arXiv subjects

Jonas Wessely

Publications and source records attributed to Jonas Wessely.

7 recordsLinked to original sources

arXiv2026

Multi-scattering processes and spectral properties of low-energy QCD

We compute quark and meson spectral functions in low-energy QCD, including all-order scatterings and decays of pions and the scalar $\sigma$-mode. For low energies the gluons decouple and the dynamics of two-flavour QCD is well-described by a Quark-Meson model. The computations are performed directly in Minkowski space, using the spectral functional renormalisation group. The full mesonic realtime dynamics is captured with the emergent composite approach which is extended here to realtime processes. The inclusion of all-order scatterings and decays is achieved through the self-consistent treatment of the scattering tails and the momentum-dependent resummation of the four-meson vertex via its Bethe-Salpeter equation. We illustrate the importance of higher-order scatterings using the example of the $\pi \to 3\pi$ scattering threshold - the lowest kinematically accessible channel for the pion.

hep-ph↗

arXiv2025

Self-consistent graviton spectral function in Lorentzian quantum gravity

We present the first fully self-consistent computation of the graviton spectral function in quantum gravity, using the spectral renormalisation group for gravity put forward in arXiv:2111.13232v2 [hep-th] within a physical mass-shell renormalisation scheme. Here, self-consistency refers to the fact that the full non-perturbative spectral function is used in the diagrams, including the scattering continuum. We find a positive graviton spectral function with a massless one-graviton peak and a multi-graviton continuum with a close-to-quadratic spectral decay in the ultraviolet. Within the physical on-shell renormalisation scheme, the graviton satisfies the sum rule of an asymptotic state and features a unit total spectral weight. We briefly discuss the implications of the physical formulation for the computation of scattering processes and investigations of unitarity in asymptotically safe quantum gravity.

hep-th↗

arXiv2025

Critical scaling for spectral functions

We study real-time scalar $\phi^4$-theory in 2+1 dimensions near criticality. Specifically, we compute the single-particle spectral function and that of the $s$-channel four-point function in and outside the scaling regime. The computation is done with the spectral functional Callan-Symanzik equation, which exhibits manifest Lorentz invariance and preserves causality. We extract the scaling exponent $\eta$ from the spectral function and compare our result with that from a Euclidean fixed point analysis.

hep-th↗

arXiv2024

The causal structure of the quark propagator

We study the causal structure of the quark propagator with the spectral DSE. The spectral gap equation is solved with the input of the spectral representation of the gluon and a causal STI-construction for the quark-gluon vertex. The latter includes a potential infrared enhancement of the vertex strength of the classical tensor structure that accommodates for the physical strength of chiral symmetry breaking. We find a critical vertex strength, below which the quark has a K\"all\'en-Lehmann representation. While the nature of the first singularity does not change above the critical strength, we find that the quark propagator features at least two additional pairs of complex conjugate poles that are located approximately at the sum of quark pole mass and peak position of the quark-gluon coupling. These additional poles lead to violations of causality, if they persist in $S$-matrix elements. While the vertex strength of the classical tensor structure in full QCD is below the critical one, that of commonly used vertex models, which rely solely on the classical vertex structure, is typically above it. Finally, we discuss how these additional poles could be avoided in full QCD, where part of chiral symmetry breaking is generated by the other tensor structures in the quark-gluon vertex.

hep-ph↗

arXiv2023

Bound states from the spectral Bethe-Salpeter equation

We compute the bound state properties of three-dimensional scalar $ϕ^4$ theory in the broken phase. To this end, we extend the recently developed technique of spectral Dyson-Schwinger equations to solve the Bethe-Salpeter equation and determine the bound state spectrum. We employ consistent truncations for the two-, three- and four-point functions of the theory that recover the scaling properties in the infinite coupling limit. Our result for the mass of the lowest-lying bound state in this limit agrees very well with lattice determinations.

hep-ph↗

arXiv2023

Renormalised spectral flows

We derive renormalised finite functional flow equations for quantum field theories in real and imaginary time that incorporate scale transformations of the renormalisation conditions, hence implementing a flowing renormalisation. The flows are manifestly finite in general non-perturbative truncation schemes also for regularisation schemes that do not implement an infrared suppression of the loops in the flow. Specifically, this formulation includes finite functional flows for the effective action with a spectral Callan-Symanzik cutoff, and therefore gives access to Lorentz invariant spectral flows. The functional setup is fully non-perturbative and allows for the spectral treatment of general theories. In particular, this includes theories that do not admit a perturbative renormalisation such as asymptotically safe theories. Finally, the application of the Lorentz invariant spectral functional renormalisation group is briefly discussed for theories ranging from real scalar and Yukawa theories to gauge theories and quantum gravity.

hep-th↗

arXiv2023

Scalar spectral functions from the spectral fRG

We compute non-perturbative spectral functions in a scalar $ϕ^4$-theory in three spacetime dimensions via the spectral functional renormalisation group. This approach allows for the direct, manifestly Lorentz covariant computation of correlation functions in Minkowski spacetime, including a physical on-shell renormalisation. We present numerical results for the spectral functions of the two- and four-point correlation functions for different values of the coupling parameter. These results agree very well with those obtained from another functional real-time approach, the spectral Dyson-Schwinger equation.

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