Aiming at a systematic inclusion of pseudoscalar and vector mesons as active degrees of freedom in an effective Lagrangian, studies have been performed in this thesis concerning the foundations of such an effective Lagrangian as well as tree-level and beyond-tree-level calculations. Hereby, vector mesons are described by antisymmetric tensor fields. First, an existing power counting scheme for both pseudoscalar and vector mesons is extended to include the pseudoscalar-meson singlet in a systematic way. Based on this, tree-level calculations are carried out which are in good agreement with the available experimental data and several processes are predicted. In particular, the ω-π0 transition form factor is in better agreement with experimental data than the prediction done in the vector-meson-dominance model. Furthermore, a Lagrangian with vector mesons is used together with the leading contributions of chiral perturbation theory in order to calculate tree-level reactions in the sector of odd intrinsic parity. It turns out that both the Lagrangian with vector mesons and the Lagrangian of chiral perturbation theory are needed to describe experimental data. Additionally, a feasibility check for one-loop calculations with pseudoscalar and vector mesons in the loop is performed. Thereby, only a limited number of interaction terms in the Lagrangian with vector mesons is used. The results are used to both renormalise the low-energy constants of chiral perturbation theory up to chiral order Q4 and to determine the influence of loops with vector mesons on masses and decay constants of pseudoscalar mesons.

Com os próximos grandes projetos the observação do Universo, a cosmologia entrará em uma era de alta precisão de medidas. Novos dados trarão um novo entendimento da evolução do Universo, seus principais componentes e do comportamento da gravi- dade. Sendo assim, é fundamental também ter uma boa predição teórica para a formação de estrutura de larga escala em regime não-linear. A melhor maneira de resolver as equações hidrodinâmicas que descrevem o nosso universo é por meio de simulações cosmológicas na rede. Entretando, estas contém desafios, como a correta inclusão de física bariônica e a diminuição do alto tempo computacional. Uma outra abordagem muito usada é o cálculo das funções de cor- relação por meio de métodos perturbativos (em inglês, Standard Perturbation Theory, ou SPT). Entretanto, esta contém problemas variados: pode não convergir para algu- mas cosmologias e, caso convirja, não há certeza de convergência para o resultado correto. Além disso, há uma escala privilegiada nos limites integrais que envolvem o método perturbativo. Nós calculamos o resultado por esse método até terceira ordem e mostramos que o termo de terceira ordem é ainda maior que o de 2-loops e 3-loops. Isso evidencia alguns problemas descritos com o método perturbativo. O método de Teorias Efetivas de Campo aplicado ao estudo de LSS busca corrigir os problemas da SPT e, desta forma, complementar os resultados de simulações na rede. Em outras áreas da física, como a Cromodinâmica Quântica de baixas energias, EFTs também são usadas como um complemento a essas simulações na rede. EFTs melhoram a predição do espectro de potência da matéria por meio da inclusão dos chamados contra-termos, que precisam ser fitados em simulações. Estes contratermos, que são parâmetros livres, contém importante informação sobre como a física em pequenas escalas afeta a física nas escalas de interesse. Explicaremos os resultados para a predição em 3-loops de EFT, trabalho inédito. É possível usar as EFTs também no problema de conectar a campo de matéria com outros traçadores, como os halos e as galáxias, chamado de bias. Com as EFTs podemos construir uma base completa de operadores para parametrizar o bias. Será explicado como utilizar esses operadores para melhorar a predição do bias em escalas não-lineares. Serão calculados esses termos de EFT em simulações. Também será mostrado como renormalizar o bias em coordenadas de Lagrange. Por fim, será explicada outra importante aplicação das EFTs em cosmologia, mais especificamente em teorias de inflação. EFTs parametrizam desvios nas teorias de um campo único no chamado regime de slow-roll. / With future cosmological surveys, cosmology will enter in the precision era. New data will improve the constraints on the standard cosmological model enhancing our knowledge about the universe history, its components and the behavior of gravity. In this context, it is vital to come up with precise theoretical predictions for the formation of large-scale structure beyond the linear regime. The best way of solving the fluid equations that describe the large-scale universe is through lattice simulations, which faces difficulties in the inclusion of accurate baryonic physics and is very computationally costly. Another approach is the theoreti- cal calculation of the correlation statistics through the