arXiv subjects

Dirk H. Rischke

Publications and source records attributed to Dirk H. Rischke.

At least 73 records · Page 4Linked to original sources

arXiv2016

Closing the equations of motion of anisotropic fluid dynamics by a judicious choice of moment of the Boltzmann equation

In Molnár et al. [Phys. Rev. D 93, 114025 (2016)] the equations of anisotropic dissipative fluid dynamics were obtained from the moments of the Boltzmann equation based on an expansion around an arbitrary anisotropic single-particle distribution function. In this paper we make a particular choice for this distribution function and consider the boost-invariant expansion of a fluid in one dimension. In order to close the conservation equations, we need to choose an additional moment of the Boltzmann equation. We discuss the influence of the choice of this moment on the time evolution of fluid-dynamical variables and identify the moment that provides the best match of anisotropic fluid dynamics to the solution of the Boltzmann equation in the relaxation-time approximation.

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arXiv2016

Role of scalar dibaryon and $f_0(500)$ in the isovector channel of low-energy neutron-proton scattering

We calculate the total and the differential cross section for $np$ scattering at low energies in the isospin $I=1$ channel within the so-called extended Linear Sigma Model. This model contains conventional (pseudo)scalar and (axial--)vector mesons, as well as the nucleon and its chiral partner within the mirror assignment. In order to obtain good agreement with experimental data analysis results we need to consider two additional resonances: the lightest scalar state $f_{0}(500)$ and a dibaryon state with quantum numbers $I=1,$ $J^{P}=0^{+}$ (also known as $^{1}S_{0}$ resonance). The resonance $f_{0}(500)$ is coupled to nucleons in a chirally invariant way through the mirror assignment and is crucial for a qualitatively correct description of the shape of the differential cross section. On the other hand, the dibaryon is exchanged in the $s$--channel and is responsible of the large cross section close to threshold. We compare our results to data analysis results performed by the SAID program of the CNS Data Analysis Center (in the following "SAID results").

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arXiv2016

Low-energy limit of the extended Linear Sigma Model

The extended Linear Sigma Model (eLSM) is an effective hadronic model based on the linear realization of chiral symmetry $SU(N_f)_L \times SU(N_f)_R$, with (pseudo)scalar and (axial-)vector mesons as degrees of freedom. In this paper, we study the low-energy limit of the eLSM for $N_f=2$ flavors by integrating out all fields except for the pions, the (pseudo-)Nambu--Goldstone bosons of chiral symmetry breaking. We only keep terms entering at tree level and up to fourth order in powers of derivatives of the pion fields. Up to this order, there are four low-energy coupling constants in the resulting low-energy effective action. We show that the latter is formally identical to Chiral Perturbation Theory (ChPT), after choosing a representative for the coset space generated by chiral symmetry breaking and expanding up to fourth order in powers of derivatives of the pion fields. Two of the low-energy coupling constants of the eLSM are uniquely determined by a fit to hadron masses and decay widths. We find that their tree-level values are in reasonable agreement with the corresponding low-energy coupling constants of ChPT. The other two low-energy coupling constants are functions of parameters that can in principle be determined by $ππ$ scattering, which has not yet been studied within the eLSM. Therefore, we use the respective values from ChPT to make a prediction for the values of these parameters in the eLSM Lagrangian.

hep-ph↗

arXiv2016

Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization

We study the one-dimensional, longitudinally boost-invariant motion of an ideal fluid with infinite conductivity in the presence of a transverse magnetic field, i.e., in the ideal transverse magnetohydrodynamical limit. In an extension of our previous work Roy et al., [Phys. Lett. B 750, 45 (2015)], we consider the fluid to have a non-zero magnetization. First, we assume a constant magnetic susceptibility $χ_{m}$ and consider an ultrarelativistic ideal gas equation of state. For a paramagnetic fluid (i.e., with $χ_{m}>0$), the decay of the energy density slows down since the fluid gains energy from the magnetic field. For a diamagnetic fluid (i.e., with $χ_{m}<0$), the energy density decays faster because it feeds energy into the magnetic field. Furthermore, when the magnetic field is taken to be external and to decay in proper time $τ$ with a power law $\simτ^{-a}$, two distinct solutions can be found depending on the values of $a$ and $χ_m$. Finally, we also solve the ideal magnetohydrodynamical equations for one-dimensional Bjorken flow with a temperature-dependent magnetic susceptibility and a realistic equation of state given by lattice-QCD data. We find that the temperature and energy density decay more slowly because of the non-vanishing magnetization. For values of the magnetic field typical for heavy-ion collisions, this effect is, however, rather small. Only for magnetic fields which are about an order of magnitude larger than expected for heavy-ion collisions, the system is substantially reheated and the lifetime of the quark phase might be extended.

