TL;DR
This paper introduces a nonperturbative approach to derive the exact all-order beta function in QCD using the background gauge field method, revealing that only the first two coefficients are non-zero, aligning with the 't Hooft scheme.
Contribution
It presents a novel nonperturbative method to determine the exact beta function in QCD, applicable to any number of flavors, and shows its equivalence to the 't Hooft scheme.
Findings
Derived the exact all-order beta function for QCD.
Showed only the first two coefficients are non-zero.
Confirmed the equivalence to the 't Hooft scheme.
Abstract
Based on specific properties of the partition function and of the quantum correlators we derive the exact form of the beta function in the background gauge field method for QCD with an arbitrary number of flavors. The all order beta function we obtain through this method has only the first two orders coefficients different than zero and thus is equivalent to the 't Hooft scheme.
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Taxonomy
TopicsQuantum Chromodynamics and Particle Interactions · Particle physics theoretical and experimental studies · High-Energy Particle Collisions Research