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Jan M. Pawlowski

Publications and source records attributed to Jan M. Pawlowski.

At least 37 records · Page 2Linked to original sources
arXiv2025

Heavy-light mesons from a flavour-dependent interaction

We introduce a new symmetry-preserving framework for the physics of heavy-light mesons, whose key element is the effective incorporation of flavour-dependent contributions into the corresponding bound-state and quark gap equations. These terms originate from the fully-dressed quark-gluon vertices appearing in the kernels of these equations, and provide a natural distinction between ``light" and ``heavy" quarks. In this approach, only the classical form factor of the quark-gluon vertex is retained, and is evaluated in the so-called ``symmetric" configuration. The standard Slavnov-Taylor identity links this form factor to the quark wave-function, allowing for the continuous transition from light to heavy quarks through the mere variation of the current quark mass in the gap equation. The method is used to compute the masses and decay constants of specific pseudoscalars and vector heavy-light systems, showing good overall agreement with both experimental data and lattice simulations.

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arXiv2025

Visions in Quantum Gravity

To deepen our understanding of Quantum Gravity and its connections with black holes and cosmology, building a common language and exchanging ideas across different approaches is crucial. The Nordita Program "Quantum Gravity: from gravitational effective field theories to ultraviolet complete approaches" created a platform for extensive discussions, aimed at pinpointing both common grounds and sources of disagreements, with the hope of generating ideas and driving progress in the field. This contribution summarizes the twelve topical discussions held during the program and collects individual thoughts of speakers and panelists on the future of the field in light of these discussions.

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arXiv2025

A comprehensive approach to the physics of mesons

We develop a novel approach for the self-consistent solution of coupled sets of Bethe-Salpeter and Schwinger-Dyson equations in QCD. This framework allows us to maintain the axial Ward-Takahashi identities of the theory within advanced approximation schemes, such as the skeleton or three-particle irreducible expansions. For this purpose we reformulate the Schwinger-Dyson equation of the axial-vector vertex such that the bulk of its quantum corrections is expressed in terms of a novel vertex. Crucially, this vertex satisfies a symmetry-induced relation of its own, which involves the full quark-gluon vertex. As a result, the Schwinger-Dyson equation reproduces the standard Ward-Takahashi identity satisfied by the axial-vector vertex. Consequently, the known relation between the quark mass function and the wave function of the pion in the chiral limit is duly fulfilled. The present approach offers valuable insights into the interplay between symmetry and dynamics, and provides a practical path towards computations of hadron physics within sophisticated approximations. In particular, the one-loop dressed truncation of the key dynamical equations, including that of the quark-gluon vertex, is shown to be completely compatible with the required symmetry relations. Further extensions and potential phenomenological applications of the developed framework are briefly discussed.

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arXiv2025

Physics-informed renormalisation group flows

The physics of strongly correlated systems offers some of the most intriguing physics challenges such as competing orders or the emergence of dynamical composite degrees of freedom. Often, the resolution of these physics challenges is computationally hard, but can be simplified enormously by a formulation in terms of the dynamical degrees of freedom and within an expansion about the physical ground state. Importantly, such a formulation does not only reduce or minimise the computational challenges, it also facilitates the access to the physics mechanisms at play. The tasks of finding the dynamical degrees of freedom and the physical ground state can be systematically addressed within the functional renormalisation group approach with flowing fields which accommodates both, emergent composites as well as the physical ground state. In the present work we use this approach to set up physics-informed renormalisation group flows (PIRG flows): Scale-dependent coordinate transformations in field space induce emergent composites, and the respective flows for the effective action generate a large set of target actions, formulated in these emergent composite fields. This novel perspective on RG flows bears a great potential both for conceptual as well as computational applications: to begin with, PIRG flows allow for a systematic search of the dynamical degrees of freedom and the respective ground state that leads to the most rapid convergence of expansion schemes, thus minimising the computational effort. Secondly, the resolution of the remaining computational tasks within a given expansion scheme can be further reduced by optimising the physics content within a given approximation. Thirdly, the maximal variability of PIRG flows can be used to reduce the analytic and numerical effort of solving the flows within a given approximation.

