2020/07/31 by Tom Steudtner
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Geometry #Group (periodic table) #Loop (graph theory) #Mathematical physics #Mathematics #Order (exchange) #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Quartic function #Scalar (mathematics) #Scalar field #Scalar field theory #hep-ph #hep-th
paper · pdf · doi:10.1007/jhep12(2020)012
match published version, corrected eq.(4.5)
openalex publication_date 2020/12/02 · arxiv created 2021/02/18 · arxiv updated 2021/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A bstract For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the MS <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>MS</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> scheme. Utilising pre-existing literature expressions for a specific model, loop integrals are avoided and templates for general theories are obtained. We reiterate known four-loop expressions, and from those derive β functions for scalar masses and cubic interactions. As an example, the results are applied to compute all renormalisation group equations in U( n ) × U( n ) scalar theories.