SMuK 2023 – wissenschaftliches Programm

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T: Fachverband Teilchenphysik

T 110: Other Theory

T 110.2: Vortrag

Donnerstag, 23. März 2023, 16:05–16:20, HSZ/0201

Two-loop Treatment of a Simple Chiral Yang–Mills Model using Non-Anticommuting γ₅ — •Baibhab Ray — Deutsches Elektronen-Synchrotron DESY, Platanenallee 6, 15738 Zeuthen — TU Dresden, Institut für Kern- und Teilchenphysik, Zellescher Weg 19, 01069 Dresden

For practical calculations of loop diagrams in perturbative quantum field theory, Dimensional Regularization (DREG) is the most commonly applied regularization scheme. In this context, fields and integrals are transformed to D dimensions and one invariably needs to decide how intrinsically four-dimensional quantities like γ₅ should be treated in D≠ 4 dimensions. The original and to date most rigorous and universal HVBM scheme (’t Hooft–Veltman/Breitenlohner–Maison) forfeits anticommutativity of γ₅ with all other γ^µ and breaks BRST symmetry in intermediate steps. The latter can be restored by means of finite, symmetry-restoring counterterms.

In this talk, I shall discuss a simple chiral Yang–Mills model with only one SU(N) gauge group and without scalar fields, and present two-loop results in the HVBM scheme. Besides acquiring the two-loop counterterm structure (involving both singular and finite counterterms), I shall demonstrate methods of cross-checking by considering the Abelian special case (which can be compared with literature), as well as comparing with Ward identities (which are derived from the relevant Slavnov–Taylor identities encoding BRST symmetry). Time permitting, I shall provide insights into the implementation in Mathematica.