M. Buballa

Technical University Darmstadt, Darmstadt, Hesse, Germany

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Publications (73)104.8 Total impact

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    Michael Buballa, Stefano Carignano
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    ABSTRACT: The chiral condensate, which is constant in vacuum, may become spatially modulated at moderately high densities and temperatures, where in the traditional picture of the QCD phase diagram a first-order chiral phase transition occurs. We review the current status of this idea, which originally dates back to Migdal's pion condensation, but recently received new momentum by studies on the nature of the chiral critical point and by the conjecture of a quarkyonic-matter phase. We discuss how these nonuniform phases emerge in generalized Ginzburg-Landau analyses as well as in specific calculations, both within effective models and in Dyson-Schwinger or large-$N_c$ approaches to QCD. Questions about the most favored shape of the modulations and in particular its dimension, and about the effects of nonzero isospin chemical potential, strange quarks, color superconductivity, and external magnetic fields, will be adressed as well.
    06/2014;
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    ABSTRACT: Inhomogeneous chiral-symmetry breaking phases at non-vanishing chemical potential and temperature are studied within a two-flavor quark-meson model in the chiral limit. The analysis is performed beyond the standard mean-field approximation by taking into account the Dirac-sea contributions of the quarks. Compared with the case where the Dirac sea is neglected, we find that the inhomogeneous phase shrinks, but in general does not disappear. It is shown within a Ginzburg-Landau analysis that the Lifshitz point of the inhomogeneous phase coincides with the tricritical point if the ratio between sigma-meson and constituent quark mass in vacuum is chosen to be $m_\sigma/M = 2$, corresponding to the fixed mass ratio in the Nambu--Jona-Lasinio model. In the present model, however, this ratio can be varied, offering the possibility to separate the two points. This is confirmed by our numerical calculations, which demonstrate a strong sensitivity of the size of the inhomogeneous phase on $m_\sigma$. Finally, we uncover a general instability of the model with respect to large wave numbers of the chiral modulations, which calls for further improvements beyond the present approximation.
    03/2014;
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    Daniel Müller, Michael Buballa, Jochen Wambach
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    ABSTRACT: The formation of inhomogeneous chiral condensates in QCD matter at nonzero density and temperature is investigated for the first time with Dyson-Schwinger equations. We consider two massless quark flavors in a so-called chiral density wave, where scalar and pseudoscalar quark condensates vary sinusoidally along one spatial dimension. We find that the inhomogeneous region covers the major part of the spinodal region of the first-order phase transition which is present when the analysis is restricted to homogeneous phases. The triple point where the inhomogeneous phase meets the homogeneous phases with broken and restored chiral symmetry, respectively, coincides, within numerical accuracy, with the critical point of the homogeneous calculation. At zero temperature, the inhomogeneous phase seems to extend to arbitrarily high chemical potentials, as long as pairing effects are not taken into account.
    Physics Letters B 08/2013; 727(1-3). · 4.57 Impact Factor
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    ABSTRACT: An important first step in the program of hadronization of chiral quark models is the bosonization in meson and diquark channels. This procedure is presented at finite temperatures and chemical potentials for the SU(2) flavor case of the NJL model with special emphasis on the mixing between scalar meson and scalar diquark modes which occurs in the 2SC color superconducting phase. The thermodynamic potential is given the Beth-Uhlenbeck form which allows a detailed discussion of bound state dissociation in hot, dense matter (Mott effect) in terms of the in-medium scattering phase shift of two-particle correlations. It is shown for the case without meson-diquark mixing that the phase shift can be separated into a continuum and a resonance part. In the latter, the Mott transition manifests itself by a change of the phase shift by \pi\ in accordance with the Levinson theorem, when a bound state transforms to a resonance in the scattering continuum. The question of a selfconsistent quasiparticle picture is discussed as a preparation for the second step in the hadronization program: the introduction of baryons and "integrating out" the diquark fields.
    05/2013;
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    Daniel Müller, Michael Buballa, Jochen Wambach
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    ABSTRACT: We investigate the phases of dense QCD matter at finite temperature with Dyson-Schwinger equations for the quark propagator for N_f=2+1 flavors. For the gluon propagator we take a fit to quenched lattice data and add quark-loop effects perturbatively in a hard-thermal-loop--hard-dense-loop approximation. We consider 2SC and CFL-like pairing with chiral up and down quarks and massive strange quarks and present results for the condensates and the phase diagram. We find a dominant CFL phase at chemical potentials larger than 500-600 MeV. At lower values of the chemical potential we find a 2SC phase, which also exists in a small band at higher temperatures for larger chemical potentials. With values of 20-30 MeV, the critical temperatures to the normal phase turn out to be quite small.
    European Physical Journal A 03/2013; 49(8). · 2.04 Impact Factor
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    Michael Buballa, Stefano Carignano
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    ABSTRACT: The existence and the properties of self-bound quark matter in the NJL model at zero temperature are investigated in mean-field approximation, focusing on inhomogeneous structures with one-dimensional spatial modulations. It is found that the most stable homogeneous solutions which have previously been interpreted as schematic quark droplets are unstable against formation of a one-dimensional soliton-antisoliton lattice. The solitons repel each other, so that the minimal energy per quark is realized in the single-soliton limit. The properties of the solitons and their interactions are discussed in detail, and the effect of vector interactions is estimated. The results may be relevant for the dynamics of expanding quark matter.
