Heavy-ion collisions at varying collision energies provide access to different regions of the QCD phase diagram. In particular collisions at intermediate energies are promising candidates to experimentally identify the postulated first order phase transition and critical end point. While heavy-ion collisions at low and high collision energies are theoretically well described by transport approaches and hydrodynamics+transport hybrid approaches, respectively, intermediate energy collisions remain a challenge. In this work, a modular hybrid approach, the SMASH-vHLLE-hybrid coupling 3+1D viscous hydrodynamics (vHLLE) to hadronic transport (SMASH), is introduced. It is validated and subsequently applied in Au+Au/Pb+Pb collisions between $\sqrt{s_\mathrm{NN}}$ = 4.3 GeV and $\sqrt{s_\mathrm{NN}}$ = 200.0 GeV to study the rapidity and transverse mass distributions of identified particles as well as excitation functions for $\mathrm{dN}/\mathrm{d}y|_{y = 0}$ and $\langle p_\mathrm{T} \rangle$. A good agreement with experimental measurements is obtained, including the baryon stopping dynamics. The transition from a Gaussian rapidity spectrum of protons at lower energies to the double-hump structure at high energies is reproduced. The centrality and energy dependence of charged particle $v_2$ is also described reasonably well. This work serves as a basis for further studies, e.g. systematic investigations of different equations of state or transport coefficients.

We use a novel real-time formulation of the functional renormalization group (FRG) for dynamical systems with reversible mode couplings to study Model G and H, which are the conjectured dynamic universality classes of the two-flavor chiral phase transition and the QCD critical point, respectively. We compute the dynamic critical exponent in both models in spatial dimensions $2

The role of spin degrees of freedom in the quark-gluon plasma (QGP) has attracted significant interest in recent years. Spin hydrodynamics extends conventional hydrodynamics by incorporating spin via the spin tensor. In the mean-field limit of the Nambu-Jona-Lasinio (NJL) model under rigid rotation, spin degrees of freedom manifest naturally as axial-vector, or spin, condensate. We investigate the interplay between chiral and spin condensates in this framework. While rotation typically suppresses the formation of a chiral condensate, the presence of a spin condensate may counteract this effect, enhancing the chiral condensate. Moreover, it can alter the nature of the chiral transition from second to first order.

The rotation effect on the QCD properties is an open question. We study the dynamic gluon mass in a dense QCD matter, the rotation is introduced by taking a covariant transformation between the flat and curved spaces. The law of causality which restricts the rotation strength of the system is carefully considered in the calculation. we find that the rotation effect is not monotonous. Overall, it behaves like an anti-screening effect, reflecting in the decreasing gluon mass, but the strength changes with the rotation. For a QCD matter with low baryon density, the screening effect in the flat space can be completely canceled by the rotation, and gluons are confined in a strongly rotating matter. When the rotation is extremely high, the matter approaches to a weakly interacting gas.

State-of-the-art additive manufacturing technologies are not only finding ever-wider applications in everyday life, but also assuming an increasingly important role in scientific research. This kind of advanced manufacturing method eliminates many of the constraints of conventional processes in fabricating components with complex external shapes or intricate internal structures, thereby providing enhanced flexibility for the design and realization of a new generation of more efficient particle accelerators and storage rings. The RACERS team initiated by the Stochastic Cooling Group at GSI, Germany, is worldwide one of the first teams working on this topic. Based on the metal 3D-printing technology, two novel accelerating structures and one efficient cooling plate for a future stochastic cooling system are under development at GSI and for the FAIR project, respectively. Some successful experience as well as learnt lessons will be presented.

The analysis of experimental results with Python often requires writing many code scripts which all need access to the same set of functions. In a common field of research, this set will be nearly the same for many users. The qspec Python package was developed to provide functions for physical formulas, simulations and data analysis routines widely used in laser spectroscopy and related fields. Most functions are compatible with numpy arrays, enabling fast calculations with large samples of data. A multidimensional linear regression algorithm enables a King plot analyses over multiple atomic transitions. A modular framework for constructing lineshape models can be used to fit large sets of spectroscopy data. A simulation module within the package provides user-friendly methods to simulate the coherent time-evolution of atoms in electro-magnetic fields without the need to explicitly derive a Hamiltonian.

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.

