# Stefania De Curtis$${}^{(a)}$$, Patrick Janot$${}^{(b)}$$, Stefano Moretti$${}^{(c)}$$ (a) INFN, Sezione di Firenze & Dept. of Physics and Astronomy, University of Florence, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy (b) CERN, EP Department, Geneva, Switzerland (c) School of Physics & Astronomy, University of Southampton, Highfield, Southampton SO17 1BJ, UK

Abstract

We assess the scope of a Future Circular Collider operating in $$e^{+}e^{-}$$ mode (FCC-ee) in accessing the parameter space of the 4-Dimensional Composite Higgs Model (4DCHM), which represents a realistic implementation of Electro-Weak Symmetry Breaking (EWSB) dynamics triggered by a pseudo-Nambu-Goldstone Boson (pNGB) emerging from the breaking of a global symmetry group $$SO(5)\to SO(4)$$ describing new strong interactions eventually resposible for Higgs compositeness. In fact, in such a framework, other composite states exist, like heavy spin-1 bosons ($$W^{\prime}$$s and $$Z^{\prime}$$s) and spin-1/2 fermions ($$b^{\prime}$$s and $$t^{\prime}$$s). Herein, we concentrate initially on the neutral gauge boson sector of this scenario, by attempting to extract the (modified) couplings of the Standard Model (SM) $$Z$$ state as well as the masses and quantum numbers of the additional $$Z^{\prime}$$ objects present in the 4DCHM. We establish the sensitivity of an FCC-ee to such parameters via the processes $$e^{+}e^{-}\to\mu^{+}\mu^{-}$$ and $$e^{+}e^{-}\to t\bar{t}$$ for a varieties of foreseen energies and luminosities, by exploiting both cross section and asymmetry observables. We finally combine the results obtained in the $$Z^{\prime}$$ sector of the 4DCHM with those emerging from foreseen Higgs measurements, as previously assessed, so as to delineate an analysis programme aimed at confirming or disproving once and for all the validity of the compositeness paradigm.

A future $$e^{+}e^{-}$$ collider will be capable to show the imprint of composite Higgs scenarios encompassing partial compositeness. Amongst the possible designs of such a machine, a Future Circular Collider of $$e^{+}e^{-}$$ beams (FCC-ee) has become a frontrunner project in terms of cost effectiveness, precision and search reach (Bicer 2014). Besides the detailed study of the Higgs boson properties, based upon the analysis of the Bjorken production channel $$e^{+}e^{-}\to ZH$$ at an energy of about 240 GeV, such a machine will have a rich programme also covering top-quark physics (at the energies of 350 to 370 GeV) and revisiting the typical LEP1/SLC and LEP2 energy ranges (from $$M_{Z}$$ to $$2M_{W}$$) with significantly increased luminosity. Of particular relevance for our purposes is the FCC-ee ability to afford one with a very accurate determination of the top-quark properties, chiefly, its mass, width and couplings to SM objects. This is because the top quark is the natural carrier of New Physics (NP) phenomena associated to the partial compositeness mechanism.

Herein we discuss such a possibility by using a particular realisation of the latter, namely, the 4-Dimensional Composite Higgs Model (4DCHM) of Ref. (Curtis 2012). This describes the intriguing possibility that the Higgs particle may be a composite state arising from some strongly interacting dynamics at a high scale. This will solve the hierarchy problem owing to compositeness form factors taming the divergent growth of the Higgs mass upon quantum effects. Furthermore, the now measured light mass of the Standard Model (SM)-like Higgs state discovered at the Large Hadron Collider (LHC) in 2012 could well be consistent with the fact that such a (now composite) object arises as a pseudo Nambu-Goldstone Boson (pNGB) from a particular coset of a global symmetry breaking. Models with a Higgs state as a pNGB generally also predict modifications of its couplings to both bosons and fermions of the SM, hence the measurement of these quantities represents a powerful way to test its possible non-fundamental nature. Furthermore, the presence of additional particles in the spectrum of generic Composite Higgs Models (CHMs) leads to both mixing effects with the SM states and new Feynman diagram topologies, both of which would represent a further source of deviations from the SM expectations.

In the near future, the LHC will be able to test Beyond the SM (BSM) scenarios more extensively, probing the existence of new particles predicted herein to an unprecedented level, potentially also at a High Luminosity (HL-LHC) option of the CERN machine (Gianotti 2005), whose approval is presently being discussed. Nevertheless, the expected bounds, though severe, might not be conclusive to completely exclude natural scenarios for the Fermi scale, such as CHMs. As an example, new gauge bosons predicted by CHMs with mass larger than $$\sim$$ 2 TeV could escape detection at the LHC in the Drell-Yan channel owing to the small $$W^{\prime}/Z^{\prime}$$ couplings to both light quarks and leptons (Accomando 2016). Likewise, while new $$b^{\prime}/t^{\prime}$$ states, presently bounded to have a mass above 800 GeV or so, may be within the reach of the current and future runs of the LHC, their peculiar decay patterns may prevent their discovery (Barducci 2014). Furthermore, concerning Higgs boson properties, the LHC will not be able to measure the Higgs couplings to better than few % thus leaving room for scenarios, like CHMs, which predict deviations within the foreseen experimental accuracy for natural choices of the compositeness scale $$f$$ (namely in the TeV range) and of the (new) strong coupling constant $$g_{\rho}$$ (namely, of order 1). For these reasons, we will tackle here the case in which LHC will discover neither a $$W^{\prime}/Z^{\prime}$$ (or it will not be able to clearly assess its properties if it does) nor a $$b/,t^{\prime}$$ (or it will discover it but without any other hints about the theory to which it belongs). In this situation, a high precision lepton collider like the FC-ee would have a great power in enlightening indirect effects of such a BSM physics scenario.