arXiv subjects

Philipp Schicho

Publications and source records attributed to Philipp Schicho.

At least 19 recordsLinked to original sources

arXiv2026

Baryon number freeze-out in the Standard Model, precisely

Weak sphaleron transitions turn a lepton asymmetry of the Standard Model plasma in the early Universe into a baryon asymmetry, conserving baryon-minus-lepton number $B-L$ and its individual flavored charges. A baryon asymmetry can thus also arise from flavored lepton asymmetries with vanishing $B-L$. Standard equilibrium calculations in the symmetric and broken phases are performed at constant temperature and hence neglect the fact that both the Higgs expectation value and the sphaleron rate vary as functions of temperature across the electroweak crossover. We derive a Boltzmann equation for the baryon number evolution across the crossover and calculate the freeze-out abundance including higher-order corrections to both the grand canonical partition function and the perturbative Higgs expectation value. This yields two sphaleron conversion factors: $C_\text{sph} = 0.3328(5)$ for $B-L$ and $\mathcal{F}_\text{sph} = 0.0279(19)$ for the flavored charges weighted by the charged-lepton Yukawa couplings.

hep-ph↗

arXiv2026

Theoretical uncertainties in reconstructing model parameters with gravitational waves from supercooled phase transitions

Future interferometers may detect a gravitational-wave (GW) signal from a cosmological first-order phase transition. Reconstructing the underlying particle-physics model from such a signal requires theoretical control over the map from microphysics to the spectrum. For classically scale-invariant extensions of the Standard Model, which generically predict strongly supercooled transitions and strong GW signals, this map depends sensitively on the treatment of quantum and thermal corrections to the nucleation rate. Taking the classically conformal ${\rm U}(1)_X$ model as representative of this class, we scan its parameter space and compare two resummation schemes. The first is a high-temperature effective field theory, matched at two-loop level and including next-to-leading-order corrections to the bounce action, with the nucleation-rate prefactor given by the full one-loop functional determinants. The second is a commonly employed daisy-resummed effective potential, with the prefactor estimated on dimensional grounds. Reconstructing the fundamental model parameters through a Fisher-matrix analysis of injected GW signals at LISA, we find that the daisy-resummation scheme is strongly disfavored, as its theoretical error dominates over the reconstruction uncertainty.

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arXiv2026

A critical look at low-scale cosmological phase transitions in the PTA era

Motivated by the recent evidence for a stochastic gravitational-wave (GW) background reported by pulsar timing array (PTA) collaborations, we perform a precision study of low-scale phase transitions in a dark Abelian Higgs sector, a minimal gauge theory of spontaneous symmetry breaking relevant for cosmological phase transitions. Using dimensionally reduced high-temperature effective field theory, we quantify the impact of thermal resummation, higher-order matching corrections, and higher-dimensional operators on the phase-transition thermodynamics and the resulting GW signal. We find that the parameter region favored by current PTA observations lies close to the boundary of validity of the effective field theory, where higher-dimensional operators become increasingly important. Even within this controlled region, the predicted signal remains disfavored by the PTA data, despite the substantial shifts induced by higher-order thermal corrections. We further delineate parameter regions where the dark and visible sectors are thermally and hydrodynamically coupled or decoupled, and revisit the dark matter phenomenology, identifying asymmetric freeze-out as naturally compatible with both the observed relic abundance and the gauge couplings favored by strong phase transitions. Our results underscore the importance of systematically controlled finite-temperature calculations for reliable GW predictions from low-scale cosmological phase transitions.

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arXiv2026

Higher-dimensional operators and Polyakov loop in hot Scalar QED from the heat kernel

Using the finite-temperature heat kernel method, we compute the gauge-invariant effective Lagrangian up to dimension-six for massive hot scalar QED. We propose two complementary methods: integrating out heavy modes at finite temperature, and deriving the finite-temperature heat kernel coefficients from the zero-temperature ones. We show that in the static limit, both lead to the same three-dimensional effective operators. We also compute the gauge-invariant Coleman-Weinberg effective potential for a constant background at finite temperature. We further examine how the Polyakov loop modifies the matching coefficients and assess its impact together with the higher-dimensional operators on the thermodynamics of cosmological first-order phase transitions, which in turn can affect an associated gravitational-wave spectrum.

