UV descriptions of composite Higgs models without elementary scalars

Abstract: We consider four-dimensional UV descriptions of composite Higgs models without elementary scalars, in which four-fermion interactions are introduced to an underlying gauge theory like in the gauged NJL model. When the anomalous dimension of the fermion bilinear is large, these interactions drive the spontaneous global symmetry breaking in the model, with the Higgs identified as a Nambu-Goldstone boson. The UV descriptions support composite top partner operators, also with large anomalous dimensions, thereby providing an explicit realisation of the idea of partial compositeness. In particular, the composite SO(6)/SO(5) model can be described by an Sp gauge theory with four flavours of fermion, together with a vector-like pair of fermions transforming in the antisymmetric representation and charged under SU(3) colour. These fermions confine to produce both the Higgs and top partner bound states. Our methods can also be applied to different coset groups, suggesting that four-fermion operators can describe the underlying UV dynamics of other composite Higgs models.

• The paper introduces a UV completion of composite Higgs models by leveraging four-fermion operators to induce spontaneous symmetry breaking and identify the Higgs as a Nambu–Goldstone boson.
• It employs a four-dimensional gauged Nambu–Jona-Lasinio framework with an Sp gauge theory and Weyl fermions to generate composite states including the Higgs and its top partners.
• The analysis shows that large anomalous dimensions from fermion bilinears enable renormalizable interactions, offering a non-supersymmetric solution to the hierarchy problem without relying on elementary scalars.

Summary of "UV Descriptions of Composite Higgs Models without Elementary Scalars"

The paper explores the ultraviolet (UV) descriptions of composite Higgs models characterized by the absence of elementary scalars, focusing on mechanisms that induce spontaneous global symmetry breaking via four-fermion interactions. The analysis specifically considers a four-dimensional UV completion of the gauged Nambu-Jona-Lasinio (NJL) model framework, where a large anomalous dimension for the fermion bilinear aids in identifying the Higgs boson as a Nambu-Goldstone boson. The discussion highlights the generation of composite states, including the Higgs and its top partner counterparts, through the mechanism of partial compositeness intrinsic to certain gauge theories.

The paper first details the theoretical foundation and implications of employing an $Sp$ gauge theory with four flavours of Weyl fermions. This approach facilitates the realization of the composite $SO(6)/SO(5)$ Higgs model via a gauge theory with antisymmetric representation and $SU(3)$ colour-charged vector-like fermions. Notably, these fermions are anticipated to confine into bound states representing the Higgs and top partners, driven by four-fermion operators that depict the critical underlying UV dynamics.

Theoretical Framework and Computational Insights

Significantly, the authors explore a phase analysis of the $SU(4)\to Sp(4)$ model, identifying the interplay between different dynamics that lead to or inhibit symmetry breaking. The paper underscores the potential for UV completeness by demonstrating how four-fermion operators become relevant in the context of large anomalous dimensions, which intriguingly render the bilinear scaling dimension approximately one. It's posited that such anisotropic scaling facilitates renormalizable interactions originating purely from fermionic and gauge sources. This approach negates the necessity for scalar fields, which traditionally pose challenges due to quadratic divergences.

The authors meticulously detail the role of $Sp(2N_c)$ gauge interactions and four-fermion operators in shaping the vacuum structure of the theory. These elements, according to the analysis, crucially ensure large mass anomalous dimensions necessary for explaining the top quark's mass hierarchy, particularly through constructing top-partner operators. The theoretical calculations indicate that the top partner dimension just scrapes past the threshold required to maintain a sizeable Yukawa coupling, pivotal in electroweak symmetry breaking.

Implications and Future Directions

The presented framework does more than just conceptualize a composite Higgs; it opens avenues for revisiting other coset structures within composite Higgs models, such as those extending beyond the minimal $SO(5)/SO(4)$ case. The exploration of alternative symmetry breaking schemes, including potential realization courses and challenges, is addressed. These discussions extend into speculative territories regarding the nature of top partners, observables in such a UV complete theory, and the comprehensive implications for crucial metrics like the S and T parameters in precision electroweak observables.

Overall, the paper impressively demonstrates the capability of extending the limitations of effective field theories by proposing a methodology for a non-supersymmetric UV completeness using fully fermionic and gauge-invariant interactions, while maintaining tractability via established quantum field theory tools. This theoretical advancement not only propounds a novel depiction of composite dynamics but also sets the stage for empirical exploration and interfacing with the broader question of the hierarchy problem in the Standard Model. Further examination into gauge couplings, anomaly cancelations, and phenomenological testability in collider physics would serve as the natural progression of research inspired by this discourse.