perturbative approach, called Standard Perturbation Theory (SPT). However, SPT has several problems: for some cosmologies, it may not converge and even when it converges, we cannot be sure it converges to the right result. Also, it contains a special scale that is the loop momenta upper-bound in the integral. In this work, we show results for the 3-loop calculation. The term of third order is larger than the terms of 2-loops and 3-loops, making explicit SPT problems. In this work, we describe the recent usage of Effective Field Theories (EFTs) on Large Scale Structure problems to correct SPT issues and complement cosmological simulations. EFTs are used in other areas of physics, such as low energy QCD, serving as a complement to lattice calculations. EFT improves the predictions for the matter power spectrum and bispectrum by adding counterterms that need to be fitted. The free parameters, instead of being a problem, bring relevant information about how the small-scale physics affects the scales for which we are trying to make statistical predictions. We show the calculation of the 3-loop EFT counterterms. EFTs are also used to explain main points connecting the matter density field with tracers like galaxies and halos. EFTs highlighted how to construct a complete basis of operators that parametrize the bias. We explain how we can use EFT to improve the bias prediction to non-linear scales. We compute the non-linear halo-bias by fitting the bias parameters in simulations. We also show the EFT renormalization in Lagrangian coordinates. Finally, we explain another critical EFT application to cosmology: in primordial physics. It can be used to parametrize deviations to the slow-roll theory within the inflationary paradigm.

Název práce: Studium efektivních Lagrangianů a jejich aplikace Autor: Jaroslav Trnka Katedra: Ústav částicové a jaderné fyziky Vedoucí disertační práce: RNDr. Jiří Novotný, CSc., ÚČJF Abstrakt: V této práci studujeme různé aspekty efektivních teorií pole pro kvan- tovou chromodynamiku (QCD). V prvních dvou kapitolách se zaměříme na efek- tivní teorii pro resonance, která interpoluje mezi nízkoenergetickou efektivní teorií (Chirální poruchová teorie) a vysokoenergetickou QCD. V rámci této teorie studu- jeme jednosmyčkovou renormalizaci, jak z pohledu výpočetního pomocí SS-PP korelátoru, tak i čistě koncepčního studiem dynamicky generovaných stupňů vol- nosti. Ve čtvrté kapitole studujeme amplitudy rozptylu v rámci nelineárního sig- ma modelu, který představuje vedoucí člen nízkoenergetické efektivní teorie pro QCD. V návaznosti na nedávné objevy v rámci Yang-Mills teorie se nám podaří v rámci tohoto modelu zkonstruovat rekurzivní relace pro stromové amplitudy. Kromě čistě teoretické důležitosti tohoto faktu představuje tato metoda efektivní výpočetní nástroj nezávislý na formulaci amplitud pomocí Feynmanovských dia- gramů. Klíčová slova: efektivní teorie pole, kvantová chromodynamika, nelineární sigma model...

Com os próximos grandes projetos the observação do Universo, a cosmologia entrará em uma era de alta precisão de medidas. Novos dados trarão um novo entendimento da evolução do Universo, seus principais componentes e do comportamento da gravi- dade. Sendo assim, é fundamental também ter uma boa predição teórica para a formação de estrutura de larga escala em regime não-linear. A melhor maneira de resolver as equações hidrodinâmicas que descrevem o nosso universo é por meio de simulações cosmológicas na rede. Entretando, estas contém desafios, como a correta inclusão de física bariônica e a diminuição do alto tempo computacional. Uma outra abordagem muito usada é o cálculo das funções de cor- relação por meio de métodos perturbativos (em inglês, Standard Perturbation Theory, ou SPT). Entretanto, esta contém problemas variados: pode não convergir para algu- mas cosmologias e, caso convirja, não há certeza de convergência para o resultado correto. Além disso, há uma escala privilegiada nos limites integrais que envolvem o método perturbativo. Nós calculamos o resultado por esse método até terceira ordem e mostramos que o termo de terceira ordem é ainda maior que o de 2-loops e 3-loops. Isso evidencia alguns problemas descritos com o método perturbativo. O método de Teorias Efetivas de Campo aplicado ao estudo de LSS busca corrigir os problemas da SPT e, desta forma, complementar os resultados de simulações na rede. Em outras áreas da física, como a Cromodinâmica Quântica de baixas energias, EFTs também são usadas como um complemento a essas simulações na rede. EFTs melhoram a predição do espectro de potência da matéria por meio da inclusão dos chamados contra-termos, que precisam ser fitados em simulações. Estes contratermos, que são parâmetros livres, contém importante informação sobre como a física em pequenas escalas afeta a física nas escalas de interesse. Explicaremos os resultados para a predição em 3-loops de EFT, trabalho inédito. É possível usar as EFTs também