[Paper Review] The Dynamical Composite Higgs

Gero von Gersdorff, Eduardo Pontón+1 more|arXiv (Cornell University)|Feb 25, 2015

Particle physics theoretical and experimental studies36 references4 citations

TL;DR

This paper proposes a minimal, non-supersymmetric ultraviolet completion of a pseudo-Nambu-Goldstone Higgs model via four-fermion interactions with a super-critical coupling, realizing SO(5)→SO(4) global symmetry breaking. The Higgs emerges as a composite bound state via the Nambu-Jona-Lasinio mechanism, with an approximate infrared fixed point ensuring insensitivity to high-energy scales; the model reproduces the observed Higgs mass, satisfies electroweak precision tests in parts of parameter space, predicts a multi-TeV singlet scalar and vector-like fermions, and is UV-completable via a renormalizable theory.

ABSTRACT

We present a simple microscopic realization of a pseudo-Nambu-Goldstone (pNGB) boson Higgs scenario arising from the breaking of $SO(5) ightarrow SO(4)$. The Higgs constituents are explicitly identified as well as the interactions responsible for forming the bound state and breaking the electroweak symmetry. This outcome follows from the presence of four-fermion interactions with a super-critical coupling, and uses the Nambu-Jona-Lasinio mechanism to break the global $SO(5)$ symmetry. The Higgs potential is found to be insensitive to high energy scales due to the existence of an approximate infrared fixed point. The appearance of vector resonances is described and the correspondence with other proposals in the literature established. The model described here is significantly simpler than other recent ultraviolet completions of pNGB scenarios. The observed Higgs mass can be accommodated, and agreement with electroweak precision tests achieved in certain regions of parameter space. There are also new vector-like fermions, some of which may lie within reach of the LHC. In addition, we predict a heavy standard model singlet scalar in the multi-TeV range. The amount of fine-tuning required in the model is studied. Finally, we show that such a scheme can be completed in the ultraviolet by a renormalizable theory.

Motivation & Objective

• To construct a minimal, non-supersymmetric UV completion of a pseudo-Nambu-Goldstone Higgs scenario that avoids quadratic divergences.
• To realize electroweak symmetry breaking through four-fermion interactions with super-critical coupling, avoiding fundamental scalars.
• To demonstrate that the Higgs potential is insensitive to high-energy scales via an approximate infrared fixed point.
• To identify the emergence of vector resonances and new vector-like fermions, some accessible at the LHC.
• To show that the model can be UV-completed by a renormalizable theory and assess the degree of fine-tuning required.

Proposed method

• The model employs four-fermion interactions with a super-critical coupling to trigger spontaneous global SO(5) symmetry breaking via the Nambu-Jona-Lasinio mechanism.
• The Higgs boson is identified as a composite bound state of fermions, with the electroweak scale generated via a one-loop Coleman-Weinberg potential from explicit global symmetry breaking.
• The effective potential is computed using a 1-loop Coleman-Weinberg calculation in the presence of field-dependent masses, with careful treatment of infrared divergences via field-dependent cutoffs.
• The model incorporates QCD interactions via renormalization group equations to study their impact on fixed-point behavior and fermion anomalous dimensions.
• The radial mode is treated as a heavy scalar field, and the compositeness condition is applied to ensure the Higgs is not fundamental.
• UV completion is achieved by embedding the four-fermion interactions into a renormalizable gauge theory with heavy vector-like fermions and a scalar singlet.

Experimental results

Research questions

• RQ1 Can a minimal, non-supersymmetric UV completion of a pseudo-Nambu-Goldstone Higgs model be constructed using four-fermion interactions?
• RQ2 Does the resulting Higgs potential remain insensitive to high-energy physics due to an approximate infrared fixed point?
• RQ3 Can the model reproduce the observed Higgs mass and satisfy electroweak precision tests within a viable parameter space?
• RQ4 What are the phenomenological signatures, such as vector-like fermions and a heavy SM singlet scalar, and are they accessible at the LHC?
• RQ5 To what extent is fine-tuning required, and can the model be UV-completed by a renormalizable theory?

Key findings

• The Higgs mass is successfully accommodated at the observed value, with the model achieving agreement with electroweak precision tests in certain regions of parameter space.
• The Higgs potential is insensitive to high-energy scales due to the presence of an approximate infrared fixed point, reducing quadratic divergences.
• The model predicts a heavy standard model singlet scalar in the multi-TeV range, arising from the radial mode of the composite Higgs.
• Vector resonances emerge naturally in the model, responsible for canceling quadratic divergences in the Higgs mass parameter from SM gauge bosons.
• New vector-like fermions are predicted, some of which may be within reach of the LHC, depending on their mass and couplings.
• The model is UV-completable by a renormalizable theory, and the amount of fine-tuning is found to be moderate, particularly when compared to fundamental scalar models.