arXiv subjects
Publications and source records attributed to York Schroder.
This talk offers a brief review of the determination of coupling constants in the framework of dimensionally reduced effective field theories for thermal QCD, specializing on its gluonic sector. Interestingly, higher-order operators that go beyond the usual super-renormalizable truncation of the effective theory need to be considered when matching parameters at three loops.
We focus on a non-abelian gauge field coupled to a single (but general) representation of a family of Nf fermions. By using the same machinery that had allowed us to evaluate the sub-leading large-Nf term of the five-loop Beta function earlier, we here report on a confirmation of the all-Nf result that has in the meantime been published by another group. Furthermore, in order to push forward the 5-loop renormalization program regarding gauge parameter dependence, we present the linear terms of the complete set of anomalous dimensions, in an expansion in the covariant gauge parameter around the Feynman gauge.
We present new analytical five-loop Feynman-gauge results for the anomalous dimensions of ghost field and -vertex, generalizing the known values for SU(3) to a general gauge group. Together with previously published results on the quark mass and -field anomalous dimensions and the Beta function, this completes the 5-loop renormalization program of gauge theories in that gauge.
We present analytical five-loop results for the quark mass and quark field anomalous dimensions, for a general gauge group and in the MSbar scheme. We confirm the values known for the gauge group SU(3) from an independent calculation, and find full agreement with results available from large-Nf studies.
We present analytical results for the $N_f^4$ and $N_f^3$ terms of the five-loop Beta function, for a general gauge group. While the former term agrees with results available from large-$N_f$ studies, the latter is new and extends the value known for SU(3) from an independent calculation.
Here, we attempt to summarize the activities of Track 3 of the 17th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2016).
We review recent progress that we have achieved in evaluating the class of fully massive vacuum integrals at five loops. After discussing topics that arise in classification, evaluation and algorithmic codification of this specific set of Feynman integrals, we present some selected new results for their expansions around $4-2\varepsilon$ dimensions.
Building upon our earlier work, we compute a Debye mass of finite-temperature Yang-Mills theory to three-loop order. As an application, we determine a $g^7$ contribution to the thermodynamic pressure of hot QCD.
We give a short review on recent progress in the field of automated calculations in finite-temperature field theory, where integration-by-parts techniques have proven (almost) as useful as in the zero-temperature case. Furthermore, we provide one concrete example of an evaluation of a new three-loop master sum-integral that exhibits maximal divergence.
We perform an integral reduction for the 3-loop effective gauge coupling and screening mass of QCD at high temperatures, defined as matching coefficients appearing in the dimensionally reduced effective field theory (EQCD). Expressing both parameters in terms of a set master (sum-) integrals, we show explicit gauge parameter independence. The lack of suitable methods for solving the comparatively large number of master integrals forbids the complete evaluation at the moment. Taking one generic class of masters as an example, we highlight the calculational techniques involved. The full result would allow to improve on one of the classic probes for the convergence of the weak-coupling expansion at high temperatures, namely the comparison of full and effective theory determinations of the spatial string tension. Furthermore, the full result would also allow to determine one new contribution of order O(g**7) to the pressure of hot QCD.
We try to give a comprehensive review of the main methods used in modern multi-loop calculations in finite-temperature field theory. While going through explicit examples, we point out similarities and differences with respect to the zero-temperature case, utilizing common techniques in a transparent way whenever possible.
Perturbation theory for non-abelian gauge theories at finite temperature is plagued by infrared divergences which are caused by magnetic soft modes ~g^2T, corresponding to gluon fields of a 3d Yang-Mills theory. While the divergences can be regulated by a dynamically generated magnetic mass on that scale, the gauge coupling drops out of the effective expansion parameter requiring summation of all loop orders for the calculation of observables. Some gauge invariant possibilities to implement such infrared-safe resummations are reviewed. We use a scheme based on the non-linear sigma model to estimate some of the contributions ~g^6 of the soft magnetic modes to the QCD pressure through two loops. The NLO contribution amounts to ~10% of the LO, suggestive of a reasonable convergence of the series.
In this article, we present a new analytic result for a certain single-mass-scale four-loop vacuum (bubble) integral. We also discuss its systematic $\e$-expansion in $d=4-2\e$ as well as $d=3-2\e$ dimensions, the coefficients of which are expressible in terms of harmonic sums at infinity.
We review recent progress made in determining the pressure of hot QCD up to the first non-perturbative term in its weak-coupling expansion.
The QCD pressure is a most fundamental quantity, for which lattice data is available up to a few times the critical temperature $T_c$. Perturbation theory, even at very high temperatures, has serious convergence problems. Combining analytical and 3d numerical methods, we show that it is possible to compute the QCD pressure from about $2 T_c$ to infinity. We also describe an algorithm to generate and classify high order Feynman diagrams which is tailored to minimize computational effort.
We evaluate the static QCD potential to two--loop order. Compared to a previous calculation a sizable reduction of the two--loop coefficient $a_2$ is found.