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arXiv2025

Physics of the gluon mass gap

It has long been known that the gluon propagator in Landau-gauge QCD exhibits a mass gap; and its emergence has been ascribed to the action of the Schwinger mechanism in the gauge sector of QCD. In the present work, we relate this property to the physical mass gap of QCD by considering two observables associated with confinement and chiral symmetry breaking, namely the confinement-deconfinement transition temperature and the pion decay constant, respectively. It turns out that the first observable is linearly proportional to the gluon mass gap, a fact that allows us to assign a direct physical meaning to this scale. Moreover, we identify three distinct momentum regimes in the gluon propagator, ultraviolet, intermediate, and deep infrared, and assess their impact on the aforementioned observables. Both observables are sensitive to the first two regions of momenta, where functional approaches essentially coincide, but are insensitive to the third, deep infrared, regime. The combined information is used for a simple fit for the gluon propagator, all of whose parameters admit a clear physical interpretation. Finally, we discuss how this fit can help us access the intertwined dynamics of confinement and chiral symmetry breaking in QCD-type theories.

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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.

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arXiv2025

Functional Renormalization Group Flows and Gauge Consistency in QED

We consider quantum electrodynamics with chiral four-Fermi interactions in the functional renormalization group approach. In gauge theories, the functional flow equation for the effective action is accompanied by the quantum master equation that governs the underlying gauge symmetry. Beyond perturbation theory, fully gauge-consistent solutions are very difficult to obtain. We devise a systematic expansion scheme in which the solutions of the flow equation also solve the Quantum Master Equation. In the present work we apply this construction within the lowest order corrections in the photon two-point functions. In this truncation we discuss the phase structure in terms of the gauge and four-Fermi couplings based on a numerical solution of the system.

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arXiv2025

Topological data analysis of the deconfinement transition in SU(3) lattice gauge theory

We study the confining and deconfining phases of pure $\mathrm{SU}(3)$ lattice gauge theory with topological data analysis. This provides unique insights into long range correlations of field configurations across the confinement-deconfinement transition. Specifically, we analyze non-trivial structures in electric and magnetic field energy densities as well as Polyakov loop traces and a Polyakov loop-based variant of the topological density. The Betti curves for filtrations based on the electric and magnetic field energy densities reveal signals of electromagnetic dualities. These dualities can be associated with an interchange in the roles of local lumps of electric and magnetic energy densities around the phase transition. Moreover, we show that plaquette susceptibilities can manifest in the geometric features captured by the Betti curves. We also compare these findings against earlier results for $\mathrm{SU}(2)$ and elaborate on the significant differences. Our results demonstrate that topological data analysis can identify clear differences between phase transitions of first and second order for non-Abelian lattice gauge theories and provides unprecedented insights into the relevant structures in their vicinity.

hep-lat↗
arXiv2025

Critical scaling for spectral functions

We study real-time scalar $ϕ^4$-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 $η$ from the spectral function and compare our result with that from a Euclidean fixed point analysis.

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arXiv2025

$e^+ e^- \to μ^+ μ^-$ in the Asymptotically Safe Standard Model

We study the electron-positron to muon--anti-muon cross-section in the asymptotically safe Standard Model. In particular, we include the graviton contributions to the scattering amplitude, which is computed from momentum-dependent timelike one-particle-irreducible correlation functions. Specifically, we employ reconstruction techniques for the graviton spectral functions. We find that the full asymptotically safe quantum cross section decreases in the ultraviolet with the centre-of-mass energy, and is compatible with unitarity bounds. Importantly, our findings provide non-trivial evidence for the unitarity of the asymptotically safe Standard Model.

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arXiv2025

Soft modes in hot QCD matter

The chiral crossover of QCD at finite temperature and vanishing baryon density turns into a second order phase transition if lighter than physical quark masses are considered. If this transition occurs sufficiently close to the physical point, its universal critical behaviour would largely control the physics of the QCD phase transition. We quantify the size of this region in QCD using functional approaches, both Dyson-Schwinger equations and the functional renormalisation group. The latter allows us to study both critical and non-critical effects on equal footing, facilitating a precise determination of the scaling regime. We find that the physical point is far away from the critical region. Importantly, we show that the physics of the chiral crossover is dominated by soft modes even far beyond the critical region. While scaling functions determine all thermodynamic properties of the system in the critical region, the order parameter potential is the relevant quantity away from it. We compute this potential in QCD using the functional renormalisation group and Dyson-Schwinger equations and provide a simple parametrisation for phenomenological applications.