    Physical review D: Particles and fields 10/2012; 87(5).
  • Stefano Carignano, Michael Buballa
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    ABSTRACT: We investigate the phase structure of the Nambu-Jona-Lasinio model at zero temperature, allowing for a two-dimensional spatial dependence of the chiral condensate. Applying the mean-field approximation, we consider various periodic structures with rectangular and hexagonal geometries, and minimize the corresponding free energy. We find that these two-dimensional chiral crystals are favored over homogeneous phases in a certain window in the region where the phase transition would take place when the analysis was restricted to homogeneous condensates. It turns out, however, that in this regime they are disfavored against a phase with a one-dimensional modulation of the chiral condensate. On the other hand, we find that square and hexagonal lattices eventually get favored at higher chemical potentials. Although stretching the limits of the model to some extent, this would support predictions from quarkyonic-matter studies.
    Physical review D: Particles and fields 10/2012; 86(7).
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    ABSTRACT: We study the Gaussian fluctuations of the two-flavor, meson-diquark bosonized NJL model for two and three colors at the color superconducting phase transition. The analysis is based on analytical properties of the polarization matrix. Pionic fluctuations are shown to be stabilised in the 2SC phase compared to the two-color result where they are right on threshold.
    Physics of Atomic Nuclei 07/2012; 75(7). · 0.54 Impact Factor
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    Sanjin Benić, David Blaschke, Michael Buballa
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    ABSTRACT: We show that the CJT thermodynamic potential of dynamical quark models with a quark propagator represented by complex conjugate mass poles inevitably exhibits thermodynamic instabilities. We find that the minimal coupling of the quark sector to a Polyakov loop potential can strongly suppress but not completely remove such instabilities. This general effect is explicitly demonstrated in the framework of a covariant, chirally symmetric, effective quark model.
    Physical review D: Particles and fields 06/2012; 86(7).
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    M. Buballa, S. Carignano, D. Nickel
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    ABSTRACT: We investigate inhomogeneous chiral symmetry breaking phases in the phase diagram of the two-flavor Nambu-Jona-Lasinio model, concentrating on phases with one-dimensional modulations. It is found that the first-order transition line in the phase diagram of homogeneous phases gets completely covered by an inhomogeneous phase which is bordered by second-order transition lines. The inhomogeneous phase turns out to be remarkably stable when vector interactions are included.
    Physics of Atomic Nuclei 06/2012; 75(6). · 0.54 Impact Factor
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    ABSTRACT: A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/N{sub c} expansion scheme. It is found that the 1/N{sub c} corrections lead to a lowering of the temperature of the chiral phase transition in comparison with the mean-field result. On the other hand, near the phase transition the 1/N{sub c} expansion breaks down and a nonperturbative scheme for the inclusion of mesonic correlations is needed in order to describe the phase transition region.
    Physics of Atomic Nuclei 06/2012; 75(6). · 0.54 Impact Factor
  • M. Buballa, K. Heckmann, J. Wambach
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    ABSTRACT: The properties of strongly interacting matter are probed in ultra-relativistic heavy-ion collisions. In the context of measurements of the elliptic flow at RHIC and the LHC the shear viscosity is of particular interest. In this presentation we discuss recent results for η/sη/s in hadronic matter at vanishing baryo-chemical potential within kinetic theory. Using the Nambu Jona-Lasinio model, special attention is paid to effects arising from the restoration of spontaneously broken chiral symmetry with increasing temperature.
    Progress in Particle and Nuclear Physics 04/2012; 67(2):348–352. · 2.26 Impact Factor
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    Stefano Carignano, Michael Buballa
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    ABSTRACT: We investigate the phase structure of the Nambu--Jona-Lasinio model at zero temperature, allowing for a two-dimensional spatial dependence of the chiral condensate. Applying the mean-field approximation, we consider various periodic structures with rectangular and hexagonal geometries, and minimize the corresponding free energy. We find that these two-dimensional chiral crystals are favored over homogeneous phases in a certain window in the region where the phase transition would take place when the analysis was restricted to homogeneous condensates. It turns out, however, that in this regime they are disfavored against a phase with a one-dimensional modulation of the chiral condensate. On the other hand, we find that square and hexagonal lattices eventually get favored at higher chemical potentials. Although stretching the limits of the model to some extent, this would support predictions from quarkyonic-matter studies.
    03/2012;
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    Klaus Heckmann, Michael Buballa, Jochen Wambach
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    ABSTRACT: We investigate the shear viscosity of a pion gas in relativistic kinetic theory, using the Nambu-Jona-Lasinio model to construct the pion mass and the pi-pi interaction at finite temperature. Whereas at low temperatures the scattering properties and, hence, the viscosity are in agreement with lowest-order chiral perturbation theory, we find strong medium modifications in the crossover region. Here the system is strongly coupled and the scattering lengths diverge, similarly as for ultra-cold Fermi gases at a Feshbach resonance. As a consequence, the ratio eta/s is found to be strongly reduced as compared to calculations without medium-modified masses and scattering amplitudes. However, the quantitative results are very sensitive to the details of the applied approximations.