no problema de conectar a campo de matéria com outros traçadores, como os halos e as galáxias, chamado de bias. Com as EFTs podemos construir uma base completa de operadores para parametrizar o bias. Será explicado como utilizar esses operadores para melhorar a predição do bias em escalas não-lineares. Serão calculados esses termos de EFT em simulações. Também será mostrado como renormalizar o bias em coordenadas de Lagrange. Por fim, será explicada outra importante aplicação das EFTs em cosmologia, mais especificamente em teorias de inflação. EFTs parametrizam desvios nas teorias de um campo único no chamado regime de slow-roll. / With future cosmological surveys, cosmology will enter in the precision era. New data will improve the constraints on the standard cosmological model enhancing our knowledge about the universe history, its components and the behavior of gravity. In this context, it is vital to come up with precise theoretical predictions for the formation of large-scale structure beyond the linear regime. The best way of solving the fluid equations that describe the large-scale universe is through lattice simulations, which faces difficulties in the inclusion of accurate baryonic physics and is very computationally costly. Another approach is the theoreti- cal calculation of the correlation statistics through the perturbative approach, called Standard Perturbation Theory (SPT). However, SPT has several problems: for some cosmologies, it may not converge and even when it converges, we cannot be sure it converges to the right result. Also, it contains a special scale that is the loop momenta upper-bound in the integral. In this work, we show results for the 3-loop calculation. The term of third order is larger than the terms of 2-loops and 3-loops, making explicit SPT problems. In this work, we describe the recent usage of Effective Field Theories (EFTs) on Large Scale Structure problems to correct SPT issues and complement cosmological simulations. EFTs are used in other areas of physics, such as low energy QCD, serving as a complement to lattice calculations. EFT improves the predictions for the matter power spectrum and bispectrum by adding counterterms that need to be fitted. The free parameters, instead of being a problem, bring relevant information about how the small-scale physics affects the scales for which we are trying to make statistical predictions. We show the calculation of the 3-loop EFT counterterms. EFTs are also used to explain main points connecting the matter density field with tracers like galaxies and halos. EFTs highlighted how to construct a complete basis of operators that parametrize the bias. We explain how we can use EFT to improve the bias prediction to non-linear scales. We compute the non-linear halo-bias by fitting the bias parameters in simulations. We also show the EFT renormalization in Lagrangian coordinates. Finally, we explain another critical EFT application to cosmology: in primordial physics. It can be used to parametrize deviations to the slow-roll theory within the inflationary paradigm.

The Swampland program is way of sorting effective field theories based on conjectures of how an effective field theory consistent with quantum gravity should look like. In this thesis we take a closer look at the No Global Symmetries Conjecture, the Weak Gravity Conjecture, the de Sitter Conjecture and the Trans-Planckian Censorship Conjecture. The Weak Gravity Conjecture generalized to arbitrary dimensions and p-forms is tested under dimensional reduction and its sharpened version is used to discuss how under this conjecture non-supersymmetric AdS geometries are unstable. The de Sitter Conjecture and the Trans-Planckian Censorship Conjecture are compared to show that they give similar predictions based on different assumptions. Lastly we provide an example of a theory emerging from the swampland that utilizes the instability of AdS geometries to model our universe as the boundary of a higher dimensional expanding bubble. / Swampland-programmet är ett sätt att sortera effektiva fältteorier baserat på antaganden om hur en effektiv fältteori förenlig med kvantgravitation bör se ut. I den här avhandlingen tittar vi närmare på No Global Symmetries-antagandet, Weak Gravity-antagandet, de Sitter-antagandet och Trans-Planckian Censorship-antagandet. Weak gravity-antagandet generaliserat till godtyckliga dimensioner och p-former testas under dimensionsreduktion och dess skärpta version används för att diskutera hur man via detta antagande finner en instabilitet i icke-supersymmetriska AdS-geometrier. De sitter-antagandet och Trans-Planckian Censorship-antagandet jämförs för att visa att de ger liknande förutsägelser baserat på olika frågeställningar. Slutligen ger vi ett exempel på en teori som växer fram ur programmet som använder instabiliteten hos AdS-geometrier genom att modellera vårt universum som randen på en expanderande bubbla i högre dimensioner.