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arXiv2026

Matching higher-dimensional operators at finite temperature for general models

High-temperature dimensional reduction provides a systematic effective field theory framework for studying finite-temperature thermodynamics and cosmological phase transitions. While the matching of super-renormalizable operators in the resulting three-dimensional effective theories is well established, the matching of higher-dimensional operators has recently been reinvigorated. These operators become phenomenologically relevant in strong first-order phase transitions where they quantify the convergence of the high-temperature expansion. This work automates the matching of generic three-dimensional dimension-five and -six operators for arbitrary models containing scalars, fermions, and gauge fields, implemented as an extension of the Mathematica package DRalgo. We present the operator basis, the matching procedure, and explicit examples including a scalar-Yukawa model, hot QCD, and the full Standard Model up to dimension six, covering operators mixing the strong and electroweak sectors as well as parity-violating contributions. Redundant operators, gauge dependence, and the corresponding field redefinitions are discussed in detail. The code and example model files are publicly available at https://github.com/DR-algo/DRalgo.

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arXiv2026

Finite-temperature operator basis on $\mathbb{R}^3 \times S^1$ for SMEFT

We present the first complete non-redundant operator basis for the Standard Model Effective Field Theory (SMEFT) at finite temperature, using the imaginary-time formalism. By employing the Hilbert series method on the space-time manifold $\mathbb{R}^3 \times S^1$, we classify all effective operators up to dimension-six. In constructing the basis, we consistently impose integration-by-parts and equations-of-motion constraints along spatial directions. We further analyze the impact of additional constraints, including the vanishing of the curl of the electric and magnetic fields and gauge choices for the temporal components on an operator basis. We also express them in terms of static three-dimensional spatial and zero-temperature SMEFT operators. At dimension five and six, we identify intrinsically thermal operators that vanish in zero temperature. Our framework is fully general and extends to arbitrary mass dimension and compact connected internal symmetry groups.

hep-th↗

arXiv2026

Hard thermal contributions to phase transition observables at NNLO

To construct the high-temperature effective field theory of gauge-Higgs models up to $\mathcal{O}(g^6)$ in the gauge coupling, we integrate out hard modes to three-loop level and use the next-to-next-to-leading order effective potential. For the Abelian Higgs model, we quantify the impact of both higher-dimensional operators and higher-loop corrections on thermodynamic parameters relevant for gravitational-wave observables, finding that one-loop dimension-six effects typically dominate over two- and three-loop corrections to super-renormalizable parameters for the strongest transitions. We derive the three-loop scalar and Debye masses for the ${\rm U(1)}$ and ${\rm SU}(N)$ gauge-Higgs models, as well as the two-loop quartic couplings for the Abelian case, show gauge independence of physical parameters, and demonstrate that no new master integrals are required for the matching, while consistency of 4d and 3d renormalizability points to previously missing contributions in these master integrals. As a byproduct, we report a previously missing contribution to the three-loop QCD Debye mass.

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arXiv2025

WallGo investigates: Theoretical uncertainties in the bubble wall velocity

We examine theoretical uncertainties in state-of-the-art calculations of the bubble wall velocity during first-order cosmological phase transitions. By utilising the software WallGo for two extensions of the Standard Model, we find several $O(1)$ uncertainties arising from the number of particles taken out of equilibrium, the logarithmically and power enhanced collision integrals, the treatment of thermal masses, the nucleation temperature, the $\tanh$ ansatz, and the perturbative order of the effective potential. However, we show that the linearisation of the Boltzmann equations is generally a good approximation with much smaller associated errors. We further clarify the limitations of the quasiparticle approximation in regions with negative mass squared. This study provides a detailed uncertainty budget and highlights where future efforts should be directed to improve the reliability of wall velocity and hence gravitational wave predictions.

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arXiv2025

Interpreting the 95 GeV resonance in the Two Higgs Doublet Model: Implications for the Electroweak Phase Transition

We investigate if the recent mass resonance excesses seen around 95 GeV at the Large Hadron Collider (LHC) can be reconciled with a first-order electroweak phase transition. Performing the first large-scale parameter scan of the Type I Two Higgs Doublet Model (2HDM) using high-temperature dimensionally reduced effective field theory, we focus on regions of parameter space consistent with interpreting the excess as an additional pseudoscalar state. We find that, in contrast to the Standard Model, the electroweak transition pattern in the 2HDM is generically first-order, proceeding either in a single or in two steps. While transition strengths can reach up to $v_c/T_C \sim 1.3$, the viable, collider-constrained parameter space yields $v_c/T_C \lesssim 1$. Thus, the gravitational wave signals lie below the projected reach of future interferometer experiments and are likely insufficient to support successful electroweak baryogenesis.

