Francesco Sannino

Motivated by the 1/Nc expansion, we present a simple model of pipi scattering as a sum of a current-algebra contact term and resonant pole exchanges. The model preserves crossing symmetry as well as unitarity up to 1.2 GeV. Key features include chiral dynamics, vector meson dominance, a broad low energy scalar (sigma) meson, and a Ramsauer-Townsend mechanism for the understanding of the 980 MeV region. We discuss in detail the regularization (corresponding to rescattering effects) necessary to make all these nice features work.

We study phenomenological constraints in a simple $S\bar{E} \chi$y extension of the Standard Model (SM) with a 125 GeV Higgs, a vector-like heavy electron $(E)$, a complex scalar electron $(S)$ and a standard model singlet Dirac fermion $(\chi)$. The interactions among the dark matter candidate $\chi$ and the standard model particles occur via loop-induced processes involving the Yukawa interaction $S\bar{E} \chi$y. The model is an explicit perturbative realization of so-called magnetic dark matter. The field content allows for a cancelation of quadratic divergences in the scalar masses at one-loop, a phenomenon which we refer to as perturbative naturality. The basic model is constrained dominantly by direct detection experiments and its parameter space can be nearly entirely covered by up-coming ton-scale direct detection experiments. We conclude this work by discussing different variations of the model.

We investigate the vacuum stability as well as the gravitational corrections in extensions of the Standard Model featuring a new complex scalar, and two Dirac fermions for different choices of the hypercharge of the scalar and one of the two fermions. The neutral fermion acquires loop-induced magnetic interactions with the Standard Model and could be identified with a dark matter candidate. To the lowest order in perturbation theory we show that these extensions can save the electroweak vacuum from being metastable. We then add the gravitational corrections to the different beta functions and discover that the models can be compatible with the asymptotically safe gravity scenario at the price of a heavier Higgs and lighter top mass.

Motivated by the 1/Nc expansion, we study a simple model in which the πK scattering amplitude is the sum of a current-algebra contact term and resonance pole exchanges. This phenomenological model is crossing symmetric and, when a putative light strange scalar meson κ is included, satisfies the unitarity bounds to well above 1 GeV. The model also features chiral dynamics, vector meson dominance and appropriate interference between the established K*0(1430) resonance and its predicted background. We briefly discuss the physical significance of the results and directions for further work.

We introduce a perturbative extension of the standard model featuring a new dark matter sector together with a 125 GeV Higgs. The new sector consists of a vector-like heavy electron E, a complex scalar electron S and a standard model singlet Dirac fermion \chi. The interactions among the dark matter candidate \chi and the standard model particles occur via loop-induced processes involving the operator SE\chi y, with y being the Yukawa-like coupling. The model is an explicit underlying realization of the light magnetic dark matter effective model introduced earlier to alleviate the tension among several direct dark matter search experiments. We further constrain the parameters of the underlying theory using results from the Large Hadron Collider. The extension can accommodate the recently observed properties of the Higgs-like state and leads to interesting predictions. Finally we show that the model's collider phenomenology and constraints nicely complement the ones coming from dark matter searches.

We summarize basic features associated to dynamical breaking of the electroweak symmetry. The knowledge of the phase diagram of strongly coupled theories as function of the number of colors, flavors and matter representation plays a fundamental role when trying to construct viable extensions of the standard model (SM). Therefore we will report on the status of the phase diagram for SU(N) gauge theories with fermionic matter transforming according to arbitrary representations of the underlying gauge group. We will discuss how the phase diagram can be used to construct unparticle models. We will then review Minimal Walking Technicolor (MWT) and other extensions, such as partially gauged and split technicolor. MWT is a sufficiently general, symmetry wise, model to be considered as a benchmark for any model aiming at breaking the electroweak symmetry dynamically. The unification of the standard model gauge couplings will be revisited within technicolor extensions of the SM. A number of appendices are added to review some basic methods and to provide useful details. In one of the appendices we will show how to gain information on the spectrum of strongly coupled theories relevant for new extensions of the SM by introducing and using alternative large N limits.