The vast majority of experiments in particle physics can be described by the Standard Model of particle physics (SM). However, there are indications for physics beyond it. The only experimentally demonstrated problem of the model is the difficulty to describe neutrino masses and leptonic mixing. There is a plethora of models that try to describe these phenomena and this thesis investigates several possibilities for new models, both full theories and effective frameworks.   The values of the parameters in a model are dependent on the energy scale and we say that the parameters run. The exact behavior of the running depends on the model and it provides a signature of the model. For a model defined at high energies it is necessary to run the parameters down to the electroweak scale in order to perform a comparison to the known values of observed quantities. In this thesis, we discuss renormalization group running in the context of extra dimensions and we provide an upper limit on the cutoff scale. We perform renormalization group running in two versions of a non-supersymmetric SO(10) model and we show that the SM parameters can be accommodated in both versions. In addition, we perform the running for the gauge couplings in a large set of radiative neutrino mass models and conclude that unification is possible in some of them.   The Higgs boson provides new possibilities to study physics beyond the SM. Its properties have to be tested with extremely high precision before it could be established whether the particle is truly the SM Higgs boson or not. In this thesis, we perform Bayesian parameter inference and model comparison. For models where the magnitude of the Higgs couplings is varied, we show that the SM is favored in comparison to all other models. Furthermore, we discuss lepton flavor violating processes in the context of the Zee model. We find that these can be sizeable and close to the experimental limits. / <p>QC 20170221</p>

Die am LHC gewonnen Ergebnisse stimmen überwiegend mit den Vorhersagen des Standardmodells der Teilchenphysik (SM) überein, doch die Notwendigkeit von Physik jenseits des Standardmodells (BSM) bleibt. Allerdings führt kein klarer Weg zu einem Nachfolger des Standardmodells. In dieser Arbeit wird daher ein allgemeines theoretisches Werkzeug für die Erforschung der Grenzen des SM verwendet: die Effektiven Feldtheorien (EFTs). In dieser Arbeit wird die Standard Model Effective Field Theory (SMEFT) benutzt, um das Potential des zukünftigen Hadronenbeschleunigers FCC-hh zu beurteilen. Hierfür wird der Vh-Produktionsprozess untersucht. Die Sensitivität dieser Kanäle wird durch die Messung von doppelt differenziellen Wirkungsquerschnitten möglich. Die Abwesenheit von Eich-Anomalien ist nötig, um die Konsistenz einer Quantenfeldtheorie zu bewahren. Es wird gezeigt, dass die SMEFT bis zur Massendimension 6 für beliebige Werte seiner WCs frei von aus Dreiecks-Anomalien stammenden Eich-Anomalien ist. Die bosonischen EFT-Techniken werden auch benutzt, um die Beziehung zwischen gemischten globalen Eich-Anomalien und Axion-Kopplungen zu Vektorbosonen in Axion-EFTs zu analysieren. Es ergibt sich, dass diese in keiner Beziehung zueinander stehen, wenn schwere chirale Fermionen ausintegriert werden. Dieser Fakt verknüpft Axion-EFTs mit chiralen Erweiterungen des Standardmodells. Für nichtabelsche Eichbosonen werden IR-Summenregeln gefunden, deren Verletzung die Anwesenheit chiraler Felder im UV-Bereich anzeigen. Es wird eine minimale Erweiterung des Standardmodells als Beispiel studiert. Letztlich wird gezeigt, wie alte Formalismen zu neuen Einsichten führen können. Helizitäts-Spinoren und Streuamplituden werden eingeführt und es wird diskutiert, wie sie die Berechnung der Amplituden erleichtern und inwiefern sie eine Alternative zu EFTs darstellen. Die VVh- und VVhh-Amplituden werden studiert und ihre Hoch-Energie-Grenzwerte einschließlich verschiedener BSM-Beiträge berechnet. / The results obtained at the LHC agree well with the predictions of the Standard Model of particle physics (SM). However, the need for Beyond the Standard Model (BSM) physics remains. But there is no clear path towards a successor for the SM. Hence, we must prepare the tools needed to explore the frontiers of physics thoroughly. In this work, we study one of the main theoretical tools that can be used for such an exploration, Effective Field Theories (EFTs). We use the Standard Model Effective Field Theory (SMEFT) to study the Vh production process at FCC-hh, assessing the discovery potential of that future collider. The sensitivity to BSM effects is improved via the measurement of doubly-differential cross-sections. We also study the relation between EFTs and anomalies. The absence of gauge anomalies is required to preserve the consistency of a Quantum Field Theory. We prove that SMEFT at dimension 6 is free from gauge anomalies coming from triangle diagrams for any value of its WCs. Then, we analyse the relationship in axion EFTs between mixed global-gauge anomalies and axion couplings to vector bosons. They turn out to be unrelated when heavy chiral fermions are integrated out, linking axion EFTs to chiral extensions of the SM. We find IR sum rules whose violation indicate the presence of chiral fields in the UV. We show and study a minimal phenomenologically relevant model as an example. Finally, we explore how revisiting old formalisms can lead to new insights. We introduce the helicity spinor and scattering amplitudes formalisms and show how they facilitate the computation of cross sections and discuss how they constitute an alternative to EFTs as a parametrisation of BSM effects. We study the VVh and VVhh amplitudes, of which we compute the high-energy limit including different BSM contributions.