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arXiv2025

Thermodynamical uncertainties for primordial black holes from cosmological phase transitions

Strongly supercooled first-order phase transitions have been proposed as a primordial black hole (PBH) production mechanism. While previous works rely on simplified models with limited thermodynamic precision, we stress that reliable theoretical PBH predictions require precise nucleation dynamics within realistic extensions of the Standard Model. By employing high-temperature dimensional reduction and computing the one-loop fluctuation determinants, we provide a state-of-the-art thermodynamic analysis and obtain an universal lower bound on the transition timescale, $\beta/H_* \simeq 5$. Then, we estimate the corresponding PBH abundance for classically conformal gauge-Higgs theories. Accounting for constraints from successful percolation and QCD chiral symmetry breaking, the parameter space where PBHs are viable dark matter candidates is severely limited.

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arXiv2025

Higher-dimensional operators at finite-temperature affect gravitational-wave predictions

We investigate the effect of higher-dimensional marginal operators on the thermodynamics of cosmological phase transitions. Using the Abelian Higgs model as a representative for radiatively-generated one-step transitions, we systematically match these operators, which arise at higher orders in the underlying high-temperature expansion of thermal effective field theory, and use field redefinitions to construct a complete, minimal, and gauge-invariant operator basis. The Abelian Higgs model shares the essential infrared structure of more realistic gauge-Higgs theories at high temperatures, allowing us to test the validity of dimensional reduction in a simplified setting. We argue that for strong transitions, temporal gauge modes, which enhance the transition strength, should be treated on equal footing with spatial ones. Marginal operators are found to weaken the transition and introduce significant uncertainties for strong transitions. For transitions strong enough to produce gravitational waves detectable by LISA, our findings suggest that the high-temperature expansion may break down entirely. This would limit the applicability of effective theory techniques, including their use in non-perturbative lattice studies.

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arXiv2025

Finite-temperature bubble nucleation with shifting scale hierarchies

Focusing on supercooled phase transitions in models with classical scale symmetry, we formulate a state-of-the art framework for computing the bubble-nucleation rate, accounting for the presence of various energy scales. In particular, we examine the limitations of derivative expansions in constructing a thermal effective field theory for bubble nucleation. We show that for gauge field fluctuations, derivative expansions diverge after the leading two orders due to the strong variation in gauge field masses between the high- and low-temperature phases. By directly computing these contributions using the fluctuation determinant, we capture these effects while also accounting for large explicit logarithms at two loops, utilising the exact renormalisation group structure of the EFT. Finally, we demonstrate how this approach significantly improves nucleation rate calculations compared to leading-order results, providing a more robust framework for predicting gravitational-wave signals from supercooled phase transitions in models such as the SU(2)cSM.

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arXiv2024

How fast does the WallGo? A package for computing wall velocities in first-order phase transitions

WallGo is an open source software for the computation of the bubble wall velocity in first-order cosmological phase transitions. It also computes the energy budget available for the generation of gravitational waves. The main part of WallGo, built in Python, determines the wall velocity by solving the scalar-field(s) equation of motion, the Boltzmann equations and energy-momentum conservation for the fluid velocity and temperature. WallGo also includes two auxiliary modules: WallGoMatrix, which computes matrix elements for out-of-equilibrium particles, and WallGoCollision, which performs higher-dimensional integrals for Boltzmann collision terms. Users can implement custom models by defining an effective potential and specifying a list of out-of-equilibrium particles and their interactions. As the first public software to compute the wall velocity including out-of-equilibrium contributions, WallGo improves the precision of the computation compared to common assumptions in earlier computations. It utilises a spectral method for the deviation from equilibrium and collision terms that provides exponential convergence in basis polynomials, and supports multiple out-of-equilibrium particles, allowing for Boltzmann mixing terms. WallGo is tailored for non-runaway wall scenarios where leading-order coupling effects dominate friction. While this work introduces the software and the underlying theory, a more detailed documentation can be found in https://wallgo.readthedocs.io.

hep-ph↗

arXiv2024

Cosmological phase transitions at three loops: the final verdict on perturbation theory

