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York Schröder

Publications and source records attributed to York Schröder.

9 recordsLinked to original sources
arXiv2026

Debye screening mass in hot QCD at three loops: Canonical form of the integrand

The Debye screening mass is a fundamental parameter characterizing the screening of chromo-electric fields in a hot quark-gluon plasma. It plays an important role in thermal field theory, entering the description of screening lengths, transport phenomena, heavy-particle interactions in the early Universe, and the dimensional reduction program that connects thermal QCD to effective three-dimensional theories. In this contribution, we revisit the reduction strategy that serves to organize the large number of terms that contribute to the screening mass at the three-loop level, applying recent advances based on canonical forms of thermal (sum-) integrands. We emphasize the role of integration variable shifts, and discuss how canonical representations of thermal integrands may simplify future high-order calculations in hot QCD.

hep-ph↗
arXiv2026

General Four-Loop Beta Function for Scalar-Fermion Theories in Three Dimensions

We present general four-loop template $β$-functions and anomalous field dimensions for renormalisable scalar-fermion theories in three dimensions. By imposing $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry, we obtain relations between the template RGE coefficients, valid in any renormalisation scheme. Directly in $d=3$, we identify a new theory with a non-trivial IR fixed point that is under perturbative control in a large-$N$ limit. We provide up-to-date numerical results for all required massive tadpole master integrals up to four loops and complement them with analytic expressions where available.

hep-th↗
arXiv2026

Factorizing two-loop vacuum sum-integrals

We derive analytic results for scalar massless bosonic vacuum sum-integrals at two loops. Building upon a recent factorization proof of massive two-loop vacuum integrals, we are able to solve the corresponding Matsubara sums and map the result onto one-loop structures, thereby proving factorization also in the sum-integral setting. Analytic results are provided for generic integer-valued propagator- and numerator-powers of the class of sum-integrals under consideration, allowing to eliminate them from any perturbative expansion, dramatically simplifying the evaluation of some observables encountered e.g. in hot QCD.

hep-ph↗
arXiv2026

A new method for taming tensor sum-integrals

We report on the computation of a class of massless bosonic three-loop vacuum sum-integrals which are key building blocks for an evaluation of the Debye screening mass in hot QCD. Generalizing known techniques and introducing the concept of tensor reduction by dimensionality shifts (known to the zero-temperature community since the work of Tarasov in 1996) to finite temperature, we are able to treat hitherto unaccessible cases, which will allow us to finalize the long-term project of NNLO Debye mass evaluation.

hep-ph↗
arXiv2024

The $g^6$ pressure of hot Yang-Mills theory: Canonical form of the integrand

We present major progress towards the determination of the last missing piece for the pressure of a Yang-Mills plasma at high temperatures at order $g^6$ in the strong coupling constant. This order is of key importance due to its role in resolving the long-standing infrared problem of finite-temperature field theory within a dimensionally reduced effective field theory setup. By systematically applying linear transformations of integration variables, or momentum shifts, we resolve equivalences between different representations of Feynman sum-integrals. on the integrand level, transforming those into a canonical form. At the order $g^6$, this results in reducing a sum of O(100000) distinct sum-integrals which are produced from all four-loop vacuum diagrams down to merely 21. Furthermore, we succeed to map 11 of those onto known lower-loop structures. This leaves only 10 genuine 4-loop sum-integrals to be evaluated, thereby bringing the finalization of three decades of theoretical efforts within reach.

hep-ph↗
arXiv2024

Towards QCD at Five Loops

We report on recent progress on five-loop calculations in perturbative QCD. We discuss the computation of the perturbative quark condensate, decoupling in QCD, and the precision determination of charm and bottom quark masses. For the latter, we give some first results from a gauge-invariant subset of five-loop diagrams.

hep-ph↗
arXiv2022

Tackling the infamous $g^6$ term of the QCD pressure

We report on ongoing efforts to tackle an important open problem in QCD thermodynamics, namely an evaluation of the pressure to order $g^6$ in a weak-coupling expansion, corresponding to four loops. In particular, we identify a class of contributing Feynman sum-integrals with lower-loop factors, describe the formalism to tensor decompose those, and manage to map them onto scalar master sum-integrals that have already been evaluated in the literature.

hep-ph↗
arXiv2022

Recursion-free solution for two-loop vacuum integrals with "collinear" masses

We investigate the structure of a particular class of massive vacuum Feynman integrals at two loops. This class enjoys the linear relation $m_1+m_2=m_3$ between its three propagator masses, corresponding to zeros of the associated Källén function. Apart from having applications in thermal field theory, the integrals can be mapped onto one-loop three-point functions with collinear external momenta, suggesting the term "collinear" masses. We present a closed-form solution for these integrals, proving that they can always be factorized into products of one-loop cases, for all integer-valued propagator powers.

hep-ph↗