Beyond the minimal composite Higgs model

Abstract

If electroweak symmetry breaking arises via strong dynamics, electroweak precision tests and flavour physics experiments suggest that the minimal model should closely resemble the Standard Model at the LHC. I describe two directions going beyond the minimal model that result in radically different physics at the LHC. One direction extends the Higgs sector and the other involves composite leptoquark states. IntroductionStrong coupling provides a solution of the electroweak hierarchy problem that is natural in the literal sense of the word. That is to say, we already have an example in Nature where a hierarchy, namely the one between the proton mass and, say, the Planck scale, is generated by a stronglycoupled theory, QCD. As such, and given the problems suffered by the only weakly-coupled candidate that can stabilize the hierarchy, namely supersymmetry, strongly-coupled dynamics remains an attractive mechanism for electroweak symmetry breaking.But strongly-coupled dynamics has severe problems of its own, in the form of clashes with electroweak precision tests and flavour-changing neutral currents. The former can be solved, to some extent, by clever use of symmetries. To see how this may occur, let me first remark that we do not yet know what the 'symmetry' of electroweak symmetry is. Certainly, we do know that it contains the SU (3) × SU (2) L × U (1) Y of the Standard Model (SM) as a gauged subgroup, but it is quite possible that the true global symmetry of the strongly-coupled sector is somewhat larger. If we enlarge the SU (2) L × U (1) Y to SU (2) L × SU (2) R ≃ SO(4) (which is an accidental symmetry of the renormalizable SM Higgs potential), then we find that the W and Z bosons automatically obtain their measured mass ratio. 1 Furthermore, by adding the discrete parity that interchanges L ↔ R (or equivalently enlarging SO(4) to O(4)), we can suppress unwanted corrections to the coupling Zbb. 2 The remaining nuisance is the S-parameter, which, alas, no symmetry can forbid without simultaneously forbidding electroweak symmetry breaking. Nevertheless, one can still use symmetry to argue that S, although it cannot vanish, could be small.The argument goes as follows. If SU (2) L were a symmetry of the vacuum, then S would indeed vanish. 3 This implies that S must be proportional to some positive power of the electroweak vev, v; in fact, since S transforms as an SU (2) L triplet, whilst v transforms as a doublet, we have that S ∝ v 2 . Now, S is dimensionless, so we must have that S ≃ v 2 /f 2 , where the scale f is set by the strong dynamics; if we could arrange for v/f to be somewhat less than unity, by some dynamical accident, then we might end up with an acceptably-small value for S. One way to do this is to further enlarge the global symmetry of the strong sector to SO(5) and then to decree that strong dynamics breaks it to SO(4). 4 The theory then contains four

What is the γγ resonance at 750 GeV?

“…For example, in composite Higgs models based on the coset SO(6)/SO(5) [49], one obtains an extra singlet PNGB. Similarly to the Higgs multiplet, these extra PNGB acquire a mass from the explicit breaking of G.…”

Composite scalar dark matter

“…The most minimal extension to this symmetry pattern is the SO(6)/SO(5) model, that contains five pNGBs in the spectrum: the Higgs doublet H and a gauge singlet η [10]. Interestingly, the pattern SO(6)/SO(5) is the minimal example with a known ultraviolet completion in terms of techni-quarks [11].…”

“…If not otherwise specified, we will assume for simplicity family independent coefficients, c u = c c = c t and c d = c s = c b . This choice is partly motivated by the bounds on flavour violation [10].…”

“…This coset was first studied in ref. [10], with focus on the modifications of the Higgs phenomenology in the presence of a real scalar singlet. Here we demand that η plays the role of DM particle and we derive its properties, under the requirement of a consistent EWSB.…”

LHC bounds on lepton number violation mediated by doubly and singly-charged scalars

“…For example, effective operators contributing to these processes are suppressed by at least two powers of the cutoff scale Λ (see appendix A). As a matter of fact, these contact interactions arise naturally in the context, for instance, of non-minimal Composite Higgs Models [98][99][100][101][102]. On the other hand, possibly s−channel contributions are in addition suppressed by small far off-shell propagators; 17 while t−channel contributions are forbidden, since doubly-charged scalars do not have trilinear couplings to a quark pair.…”