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arXiv2016

Masses of Heavy and Light Scalar Tetraquarks in a Non-Relativistic Quark Model

Scalar tetraquark states are studied within the diquark-antidiquark picture in a non-relativistic approach. We consider two types of confining potentials, a quadratic and a linear one, to which we also add spin-spin, isospin-isospin, and spin-isospin interactions. We calculate the masses of the scalar diquarks and of the ground-state open and hidden charmed and bottom scalar tetraquarks. Our results indicate that the scalar resonances $D_{0}^{\ast}(2400)$ and $D_{s}(2632)$ have a sizable tetraquark amount in their wave function, while, on the other hand, it turns out that the scalar states $D_{s0}^{\ast}(2317)$ and $X(3915)$ should not be considered as being predominantly diquark-antidiquark bound states. We also investigate the masses of light scalar diquarks and tetraquarks, which are comparable to the measured masses of the light scalar mesons.

hep-ph↗

arXiv2016

A Three-Flavor Chiral Effective Model with Four Baryonic Multiplets within the Mirror Assignment

In the case of three quark flavors, (pseudo)scalar diquarks transform as antiquarks under chiral transformations. We construct four spin-1/2 baryonic multiplets from left- and right-handed quarks as well as left- and right-handed diquarks. The fact that two of these multiplets transform in a "mirror" way allows for chirally invariant mass terms. We then embed these baryonic multiplets into the Lagrangian of the so-called extended Linear Sigma Model, which features (pseudo)scalar and (axial-)vector mesons, as well as glueballs. Reducing the Lagrangian to the two-flavor case, we obtain four doublets of nucleonic states. These mix to produce four experimentally observed states with definite parity: the positive-parity nucleon $N(939)$ and Roper resonance $N(1440)$, as well as the negative-parity resonances $N(1535)$ and $N(1650)$. We determine the parameters of the nucleonic part of the Lagrangian from a fit to masses and decay properties of the aforementioned states. Studying the limit of vanishing quark condensate, we conclude that $N(939)$ and $N(1535)$, as well as $N(1440)$ and $N(1650)$ form pairs of chiral partners.

hep-ph↗

arXiv2016

$a_{0}(980)$ revisited

Light scalar hadrons can be understood as dynamically generated resonances. These arise as `companion poles' in the propagators of quark-antiquark seed states when accounting for meson-loop contributions to the self-energies of the latter. Along this line, we extend previous calculations of Törnqvist and Roos and of Boglione and Pennington, where the resonance $a_{0}(980)$ appears as companion pole in the propagator of $a_{0}(1450)$ which is predominantly a quark-antiquark state. We also construct an effective Lagrangian where $a_{0}(1450)$ couples to pseudoscalar mesons with both non-derivative and derivative interactions. Computing the one-loop self-energy, we demonstrate that the propagator has two poles: a companion pole corresponding to $a_{0}(980)$ and a pole of the seed state $a_{0}(1450)$. The positions of these poles are in quantitative agreement with experimental data.

hep-ph↗

arXiv2016

Inhomogeneous condensation in effective models for QCD using the finite-mode approach

We use a numerical method, the finite-mode approach, to study inhomogeneous condensation in effective models for QCD in a general framework. Former limitations of considering a specific ansatz for the spatial dependence of the condensate are overcome. Different error sources are analyzed and strategies to minimize or eliminate them are outlined. The analytically known results for $1+1$ dimensional models (such as the Gross-Neveu model and extensions of it) are correctly reproduced using the finite-mode approach. Moreover, the NJL model in $3+1$ dimensions is investigated and its phase diagram is determined with particular focus on the inhomogeneous phase at high density.

