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The Unnatural Composite Higgs

A simple way to trivially satisfy precision-electroweak and flavor constraints in composite Higgs models is to require a large global symmetry breaking scale, f > 10 TeV. This leads to a tuning of order 10 -4 ; to obtain the observed Higgs mass, but gives rise to a 'split' spectrum where the strong-sector resonances with masses greater than 10 TeV are separated from the pseudo Nambu-Goldstone bosons, which remain near the electroweak scale. To preserve gauge-coupling unification (due to a composite top quark), the symmetry breaking scale satisfies an upper bound f < 100-1000 TeV, which implies that the resonances are not arbitrarily heavy and may be accessible at future colliders. Furthermore, by identifying dark matter with a pseudo Nambu-Goldstone boson, the smallest coset space containing a stable, scalar singlet and an unbroken SU(5) symmetry is SU(7) / SU(6) x U(1). Interestingly, this coset space also contains a metastable color-triplet pseudo Nambu-Goldstone boson that can decay via a displaced vertex when produced at colliders, leading to a distinctive signal of unnaturalness.