Constraining fine tuning in composite Higgs models with partially composite leptons

Abstract

Minimal Composite Higgs Models (MCHM) have long provided a solution to the hierarchy problem of the Standard Model, yet suffer from various sources of fine tuning that are becoming increasingly problematic with the lack of new physics observations at the LHC. We develop a new fine tuning measure that accurately counts each contribution to fine tuning (single, double, triple, etc) that can occur in a theory with n p parameters, that must reproduce n o observables. We then use a novel scanning procedure to perform a comprehensive study of three different two-site, 4D, SO(5) → SO(4) MCHMs with all third generation fermions included, distinguished by the choice of the lepton embeddings. These are the MCHM 5-5-5 5-5-5 , MCHM 5-5-5 14-14-10 and MCHM 5-5-5 14-1-10 , where MCHM q−t−b l−τ −ν has the lepton doublet partner in representation l, tau partner in representation τ , and so on. We find that embedding at least one massive lepton in the symmetric 14 of SO (5) moderately reduces the tuning for the case of low top partner masses (in line with previous results), but that this is balanced against the increased complexity of the model when one properly accounts for all sources of fine tuning. We study both the current relative fine-tuning of each scenario, and the future prospects. Noting that the different scenarios behave differently with respect to future improvements in collider measurements, we find that the MCHM 5-5-5 14-1-10 enjoys a relatively low increase in fine tuning even for a future lower bound on the top partner masses of 3.4 TeV (or equivalently a maximum Higgs-fermion or Higgs-gluon coupling deviation of 2%).

Exploring fine-tuning of the Next-to-Minimal Composite Higgs Model

“…This can be attributed to a small punishment for increasing the parameter set from nine to ten. A thorough discussion of parameter set scaling in the higher order tuning measure can be found in reference [19]. This agrees with a first-order expectation, since NMCHM observables are generically proportional to MCHM observables according to m NMCHM ∝ m MCHM sin θ, and θ is a free parameter.…”

“…This generalises to more than three observables in a straight-forward way (see Reference [19] for details). The full tuning ∆ is then the sum of all orders of tuning,…”

The Discreet Charm of Higgsino Dark Matter: A Pocket Review

“…For the specific case of the ∼ 1 TeV higgsino, a failure to observe a signal in, say, the next round of XENON-1T data will imply a fine tuning greater than one part in 10 3 , with rapid increase with each successive milestone exclusion. 5 However, we emphasize that a large fine tuning is by no means exclusive to the CMSSM, to higgsino DM, or even to SUSY in general (see, e.g., [150] for fine tuning in a non-SUSY scenario). As a matter of fact, the majority of phenomenological DM models found in the literature do not even attempt to construct a UV completion that could directly relate their free parameters to the physics of the high scale.…”

Improving fine-tuning in composite Higgs models

“…In general, the vev-tuning in this class of models is expected to be greater than ∆. In most cases it can be estimated as ∼ ∆/κ, where κ( 1) is a model dependent parameter [11,12,13,14,15]. In this paper we assume that ∆ quantifies the minimal tuning in the Higgs vev.…”

“…A complementary method based on statistical approach to estimate the fine-tuning can be found in[15].…”