arXiv subjects

Marco Hofmann

Publications and source records attributed to Marco Hofmann.

10 recordsLinked to original sources

arXiv2026

A doubly critical point in the color-superconducting regime of the RG-consistent NJL model

Nambu--Jona-Lasinio (NJL) models of color-superconducting quark matter suffer from cutoff artifacts once temperature or quark chemical potential become comparable to the model cutoff. These artifacts can be removed employing a renormalization-group (RG) consistent regularization scheme. In this article we perform a systematic study of neutral beta-equilibrated quark matter within the three-flavor NJL model with RG consistent regularization. Varying the coupling constant in the scalar diquark channel, we map out the phase diagram in the plane of chemical potential and temperature, and identify the gapless domains. We particularly focus on the melting pattern of the color-flavor locked (CFL) phase. At larger couplings the CFL phase melts through a so-called $d$SC phase, as expected from leading-order Ginzburg--Landau analyses. Lowering the coupling, the phase structure becomes markedly richer: While at large densities the CFL phase still melts through a $dSC$ phase, we find a $uSC$ phase at lower chemical potential. These phases, $uSC$ and $dSC$ meet at a doubly critical point whose existence had been anticipated long ago but was never demonstrated explicitly in a model.

hep-ph↗

arXiv2026

The petit four of color-superconducting phases in proto-neutron star evolution

At high densities and moderate temperatures, hadronic matter is expected to undergo a first-order phase transition into a color-superconducting (CSC) state. A proto-neutron star describes the earliest evolutionary stages during the first seconds to minutes after core-collapse supernovae and therefore has the potential to assess the appearance of CSC phases at such high densities and moderate temperatures. To address this, we incorporate proto-neutron star conditions, considering neutrino-trapped and neutrino-transparent ones, into the equation of state including color-superconducting phases in a recently developed RG-consistent NJL model. Since the total baryon number of a proto-neutron star is conserved during its later evolution, tracking stellar configurations from an initial mass of the hot proto-neutron star to the final cold neutron star along isolines of baryon number allows us to investigate whether color-superconducting phases can form at any point along this trajectory. By mapping this multidimensional transition in the hot furnace of a core-collapse supernovae cooling from a neutrino-trapped birth state to a cold, neutrino-transparent final state, we reveal four distinct core evolution scenarios-our "petit four" of proto-neutron star evolution: a delayed collapse from the CSC phase to a black hole, a persistent CSC phase, a vanishing CSC phase, and a fleeting CSC phase. For our specific parameterization of the hadronic and the CSC equation of state, we find that a stable color-superconducting phase can only be sustained in the final cold neutron star for a narrow, high-mass region.

nucl-th↗

arXiv2026

Studying the QCD Matter produced in Heavy-Ion Collisions using the MUSES Calculation Engine

The equation of state of hot and dense matter is essential for describing heavy-ion collisions at all collision energies. Here, we explore the capabilities of the latest version of the MUSES Calculation Engine, $\textit{Calliope}$, focusing on software modules and workflows that compute the equation of state and observable properties of the matter produced in heavy-ion collisions. These include several equations of state, ranging from first-principles lattice QCD to phenomenological approaches, with or without a critical point, and with phase-space dimensionality ranging from two dimensions defined by temperature $T$ and baryon chemical potential $\mu_B$, to four dimensions after the addition of strangeness and electric-charge chemical potentials $\mu_S$ and $\mu_Q$. We also discuss modules that provide additional thermodynamic quantities and observables relevant for heavy-ion modeling, including elements of the pressure Hessian matrix and transport coefficients. Workflow examples are constructed that merge two equations of state thermodynamically consistently to extend phase-diagram coverage, and feed the results into an equation of state inverter to produce inputs suitable for hydrodynamic simulations. Finally, we apply this framework to perform a relativistic viscous hydrodynamic simulation with equations of state with an extended $T$ and $\mu_B$ coverage and a movable critical point, including effects from transport coefficients that phenomenologically encode critical scaling, at collision energies $\sqrt{s_{NN}}=7.7, 19.6$, and $39$ GeV.