Submitted by Biblioteca do Instituto de Física (bif@ndc.uff.br) on 2017-03-07T18:35:27Z No. of bitstreams: 1 TESE.pdf: 797081 bytes, checksum: 36b77c687969ac7b12aeef2589d1d766 (MD5) / Made available in DSpace on 2017-03-07T18:35:27Z (GMT). No. of bitstreams: 1 TESE.pdf: 797081 bytes, checksum: 36b77c687969ac7b12aeef2589d1d766 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Conselho Nacional de Desenvolvimento Científico e Tecnológico / Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro / O confinamento de quarks e glúons continua sendo um dos maiores problemas da Física atual, mesmo depois de passados 50 anos da criação da cromodinâmica quântica. Existem diversas abordagens que procuram uma explicação para este comportamento. Um destes cenários consiste na supercondutividade dual, proposta por G. t’Hooft em 1978. Aqui, ele discute como a condensação de objetos cromomagnéticos poderia originar um potencial linear entre cargas cromoelétricas. Este mecanismo é um dos mais aceitos atualmente e nos dirige à algumas perguntas cruciais: como estes objetos poderiam se tornar relevantes em teorias de Yang-Mills puras? quais os tipos de objetos que devemos levar em consideração para gerar as propriedades do potencial confinante? Embora a primeira pergunta seja difícil de responder, a segunda pode ser atacada por técnicas diferentes, suportadas pelas descrições na rede e por descrições efetivas de ensembles 1. Nesta tese, me dedico a estudar uma classe de objetos que s˜ao bons candidatos a resolverem a segunda questão: monopólos e vórtices de centro. Quando estamos lidando com as teorias de Yang-Mills puras SU(N), o problema consiste que, em nível clássico, estes defeitos são singulares. Porém, recebendo suporte da rede (nosso laboratório em teoria quântica de campos), podemos imaginar que, devido a flutuações quânticas do vácuo, estes objetos poderiam adquirir algumas propriedades dimensionais, como tensão,rigidez e interações que ajudariam a caracterizar o ensemble magnético nos levando a descrições de campos efetivas, que podem ser utilizadas para extrair a corda elétrica confinante. Utilizando técnicas oriundas da física de polímeros obtivemos equações de difusão que representam objetos unidimensionais, como vórtices de centro em 3D ou monopólos em 4D. O surgimento de uma derivada covariante abeliana, no caso do ensemble de vórtices de centro e instantons correlacionados em 3D, e de uma derivada covariante não abeliana, no caso do ensemble de monopólos coloridos em 4D, foi fundamental paragerar os modelos efetivos correspondentes. Acreditamos que estas equações de difusão poderão ser úteis, no futuro, para relacionar as propriedades do potencial entre quarks e aquelas de seus possíveis ensembles correspondentes. / Nowadays, quark and gluon confinement continues to be one of the most important problems in Physics. It remains unsolved, although 50 years have passed since the foundations of quantum chromodynamics. There are various approaches aimed at explaining this behaviour. One of them is the dual superconductor scenario proposed by G. t’Hooft in 1978. The general idea is that the condensation of chromomagnetics objects could originate a linear potential between chromoelectric charges. This is a promising mechanism that posses some crucial questions: how could these objects be relevant in pure YangMills? what type of object would be needed in order to generate the properties of the confining potential? While the first question is very difficult, the second one can be approached by different techniques, guided by the lattice and effective ensemble descriptions. In this thesis, I’ve been working on some good candidates to solve the second question: monopoles and center vortices. When dealing with pure SU(N) Yang-Mills theory, the problem is that at the classical level these magnetic defects are singular. Nevertheless, supported by the lattice (our laboratory in quantum field theory), we can imagine that, due to quantum vacuum fluctuations, they could acquire dimensionful properties. The tension, stiffness, as well as possible interactions that characterize the magnetic ensemble lead to effective field descriptions, that could be used to extract the corresponding confining electric string. Based on techniques borrowed from the physics of polymers, we obtained diffusion equations that describe magnetic one-dimensional objects, such as center vortices in 3D and monopoles in 4D. The appearance of an Abelian covariant derivative, for an ensemble of chains in 3D, and a non Abelian one, in the case of coloured loops in 4D, was essential to generate the corresponding effective descriptions. We believe that these diffusion equations could be helpful in the future, to relate the properties of the interquark potential and those of the possible underlying ensembles.