    European Physical Journal A 02/2012; 48(10). · 2.04 Impact Factor
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    J. Wambach, K. Heckmann, M. Buballa
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    ABSTRACT: The properties of strong-interaction matter are probed in ultra-relativistic heavy-ion collisions. In the context of measurements of the elliptic flow at RHIC and the LHC the shear viscosity is of particular interest. In this presentation we discuss recent results for eta/s in hadronic matter at vanishing baryo-chemical potential within kinetic theory. Using the Nambu-Jona-Lasinio model, special attention is paid to effects arising from the restoration of spontaneously broken chiral symmetry with increasing temperature.
    11/2011;
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    Stefano Carignano, Michael Buballa
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    ABSTRACT: We present some recent developments in our study of inhomogeneous chiral symmetry breaking phases in the Nambu--Jona-Lasinio model. First, we investigate different kinds of one- and two-dimensional spatial modulations of the chiral condensate within the inhomogeneous "island" and compare their free energies. Next, we employ the Polyakov-loop extended version of the model to study the effects of varying the number of colors on the inhomogeneous region. Finally, we discuss the properties of an inhomogeneous "continent" which appears in our model at higher chemical potentials, and analyze its origin.
    11/2011;
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    David Scheffler, Michael Buballa, Jochen Wambach
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    ABSTRACT: Motivated by lattice QCD studies we investigate the RW transition endpoint at imaginary chemical potential in a two-flavor PNJL model. We focus on the quark-mass dependence of the endpoint using different forms of the Polyakov-loop potential.
    11/2011;
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    ABSTRACT: A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/Nc expansion scheme. The parameters of the nonlocal model are refitted so that the physical values of the pion mass and the weak pion decay constant are obtained. The size of the 1/Nc correction to the quark condensate is carefully studied and compared with the usual local Nambu–Jona-Lasinio model. It is found that even the sign of the corrections can be different. This can be attributed to the mesonic cutoff of the local model. The model is also applied to finite temperature. We find that the 1/Nc corrections dominate the melting of the chiral condensate at low temperatures, T≲100 MeV, in agreement with chiral perturbation theory. On the other hand, the relative importance of the 1/Nc corrections in the crossover regime depends on the parameter T0 of the Polyakov-loop potential. For T0=270 MeV, corresponding to a fit of lattice data for pure gluodynamics, the correction terms are large and lead to a lowering of the chiral phase-transition temperature in comparison with the mean-field result. Near the phase transition the 1/Nc expansion breaks down and a nonperturbative scheme is needed to include mesonic correlations in that regime. Lowering T0 leads to a more rapid crossover even at the mean-field level and the unstable region for the 1/Nc corrections shrinks. For T0≲220 MeV the temperatures of deconfinement and chiral restoration are practically synchronized.
    Physical review D: Particles and fields 06/2011; 83(11).
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    H. Basler, M. Buballa
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    ABSTRACT: The phase diagram of strongly interacting matter is studied within a three-flavor Nambu–Jona-Lasinio model, which contains the coupling between chiral and diquark condensates through the axial anomaly. Our results show that it is essential to include the two-flavor color superconducting (2SC) phase in the analysis. While this is expected for realistic strange-quark masses, we find that even for equal up, down, and strange bare quark masses 2SC pairing can be favored due to spontaneous flavor symmetry breaking by the axial anomaly. This can lead to a rich phase structure, including BCS- and Bose-Einstein condensate-like 2SC and color-flavor locked phases and new endpoints. On the other hand, the low-temperature critical endpoint, which was found earlier in the same model without 2SC pairing, is almost removed from the phase diagram and cannot be reached from the low-density chirally broken phase without crossing a preceding first-order phase boundary. For physical quark masses no additional critical endpoint is found.
    Physical review D: Particles and fields 11/2010; 82(9).
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    Stefano Carignano, Dominik Nickel, Michael Buballa
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    ABSTRACT: We investigate the role of the isoscalar vector interaction and the dynamics of the Polyakov loop on inhomogeneous phases in the phase diagram of the two-flavor Nambu-Jona--Lasinio (NJL) model. Thereby we concentrate on phases with a one-dimensional modulation, explicitly domain-wall solitons and, for comparison, the chiral spiral. While the inclusion of the Polyakov loop merely leads to quantitative changes compared to the original NJL model, the presence of a repulsive vector-channel interaction has significant qualitative effects: Whereas for homogeneous phases the first-order phase transition gets weakened and eventually turns into a second-order transition or a cross-over, the domain of inhomogeneous phases is less affected. In particular the location of the Lifshitz point in terms of temperature and density is not modified. Consequently, the critical point disappears from the phase diagram and only a Lifshitz point (showing a different critical behavior) remains. As a result, susceptibilities remain finite.
    Physical review D: Particles and fields 07/2010; 82(5).