nucl-th↗

arXiv2025

A finite temperature framework for quark matter with color-superconducting phases

Current observations of neutron stars and measurements of gravitational waves only provide constraints on the zero temperature ($T=0$) equation of state (EoS) of dense matter. The detection of the post-merger gravitational-wave signal from a binary neutron star merger would additionally provide access to finite-temperature properties of the EoS which contain more information about the composition and the interactions of dense matter than the cold EoS alone. In particular deconfined quark matter may be probed by its characteristic finite temperature effects. This is especially the case for color-superconducting phases, in which the quasiparticle contribution to the thermal pressure is exponentially suppressed at low temperatures. Here we develop a new finite $T$ framework to model the thermal EoS for dense quark matter based on the cold quark matter EoS which is useful for numerical relativity simulations. We test the validity of the framework against a three-flavor NJL mean-field calculation, both with and without diquark pairing. We find that even for the complicated phase diagram of the NJL model including multiple different phases the framework is accurate to the few percent level for temperatures up to $T\sim 50\,$MeV.

astro-ph.HE↗

arXiv2025

Neutrino absorption in two-flavor color-superconducting quark matter

We calculate the absorption mean free paths of electron and muon neutrinos in two-flavor color-superconducting (2SC) quark matter in the density and temperature range that is relevant to binary neutron star mergers. We model the strong interaction between quarks using a Nambu--Jona-Lasinio model, performing calculations self-consistently in the mean-field approximation. Since the 2SC gap is large we restrict our analysis to the contribution of unpaired quarks. We find that at low temperatures absorption by a down quark $\nu+d \to u+e^-/\mu^-$ is kinematically not allowed, so absorption by a strange quark $\nu+s \to u+e^-/\mu^-$ dominates the mean free path. As temperature or neutrino energy rises, the $d$ quark absorption channel becomes active, and the mean free path shrinks. We find that in equilibrated 2SC matter with an electron lepton fraction $Y_{L_e}=0.1$, the neutrinos form a degenerate gas with a mean free path of meters or less, independent of the temperature.

nucl-th↗

arXiv2025

Removing cutoff artifacts in the NJL model by a Renormalization Group consistent treatment

We summarize how a renormalization-group (RG)-consistent treatment removes well-known artifacts in NJL-model descriptions of color-superconducting quark matter. We introduce two RG-consistent schemes, "minimal" and "massless", and present analytic solutions for the diquark gap at $T=0$ and for the phase boundary $T_c(\mu)$ in symmetric massless matter, representing the high-density limit of the model. We compare the pairing gaps, phase diagram, and speed of sound with results obtained using conventional regularization.

hep-ph↗

arXiv2025

Comprehensive Analysis of Constructing Hybrid Stars with an RG-consistent NJL Model

In this work, we investigate the properties of hadronic and quark matter that would allow for a first order phase transition between them within neutron stars. To this end, we use a parameterizable Relativistic Mean-Field (RMF) description for the hadronic phase and a Renormalization Group-consistent Nambu-Jona-Lasino (RG-NJL) model for the quark phase. This also enables us to consider sequential phase transitions involving a two-flavor color-superconducting (2SC) and a color-flavor-locked (CFL) phase. We find large ranges for all parameters that facilitate a phase transition, even when constrained by current astrophysical data. We further attempt to filter out stars with a high chance of detectability by mass-radius measurement, i.e., stars with identical mass but different radii, so-called twin stars. However, we find that such configurations are outside the constrained parameter spaces. Instead, most of the mass-radius relations that feature a phase transition appear to be indistinguishable from a purely hadronic description.

astro-ph.HE↗

arXiv2024

Astrophysical constraints on color-superconducting phases in compact stars within the RG-consistent NJL model

