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In this paper (second in the series) we study the properties of tree-level binary amplitudes of the infinite-component effective field theory of strong interaction obeying the requirements of quark-hadron duality and maximal analyticity. In contrast to the previous paper, here we derive the results following from less restrictive --- Regge-like --- boundedness conditions. We develop the technique of Cauchys forms in two variables and show the string-like structure of a theory. Next, we derive the full set of bootstrap constraints for the resonance parameters in (pi,K) system. Numerical test shows: (1) those constraints are consistent with data on well established vector resonances; (2) two light broad resonances -- sigma- and kappa-mesons -- are needed to saturate sum rules following from Chiral symmetry and analyticity. As a by-product we obtain expressions for the parameters of Chiral expansions and give corresponding estimates.
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Standard Model (SM) of particle physics has achieved enormous success in describing the interactions among the known fundamental constituents of nature, yet it fails to describe phenomena for which there is very strong experimental evidence, such as the existence of dark matter, and which point to the existence of new physics not included in that model; beyond its existence, experimental data, however, have not provided clear indications as to the nature of that new physics. The effective field theory (EFT) approach, the subject of this review, is designed for this type of situations; it provides a consistent and unbiased framework within which to study new physics effects whose existence is expected but whose detailed nature is known very imperfectly. We will provide a description of this approach together with a discussion of some of its basic theoretical aspects. We then consider applications to high-energy phenomenology and conclude with a discussion of the application of EFT techniques to the study of dark matter physics and it possible interactions with the SM. In several of the applications we also briefly discuss specific models that are ultraviolet complete and may realize the effects described by the EFT.
Dark mesons are bosonic composites of a new, strongly-coupled sector beyond the Standard Model. We consider several dark sectors with fermions that transform under the electroweak group, as arise from a variety of models including strongly-coupled theories of dark matter (e.g., stealth dark matter), bosonic technicolor (strongly-coupled indcued electroweak symmetry breaking), vector-like confinement, etc. We consider theories with two and four flavors under an $SU(N)$ strong group that acquire variously chiral, vector-like, and mixed contributions to their masses. We construct the non-linear sigma model describing the dark pions and match the ultraviolet theory onto a low energy effective theory that provides the leading interactions of the lightest dark pions with the Standard Model. We uncover two distinct classes of effective theories that are distinguishable by how the lightest dark pions decay: Gaugephilic: where $pi^0 rightarrow Z h$, $pi^pm rightarrow W h$ dominate once kinematically open, and Gaugephobic: where $pi^0 rightarrow bar{f} f$, $pi^pm rightarrow bar{f} f$ dominate. Custodial $SU(2)$ plays a critical role in determining the philic or phobic nature of a model. In dark sectors that preserve custodial $SU(2)$, there is no axial anomaly, and so the decay $pi^0 rightarrow gammagamma$ is highly suppressed. In a companion paper, we study dark pion production and decay at colliders, obtaining the constraints and sensitivity at the LHC.
We summarize our latest developments in perturbative treating the effective theories of strong interactions. We discuss the principles of constructing the mathematically correct expressions for the S-matrix elements at a given loop order and briefly review the renormalization procedure. This talk shall provide the philosophical basement as well as serve as an introduction for the material presented at this conference by A. Vereshagin and K. Semenov-Tian-Shansky.
There are indications that some theories with spontaneous symmetry breaking also feature a light scalar in their spectrum, with a mass comparable to the one of the Goldstone modes. In this paper, we perform the one-loop renormalization of a theory of Goldstone modes invariant under a chiral $SU(n)times SU(n)$ symmetry group coupled to a generic scalar singlet. We employ the background field method, together with the heat kernel expansion, to get an expression for the effective action at one loop and single out the anomalous dimensions, which can be read off from the second Seeley-DeWitt coefficient. As a relevant application, we use our master formula to renormalize chiral-scale perturbation theory, an alternative to $SU(3)$ chiral perturbation theory where the $f_0(500)$ meson is interpreted as a dilaton. Based on our results, we briefly discuss strategies to test and discern both effective field theories using lattice simulations.
We study effective theories of an axion in spontaneously broken supersymmetric theories. We consider a system where the axion supermultiplet is directly coupled to a supersymmetry breaking sector whereas the standard model sector is communicated with those sectors through loops of messenger fields. The gaugino masses and the axion-gluon coupling necessary for solving the strong CP problem are both obtained by the same effective interaction. We discuss cosmological constraints on this framework.
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