We complete the perturbative program for equilibrium thermodynamics of cosmological first-order phase transitions by determining the finite-temperature effective potential of gauge-Higgs theories at next-to-next-to-next-to-next-to-leading order (N$^4$LO). The computation of the three-loop effective potential required to reach this order is extended to generic models in dimensionally reduced effective theories in a companion article. Our N$^4$LO result is the last perturbative order before confinement renders electroweak gauge-Higgs theories non-perturbative at four loops. By contrasting our analysis with non-perturbative lattice results, we find a remarkable agreement. As a direct application for predictions of gravitational waves produced by a first-order transition, our computation provides the final fully perturbative results for the phase transition strength and speed of sound.

hep-ph↗

arXiv2024

Impact of theoretical uncertainties on model parameter reconstruction from GW signals sourced by cosmological phase transitions

Different computational techniques for cosmological phase transition parameters can impact the Gravitational Wave (GW) spectra predicted in a given particle physics model. To scrutinize the importance of this effect, we perform large-scale parameter scans of the dynamical real-singlet extended Standard Model using three perturbative approximations for the effective potential: the $\overline{\rm MS}$ and on-shell schemes at leading order, and three-dimensional thermal effective theory (3D EFT) at next-to-leading order. While predictions of GW amplitudes are typically unreliable in the absence of higher-order corrections, we show that the reconstructed model parameter spaces are robust up to a few percent in uncertainty. While 3D EFT is accurate from one loop order, theoretical uncertainties of reconstructed model parameters, using four-dimensional standard techniques, remain dominant over the experimental ones even for signals merely strong enough to claim a detection by LISA.

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arXiv2023

The force-force correlator at the hard thermal scale of hot QCD

High-energy particles traversing the Quark-Gluon plasma experience modified (massive) dispersion, although their vacuum mass is negligible compared to the kinetic energy. Due to poor convergence of the perturbative series in the regime of soft loop momenta, a more precise determination of this effective mass is needed. This paper continues our investigation on the factorisation between strongly-coupled infrared classical and perturbative ultraviolet behavior. The former has been studied non-perturbatively within EQCD by determining a non-local operator on the lattice. By computing the temperature-scale contribution to the same operator in 4D QCD at next-to-leading order (NLO), we remove the ultraviolet divergence of the EQCD calculation with an opposite infrared divergence from the hard thermal scale. The result is a consistent, regulator-independent determination of the classical contribution where the emergence of new divergences signals sensitivities to new regions of phase space. We address the numerical impact of the classical and NLO thermal corrections on the convergence of the factorised approach and on the partial applicability of our results to calculations of transport coefficients.

hep-ph↗

arXiv2023

Hard parton dispersion in the quark-gluon plasma, non-perturbatively

The in-medium dispersion of hard partons, encoded in their so-called asymptotic mass, receives large non-perturbative contributions from classical gluons, i.e. soft gluons with large occupation numbers. Here, we discuss how the analytical properties of thermal amplitudes allow for a non-perturbative determination of the infrared classical contribution through lattice determinations in the dimensionally-reduced effective theory of hot QCD, EQCD. We show how these lattice determinations need to be complemented by perturbative two-loop matching calculations between EQCD and QCD, so that the unphysical (classical) ultraviolet behavior of EQCD is replaced by its proper quantum QCD counterpart. We show how lattice and perturbative EQCD are in good agreement in the UV and present an outlook on the two-loop quantum QCD contribution.

hep-ph↗

arXiv2023

Integrating by parts at finite density

Both nonzero temperature and chemical potentials break the Lorentz symmetry present in vacuum quantum field theory by singling out the rest frame of the heat bath. This leads to complications in the application of thermal perturbation theory, including the appearance of novel infrared divergences in loop integrals and an apparent absence of four-dimensional integration-by-parts (IBP) identities, vital for high-order computations. Here, we propose a new strategy that enables the use of IBP techniques in the evaluation of Feynman integrals, in particular vacuum or bubble diagrams, in the limit of vanishing temperature $T$ but nonzero chemical potentials $\mu$. The central elements of the new setup include a contour representation for the temporal momentum integral, the use of a small but nonzero $T$ as an IR regulator, and the systematic application of both temporal and spatial differential operators in the generation of linear relations among the loop integrals of interest. The relations we derive contain novel inhomogeneous terms featuring differentiated Fermi-Dirac distribution functions, which severely complicate calculations at nonzero temperature, but are shown to reduce to solvable lower-dimensional objects as $T$ tends to zero. Pedagogical example computations are kept at the one- and two-loop levels, but the application of the new method to higher-order calculations is discussed in some detail.

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