# A Natural Composite Higgs via Universal Boundary Conditions

### Submission summary

 As Contributors: Simone Blasi Arxiv Link: https://arxiv.org/abs/2004.06120v3 (pdf) Date submitted: 2020-12-29 11:09 Submitted by: Blasi, Simone Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory High-Energy Physics - Phenomenology Approaches: Theoretical, Phenomenological

### Abstract

We present a novel realization of a composite Higgs, which can naturally produce top partners above the current LHC bounds without increasing the tuning above 10%. The essential ingredients are softened breaking of the Higgs shift symmetry as well as maximal symmetry, which turn out to perfectly complement each other. The 5D realization of this model is particularly simple: universal UV and IR boundary conditions for the bulk fermions containing the SM fields will cure the problems of existing holographic composite Higgs models and provide a complete viable model for a naturally light Higgs without much tuning.

###### Current status:
Has been resubmitted

### List of changes

1. Discussion on the expected bounds from HL-LHC on composite Higgs models in terms of light top partners vs Higgs couplings (page 17).

2. Clarification of the spurious nature of the SO(5)' transformation acting on the Goldstone matrix (page 6 and caption of Table 1).

3. Paragraph added on the possible microscopic interpretation of soft breaking (page 8).

4. Clarification of the assumptions concerning maximal symmetry (footnote at page 7).

5. Inclusion of the explicit form of the IR-localized action considered in Section 5 (Eq. 5.3 at page 19).

### Submission & Refereeing History

Resubmission 2004.06120v4 on 4 May 2021

Resubmission 2004.06120v3 on 29 December 2020
Submission 2004.06120v2 on 3 August 2020

## Reports on this Submission

### Report

The clarifications added in the current version do indeed improve the quality of the manuscript. I have some followup comment, reported below, to the authors' reply. Based on these comments the authors might want to make some further adjustment to the text. But I leave the choice to them.

Concerning Higgs coupling constraints: the most up-to-date HL-LHC Higgs coupling measurements projections are reported in https://arxiv.org/pdf/1905.03764.pdf. In particular one can look at Table 9 (in particular, to the single-operator sensitivity to $c_\phi$, which is the relevant one in composite Higgs at large $g_*$). This is quite stronger than what previously considered to be possible, and correspondingly the reach on $f$ one extracts from Figure 7 left panel is higher than the $1.6\,$TeV mentioned in the manuscript for the reach from top partners direct searches . In the text describing the table in https://arxiv.org/pdf/1905.03764.pdf it is explained that the sensitivity to $c_\phi$ reported in the table is still subject to large uncertainties. However I guess this suggests that one should be carful before stating with certitude that top partners direct searches will be the strongest probe of Composite Higgs at the end of the HL-LHC.

Concerning the microscopic origin of the soft-breaking structure: it is indisputable that elementary degrees of freedom having to transform under the global group of the composite sector restricts the viable options for the microscopic origin of the symmetry. In particular, the symmetry cannot emerge anymore as an Accidental (in the proper sense detailed below) Flavour-type symmetry of the Composite Sector.

Finally, about Maximal symmetry being possibly "Accidental": I really do not understand what this means. There exist a sharp notion of Accidental Symmetries, based on operator classification at a given order (like baryon and lepton number in the SM). Maximal Symmetry definitely does not emerge in this way. I am not sure that the authors have something concrete in mind when they refer to the dynamics of the composite sector, to which condensates form or do not form. In any case, I recommend them not to use the word "accidental" to describe what they have in mind because this is very confusing.

On general grounds, it is technically legitimate to state that the Holographic model is a "UV completion". However it is so in a rather limited sense, due to the limited cutoff of the Holographic model and to the lack of a String origin of the Holographic model itself. The ingredients employed in the model do indeed make sense in the Holographic setup. While they make less sense in the perspective of a possible UV-completion based on strong dynamics in 4d and extending up to energies well above the TeV scale. This is in my view the main limitation of the work, which however remains interesting especially with the clarifications included in the revised version.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -

Author Simone Blasi on 2021-05-04
(in reply to Report 1 on 2021-02-03)
Category:
remark