Related papers: Stop comparing resummation methods
A key issue in making precise predictions in perturbative QCD is the uncertainty in setting the renormalization scale. If in principle, the entire perturbative series is void of this issue, in practice the perturbative corrections are known…
This paper develops a process-based account of scientific explanation that reconceives grounding in terms of stabilisation. Grounding theories capture hierarchical dependence but lack criteria for when explanations remain adequate under…
Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…
The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory…
A non-perturbative method which can go beyond the weak coupling perturbation theory is introduced. Essential idea is to formulate a set of exact differential equations as a function of the coupling strength $g$. Unlike other resummation in…
A method to quantitatively assess the consistency of power-counting proposals in Effective Field Theories (EFT) which are non-perturbative at leading order is presented. The Renormalisation Group evolution of an observable predicts the…
The resummation of large thermal corrections to the effective potential is mandatory for the accurate prediction of phase transitions. We discuss the accuracy of different prescriptions to perform this resummation at the one- and two-loop…
We present a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are…
We consider all radiative corrections to the total electron-positron cross section showing how the renormalization group equation can be used to sum the logarithmic contributions in two ways. First of all, one can sum leading-log etc.…
Hamiltonian Truncation Effective Theory is a framework that aims to improve the results of Hamiltonian truncation in a systematic, order-by-order fashion using Effective Field Theory methodology. The result is a truncated effective…
The perturbative effective potential calculated in Landau gauge suffers from infrared problems due to Goldstone boson loops. These divergences are spurious and can be removed by a resummation procedure that amounts to a shift of the mass of…
We use the scalar model with quartic interaction to illustrate how a nonperturbative variational technique combined with renormalization group (RG) properties efficiently resums perturbative expansions in thermal field theories. The…
Standard perturbation theory (SPT) for large-scale matter inhomogeneities is unsatisfactory for at least three reasons: there is no clear expansion parameter since the density contrast is not small on all scales; it does not fully account…
The naive perturbation expansion for many-fermion systems is infrared divergent. One can remove these divergences by introducing counterterms. To do this without changing the model, one has to solve an inversion equation. We call this…
We reconsider the gauge hierarchy problem from the viewpoint of effective field theories and a high-energy physics, motivated by the alternative scenario that the standard model holds up to a high-energy scale such as the Planck scale. The…
We introduce a dynamic approach to probabilistic forecast reconciliation at scale. Our model differs from the existing literature in this area in several important ways. Firstly we explicitly allow the weights allocated to the base…
Promoting a theory with a finite number of terms into an effective field theory with an infinite number of terms worsens simplicity, predictability, falsifiability, and other attributes often favored in theory choice. However, the…
A recently developed variational resummation technique incorporating renormalization group properties has been shown to solve the scale dependence problem that plagues the evaluation of thermodynamical quantities, e.g., within the framework…
The truncation scheme dependence of the exact renormalization group equations is investigated for scalar field theories in three dimensions. The exponents are numerically estimated to the next-to-leading order of the derivative expansion.…
Perturbation theory alone fails to describe thermodynamics of the electroweak phase transition. We review a technique combining perturbative and non-perturbative methods to overcome this challenge. Accordingly, the principal theme is a…