Vacuum alignment and radiatively induced Fermi scale

We extend the discussion about vacuum misalignment by quantum corrections in models with composite pseudo-Goldstone Higgs boson to renormalisable models with elementary scalars. As a concrete example, we propose a framework, where the hierarchy between the unification and the Fermi scale emerges radiatively. This scenario provides an interesting link between the unification and Fermi scale physics.Comment: 7 pages. To appear in the proceedings of the 5th International Conference on New Frontiers in Physics ICNFP2016, July 06 - 14, 2016. Based on arXiv:1511.01910 and arXiv:1608.07442. arXiv admin note: text overlap with arXiv:1609.0849

The β\beta-function for Yukawa theory at large NfN_f

We compute the $\beta$-function for a massless Yukawa theory in a closed form at the order $\mathcal{O}(1/N_f)$ in the spirit of the expansion in a large number of flavours $N_f$. We find an analytic expression with a finite radius of convergence, and the first singularity occurs at the coupling value $K=5$.Comment: 15 pages, 2 figures. v3 error in the computation of the n-loop scalar self-energy corrected. The first singularity occurs at $K=5$, qualitatively the analysis is unchange

The abelian gauge-Yukawa β\beta-functions at large NfN_f

We study the impact of the Yukawa interaction in the large-$N_f$ limit to the abelian gauge theory. We compute the coupled $\beta$-functions for the system in a closed form at $\mathcal{O}(1/N_f)$.Comment: 13 pages, 6 figures. v3 matches the published versio

Axiflavon-Higgs Unification

In this talk, a unified model of scalar particles that addresses the flavour hierarchies, solves the strong CP problem, delivers a dark matter candidate, and radiatively triggers electroweak symmetry breaking is discussed. The recently proposed axiflavon is embedded together with an (elementary) Goldstone Higgs-sector in a single multiplet (and thereby also a model of flavour and strong CP conservation for the latter is provided). Bounds on the axion decay constant follow from requiring a SM-like Higgs potential at low energies and are confronted with constraints from flavour physics and astrophysics. In the minimal implementation, the axion decay constant is restricted to $f_a \approx (10^{11}-10^{12})$ GeV, while adding right-handed neutrinos allows for a heavy-axion model at lower energies, down to $f_a \sim 10$ TeV.Comment: Contribution to the 2019 EW session of the 54th Rencontres de Moriond, 6 pages, 2 figure

Bubble-resummation and critical-point methods for β\beta-functions at large NN

We investigate the connection between the bubble-resummation and critical-point methods for computing the $\beta$-functions in the limit of large number of flavours, $N$, and show that these can provide complementary information. While the methods are equivalent for single-coupling theories, for multi-coupling case the standard critical exponents are only sensitive to a combination of the independent pieces entering the $\beta$-functions, so that additional input or direct computation are needed to decipher this missing information. In particular, we evaluate the $\beta$-function for the quartic coupling in the Gross-Neveu-Yukawa model, thereby completing the full system at $\mathcal{O}(1/N)$. The corresponding critical exponents would imply a shrinking radius of convergence when $\mathcal{O}(1/N^2)$ terms are included, but our present result shows that the new singularity is actually present already at $\mathcal{O}(1/N)$, when the full system of $\beta$-functions is known.Comment: 11 pages, 7 figures; v2: references added, matches the published versio

Elementary Goldstone Higgs Boson and Dark Matter

We investigate a perturbative extension of the Standard Model featuring elementary pseudo-Goldstone Higgs and dark matter particles. These are two of the five Goldstone bosons parametrising the SU(4)/Sp(4) coset space. They acquire masses, and therefore become pseudo-Goldstone bosons, due to the embedding of the Yukawa and the electroweak gauge interactions that do not preserve the full SU(4) symmetry. At the one-loop order the top corrections dominate and align the vacuum in the direction where the Higgs is mostly a pseudo-Goldstone boson. Because of the perturbative and elementary nature of the theory, the quantum corrections are precisely calculable. The remaining pseudo-Goldstone boson is identified with the dark matter candidate because it is neutral with respect to the Standard Model and stable. By a direct comparison with the Large Hadron Collider experiments, the model is found to be phenomenologically viable. Furthermore the dark matter particle leads to the observed thermal relic density while respecting the most stringent current experimental constraints.Comment: 26 pages, 6 figures. Revised version to match the published on

A partially composite Goldstone Higgs

We consider a model of dynamical electroweak symmetry breaking with a partially composite Goldstone Higgs. The model is based on a strongly-interacting fermionic sector coupled to a fundamental scalar sector via Yukawa interactions. The SU(4) x SU(4) global symmetry of these two sectors is broken to a single SU(4) via Yukawa interactions. Electroweak symmetry breaking is dynamically induced by condensation due to the strong interactions in the new fermionic sector which further breaks the global symmetry SU(4) to Sp(4). The Higgs boson arises as a partially composite state which is an exact Goldstone boson in the limit where SM interactions are turned off. Terms breaking the SU(4) global symmetry explicitly generate a mass for the Goldstone Higgs. The model realizes in different limits both (partially) composite Higgs and (bosonic) Technicolor models, thereby providing a convenient unified framework for phenomenological studies of composite dynamics. It is also a dynamical extension of the recent elementary Goldstone-Higgs model.Comment: 7 pages, 7 figure