We determine parameters of the renormalization group-consistent three-flavor color-superconducting Nambu-Jona-Lasinio (NJL) model that are suited to investigate possible compact-star configurations. Our goal is to provide quark-matter equations of state (EoS) that can be used for hadron-quark hybrid-star constructions. To that end, we mainly focus on the parameters of the quark-matter model. By varying the vector and diquark coupling constants, we analyze their impact on the EoS, the speed of sound, the maximum diquark gap, and the mass-radius relation. In almost all configurations, a stable color-flavor-locked (CFL) phase appears in the core of the maximum-mass configurations, typically spanning several kilometers in radius. In other cases, the star's two-flavor color-superconducting (2SC) branch of the EoS becomes unstable before reaching the CFL transition density. At neutron-star densities, the speed of sound squared reaches up to $c_s^2 \sim 0.6$ and the CFL gap up to $\Delta\sim250\,$MeV. We argue that adding a hadronic EoS at lower densities by performing a Maxwell construction does not increase the maximum mass substantially. Thus we use the $2.0 M_{\odot}$ constraint to constrain the NJL model parameters that are suited for the construction of hybrid-star EoS. We construct three examples of the hybrid-star model, demonstrating that there is room for different color-superconducting compositions. The hybrid EoSs obtained in this way can have no 2SC matter or different ratios of 2SC and CFL quark matter in the core. We show that early hadron-quark transitions are possible that can modify the tidal deformability at 1.4 $M_\odot$. We find that these EoSs are consistent with the imposed constraints from astrophysics and perturbative QCD. They allow for different hybrid-star scenarios with a hadronic EoS that is soft at low to intermediate densities ($\sim 1-3\, n_{\text{sat}}$).

hep-ph↗

arXiv2024

Renormalization-group consistent treatment of color superconductivity in the NJL model

The Nambu-Jona-Lasinio (NJL) model and specifically its extension to color superconductivity (CSC) is a popular effective model for investigating dense quark matter. However, the reliability of its results is challenged by cutoff artifacts, which emerge if temperature or chemical potential are of the order of the cutoff energy scales. In this work, we generalize an idea from [Braun et al. SciPost Phys., 6:056, 2019], which is based on the requirement of renormalization-group (RG) consistency and has successfully been applied to the two-flavor Quark-Meson-Diquark model, to the NJL model for electrically and color-neutral three-flavor color-superconducting quark matter. To this end, we analyze the medium divergences of the model and eliminate them by appropriate counterterms, introducing three different schemes. We show that the RG-consistent treatment removes the cutoff artifacts of the conventional regularization and enables the investigation of CSC matter at higher densities by the model. Our studies reveal the emergence of a so-called d-quark superconducting (dSC) phase within the melting pattern of the Color-Flavor Locked (CFL) phase at high chemical potentials, consistent with earlier Ginzburg-Landau analyses.

hep-ph↗

arXiv2021

Dephasing versus collapse: Lessons from the tight-binding model with noise

Condensed matter physics at room temperature usually assumes that electrons in conductors can be described as spatially narrow wave packets - in contrast to what the Schr\"odinger equation would predict. How a finite-temperature environment can localize wave functions is still being debated. Here, we represent the environment by a fluctuating potential and investigate different unravellings of the Lindblad equation that describes the one-dimensional tight-binding model in the presence of such a potential. While all unravellings show a fast loss of phase coherence, only part of them lead to narrow wave packets, among them the quantum-state diffusion unravelling. Surprisingly, the decrease of the wave packet width for the quantum state diffusion model with increasing noise strength is slower than that of the phase coherence length. In addition to presenting analytical and numerical results, we also provide phenomenological explanations for them. We conclude that as long as no feedback between the wave function and the environment is taken into account, there will be no unique description of an open quantum system in terms of wave functions. We consider this to be an obstacle to understanding the quantum-classical transition.

quant-ph↗