Scalar Democracy

Abstract

We conjecture that there exists a scalar bound state for every pair of fundamental fermions at a UV ("composite") scale, Λ v weak . This implies a large number of universally coupled, sub-critical Higgs doublets. All but the Standard Model Higgs are "dormant," with large positive squared masses and each receives a small vacuum expectation values via mixing with the Standard Model Higgs. Universal couplings, modulo renormalization group running effects, flips the flavor problem into the masses and mixings of the Higgs system. Doublets associated with heavy fermion masses, b, c, τ likely lie in the multi-TeV range, but may be observable at the current LHC, or a high-luminosity and/or an energy-upgraded LHC. In the lepton sector we are lead to a Higgs seesaw for neutrino masses, and corollary processes of observable flavor violation. The observation of the first sequential doublet coupled to bb with masses 3.5 TeV would lend credence to the hypothesis.

Where are the Next Higgs Bosons?

“…We will focus, for simplicity, upon the third generation, and will ignore masses and mixings involving the lighter two generations. We note that, in a previous study, [2], the flavor constraints on this system were found to be consistent.…”

“…In a larger framework with a UV completion, such as Ref. [2], at a mass scale, m > M b , both g t (m) and g b (m) will have a common renormalization group equation modulo U(1) Y effects. We implicitly assume that, at some very high scale Λ v, the SU(2…”

“…Since the RG equations for the leptons do not involve QCD, we typically find g τ (m τ ) = g ν (m τ ) 0.7 for Λ ∼ M Planck [2]. More generally we define the parameters…”

“…This coupling is thus determined by the known top quark Higgs-Yukawa coupling, y t = g 1. A schematic proposal for a UV completion theory that leads to G, based upon far UV compositeness, was proposed in [2]. In that scheme y t = g g b 1 is actually predicted by the infrared fixed point [3,4].…”

“…. The tachyonic (negative) M 2 0 can thus be generated from an unknown input value, M 2 H , but we should not fine tune the difference, M 2 H − µ 4 /M 2 . This requirement establishes the scale of M b ∼ 5 TeV.…”