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A bstract In composite Higgs models the Higgs is a pseudo-Goldstone boson of a high-energy strong dynamics. We have constructed the effective chiral Lagrangian for a generic symmetric coset, restricting to CP-even bosonic operators up to four momenta which turn out to depend on seven parameters, aside from kinetic terms. Once the same sources of custodial symmetry breaking as in the Standard Model are considered, the total number of operators in the basis increases up to ten, again aside from kinetic terms. Under these assumptions, we have then particularised the discussion to three distinct frameworks: the original SU(5)/SO(5) Georgi-Kaplan model, the minimal custodial-preserving SO(5)/SO(4) model and the minimal SU(3)/(SU(2) × U(1)) model, which intrinsically breaks custodial symmetry. The projection of the high-energy electroweak effective theory into the bosonic sector of the Standard Model is shown to match the low-energy chiral effective Lagrangian for a dynamical Higgs, and it uncovers strong relations between the operator coefficients. Finally, the relation with the bosonic basis of operators describing linear realisations of electroweak symmetry breaking is clarified.

Abstract We present a novel mechanism for realistic electroweak symmetry breaking in Twin Higgs/neutral naturalness models where the Z 2 exchange symmetry can remain exactly unbroken. The exchange symmetry in the Yukawa sector will be implemented as an “N-trigonometric parity” sin N h f ↔ cos N h f $$ \\sin N\\frac{h}{f}\\leftrightarrow \\cos N\\frac{h}{f} $$ . The Yukawa couplings will be suppressed leading to an N-suppressed Higgs quadratic term, without significantly affecting the quartic. We present a concrete implementation of this idea for general (odd) values of N using maximal symmetry, and a realistic benchmark model for N = 3. We find that the tuning in the resulting Higgs potential is negligible, and also show that two-loop N-suppression violating gauge contributions can be sufficiently small. The Higgs potential and its couplings in top sector are different from other neutral naturalness models, which are the main predictions of our model and can be tested in colliders.

A bstract The LHCb measurement of the μ/e ratio R K ∗ indicates a deficit with respect to the Standard Model prediction, supporting earlier hints of lepton universality violation observed in the R K ratio. We show that the R K and R K ∗ ratios alone constrain the chiralities of the states contributing to these anomalies, and we find deviations from the Standard Model at the 4 σ level. This conclusion is further corroborated by hints from the theoretically challenging b → sμ + μ − distributions. Theoretical interpretations in terms of Z ′, lepto-quarks, loop mediators, and composite dynamics are discussed. We highlight their distinctive features in terms of the chirality and flavour structures relevant to the observed anomalies.

Abstract The LHCb measurement of the μ/e ratio R K ∗ indicates a deficit with respect to the Standard Model prediction, supporting earlier hints of lepton universality violation observed in the R K ratio. We show that the R K and R K ∗ ratios alone constrain the chiralities of the states contributing to these anomalies, and we find deviations from the Standard Model at the 4σ level. This conclusion is further corroborated by hints from the theoretically challenging b → sμ + μ − distributions. Theoretical interpretations in terms of Z′, lepto-quarks, loop mediators, and composite dynamics are discussed. We highlight their distinctive features in terms of the chirality and flavour structures relevant to the observed anomalies.

A bstract We propose a four dimensional description of Composite Higgs Models which represents a complete framework for the physics of the Higgs as a pseudo-Nambu-Goldstone boson. Our setup captures all the relevant features of 5D models and more in general of composite Higgs models with partial compositeness. We focus on the minimal scenario where we include a single multiplet of resonances of the composite sector, as these will be the only degrees of freedom which might be accessible at the LHC. This turns out to be sufficient to compute the effective potential and derive phenomenological consequences of the theory. Moreover our simplified approach is well adapted to simulate these models at the LHC. We also consider the impact of non-minimal terms in the effective lagrangian which do not descend from a 5D theory and could be of phenomenological relevance, for example contributing to the S  − parameter.

A bstract We present a comprehensive study of the electroweak phase transition in composite Higgs models, where the Higgs arises from a new, strongly-coupled sector which confines near the TeV scale. This work extends our study in ref. [ 1 ]. We describe the confinement phase transition in terms of the dilaton, the pseudo-Nambu-Goldstone boson of broken conformal invariance of the composite Higgs sector. From the analysis of the joint Higgs-dilaton potential we conclude that in this scenario the electroweak phase transition can naturally be first-order, allowing for electroweak baryogenesis. We then extensively discuss possible options to generate a sufficient amount of CP violation — another key ingredient of baryogenesis — from quark Yukawa couplings which vary during the phase transition. For one such an option, with a varying charm quark Yukawa coupling, we perform a full numerical analysis of tunnelling in the Higgs-dilaton potential and determine regions of parameter space which allow for successful baryogenesis. This scenario singles out the light dilaton region while satisfying all experimental bounds. We discuss future tests. Our results bring new opportunities and strong motivations for electroweak baryogenesis.

A bstract I present a model addressing coherently the naturalness problem of the electroweak scale and the observed pattern of deviations from the Standard Model in semileptonic decays of B mesons. The Higgs and the two scalar leptoquarks responsible for the B -physics anomalies, S 1 = 3 ¯ , 1 , 1 / 3 and S 3 = 3 ¯ , 3 , 1 / 3 , arise as pseudo Nambu-Goldstone bosons of a new strongly coupled sector at the multi-TeV scale. I focus on an explicit realization of such a dynamics in terms of a new strongly coupled gauge interaction and extra vectorlike fermions charged under it. The model presents a very rich phenomenology, ranging from flavour observables, Higgs and electroweak precision measurements, and direct searches of new states at the LHC.

A bstract Dark Matter could be a composite state of a confining sector with an approximate scale symmetry. We consider the case where the associated pseudo-Goldstone boson, the dilaton, mediates its interactions with the Standard Model. When the confining phase transition in the early universe is supercooled, its dynamics allows for Dark Matter masses up to 10 6 TeV. We derive the precise parameter space compatible with all experimental constraints, finding that this scenario can be tested partly by telescopes and entirely by gravitational waves.

A bstract Strongly-coupled theories at the TeV can naturally drive a long period of supercooling in the early universe. Trapped into the deconfined phase, the universe could inflate and cool down till the temperature reaches the QCD strong scale. We show how at these low temperatures QCD effects are important and could trigger the exit from the long supercooling era. We also study the implications on relic abundances. In particular, the latent heat released at the end of supercooling could be the reason for the similarities between dark matter and baryon energy densities. The axion abundance could also be significantly affected, allowing for larger values of the axion decay constant. Finally, we discuss how a long supercooling epoch could lead to an enhanced gravitational wave signal.