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Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Nonrenormalization and Operator Mixing via On-Shell Methods.

Zvi Bern^1,2, Julio Parra-Martinez¹, Eric Sawyer¹

¹Mani L. Bhaumik Institute for Theoretical Physics, UCLA Department of Physics and Astronomy, Los Angeles, California 90095, USA.

Physical Review Letters

|February 22, 2020

Summary

This summary is machine-generated.

A new theorem in quantum field theory restricts how operators mix, preventing longer operators from changing shorter ones. This finding simplifies calculations in the Standard Model Effective Field Theory.

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Area of Science:

Theoretical particle physics
Quantum field theory
High-energy physics

Background:

Operator mixing is crucial for understanding quantum field theories.
Nonrenormalization theorems simplify calculations by limiting operator evolution.
Previous methods relied on specific symmetries like helicity selection rules.

Purpose of the Study:

To develop a general perturbative nonrenormalization theorem for operator mixing.
To apply this theorem to the Standard Model Effective Field Theory.
To identify and explain new zeros in anomalous dimension matrices.

Main Methods:

Utilizing on-shell methods.
Analyzing unitarity cuts of form factors to understand anomalous dimensions.
Perturbative calculations in massless four-dimensional quantum field theories.

Main Results:

A new nonrenormalization theorem for operator mixing was established.
Longer operators are restricted from renormalizing shorter operators at the first order.
Nontrivial zeros in the anomalous-dimension matrix for operators of dimension five through seven were found, extending beyond helicity selection rules.
Explicit two-loop calculations were performed.

Conclusions:

The new theorem provides a general framework for understanding operator mixing.
It reveals new constraints on renormalization in quantum field theories.
The findings have implications for precision calculations in the Standard Model Effective Field Theory.