We explore the paradigm according to which inflation is driven by a four-dimensional strongly coupled dynamics coupled non-minimally to gravity. We start by introducing the general setup, both in the metric and Palatini formulation, for generic models of composite inflation. We then analyze the relevant example where the inflaton is identified with the glueball field of a pure Yang-Mills theory. We introduce the dilatonic-like glueball action which is obtained by requiring saturation of the underlying Yang-Mills trace anomaly at the effective action level. We couple the resulting action non-minimally to gravity. We demonstrate that it is possible to achieve successful inflation with the confining scale of the underlying Yang-Mills theory naturally of the order of the grand unified energy scale. We also argue that within the metric formulation models of composite inflation lead to a more consistent picture than within the Palatini one. Finally we show that, in the metric formulation, the model nicely respects tree-level unitarity for the scattering of the inflaton field all the way to the Planck scale.

We unveil the temperature-dependent electroweak phase transition in new extensions of the standard model in which the electroweak symmetry is spontaneously broken via strongly coupled, nearly conformal dynamics achieved by the means of multiple matter representations. In particular, we focus on the low energy effective theory introduced to describe ultra minimal walking technicolor at the phase transition. Using the one-loop effective potential with ring improvement, we identify regions of parameter space, which yield a strong first-order transition. A striking feature of the model is the existence of a second phase transition associated to the electroweak-singlet sector. The interplay between these two transitions leads to an extremely rich phase diagram.

We investigate models in which inflation is driven by an ultraviolet safe and interacting scalar sector stemming from a new class of nonsupersymmetric gauge field theories. These new theories, differently from generic scalar models, are well defined to arbitrary short distances because of the existence of a controllable ultraviolet interacting fixed point. The scalar couplings at the ultraviolet fixed point and their overall running are predicted by the geometric structure of the underlying theory. We analyse the minimal and non-minimal coupling to gravity of these theories and the consequences for inflation. In the minimal coupling case the theory requires large non-perturbative quantum corrections to the quantum potential for the theory to agree with data, while in the non- minimal coupling case the perturbative regime in the couplings of the theory is preferred. Requiring the theory to reproduce the observed amplitude of density perturbations constrain the geometric data of the theory such as the number of colors and flavors for generic values of the non-minimal coupling.

In the large Nc approximation to QCD, the leading ππ scattering amplitude is expressed as the sum of an infinite number of tree diagrams. We investigate the possibility that an adequate approximation at energies up to somewhat more than 1 GeV can be made by keeping diagrams which involve the exchange of resonances in this energy range in addition to the simplest chiral contact terms. In this approach crossing symmetry is automatic but individual terms tend to drastically violate partial wave unitarity. We first note that the introduction of the ρ meson in a chirally invariant manner substantially delays the onset of drastic unitarity violation which would be present for the current algebra term alone. This suggests a possibility of local (in energy) cancellation which we then explore in a phenomenological way. We include exchanges of leading resonances up to the 1.3 GeV region. However, unitarity requires more structure which we model by a four derivative contact term or by a low-lying scalar resonance which is presumably subleading in the 1/Nc expansion, but may nevertheless be important. The latter two flavor model gives a reasonable description of the phase shift δ00 up until around 860 MeV, before the effects associated with the KK¯ threshold come into play.

We unveil the general features of the phase diagram for any gauge theory with fermions transforming according to distinct representations of the underlying gauge group, at the four-loop order. We classify and analyze the zeros of the perturbative beta function and discover the existence of a rich phase diagram. The anomalous dimension of the fermion masses, at the infrared stable fixed point, are presented. We show that the infrared fixed point, and associated anomalous dimension, are well described by the all-orders beta function for any theory. We also argue the possible existence, to all orders, of a nontrivial ultraviolet fixed point for gauge theories at large number of flavors.

