arXiv subjects

Ralf-Arno Tripolt

Publications and source records attributed to Ralf-Arno Tripolt.

At least 19 recordsLinked to original sources

arXiv2022

Study for a model-independent pole determination of overlapping resonances

We apply a model-independent reconstruction method to experimental data in order to identify complex poles of overlapping resonances. The algorithm is based on the Schlessinger Point Method where data points are interpolated using a continued-fraction expression. Statistical uncertainties of the experimental data are propagated with resampling. In order to demonstrate the feasibility of this method, we apply it to the $S$-wave $J/ψ\to γπ^0π^0$ decay. We benchmark the method on known analytic models, which allows us to estimate the deviation from the true value. We then perform the pole extraction from BESIII data, and identify the $f_0(1500)$, $f_0(1710)$, and $f_0(2020)$ scalar states. Our results are in reasonable agreement with recent results, which suggests the proposed method as a promising model-independent alternative for the determination of resonance poles that is solely based on available experimental data.

hep-ph↗

arXiv2022

Electromagnetic Probes: Theory and Experiment

We review the current state of research on electromagnetic probes in the context of heavy-ion collisions. The focus is on thermal photons and dileptons which provide unique insights into the properties of the created hot and dense matter. This review is intended to provide an introductory overview of the topic as well as a discussion of recent theoretical and experimental results. In particular, we discuss the role of vector-meson spectral functions in the calculation of photon and dilepton rates and present recent results obtained from different frameworks. Furthermore, we will highlight the special role of photons and dileptons to provide information on observables such as the temperature, the lifetime, the polarization and the electrical conductivity of the produced medium as well as their use to learn about chiral symmetry restoration and phase transitions.

hep-ph↗

arXiv2022

Real-time observables from Euclidean thermal correlation functions

In this work we apply a local quantum field theory approach in order to analyse the connection between real-time observables and Euclidean thermal correlation functions. In particular, using data generated from the functional renormalisation group in the quark-meson model, we demonstrate that in-medium effects can be directly extracted from the spatial momentum dependence of the Euclidean propagators, in contrast to conventional approaches, which rely on the reconstruction from different Matsubara frequencies. As an application, we determine the analytic features that arise from the discrete spectral contribution to the pion correlation function, and calculate the non-perturbative shear viscosity arising from these states.

hep-ph↗

arXiv2021

Self-consistent $O(4)$ model spectral functions from analytically continued FRG flows

In this paper we explore practicable ways for self-consistent calculations of spectral functions from analytically continued functional renormalization group (aFRG) flow equations. As a particularly straightforward one we propose to include parametrizations of self-energies based on explicit analytic one-loop expressions. To exemplify this scheme we calculate the spectral functions of pion and sigma meson of the $O(4)$ model at vanishing temperature in the broken phase. Comparing the results with those from previous aFRG calculations, we explicitly demonstrate how self-consistency at all momenta fixes the tight relation between particle masses and decay thresholds. In addition, the two-point functions from our new semi-analytic FRG scheme have the desired domain of holomorphy built in and can readily be studied in the entire cut-complex frequency plane, on physical as well as other Riemann sheets. This is very illustrative and allows, for example, to trace the flow of the resonance pole of the sigma meson across an unphysical sheet. In order to assess the limitations due to the underlying one-loop structure, we also introduce a fully self-consistent numerical scheme based on spectral representations with scale-dependent spectral functions. The most notable improvement of this numerically involved calculation is that it describes the three-particle resonance decay of an off-shell pion, $π^* \to σπ\to3π$. Apart from this further conceptual improvement, overall agreement with the results from the considerably simpler semi-analytic one-loop scheme is very encouraging, however. The latter can therefore provide a sound and practicable basis for self-consistent calculations of spectral functions in more realistic effective theories for warm and dense matter.

hep-ph↗

arXiv2021

Spectral representation of the shear viscosity for local scalar QFTs at finite temperature

In local scalar quantum field theories (QFTs) at finite temperature correlation functions are known to satisfy certain non-perturbative constraints, which for two-point functions in particular implies the existence of a generalisation of the standard Källén-Lehmann representation. In this work, we use these constraints in order to derive a spectral representation for the shear viscosity arising from the thermal asymptotic states, $η_{0}$. As an example, we calculate $η_{0}$ in $ϕ^{4}$ theory, establishing its leading behaviour in the small and large coupling regimes.

