# The running coupling of the minimal sextet composite Higgs model

Z. Fodor, Kieran Holland, Julius Kuti, Santanu Mondal, Daniel Nogradi, Chik Him Wong

Research output: Contribution to journalArticle

25 Citations (Scopus)

### Abstract

Abstract: We compute the renormalized running coupling of SU(3) gauge theory coupled to Nf = 2 flavors of massless Dirac fermions in the 2-index-symmetric (sextet) representation. This model is of particular interest as a minimal realization of the strongly interacting composite Higgs scenario. A recently proposed finite volume gradient flow scheme is used. The calculations are performed at several lattice spacings with two different implementations of the gradient flow allowing for a controlled continuum extrapolation and particular attention is paid to estimating the systematic uncertainties. For small values of the renormalized coupling our results for the β-function agree with perturbation theory. For moderate couplings we observe a downward deviation relative to the 2-loop β-function but in the coupling range where the continuum extrapolation is fully under control we do not observe an infrared fixed point. The explored range includes the locations of the zero of the 3-loop and the 4-loop β-functions in the MS¯$$\overline{\mathrm{MS}}$$ scheme. The absence of a non-trivial zero in the β-function in the explored range of the coupling is consistent with our earlier findings based on hadronic observables, the chiral condensate and the GMOR relation. The present work is the first to report continuum non-perturbative results for the sextet model.

Original language English 39 Journal of High Energy Physics 2015 9 https://doi.org/10.1007/JHEP09(2015)039 Published - Sep 14 2015

### Fingerprint

composite materials
continuums
extrapolation
condensates
gauge theory
estimating
perturbation theory
fermions
spacing
deviation

### Keywords

• Beyond Standard Model
• Higgs Physics
• Lattice Gauge Field Theories

### ASJC Scopus subject areas

• Nuclear and High Energy Physics

### Cite this

The running coupling of the minimal sextet composite Higgs model. / Fodor, Z.; Holland, Kieran; Kuti, Julius; Mondal, Santanu; Nogradi, Daniel; Wong, Chik Him.

In: Journal of High Energy Physics, Vol. 2015, No. 9, 39, 14.09.2015.

Research output: Contribution to journalArticle

Fodor, Z. ; Holland, Kieran ; Kuti, Julius ; Mondal, Santanu ; Nogradi, Daniel ; Wong, Chik Him. / The running coupling of the minimal sextet composite Higgs model. In: Journal of High Energy Physics. 2015 ; Vol. 2015, No. 9.
title = "The running coupling of the minimal sextet composite Higgs model",
abstract = "Abstract: We compute the renormalized running coupling of SU(3) gauge theory coupled to Nf = 2 flavors of massless Dirac fermions in the 2-index-symmetric (sextet) representation. This model is of particular interest as a minimal realization of the strongly interacting composite Higgs scenario. A recently proposed finite volume gradient flow scheme is used. The calculations are performed at several lattice spacings with two different implementations of the gradient flow allowing for a controlled continuum extrapolation and particular attention is paid to estimating the systematic uncertainties. For small values of the renormalized coupling our results for the β-function agree with perturbation theory. For moderate couplings we observe a downward deviation relative to the 2-loop β-function but in the coupling range where the continuum extrapolation is fully under control we do not observe an infrared fixed point. The explored range includes the locations of the zero of the 3-loop and the 4-loop β-functions in the MS¯$$\overline{\mathrm{MS}}$$ scheme. The absence of a non-trivial zero in the β-function in the explored range of the coupling is consistent with our earlier findings based on hadronic observables, the chiral condensate and the GMOR relation. The present work is the first to report continuum non-perturbative results for the sextet model.",
keywords = "Beyond Standard Model, Higgs Physics, Lattice Gauge Field Theories",
author = "Z. Fodor and Kieran Holland and Julius Kuti and Santanu Mondal and Daniel Nogradi and Wong, {Chik Him}",
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language = "English",
volume = "2015",
journal = "Journal of High Energy Physics",
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T1 - The running coupling of the minimal sextet composite Higgs model

AU - Fodor, Z.

AU - Holland, Kieran

AU - Kuti, Julius

AU - Mondal, Santanu

AU - Wong, Chik Him

PY - 2015/9/14

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N2 - Abstract: We compute the renormalized running coupling of SU(3) gauge theory coupled to Nf = 2 flavors of massless Dirac fermions in the 2-index-symmetric (sextet) representation. This model is of particular interest as a minimal realization of the strongly interacting composite Higgs scenario. A recently proposed finite volume gradient flow scheme is used. The calculations are performed at several lattice spacings with two different implementations of the gradient flow allowing for a controlled continuum extrapolation and particular attention is paid to estimating the systematic uncertainties. For small values of the renormalized coupling our results for the β-function agree with perturbation theory. For moderate couplings we observe a downward deviation relative to the 2-loop β-function but in the coupling range where the continuum extrapolation is fully under control we do not observe an infrared fixed point. The explored range includes the locations of the zero of the 3-loop and the 4-loop β-functions in the MS¯$$\overline{\mathrm{MS}}$$ scheme. The absence of a non-trivial zero in the β-function in the explored range of the coupling is consistent with our earlier findings based on hadronic observables, the chiral condensate and the GMOR relation. The present work is the first to report continuum non-perturbative results for the sextet model.

AB - Abstract: We compute the renormalized running coupling of SU(3) gauge theory coupled to Nf = 2 flavors of massless Dirac fermions in the 2-index-symmetric (sextet) representation. This model is of particular interest as a minimal realization of the strongly interacting composite Higgs scenario. A recently proposed finite volume gradient flow scheme is used. The calculations are performed at several lattice spacings with two different implementations of the gradient flow allowing for a controlled continuum extrapolation and particular attention is paid to estimating the systematic uncertainties. For small values of the renormalized coupling our results for the β-function agree with perturbation theory. For moderate couplings we observe a downward deviation relative to the 2-loop β-function but in the coupling range where the continuum extrapolation is fully under control we do not observe an infrared fixed point. The explored range includes the locations of the zero of the 3-loop and the 4-loop β-functions in the MS¯$$\overline{\mathrm{MS}}$$ scheme. The absence of a non-trivial zero in the β-function in the explored range of the coupling is consistent with our earlier findings based on hadronic observables, the chiral condensate and the GMOR relation. The present work is the first to report continuum non-perturbative results for the sextet model.

KW - Beyond Standard Model

KW - Higgs Physics

KW - Lattice Gauge Field Theories

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