The ’t Hooft and Corrigan-Ramond limits of massless one-flavor QCD consider the two Weyl fermions to be, respectively, in the fundamental representation and the two index antisymmetric representation of the gauge group. We introduce a limit in which one of the two Weyl fermions is in the fundamental representation and the other in the two index antisymmetric representation of a generic SU(N) gauge group. This theory is chiral and to avoid gauge anomalies a more involved chiral theory is needed. This is the generalized Georgi-Glashow model with one vectorlike fermion. We show that there is an interesting phase in which the considered chiral gauge theory, for any N, Higgses via a bilinear condensate: The gauge interactions break spontaneously to ordinary massless one-flavor SU(3) QCD. The additional elementary fermionic matter is uncharged under this SU(3) gauge theory. It is also seen that when the number of colors reduce to three it is exactly this hidden QCD which is revealed.

We study the meson spectrum of the SU(2) gauge theory with two Wilson fermions in the fundamental representation. The theory unifies both Technicolor and composite Goldstone Boson Higgs models of electroweak symmetry breaking. We have calculated the masses of the lightest spin one vector and axial vector mesons. In addition, we have also obtained preliminary results for the mass of the lightest scalar (singlet) meson state. The simulations have been done with multiple masses and two different lattice spacings for chiral and continuum extrapolations. The spin one meson masses set lower limits for accelerator experiments, whereas the scalar meson will mix with a pGB of the theory and produce two scalar states. The lighter of the states is the 125 GeV Higgs boson, and the heavier would be a new yet unobserved scalar state.

We relate the asymmetries in the charged pions energy in the decay into π+π-π0 of K L and of the tagged neutral kaons. The former asymmetry is a given combination ofRe (\varepsilon ), Im (\varepsilon ), and üɛ'ü. Moreover, the non-violating CP asymmetry allows a test for theχ PT predictions within the Zel'dovich approach for the final state interaction.

We investigate the physical spectrum of vector-like SU(N) gauge theories with infrared coupling close to but above the critical value for a conformal phase transition. We use dispersion relations, the momentum dependence of the dynamical fermion mass and resonance saturation. We argue that the second spectral function sum rule is substantially affected by the continuum contribution, allowing for a reduction of the axial-vector-vector mass splitting with respect to QCD-like theories. Possible consequences for technicolor theories are described.

We investigate generic properties of the conformal phase transition in gauge theories featuring Higgs-like fundamental particles. These theories provide an excellent arena to properly investigate conformal dynamics and discover novel features. We show that the phase transition at the boundary of the Higgs conformal window is not smooth but a jumping one for the known perturbative examples. In addition the general conditions under which the transition is either jumping or smooth are provided. Jumping implies that the massive spectrum of the theory will jump at the phase transition. It, however, still allows for one of the states, the would be dilaton of the theory, to be lighter than the heaviest states in the broken phase. Finally we exhibit a calculable Higgs model in which we can, in perturbation theory, determine the Higgs conformal window, the spectrum in the conformally broken phase and demonstrate it to possess a jumping type conformal phase transition.

Motivated by the 1/Nc expansion, we present a simple model of pion-pion scattering as a sum of a `current-algebra' contact term and resonant pole exchanges. The model preserves crossing symmetry as well as unitarity up to 1.2 GeV. Key features include chiral dynamics, vector meson dominance, a broad low energy scalar (sigma) meson and a `Ramsauer-Townsend' mechanism for the understanding of the 980 MeV region. We discuss in detail the `regularization' (corresponding to rescattering effects) necessary to make all these nice features work.

The purpose of the Workshop is to have intensive discussions on both theoretical and phenomenological aspects of strong coupling gauge theories (SCGTs), with particular emphasis on the model buildings to be tested in the LHC experiments. Dynamical issues are discussed in lattice simulations and various analytical methods. This proceedings volume is a collection of the presentations made at the Workshop by many leading scientists in the field.