arXiv subjects

Kaapo Seppänen

Publications and source records attributed to Kaapo Seppänen.

9 recordsLinked to original sources

arXiv2026

Complete four-loop pressure of cold QED

Extending the weak-coupling expansion of the pressure of a cold and dense ultrarelativistic electron gas to next-to-next-to-next-to-leading order (N3LO) in the gauge coupling has remained an open problem since the classic N2LO result of Freedman and McLerran, published in 1977. Here, we present the full N3LO pressure, the first thermodynamic quantity determined to this order in a physical gauge theory. The pressure exhibits good perturbative convergence and weak renormalization-scale dependence even at sizable couplings, while a Bayesian analysis of missing higher-order contributions indicates uncertainties that can exceed those inferred from scale variation alone.

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arXiv2026

Static linear response of hot and dense QCD matter to electromagnetic fields: Leading hard and soft QCD corrections

We compute the static electromagnetic susceptibilities of a hot and dense quark-gluon plasma using perturbative Quantum Chromodynamics (QCD). Our evaluation includes the leading $\mathcal{O}(α_s)$ correction as well as the leading soft, resummed contribution of $\mathcal{O}(α_s^{3/2})$ within electrostatic QCD. By matching to Lattice QCD at vanishing baryon chemical potential through Lattice perturbation theory, we establish a connection between perturbative results and Lattice simulations and assess the size of higher-order corrections. This extends the electromagnetic susceptibilities to finite baryon chemical potential, where Lattice methods are not applicable and establishes first-principle constraints on the quark-gluon plasma's electromagnetic response at temperatures and densities relevant for intermediate-energy heavy-ion collisions.

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arXiv2026

A new approach to determine the thermodynamics of deconfined matter to high accuracy

We demonstrate that at finite density and sufficiently high temperatures, phase-quenched (PQ) lattice simulations combined with perturbation theory provide a new precision approach to determining the thermodynamics of QCD across a wide arc of the phase diagram where the strong coupling constant $α_s$ remains small. In this regime, nonperturbative pairing effects in the PQ theory are parametrically suppressed, so that the difference between the PQ and full QCD pressures becomes a small perturbative correction. We compute this correction up to and including $O(α_s^{7/2})$ using electrostatic QCD together with a novel numerical method to compute four-loop sum-integrals. This enables the determination of the perturbative QCD pressure with precision beyond the current state of the art while including nonperturbative pure-gluonic contributions from the lattice.

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arXiv2025

Cosmological phase transitions without high-temperature expansions

We introduce a new framework for perturbatively computing equilibrium thermodynamic properties of cosmological phase transitions to high loop orders, using the full four-dimensional resummed thermal effective potential and avoiding the limitations of standard high-temperature approximations. By systematically disentangling the physics of hard and soft momentum scales, our approach unifies their treatment within a single expression, enabling consistent handling of both vacuum and thermal divergences across all mass regimes. This core innovation enables the efficient numerical evaluation of massive multiloop thermal sum-integrals, achieved through a finite-temperature generalization of Loop-Tree Duality -- an advanced algorithmic technique originally developed to render vacuum Feynman integrals numerically tractable via Monte Carlo methods. As a proof of principle, we apply the framework to a scalar-Yukawa model, presenting a complete two-loop calculation and a novel three-loop extension -- the first fully massive three-loop sum-integral computation without relying on high-temperature expansions. Our approach opens the door to precise perturbative predictions of the phase structure in a broad class of beyond-the-Standard-Model scenarios, including those featuring strong first-order phase transitions relevant for gravitational-wave signals, where conventional high-temperature approximations break down.

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arXiv2024

Perturbative QCD meets phase quenching: The pressure of cold quark matter

Nonperturbative inequalities constrain the thermodynamic pressure of Quantum Chromodynamics (QCD) with its phase-quenched version, a Sign-Problem-free theory amenable to lattice treatment. In the perturbative regime with a small QCD coupling constant $α_s$, one of these inequalities manifests as an $O(α_s^3)$ difference between the phase-quenched and QCD pressures at large baryon chemical potential. In this work, we generalize state-of-the-art algorithmic techniques used in collider physics in vacuum quantum field theory to address large-scale multiloop computations at finite chemical potential, by direct numerical integration of Feynman diagrams in momentum space. Using this novel approach, we evaluate this $O(α_s^3)$ difference and show that it is a gauge-independent and small positive number compared to the known perturbative coefficients at this order. This implies that at high baryon densities, phase-quenched lattice simulations can provide a complementary nonperturbative method for accurately determining the pressure of cold quark matter at $O(α_s^3)$.

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arXiv2023

Equation of State of Cold Quark Matter to $O(α_s^3 \ln α_s)$

Accurately understanding the equation of state (EOS) of high-density, zero-temperature quark matter plays an essential role in constraining the behavior of dense strongly interacting matter inside the cores of neutron stars. In this Letter, we study the weak-coupling expansion of the EOS of cold quark matter and derive the complete, gauge-invariant contributions from the long-wavelength, dynamically screened gluonic sector at next-to-next-to-next-to-leading order (N3LO) in the strong coupling constant $α_s$. This elevates the EOS result to the $O(α_s^3 \ln α_s)$ level, leaving only one unknown constant from the unscreened sector at N3LO, and places it on par with its high-temperature counterpart from 2003.

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arXiv2023

Soft gluon self-energy at finite temperature and density: hard NLO corrections in general covariant gauge

We compute the next-to-leading order (NLO) hard correction to the gluon self-energy tensor with arbitrary soft momenta in a hot and/or dense weakly coupled plasma in Quantum Chromodynamics. Our diagrammatic computations of the two-loop and power corrections are performed within the hard-thermal-loop (HTL) framework and in general covariant gauge, using the real-time formalism. We find that after renormalization our individual results are finite and gauge-dependent, and they reproduce previously computed results in Quantum Electrodynamics in the appropriate limit. Combining our results, we also recover a formerly known gauge-independent matching coefficient and associated screening mass in a specific kinematic limit. Our NLO results supersede leading-order HTL results from the 1980s and pave the way to an improved understanding of the bulk properties of deconfined matter, such as the equation of state.

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arXiv2022

Degenerate fermionic matter at N$^3$LO: Quantum Electrodynamics

We determine the pressure of a cold and dense electron gas to a nearly complete next-to-next-to-next-to-leading order (N$^3$LO) in the fine-structure constant $α_e$, utilizing a new result for the two-loop photon self-energy from a companion paper. Our result contains all infrared-sensitive contributions to the pressure at this order, including the coefficient of the $O(α_e^3 \ln α_e^{ })$ term, and leaves only a single coefficient associated with the contributions of unresummed hard momenta undetermined. Moreover, we explicitly demonstrate the complete cancellation of infrared divergences according to the effective field theory paradigm by determining part of the hard contributions at this order. Our calculation provides the first improvement to a 45-year-old milestone result and demonstrates the feasibility of the corresponding N$^3$LO calculation for cold and dense quark matter.

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arXiv2022

Soft photon propagation in a hot and dense medium to next-to-leading order

We present the first complete calculation of the soft photon self-energy to the next-to-leading order in a hot and/or dense ultrarelativistic plasma in Quantum Electrodynamics (QED). The calculation is performed within the real-time formalism utilizing dimensional regularization in $4-2ε$ dimensions, while the result is reported including explicit $O(ε)$ terms in the zero-temperature limit. This information is required to extend the perturbative calculation of the pressure of cold and dense QED matter to partial next-to-next-to-next-to-leading order in a weak-coupling expansion, reported in a companion paper. These results pave the way for a similar future calculation in Quantum Chromodynamics.

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