Fixed Point and Beta Function of Strongly Coupled Gauge Theories

**Principal Investigator:**

Chik Him Wong

**Affiliation:**

University of Wuppertal (Germany)

**Local Project ID:**

chwu33

**HPC Platform used:**

JUWELS and JUQUEEN of JSC

**Date published:**

The Standard Model (SM) refers to the theory that classifies all known subatomic particles and describes the electromagnetic, weak and strong interactions among them. Experimental evidence collected so far are all in excellent agreement with the theory. Despite the remarkable success, it lacks explanation for some phenomena such as dark matter and is theoretically unsatisfactory regarding the so-called “hierarchy problem”.

In an attempt to extend the SM, lots of Beyond Standard Model (BSM) theories have been proposed. One class of such theories postulates that the observed Higgs boson, rather than a fundamental particle as described by SM, is indeed a composite particle composed of new subatomic particles bounded by new interactions. Such new particles and interactions not only lift the hierarchy problem, but also lead to new composite particles that may naturally become dark matter. These theories can be realized by nearly conformal Strongly Coupled Gauge Theories (SCGTs).

Strongly Coupled Gauge Theories (SCGTs) play an important role in High Energy Physics. A well-known example is Quantum Chromodynamics (QCD), which describes the strong force among subatomic particles. The properties of SCGTs is characterized by the rate of change in the interaction strength with respect to probing energy, which is known as the beta function. For a nearly conformal SCGT, the beta function becomes very close to zero below certain probing energy and such threshold is called a pseudo infrared fixed point. Nearly conformal SCGTs are of particular interest since they are more likely to be compatible with existing experimental constraints, which is an essential criterium of being a viable BSM candidate.

The behavior of the beta function depends on the number of fermion flavors, the types of fermions (representation) and interaction (symmetry group). Therefore it is important to identify which combinations give a pseudo infrared fixed point in the beta functions. In order to quantitatively investigate this, a numerical calculation is needed.

The computation of beta functions of nearly conformal theories is very challenging. One needs to focus on several models among infinitely many models, chosen by theoretical predictions. The calculation of beta functions of each of these models are highly involved and have to be numerically simulated. Space-time is replaced by a four-dimensional discrete lattice. For nearly conformal theories, the correlation lengths become very long, imposing difficulties of removing the discretization effects and thus requires very large lattices. This implies that the simulations are only possible on powerful high performance computing systems (HPC) such as the GCS supercomputer JUQUEEN and JUWELS at the Jülich Supercomputing Center (JSC).

In this project, the Lattice Higgs Collaboration (LatHC), which consists of scientists from University of Wuppertal, Eotvos University, University of the Pacific and University of California, San Diego, investigates the beta function of several SCGTs. They include SU(3) models with 4,8,10,12,13 flavors of fermions in the fundamental representation, and 2 flavors of fermions in sextet representation. It is observed that the beta function decreases with increasing number of fermion flavors, providing a quantitative non-perturbative evidence of nearly conformal behavior of many flavored SCGTs, which is qualitatively predicted by perturbative calculations. It is also observed that the sextet model exhibits near conformality as predicted theoretically. These provide quantitative estimates how SCGTs approach conformality as the number of flavors and representations vary, which is crucial in the search of BSM candidates.

**Team: Lattice Higgs Collaboration (LatHC)**

- Zoltan Fodor (Eotvos U. & IAS, Julich & Wuppertal U.)
- Kieran Holland (U. Pacific, Stockton & U. Bern, AEC)
- Julius Kuti (UC, San Diego)
- Daniel Nogradi (Eotvos U. & Eotvos Lorand U., Budapest, Inst. Theor. Phys.)
- Chik Him Wong (Wuppertal U.)

**Scientific Contact:**

Dr. Chik Him (Ricky) Wong

Institute for Theoretical Particle Physics

Faculty of Mathematics and Natural Sciences

Bergische Universität Wuppertal, D-42097 Wuppertal (Germany)

e-mail: c wong [at] uni-wuppertal.de

*JSC project ID: chwu33*

*March 2020*