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Nonperturbative Renormalization of Operators in Near-Conformal Systems Using Gradient Flows
Andrea Carosso1, Anna Hasenfratz1, Ethan T Neil1,2
1Department of Physics, University of Colorado, Boulder, Colorado 80309, USA.
Physical Review Letters
|December 1, 2018
Summary
We developed a new numerical method for renormalization group studies, simplifying calculations in quantum chromodynamics. This technique yields key insights into the mass and nucleon anomalous dimensions for SU(3) gauge theory.
Area of Science:
- High Energy Physics
- Quantum Field Theory
- Computational Physics
Background:
- Renormalization group transformations are crucial for understanding quantum field theories at different scales.
- Traditional numerical methods like ensemble matching can be computationally expensive.
- SU(3) gauge theory with multiple fermions is a key model for studying strong interactions.
Purpose of the Study:
- To introduce a novel, continuous real space renormalization group transformation based on gradient flow.
- To enable efficient numerical studies of renormalization without ensemble matching.
- To investigate SU(3) gauge theory with 12 fermions in the fundamental representation.
Main Methods:
- Development of a continuous real space renormalization group transformation utilizing gradient flow.
- Application of the new method to a pilot study of SU(3) gauge theory.
- Numerical calculation of anomalous dimensions.
Main Results:
- The mass anomalous dimension (γm) was found to be 0.23(6), aligning with existing theoretical and lattice results.
- The nucleon anomalous dimension (γN) was calculated for the first time in this theory, yielding 0.05(5).
Conclusions:
- The proposed gradient flow-based renormalization group transformation offers an efficient alternative for numerical studies.
- The results provide valuable data for understanding the behavior of SU(3) gauge theory with 12 fermions.
- This method opens new avenues for lattice calculations in quantum chromodynamics.
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