We provide results for the spectrum of scalar and pseudoscalar glueballs in pure Yang-Mills theory using a parameter-free fully self-contained truncation of Dyson-Schwinger and Bethe-Salpeter equations. The only input, the scale, is fixed by comparison with lattice calculations. We obtain ground state masses of $1.9\,\text{GeV}$ and $2.6\,\text{GeV}$ for the scalar and pseudoscalar glueballs, respectively, and $2.6\,\text{GeV}$ and $3.9\,\text{GeV}$ for the corresponding first excited states. This is in very good quantitative agreement with available lattice results. Furthermore, we predict masses for the second excited states at $3.7\,\text{GeV}$ and $4.3\,\text{GeV}$. The quality of the results hinges crucially on the self-consistency of the employed input. The masses are independent of a specific choice for the infrared behavior of the ghost propagator providing further evidence that this only reflects a nonperturbative gauge completion.

Femtoscopy offers a sensitive probe of hadron emission sources and hadronic interactions. In this study, we examine relativistic corrections to scattering phase shifts and correlation functions using the two-body Dirac equation framework. We analyze the impact of the Darwin term and spin-dependent potentials, showing that these relativistic effects, especially spin-related interactions, significantly enhance the proton-proton correlation function. Our findings emphasize the necessity of including relativistic corrections for precise femtoscopic analyses.

We compute hybrid static potentials in SU(2) lattice gauge theory using a multilevel algorithm and three different small lattice spacings. The resulting static potentials, which are valid for quark-antiquark separations as small as 0.05 fm, are important e.g. when computing masses of heavy hybrid mesons in the Born-Oppenheimer approximation. We also discuss and exclude possible systematic errors from topological freezing, the finite lattice volume and glueball decays.

The role of spin degrees of freedom in the quark-gluon plasma (QGP) has attracted significant interest in recent years. Spin hydrodynamics extends conventional hydrodynamics by incorporating spin via the spin tensor. In the mean-field limit of the Nambu-Jona-Lasinio (NJL) model under rigid rotation, spin degrees of freedom manifest naturally as axial-vector, or spin, condensate. We investigate the interplay between chiral and spin condensates in this framework. While rotation typically suppresses the formation of a chiral condensate, the presence of a spin condensate may counteract this effect, enhancing the chiral condensate. Moreover, it can alter the nature of the chiral transition from second to first order.

We demonstrate that the reformulation of renormalization group (RG) flow equations as non-linear heat equations has severe implications on the understanding of RG flows in general. We demonstrate by explicitly constructing an entropy function for a zero-dimensional $\mathbb{Z}_2$-symmetric model that the dissipative character of generic non-linear diffusion equations is also hard-coded in the functional RG equation. This renders RG flows manifestly irreversible, revealing the semi-group property of RG transformations on the level of the flow equation itself. Additionally, we argue that the dissipative character of RG flows, its irreversibility and the entropy production during the RG flow may be linked to the existence of a so-called $\mathcal{C}$-/$\mathcal{A}$-function. In total, this introduces an asymmetry in the so-called RG time -- in complete analogy to the thermodynamic arrow of time -- and allows for an interpretation of infrared actions as equilibrium solutions of dissipative RG flows equations. The impossibility of resolving microphysics from macrophysics is evident in this framework. Furthermore, we directly link the irreversibility and the entropy production in RG flows to an explicit numerical entropy production, which is manifest in diffusive and non-linear partial differential equations (PDEs) and a standard mathematical tool for the analysis of PDEs. Using exactly solvable zero-dimensional $\mathbb{Z}_2$-symmetric models, we explicitly compute the (numerical) entropy production related to the total variation non-increasing property of the PDE during RG flows toward the infrared limit. Finally, we discuss generalizations of our findings and relations to the $\mathcal{C}$-/$\mathcal{A}$-theorem as well as how our work may help to construct truncations of RG flow equations in the future, including numerically stable schemes for solving the corresponding PDEs.

We study charge diffusion in relativistic resistive second-order dissipative magnetohydrodynamics. In this theory, charge diffusion is not simply given by the standard Navier-Stokes form of Ohm's law, but by an evolution equation which ensures causality and stability. This, in turn, leads to transient effects in the charge diffusion current, the nature of which depends on the particular values of the electrical conductivity and the charge-diffusion relaxation time. The ensuing equations of motion are of so-called stiff character, which requires special care when solving them numerically. To this end, we specifically develop an implicit-explicit Runge-Kutta method for solving relativistic resistive second-order dissipative magnetohydrodynamics and subject it to various tests. We then study the system's evolution in a simplified 1+1-dimensional scenario for a heavy-ion collision, where matter and electromagnetic fields are assumed to be transversely homogeneous, and investigate the cases of an initially non-expanding fluid and a fluid initially expanding according to a Bjorken scaling flow. In the latter case, the scale invariance is broken by the ensuing self-consistent dynamics of matter and electromagnetic fields. However, the breaking becomes quantitatively important only if the electromagnetic fields are sufficiently strong. The breaking of scale invariance is larger for smaller values of the conductivity. Aspects of entropy production from charge diffusion currents and stability are also discussed.

