# Two-loop ADMs in the LEFT and related issues

- Institution: CERN
- Department: Open meetings
- Speaker: Marko Pesut
- Year: 2025
- Language: English
- Source: [CERN](https://videos.cern.ch/record/3021501)
- Licence: [CERN](http://copyright.web.cern.ch)
- Who can watch: Teens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

We derive the complete set of two-loop anomalous dimensions describing the mixing of four-fermion operators in the Low Energy Effective Field Theory (LEFT). The calculation is performed in Naive Dimensional Regularization with anticommuting $\gamma_5$ (the NDR scheme), and the results are given in the "JMS basis" of dimension-six operators. The derivation relies on known results for UV poles in two-loop diagrams in QCD, which are then used to derive the two-loop Anomalous Dimension Matrix (ADM) for the full set of four-fermion operators including O($\alpha_s^2$), O($\alpha_s\alpha$) and O($\alpha^2$) corrections. The method employed is an extension of a common approach to deal with traces containing $\gamma_5$ in NDR. Our results have been implemented in the public code DsixTools. We also discuss and provide the results in the LEFT with 5, 4 and 3 active quark flavors..

0:00:00 Slide 1

0:09:32 Slide 2

0:10:48 Slide 3

0:12:47 Slide 4

0:14:33 Slide 5

0:15:42 Slide 6

0:17:22 Slide 7

## Lectures

1. [Two-loop ADMs in the LEFT and related issues](https://invisiblenetwork.ai/learn/cern/3021501/19df87d80927), 21 min (CERN's player)