet hadronization model in the Monte Carlo simulations that includes the transverse momentum of the produced hadrons. The strong decays of the vector mesons and the subsequent modification of the pseudoscalar meson DFFs are also considered. The resulting pseudoscalar meson DFFs are strongly influenced by the decays of the relevant vector mesons. This is because of the large combinatorial factors involved in counting the number of the hadron pairs that include the decay products. The evolution of the DFFs from the model scale to a typical experimental scale has also been performed.

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arXiv2013

The Effect of Vector Meson Decays on Dihadron Fragmentation Functions

Dihadron Fragmentation Functions (DFF) provide a vast amount of information on the intricate details of the parton hadronization process. Moreover, they provide a unique access to the "clean" extraction of nucleon transversity parton distribution functions in semi inclusive deep inelastic two hadron production process with a transversely polarised target. On the example of the u \to π^+ π^-, we analyse the properties of unpolarised DFFs using their probabilistic interpretation. We use both the NJL-jet hadronization model and PYTHIA 8.1 event generator to explore the effect of the strong decays of the vector mesons produced in the quark hadronization process on the pseudoscalar DFFs. Our study shows that, even though it is less probable to produce vector mesons in the hadronization process than pseudo scalar mesons of the same charge, the products of their strong decays drastically affect the DFFs for pions because of the large combinatorial factors. Thus, an accurate description of both vector meson production and decays are crucial for theoretical understanding of DFFs.

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arXiv2012

Collins Fragmentation Function within NJL-jet Model

The NJL-jet model is extended to accommodate hadronization of a transversely polarized quark in order to explore the Collins effect within a multihadron emission framework. This is accomplished by calculating the polarized quark spin flip probabilities after a pseudoscalar hadron emission and the elementary Collins functions. The model is used to calculate the number densities of the hadrons produced in the polarized quark's decay chain. The full Collins fragmentation function is extracted from the sine modulation of the polarized number densities with respect to the polar angle between the initial quark's spin and hadron's transverse momentum. Two cases are studied here. First, a toy model for elementary Collins function is used to study the features of the transversely polarized quark-jet model. Second, a full model calculation of transverse momentum dependent pion and kaon Collins functions is presented. The remarkable feature of our model is that the 1/2 moments of the favored Collins fragmentation functions are positive and peak at large values of z but decrease and oscillate at small values of z. The 1/2 moments of the unfavored Collins functions have comparable magnitude and opposite sign to the favored functions, vanish at large z and peak at small values of z. This feature is observed for both the toy and full models and can be attributed to the quark-jet picture of hadronization. Moreover, the transverse momentum dependencies of the model Collins functions differ significantly from the Gaussian form widely used in the empirical parametrizations. Finally, a naive interpretation of the Schafer-Teryaev sum rule is proven not to hold in our model, where the transverse momentum conservation is explicitly enforced. This is attributed to the sizable average transverse momentum of the remnant quark that needs to be accounted for to satisfy the transverse momentum sum-rule.

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arXiv2012

Higher Order Collins Modulations in Transversely Polarized Quark Fragmentation

The Collins effect describes the modulation of the hadron production by a transversely polarized quark with the sine of the polar angle, $φ$, between the produced hadron's transverse momentum and the quark spin. We employ a quark-jet model to describe multiple hadron emissions by such a quark, taking the Collins effect into account. The resulting hadron distributions exhibit modulation up to fourth order in $\sin(φ)$ when only two hadron emissions are allowed, rising with any further increase in the number of emitted hadrons. These new effects are a direct consequence of the quark-jet mechanism for quark hadronization, which do not depend on the details of the model used for elementary hadron emission. The size and the sign of the higher order terms are directly connected with the probabilities of quark spin flip in the elementary emission process, with opposing sign favored and unfavored Collins functions only being generated if quark spin flip is preferential. Experimental studies of these effects should therefore provide a critical test of the quark hadronization mechanism, which in turn will lead to a deeper understanding of the transverse spin structure of hadrons.

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