We use antistatic-antistatic potentials computed with lattice QCD and a coupled-channel Born-Oppenheimer approach to explore the existence of a $\bar{b} \bar{b} u d$ tetraquark resonance with quantum numbers $I(J^P) = 0(1^-)$. A pole in the $\mbox{T}$ matrix signals a resonance with mass $m = 2 m_B + 94.0^{+1.3}_{-5.4} \, \text{MeV}$ and decay width $\Gamma = 140^{+86}_{-66} \, \text{MeV}$, i.e. very close to the $B^\ast B^\ast$ threshold. We also compute branching ratios, which clearly indicate that this resonance is mainly composed of a $B^\ast B^\ast$ meson pair with a significantly smaller $B B$ contribution. By varying the potential matrix responsible for the coupling of the $B B$ and the $B^\ast B^\ast$ channel as well as the $b$ quark mass, we provide additional insights and understanding concerning the formation and existence of the resonance. We also comment on the importance of our findings and the main takeaways for a possible future full lattice QCD investigation of this $I(J^P) = 0(1^-)$ $\bar{b} \bar{b} u d$ tetraquark resonance.

The $SU(3)$ spin model with chemical potential corresponds to a simplified version of QCD with static quarks in the strong coupling regime. It has been studied previously as a testing ground for new methods aiming to overcome the sign problem of lattice QCD. In this work we show that the equation of state and the phase structure of the model can be determined to reasonable accuracy by a linked cluster expansion. In particular, we compute the free energy to 14-th order in the nearest neighbour coupling. The resulting predictions for the equation of state and the location of the critical end point agree with numerical determinations to ${\cal O}(1\%)$ and ${\cal O}(10\%)$, respectively. While the accuracy for the critical couplings is still limited at the current series depth, the approach is equally applicable at zero and non-zero imaginary or real chemical potential, as well as to effective QCD Hamiltonians obtained by strong coupling and hopping expansions.

Dense QCD matter may exhibit crystalline phases. Their existence is reflected in a moat regime, where mesonic correlations feature spatial modulations. We study the realtime properties of pions at finite temperature and density in QCD in order to elucidate the nature of this regime. We show that the moat regime arises from particle-hole-like fluctuations near the Fermi surface. This gives rise to a characteristic peak in the spectral function of the pion at nonzero \emph{spacelike} momentum. This peak can be interpreted as a new quasi particle, the moaton. In addition, our framework also allows us to directly test the stability of the homogeneous chiral phase against the formation of an inhomogeneous condensate in QCD. We find that the formation of such a phase is highly unlikely for baryon chemical potentials $\mu_B \leq 630$\,MeV.

Anisotropic flow emerges in all three of hybrid approaches: initial conditions, viscous relativistic hydrodynamics as well as hadronic transport. Previous works focus mainly on a constant or temperature dependent shear viscosity $\eta/s$. Here instead, we study qualitatively the effect of a generalized $\eta/s(T,\mu_B)$ in the hybrid approach SMASH-vHLLE-hybrid. The parameterization takes into account the constraints of matching to the transport coefficients in the hadronic phase, as well as of recent Bayesian analysis results. We compare the effect of the different parameterizations in the intermediate energy region of $\sqrt{s_{NN}}$=7.7 - 39.0 GeV. We observe that using the energy density dependent parameterization decreases the effect of the point of particlization. In addition, we quantify the uncertainty due to different initial state profiles, including the SMASH initial conditions as well as TrENTo and IP-Glasma profiles. It can be shown that the initial state transverse momentum impacts final state momentum anisotropy.

We compute gluelump masses and mass differences using SU(3) lattice gauge theory. We study states with total angular momentum up to $J = 3$, parity $P = +,-$and charge conjugation$C = +,-$. Computations on four ensembles with rather fine lattice spacings in the range $0.040 \, \text{fm} \ldots 0.093 \, \text{fm}$ allow continuum extrapolations of gluelump mass differences. We complement existing results on hybrid static potentials with the obtained gluelump masses, which represent the limit of vanishing quark-antiquark separation. We also discuss the conversion of lattice gluelump masses to the Renormalon Subtracted scheme, which is e.g. important for studies of heavy hybrid mesons in the Born-Oppenheimer approximation.