A novel method to treat effects from evanescent operators in next-to-leading order (NLO) computations is introduced. The approach allows, besides further simplifications, to discard evanescent-to-physical mixing contributions in NLO calculations. The method is independent of the treatments of and can therefore be combined with different renormalization schemes. We illustrate the utility of this result by reproducing literature results of two-loop anomalous dimension matrices for both and transitions.
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http://dx.doi.org/10.1140/epjc/s10052-024-13101-0 | DOI Listing |
Eur Phys J C Part Fields
July 2024
Physik-Institut, Universität Zürich, 8057 Zurich, Switzerland.
A novel method to treat effects from evanescent operators in next-to-leading order (NLO) computations is introduced. The approach allows, besides further simplifications, to discard evanescent-to-physical mixing contributions in NLO calculations. The method is independent of the treatments of and can therefore be combined with different renormalization schemes.
View Article and Find Full Text PDFPhys Rev E
May 2024
Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia.
By using the field theoretic renormalization group technique together with the operator product expansion, simultaneous influence of the spatial parity violation and finite-time correlations of an electrically conductive turbulent environment on the inertial-range scaling behavior of correlation functions of a passively advected weak magnetic field is investigated within the corresponding generalized Kazantsev-Kraichnan model in the second order of the perturbation theory (in the two-loop approximation). The explicit dependence of the anomalous dimensions of the leading composite operators on the fixed point value of the parameter that controls the presence of finite-time correlations of the turbulent field as well as on the parameter that drives the amount of the spatial parity violation (helicity) in the system is found even in the case with the presence of the large-scale anisotropy. In accordance with the Kolmogorov's local isotropy restoration hypothesis, it is shown that, regardless of the amount of the spatial parity violation, the scaling properties of the model are always driven by the anomalous dimensions of the composite operators near the isotropic shell.
View Article and Find Full Text PDFPhys Rev Lett
February 2024
PRISMA+ Cluster of Excellence, Johannes Gutenberg University, 55099 Mainz, Germany.
In cross sections with angular cuts, an intricate pattern of enhanced higher-order corrections known as nonglobal logarithms arises. The leading logarithmic terms were computed numerically two decades ago, but the resummation of subleading nonglobal logarithms remained a challenge that we solve in this Letter using renormalization group methods in effective field theory. To achieve next-to-leading logarithmic accuracy, we implement the two-loop anomalous dimension governing the resummation of nonglobal logarithms into a large-N_{c} parton shower framework, together with one-loop matching corrections.
View Article and Find Full Text PDFPhys Rev E
February 2023
Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia.
Using the field theoretic formulation of the kinematic magnetohydrodynamic turbulence, the explicit expressions for the anomalous dimensions of leading composite operators, which govern the inertial-range scaling properties of correlation functions of the weak magnetic field passively advected by the electrically conductive turbulent environment driven by the Navier-Stokes velocity field, are derived and analyzed in the second order of the corresponding perturbation expansion (in the two-loop approximation). Their properties are compared to the properties of the same anomalous dimensions obtained in the framework of the Kazantsev-Kraichnan model of the kinematic magnetohydrodynamics with the Gaussian statistics of the turbulent velocity field as well as to the analogous anomalous dimensions of the leading composite operators in the problem of the passive scalar advection by the Gaussian (the Kraichnan model) and non-Gaussian (driven by the Navier-Stokes equation) turbulent velocity field. It is shown that, regardless of the Gaussian or non-Gaussian statistics of the turbulent velocity field, the two-loop corrections to the leading anomalous dimensions are much more important in the case of the problem of the passive advection of the vector (magnetic) field than in the case of the problem of the passive advection of scalar fields.
View Article and Find Full Text PDFPhys Rev E
December 2022
Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, 75005 Paris, France.
We study quenched disordered polymerized membranes in their flat phase by means of a three-loop perturbative analysis performed in dimension D=4-ε. We derive the renormalization group equations at this order and solve them up to order ε^{3}. Our results confirm those obtained by Coquand et al.
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