PDF《CP3-Origins-2017-008 DNRF90》

CP3-Origins-2017-008 DNRF90 A UV Complete Compositeness Scenario: LHC Constraints Meet The Lattice Luigi Del Debbio,1 Christoph Englert,2 and Roman Zwicky1

1 Higgs Centre for Theoretical Physics, School of Physics &

Astronomy, University of Edinburgh, EH9 3FD, UK

2 SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK We investigate a recently proposed UV-complete composite Higgs scenario in the light of the ?rst LHC runs.

The model is based on a SU(4) gauge group with global ?avour symmetry breaking SU(5) → SO(5), giving rise to pseudo Nambu-Goldstone bosons in addition to the Higgs doublet. This includes a real and a complex electroweak triplet with exotic electric charges. Including these, as well as constraints on other exotic states, we show that LHC measurements are not yet sensitive enough to signi?cantly constrain the model'

s low energy constants. The Higgs potential is described by two parameters which are on the one hand constrained by the LHC measurement of the Higgs mass and Higgs decay channels and on the other hand can be computed from correlation functions in the UV-complete theory. Hence to exclude the model at least one constant needs to be determined and to validate the Higgs potential both constants need to be reproduced by the UV-theory. Due to its UV-formulation, a certain number of low energy constants can be computed from ?rst principle numerical simulations of the theory formulated on a lattice, which can help in establishing the validity of this model. We assess the potential impact of lattice calculations for phenomenological studies, as a preliminary step towards Monte Carlo simulations. Contents I. Introduction

1 II. Ferretti'

s model

2 Lessons from the Lattice and the LHC

4 Higgs Potential

4 Quark Condensates and Goldstone Boson Decay Constants

5 III. Parameter regions after LHC measurements

5 Constraints from coloured Exotica

6 Constraints from Higgs signal strengths

6 Constraints from exotic Higgs searches

6 Doubly Charged Scalars

6 Charged Scalars

7 Neutral Scalars

8 IV. Summary and Conclusions

9 A. Four point-functions

10 B. Analysis of loop-induced decays of the non-Higgs scalar states

10 References

11 I. INTRODUCTION The discovery of a Standard Model (SM) like Higgs boson has so far not revealed concrete hints towards an understanding of the electroweak symmetry breaking (EWSB). The concept of Higgs naturalness stands ques- tioned in many established BSM scenarios such as super- symmetry but also in theories of Higgs compositeness. It is conceivable that future LHC runs, exploring higher energy scales with large statistics, will improve the situa- tion. Due to the non-perturbative nature of the compos- ite Higgs models, their phenomenological investigations are typically informed by means of e?ective theories, in a way that is completely analogous to the description of the low energy dynamics of QCD by chiral perturbation theory. Although these methods have been very success- ful in understanding the low energy properties of QCD, the ultimate goal is obviously to analyse the phenomeno- logical properties of a composite Higgs scenario by inves- tigating concrete UV-complete candidate theories using non-perturbative techniques to gain a more complete pic- ture of their dynamics from ?rst principles. The minimal composite Higgs model (MCHM) [1C3] based on global symmetry breaking pattern SO(5) → SO(4) is the prototype of composite Higgs model. The four arising Nambu-Goldstone bosons (NGBs) transform as a bi-doublet under SU(2) * SU(2) SO(4) and can therefore be identi?ed with the Higgs doublet in the SM. Breaking the global symmetry by gauging the weak inter- action SU(2)L *U(1)Y ? SO(4) in the presence of heavy composite fermions induces a Higgs potential. Whether or not the potential triggers EWSB can only be investi- gated for de?nite in a UV complete scenario. The scale of the composite sector is parametrised by f and its value compared to v, ξ ≡ v2 /f2 (v