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arXiv2015

Phenomenology of charmed mesons in the extended Linear Sigma Model

We study the so-called extended linear sigma model for the case of four quark flavors. This model is based on global chiral symmetry and dilatation invariance and includes, besides scalar and pseudoscalar mesons, vector and axial-vector mesons. Most of the parameters of the model have been determined in previous work by fitting properties of mesons with three quark flavors. Only three new parameters, all related to the current charm quark mass, appear when introducing charmed mesons. Surprisingly, within the accuracy expected from our approach, the masses of open charmed mesons turn out to be in quantitative agreement with experimental data. On the other hand, with the exception of $J/ψ$, the masses of charmonia are underpredicted by about 10\%. It is remarkable that our approach correctly predicts (within errors) the mass splitting between spin-0 and spin-1 negative-parity open charm states. This indicates that, although the charm quark mass breaks chiral symmetry quite strongly explicitly, this symmetry still seems to have some influence on the properties of charmed mesons.

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arXiv2015

Functional Renormalization Group Study of the Chiral Phase Transition Including Vector and Axial-vector Mesons

The transition in quantum chromodynamics (QCD) from hadronic matter to the quark-gluon plasma (QGP) at high temperatures and/or net-baryon densities is associated with the restoration of chiral symmetry and can be investigated in the laboratory via heavy-ion collisions. We study this chiral transition within the functional renormalization group (FRG) approach applied to the two-flavor version of the extended Linear Sigma Model (eLSM). The eLSM is an effective model for the strong interaction and features besides scalar and pseudoscalar degrees of freedom also vector and axial- vector mesons. We discuss the impact of the quark masses and the axial anomaly on the order of the chiral transition. We also confirm the degeneracy of the masses of chiral partners above the transition temperature. We find that the mass of the $a_1$ meson ($ρ$ meson) decreases (increases) towards the chiral transition.

hep-ph↗

arXiv2015

Classical and quantum theory of the massive spin-two field

In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz-Pauli constraints via three different methods: the eigenvalue equations for the Casimir invariants of the Poincaré group, a Lagrangian approach, and a covariant Hamilton formalism. We also present the conserved quantities, the solution of the equations of motion in terms of polarization tensors, and the tree-level propagator. We then discuss canonical quantization by postulating commutation relations for creation and annihilation operators. We express the energy, momentum, and spin operators in terms of the former. As an application, quark-antiquark currents for tensor mesons are presented. In particular, the current for tensor mesons with quantum numbers $J^{PC}=2^{-+}$ is, to our knowledge, given here for the first time.

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arXiv2015

Thermodynamics of asymptotically safe theories

We investigate the thermodynamic properties of a novel class of gauge-Yukawa theories that have recently been shown to be completely asymptotically safe, because their short-distance behaviour is determined by the presence of an interacting fixed point. Not only do all the coupling constants freeze at a constant and calculable value in the ultraviolet, their values can even be made arbitrarily small for an appropriate choice of the ratio $N_c/N_f$ of fermion colours and flavours in the Veneziano limit. Thus, a perturbative treatment can be justified. We compute the pressure, entropy density, and thermal degrees of freedom of these theories to next-to-next-to-leading order in the coupling constants.

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arXiv2014

Chiral density wave in nuclear matter

Inspired by recent work on inhomogeneous chiral condensation in cold, dense quark matter within models featuring quark degrees of freedom, we investigate the chiral density-wave solution in nu- clear matter at zero temperature and nonvanishing baryon number density in the framework of the so-called extended linear sigma model (eLSM). The eLSM is an effective model for the strong interaction based on the global chiral symmetry of quantum chromodynamics (QCD). It contains scalar, pseudoscalar, vector, and axial-vector mesons as well as baryons. In the latter sector, the nucleon and its chiral partner are introduced as parity doublets in the mirror assignment. The eLSM simultaneously provides a good description of hadrons in vacuum as well as nuclear matter ground-state properties. We find that an inhomogeneous phase in the form of a chiral density wave is realized, but only for densities larger than 2.4 ρ0, where ρ0 is the nuclear matter ground-state density.