hep-th↗

arXiv2021

Vector and Axial-Vector Mesons in Nuclear Matter

As a first step towards a realistic phenomenological description of vector and axial-vector mesons in nuclear matter, we calculate the spectral functions of the $ρ$ and the $a_1$ meson in a chiral baryon-meson model as a low-energy effective realization of QCD, taking into account the effects of fluctuations from scalar mesons, nucleons, and vector mesons within the Functional Renormalization Group (FRG) approach. The phase diagram of the effective hadronic theory exhibits a nuclear liquid-gas phase transition as well as a chiral phase transition at a higher baryon-chemical potential. The in-medium $ρ$ and $a_1$ spectral functions are calculated by using the previously introduced analytically-continued FRG (aFRG) method. Our results show strong modifications of the spectral functions in particular near the critical endpoints of both phase transitions which may well be of relevance for electromagnetic rates in heavy-ion collisions or neutrino emissivities in neutron-star merger events.

hep-ph↗

arXiv2020

Fermionic excitations at finite temperature and density

We study fermionic excitations in a hot and dense strongly interacting medium consisting of quarks and (pseudo-)scalar mesons. In particular, we use the two-flavor quark-meson model in combination with the Functional Renormalization Group approach, which allows to take into account the effects from thermal and quantum fluctuations. The resulting fermionic excitation spectrum is investigated by calculating the quark spectral function at finite temperature, quark chemical potential, and spatial momentum. This involves an analytic continuation from imaginary to real energies by extending the previously introduced analytically-continued FRG (aFRG) method to the present case. We identify three different collective excitations in the medium: the ordinary thermal quark, the plasmino mode, and an ultra-soft "phonino" mode. The dispersion relations of these modes are extracted from the quark spectral function. When compared to corresponding results from an FRG-improved one-loop calculation remarkable agreement is found.

hep-ph↗

arXiv2020

Electromagnetic and weak probes: theory

An overview of the latest theoretical developments and results on electromagnetic and weak probes in relativistic heavy-ion collisions is presented. The possibilities to use electromagnetic probes, i.e., photons and dileptons, as a spectrometer, thermometer, chronometer, polarimeter, barometer, and multimeter of the collision system, as well as to explore the QCD phase diagram and to locate phase transitions such as the critical endpoint, are discussed.

hep-ph↗

arXiv2020

Spectral functions of confined particles

We determine the gluon and ghost spectral functions along with the analytic structure of the associated propagators from numerical data describing gauge correlators at space-like momenta obtained by either solving the Dyson-Schwinger equations or through lattice simulations. Our novel reconstruction technique shows the expected branch cut for the gluon and the ghost propagator, which, in the gluon case, is supplemented with a pair of complex conjugate poles. Possible implications of the existence of these poles are briefly addressed.

hep-ph↗

arXiv2018

Numerical analytic continuation of Euclidean data

In this work we present a direct comparison of three different numerical analytic continuation methods: the Maximum Entropy Method, the Backus-Gilbert method and the Schlessinger point or Resonances Via Padé method. First, we perform a benchmark test based on a model spectral function and study the regime of applicability of these methods depending on the number of input points and their statistical error. We then apply these methods to more realistic examples, namely to numerical data on Euclidean propagators obtained from a Functional Renormalization Group calculation, to data from a lattice Quantum Chromodynamics simulation and to data obtained from a tight-binding model for graphene in order to extract the electrical conductivity.

hep-ph↗

arXiv2018

Resonance poles and threshold energies for hadron physical problems by a model-independent universal algorithm

We show how complex resonance poles and threshold energies for systems in hadron physics can be accurately obtained by using a method based on the Padé-approximant which was recently developed for the calculation of resonance poles for atomic and molecular auto-ionization systems. The main advantage of this method is the ability to calculate the resonance poles and threshold energies from \emph{real} spectral data. In order to demonstrate the capabilities of this method we apply it here to an analytical model as well as to experimental data for the squared modulus of the vector pion form factor, the S0 partial wave amplitude for $ππ$ scattering and the cross section ratio $R(s)$ for $e^+e^-$ collisions. The extracted values for the resonance poles of the $ρ(770)$ and the $f_0(500)$ or $σ$ meson are in very good agreement with the literature. When the data are noisy the prediction of decay thresholds proves to be less accurate but feasible.

hep-ph↗

arXiv2018

Fermionic spectral functions with the Functional Renormalization Group

We present first results on the calculation of fermionic spectral functions from analytically continued flow equations within the Functional Renormalization Group approach. Our method is based on the same analytic continuation from imaginary to real frequencies that was developed and used previously for bosonic spectral functions. In order to demonstrate the applicability of the method also for fermionic correlations we apply it here to the real-time quark propagator in the quark-meson model and calculate the corresponding quark spectral functions in the vacuum.