Après une introduction générale, ce manuscrit contient deux chapitres préliminaires, l'un décrivant le contexte physique et l'autre les techniques mathématiques utilisées lors de cette thèse.Nous présentons ensuite les travaux développés au cours de cette thèse. Nous commençons par l'extraction de la correction du couplage de Yukawa du quark bottom dans la théorie effective du boson de Higgs par un calcul de correspondance à deux boucles entre cette théorie effective et le modèle standard. Cette correction était la pièce manquante pour l'amélioration de la prédiction de la section efficace de production du boson de Higgs en association avec deux quarks bottom.Les deux chapitres suivants couvrent différents aspects du calcul de la correction au deuxième ordre de la section efficace de production d'un boson de Higgs par fusion de gluon dans la théorie effective du modèle standard. Nous présentons d'abord le calcul des corrections virtuelles de ce processus et exploitons la structure établie des divergences ultraviolettes à une boucle et des divergences infrarouges pour extraire un contre terme à deux boucles qui nous a permis de renormaliser l'amplitude, que nous avons ensuite prolongé analytiquement aux régions physiques.Nous combinons alors ce résultat avec le calcul automatique des corrections par émission réelles par le logiciel Madgraph5_aMC@NLO, qui a permis l'intégration de la section efficace. Nous présentons les résultats pour la section efficace totale et deux distributions de variables cinématiques et commentons l'impact des corrections radiatives sur ces prédictions / After a general introduction, this manuscript presents two preliminary chapters, describing first the physics context and the mathematical techniques used in this thesis.We then present the work performed in this thesis. We start with extraction of the power-suppressed of the Yukawa coupling of the bottom quark in the Higgs Effective Field Theory (HEFT) by a two-loop matching calculation between the Standard Model and the HEFT. This correction was the missing piece to improve the prediction of the production cross section of a Higgs boson in association to a pair of bottom quarks.The two next chapters present different aspects of the NLO corrections to Higgs boson production through gluon fusion in the standard model effective field theory. We first present the evaluation of the virtual corrections to this process and use the known one-loop ultraviolet and infrared divergence structure to extract a two-loop counterterm that allowed us to renormalize the amplitude, which we then analytically continued to the physical regions.We then combine this result with the automatic calculation of the real emission corrections in the program Madgraph5_aMC@NLO. The results are presented for the total cross section and differential distributions and comment on the effect of radiative corrections on these predictions

The F and G formfactors of Kl4 decays are calculated to O(p4 ) in isospin limit in Resummed Chiral Perturbation Theory. Formulae for reparametrization of low-energy constants L1 - L3 in terms of physical observables are derived. They are used to obtain values of these low-energy constants from recent experimental data, theoretical error of the result is estimated and dependence on parameters X, Z of spontaneous symmetry breaking of SU(3) × SU(3) chiral symmetry and quark mass ratio r is investigated. Convergence of the formfactors in Resummed Chiral Perturbation Theory is discussed and it is suggested that inclusion of σ as an explicit degree of freedom into Chiral Perturbation Theory could significantly improve overall covergence of chiral series. 1