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arXiv2014

Functional renormalization group study of the two-flavor linear sigma model in the presence of the axial anomaly

The $SU(2)_A \times U(2)_V$-symmetric chiral linear sigma model in the presence of the axial anomaly is studied in the local-potential approximation of the Functional Renormalization Group (FRG). The renormalization group (RG) flow is investigated in a truncation which reproduces recent results for the $U(2)_A \times U(2)_V$-symmetric model in the limit of vanishing axial anomaly strength. We search for the conjectured O(4) fixed point in the presence of the $U(1)_A$ anomaly and analyze its stability properties.

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arXiv2014

Is f0(1710) a glueball?

We study the three-flavor chirally and dilatation invariant extended Linear Sigma Model with (pseudo)scalar and (axial-)vector mesons as well as a scalar dilaton field whose excitations are interpreted as a glueball. The model successfully describes masses and decay widths of quark-antiquark mesons in the low-energy region up to 1.6 GeV. Here we study in detail the vacuum properties of the scalar-isoscalar channel and find that (i) a narrow glueball is only possible if the vacuum expectation value of the dilaton field is (at tree-level) quite large (i.e., larger than what lattice QCD and QCD sum rules suggest) and (ii) that only solutions in which f0(1710) is predominantly a glueball are found. Moreover, the resonance f0(1370) turns out to be mainly nonstrange quark-antiquark state and thus corresponds to the chiral partner of the pion, while the resonance f0(1500) is mainly strange quark-antiquark state.

hep-ph↗

arXiv2014

Meson production in proton-proton scattering within an extended linear sigma model

We study the production of non-strange mesons in proton-proton scattering reactions within an effective model of mesons and baryons with global chiral symmetry. The model includes the nucleon ($N$) and its chiral partner ($N^{\ast}$) and their couplings to the $N_{f}=2$ multiplets of (pseudo-)scalar and (axial-)vector mesons. Results for the production of $ω$ and $η$ mesons are presented.

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arXiv2014

Rotating hybrid compact stars

Starting from equations of state of nucleonic and color-superconducting quark matter and assuming a first-order phase transition between these, we construct an equation of state of stellar matter, which contains three phases: a nucleonic phase, as well as two-flavor and three-flavor color-superconducting phases of quarks. Static sequences of the corresponding hybrid stars include massive members with masses of $\sim 2 M_{\odot}$ and radii in the range of $13< R < 16$ km. We investigate the integral parameters of rapidly rotating stars and obtain evolutionary sequences that correspond to constant rest-mass stars spinning down by electromagnetic and gravitational radiation. Physically new transitional sequences are revealed that are distinguished by a phase transition from nucleonic to color-superconducting matter for some configurations that are located between the static and Keplerian limits. The snapshots of internal structure of the star, displaying the growth or shrinkage of superconducting volume as the star's spin changes, are displayed for constant rest mass stars. We further obtain evolutionary sequences of rotating supramassive compact stars and construct pre-collapse models that can be used as initial data to simulate a collapse of color-superconducting hybrid stars to a black hole.

astro-ph.SR↗

arXiv2014

Charmonium Spectral Functions and Transport Properties of Quark-Gluon Plasma

We study vacuum masses of charmonia and the charm-quark diffusion coefficient in the quark-gluon plasma based on the spectral representation for meson correlators. To calculate the correlators, we solve the quark gap equation and the inhomogeneous Bethe-Salpeter equation in the rainbow-ladder approximation. It is found that the ground-state masses of charmonia in the pseudoscalar, scalar, and vector channels can be well described. For $1.5\,T_c<T<3.0\,T_c$, the value of the diffusion coefficient $D$ is comparable with that obtained by lattice QCD and experiments: $3.4<2πTD<5.9$. Relating the diffusion coefficient with the ratio of shear viscosity to entropy density $η/s$ of the quark-gluon plasma, we obtain values in the range $0.09<η/s<0.16$.

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