hep-ph↗

arXiv2018

In-medium spectral functions and dilepton rates with the Functional Renormalization Group

We present recent results on in-medium spectral functions of vector and axial-vector mesons, the electromagnetic (EM) spectral function and dilepton rates using the Functional Renormalization Group (FRG) approach. Our method is based on an analytic continuation procedure that allows us to calculate real-time quantities like spectral functions at finite temperature and chemical potential. As an effective low-energy model for Quantum Chromodynamics (QCD) we use an extended linear-sigma model including quarks where (axial-)vector mesons as well as the photon are introduced as gauge bosons. In particular, it is shown how the $ρ$ and the $a_1$ spectral function become degenerate at high temperatures or chemical potentials due to the restoration of chiral symmetry. Preliminary results for the EM spectral function and the dilepton production rate are discussed with a focus on the possibility to identify signatures of the chiral crossover and the critical endpoint (CEP) in the QCD phase diagram.

hep-ph↗

arXiv2018

Color superconductivity from the chiral quark-meson model

We study the two-flavor color superconductivity of low-temperature quark matter in the vicinity of chiral phase transition in the quark-meson model where the interactions between quarks are generated by pion and sigma exchanges. Starting from the Nambu-Gor'kov propagator in real-time formulation we obtain finite temperature (real axis) Eliashberg-type equations for the quark self-energies (gap functions) in terms of the in-medium spectral function of mesons. Exact numerical solutions of the coupled nonlinear integral equations for the real and imaginary parts of the gap function are obtained in the zero temperature limit using a model input spectral function. We find that these components of the gap display a complicated structure with the real part being strongly suppressed above $2Δ_0$, where $Δ_0$ is its on-shell value. We find $Δ_0\simeq 40$ MeV close to the chiral phase transition.

hep-ph↗

arXiv2018

The low-temperature behavior of the quark-meson model

We revisit the phase diagram of strong-interaction matter for the two-flavor quark-meson model using the Functional Renormalization Group. In contrast to standard mean-field calculations, an unusual phase structure is encountered at low temperatures and large quark chemical potentials. In particular, we identify a regime where the pressure decreases with increasing temperature and discuss possible reasons for this unphysical behavior.

hep-ph↗

arXiv2017

Spectral Functions from the Functional Renormalization Group

We present results for in-medium spectral functions obtained within the Functional Renormalization Group framework. The analytic continuation from imaginary to real time is performed in a well-defined way on the level of the flow equations. Based on this recently developed method, results for the sigma and the pion spectral function for the quark-meson model are shown at finite temperature, finite quark-chemical potential and finite spatial momentum. It is shown how these spectral function become degenreate at high temperatures due to the restoration of chiral symmetry. In addition, results for vector- and axial-vector meson spectral functions are shown using a gauged linear sigma model with quarks. The degeneration of the $ρ$ and the $a_1$ spectral function as well as the behavior of their pole masses is discussed.

hep-ph↗

arXiv2016

In-Medium Spectral Functions of Vector- and Axial-Vector Mesons from the Functional Renormalization Group

In this work we present first results on vector and axial-vector meson spectral functions as obtained by applying the non-perturbative functional renormalization group approach to an effective low-energy theory motivated by the gauged linear sigma model. By using a recently proposed analytic continuation method, we study the in-medium behavior of the spectral functions of the $ρ$ and $a_1$ mesons in different regimes of the phase diagram. In particular, we demonstrate explicitly how these spectral functions degenerate at high temperatures as well as at large chemical potentials, as a consequence of the restoration of chiral symmetry. In addition, we also compute the momentum dependence of the $ρ$ and $a_1$ spectral functions and discuss the various time-like and space-like processes that can occur.

hep-ph↗

arXiv2016

Spectral functions and in-medium properties of hadrons

The in-medium modifications of hadron properties such as masses and decay widths have been a major focus of the scientific work of Gerry Brown and the insights gained by him and his collaborators made them major drivers of this field for several decades. Their prediction of experimental signals in di-lepton pair production in relativistic heavy-ion collisions were instrumental in initiating large experimental campaigns which continue until today. In this chapter we review recent results which elucidate the relation of hadronic spectral properties at finite temperature and density to the restoration of spontaneously broken chiral symmetry.

hep-ph↗