## SciPost Submission Page

# A Natural Composite Higgs via Universal Boundary Conditions

### by Simone Blasi, Csaba Csaki, Florian Goertz

### Submission summary

As Contributors: | Simone Blasi |

Arxiv Link: | https://arxiv.org/abs/2004.06120v2 (pdf) |

Date submitted: | 2020-08-03 17:56 |

Submitted by: | Blasi, Simone |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | 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:

### Submission & Refereeing History

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## Reports on this Submission

### Anonymous Report 1 on 2020-9-3 Invited Report

### Report

The paper proposes a new holographic (5d) realisation of the Composite Higgs scenario. In the new model the amount cancellation (fine-tuning) required to keep the EWSB scale "v" separated from the Higgs Goldstone decay constant "f" is at the level of (f/v)^2, which is believed to be the minimal possible tuning in these constructions. At the same time, and this is what makes the model different from other departures from the "Minimal" model, the model does not require extra tuning to avoid unobserved light Top Partner fermion resonances for the Higgs being as light as we observe it.

I have two concerns about the relevance of the paper. The first one is phenomenological as it is unclear if anomalously light top partner direct searches will be or not the strongest probes of Higgs compositeness at the end of the HL-LHC. Departures of the Higgs couplings from the SM predictions, of order (v/f)^2 and hence directly related with the "minimal" tuning, will be probed accurately. I have not found mention of this aspect in the manuscript, but it seems clear that this kind of effects are not reduced in the model under consideration relative to the generic expectation.

The second concern is that the phenomenological virtues of the model do not come from robust structural assumptions or emergent phenomena that are deeply rooted in the theory. The first ingredient of the model is Maximal Symmetry, reviewed in section 2. This is an SO(5)' group, different from the SO(5) Goldstone symmetry, that acts on the fermionic composite resonances and that is enforced by a choice of the composite resonance masses. I believe that this symmetry can not be promoted to a true symmetry of the Composite Sector of the theory. Or, equivalently, the choice of the mass spectrum that respects the symmetry cannot be viewed as the consequence of some global symmetry that is respected by the underlying Composite Sector Dynamics. I think it is pretty obvious that the symmetry cannot be uplifted to a true symmetry of the theory, and the manuscript does not claim otherwise.

However the manuscript claims that the symmetry can be extended also to the composite fermions-Higgs interaction, by acting on the Goldstone Boson Higgs as in eq.(2.13). I am confused by that equation. The Sigma matrix is not a generic matrix, but it is of the form (2.9) and the only degrees of freedom it contains are the Goldstone scalars that are present in the U Goldstone matrix. I do not see how the transformation in eq.(2.13) could be realised as a transformation acting only on those degrees of freedom. Actually it seems to me that eq.(2.13), using eq.(2.11) for V, can be turned into the operation U^2--> gL U^2 gL^\dagger, with gL a generic SO(5) matrix, which is clearly not permitted since U only contains the exponent of broken generators. This aspect should be definitely clarified if the manuscript has to be further considered for publication.

The second element of the model is Goldstone symmetry "soft breaking", also reviewed in Section 2. This is based on adding extra elementary degrees of freedom that fill a five-plet of the SO(5) Goldstone symmetry and couple them to the Composite Sector in a way that respects the symmetry. The SM fermions Yukawa coupling and the explicit symmetry breaking emerge from elementary-to-elementary mass-mixings. The setup allows to relax the connection between the Higgs mass and the mass of the Top Partners. It is technically correct to add extra degrees of freedom to the theory, and it is technically correct to assign to them transformation properties under SO(5) and postulate a specific patter of breaking of the symmetry. However it is unclear which microscopic assumption on the underlying theory would produce the advocated symmetry structure: the elementary fermions know nothing about the SO(5) global symmetry of the composite constituents, a priori.

The structural considerations above are not made explicit in the manuscript. It is admitted that the required structure is somehow ad hoc, but this is not sufficient. Being or not "ad hoc" can be matter of taste. Being or not able to sharply state the microscopic UV theory assumptions that produce the desired effect in the low-energy theory is an objective statement. Emphasis is given in the manuscript to the "simplicity" of the 5d holographic model that realises all these required structures. On one hand I agree that from the 5d perspective the model is not more involved than the ordinary Minimal Composite Higgs Model (MCHM). On the other hand the MCHM can be viewed as a generic realisation of a clear set of well-defined microscopic assumptions on the Composite and Elementary sectors of the 4d underlying theory. The new ingredients of the present model instead (Maximal Symmetry, in the first place) do not emerge from microscopic assumptions.

In conclusion, I am not enthusiastic about the paper. In itself, the fact that minor deformations and/or special choices of the MCHM parameters can reduce the fine tuning and lift the Top Partners, is not surprising. It would have been interesting if these choices/deformations had been found to emerge from structural microscopic assumptions, which is not the case here. On the other hand it is interesting to see one concrete example, and definitely a lot of work is done in the paper to explain why the non-generic features introduced in the construction (in the first place, the fact that the IR boundary conditions do not split SO(4) multiplets, in order to produce Maximal Symmetry) do indeed produce an interesting phenomenology.

So I believe that the paper can be published, provided the limitations are more clearly spelled out.

### Requested changes

1-One should discuss the impact of Higgs coupling measurements and state if or not the model behaves differently from the standard one.

2-The meaning of Eq.(2.13) should be clarified, in light of the comment made in the report.

3-It should be stated clearly which aspects of the construction are structural assumption about the underlying microscopic theory and which ones are not. in light of the remarks made in the report.