Vacuum misalignment in presence of four-Fermi operators

Abstract

We consider the issue of vacuum misalignment induced by four-Fermi couplings in a generic strongly coupled four-dimensional gauge theory. After briefly reviewing the general formalism, we focus on the case of partial compositness-like operators at leading order, which is relevant in applications to phenomenology. We show that the interactions between an elementary fermion and composite spin-1/2 operators in various representations contribute to the effective potential with relative sign differences. Thus the correct sign required to misalign the vacuum is guaranteed to occur for some representations but not all of them. The overall sign dictating the specific representations responsible for misalignment can in principle be determined on the lattice. We also comment on the likely sign for some simple cases.

arXiv comment15 pages, 1 captioned figure. Comments are welcome

References in corpus (20)

• The Minimal Composite Higgs Model
• The Littlest Higgs
• Higgs as a Holographic Pseudo-Goldstone Boson
• Fermionic UV completions of Composite Higgs models
• UV descriptions of composite Higgs models without elementary scalars
• Fundamental Composite (Goldstone) Higgs Dynamics
• Gauge theories of Partial Compositeness: Scenarios for Run-II of the LHC
• UV Completions of Partial Compositeness: The Case for a SU(4) Gauge Group
• Fundamental Composite 2HDM: SU(N) with 4 flavours
• Baryon spectrum of SU(4) composite Higgs theory with two distinct fermion representations
• A UV complete partially composite-pNGB Higgs
• UV complete composite Higgs models
• Top quark induced effective potential in a composite Higgs model
• Vacuum misalignment and pattern of scalar masses in the SU(5)/SO(5) composite Higgs model
• Effective potential in ultraviolet completions for composite Higgs models
• Lattice studies of the $Sp(4)$ gauge theory with two fundamental and three antisymmetric Dirac fermions
• Glueballs and Strings in $Sp(2N)$ Yang-Mills theories
• Anomalous dimensions of potential top-partners
• Modelling vector-like quarks in partial compositeness framework
• One-loop anomalous dimension of top-partner hyperbaryons in a family of composite Higgs models

Cited by in corpus (2)

• Vector-like quarks: status and new directions at the LHC
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