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arXiv2025

Finite density signatures of confining and chiral dynamics in QCD thermodynamics and fluctuations of conserved charges

We evaluate thermodynamic observables such as pressure, baryon number, entropy and energy density, as well as the second and fourth order baryon number cumulants in the phase structure of QCD. The intertwined confinement and chiral dynamics is resolved within functional QCD, aiming for quantitative accuracy at larger densities. Specifically it is shown that the self-consistent resolution of the confining gluonic background is crucial in particular for even the qualitative properties of the cumulants. Our results are in quantitative agreement with lattice and functional QCD benchmarks at vanishing and small chemical potentials. Moreover, they offer novel insights in the dynamics at larger chemical potentials including the regime of the critical end point. A welcome by-product of this analysis is the computation of the Polyakov loop potential in finite density QCD, which, alongside the aforementioned observables, can be used as input and benchmark for effective theory computations at finite density.

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arXiv2025

Tunneling with physics-informed RG flows in the anharmonic oscillator

We solve the anharmonic oscillator with physics-informed renormalisation group (PIRG) flows, with an emphasis on the weak coupling regime with its instanton-dominated tunnelling processes. We show that the instanton physics behind the exponential decay of the energy gap is already covered in the first order of the derivative expansion of the PIRG. The crucial new ingredients in the present analysis are the use of the ground state expansion within PIRG flows, as well as precision numerics based on Galerkin methods. Our result $a_{\mathrm{inst}} = 1.910(2)$ for the decay constant is in quantitative agreement with the analytic one, $a_{\mathrm{inst}} = 1.886$ with a deviation of $1\%$. This illustrates very impressively the capacity of the PIRG for fully capturing non-perturbative physics already in relatively simple approximations.

hep-th↗
arXiv2025

Physics-informed gauge theories

We use the physics-informed renormalisation group (PIRG) for the construction of gauge invariant renormalisation group flows. The respective effective action is a sum of a gauge invariant quantum part and the classical gauge fixing part which arranges for invertibility of the gauge field two-point function. Thus, the BRST transformations simply accommodate the gauge consistency of the gauge fixing sector, while the quantum part of the effective action is gauge and BRST invariant. We apply this physics-informed approach to Yang-Mills theory and gravity and show how the flowing gauge fields arrange for full gauge invariance. We also embed the background field approximation to the functional renormalisation group (fRG) in an exact gauge invariant PIRG flow. This allows us to discuss the dynamics of the correction terms, and the non-trivial ultraviolet or infrared relevant terms are elucidated within a one-loop approximation. The background field approximation of the latter is known for violating one-loop universality for specific regulators and we show how the present setup reinstates universality in a constructive way. Finally, we discuss the landscape of fRG flows in gauge theories through the lens of the novel PIRG approach as well as potential applications.

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arXiv2025

Juggling with Tensor Bases in Functional Approaches

Systematic expansion schemes in functional approaches require the inclusion of higher order vertices. These vertices are expanded in independent tensor bases with a rapidly increasing number of basis elements. Amongst the related tasks are the construction of bases and projection operators, the importance ordering of their elements, and the optimisation of such tensor bases, as well as an analysis of their regularity in momentum space. We present progress in all these directions and introduce the Mathematica package TensorBases designed for the aforementioned tasks.

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arXiv2025

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 Källén-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.

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arXiv2025

Four-quark scatterings in QCD III

We study the full infrared dynamics of 2+1 flavour QCD with the functional renormalisation group approach. We resolve self-consistently the glue dynamics as well as the dynamics of chiral symmetry breaking. The computation hosts no phenomenological parameter or external input. The only ultraviolet input parameters are the physical ones in QCD: the light and strange quark masses. They are adjusted to the physical ratios of the pion and kaon masses, divided by the pion decay constant. The results for other observables of current first-principles computations are in quantitative agreement with the physical ones. This work completes the series of papers, initiated and furthered in [1,2], on dynamical chiral symmetry breaking and the emergence of mesonic bound states within the functional renormalisation group. As a first application we discuss the formation of light mesonic bound states. Amongst other applications such as the phase structure of QCD, the current work paves the way for studying QCD parton distribution functions within the functional renormalisation group approach to first-principles QCD.

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