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The vision for 6G extends beyond mere communication, incorporating sensing capabilities to facilitate a diverse array of novel applications and services. However, the advent of joint communication and sensing (JCAS) technology introduces concerns regarding the handling of sensitive personally identifiable information (PII) pertaining to individuals and objects, along with external third-party data and disclosure. Consequently, JCAS-based applications are susceptible to privacy breaches, including location tracking, identity disclosure, profiling, and misuse of sensor data, raising significant implications under the European Union's general data protection regulation (GDPR) as well as other applicable standards. This paper critically examines emergent JCAS architectures and underscores the necessity for network functions to enable privacy-specific features in the 6G systems. We propose an enhanced JCAS architecture with additional network functions and interfaces, facilitating the management of sensing policies, consent information, and transparency guidelines, alongside the integration of sensing-specific functions and storage for sensing processing sessions. Furthermore, we conduct a comprehensive threat analysis for all interfaces, employing security threat model STRIDE and privacy threat model LINDDUN. We also summarise the identified threats using standard common weakness enumeration (CWE). Finally, we suggest the security and privacy controls as the mitigating strategies to counter the identified threats stemming from the JCAS architecture.

In this letter, we discuss a generalization of the Adler zero to loop integrands in the planar limit of the $SU(N)$ non-linear sigma model (NLSM). While possible to maintain at one-loop, the Adler zero for integrands is violated starting at the two-loop order and is only recovered after integration. Here we propose a non-zero soft theorem satisfied by loop integrands with any number of loops and legs. This requires a generalization of NLSM integrands to an off-shell framework with certain deformed kinematics. Defining an `algebraic soft limit', we identify a particularly simple non-vanishing soft behavior of integrands, which we call the `algebraic soft theorem'. We find that the proposed soft theorem is satisfied by the `surface' integrand of Arkani-Hamed, Cao, Dong, Figueiredo and He, which is obtained from the shifted ${\rm Tr}\phi^3$ surfacehedron integrand. Finally, we derive an on-shell version of the algebraic soft theorem that takes an interesting form in terms of propagator renormalization factors and lower-loop integrands in a mixed theory of pions and scalars., Comment: 6 pages

In this paper, we study celestial amplitudes of Goldstone bosons and conformal soft theorems. Motivated by the success of soft bootstrap in momentum space and the important role of the soft limit behavior of tree-level amplitudes, our goal is to extend some of the methods to the celestial sphere. The crucial ingredient of the calculation is the Mellin transformation, which transforms four-dimensional scattering amplitudes to correlation functions of primary operators in the celestial CFT. The soft behavior of the amplitude is then translated to the singularities of the correlator. Only for amplitudes in "UV completed theories" (with sufficiently good high energy behavior) the Mellin integration can be properly performed. In all other cases, the celestial amplitude is only defined in a distributional sense with delta functions. We provide many examples of celestial amplitudes in UV-completed models, including linear sigma models and Z-theory, which is a certain completion of the SU(N) non-linear sigma model. We also comment on the BCFW-like and soft recursion relations for celestial amplitudes and the extension of soft bootstrap ideas., Comment: 86 pages, 6 figures, v2: published version, minor changes, one appendix added

The nonlocal order parameters of the QCD chiral symmetry breaking, namely the nonanomalous three-point Green functions of the quark bilinears belonging to the odd intrinsic parity sector, are studied within the framework of the Resonance chiral theory. The general form of these correlators is then matched with various high energy constraints: the leading and sub-leading OPE for all three momenta simultaneously large, the leading OPE for two momenta large and the leading and sub-leading Brodsky-Lepage limit for the corresponding transition form factor. In order to satisfy these constraints, the Resonance chiral theory has to be enlarged with additional resonance multiplets and with higher derivative operators as well. We discuss a minimal extension of this kind in detail and present corresponding correlators in a closed form. The remaining free parameters are then constrained from lattice data. As a phenomenological application, we discuss the pion-pole contribution to the muon $g-2$ and the decay $\pi^0\to e^+e^-$., Comment: 59 pages, 11 figures, ver2: some changes in the text and analysis, version accepted by JHEP

We analyze a theory known as extended DBI, which interpolates between DBI and the $U(N)\times U(N)/U(N)$ non-linear sigma model and represents a nontrivial example of theories with mixed power counting. We discuss symmetries of the action and their geometrical origin; the special case of SU(2) extended DBI theory is treated in great detail. The revealed symmetries lead to a new type of graded soft theorem that allows us to prove on-shell constructibility of the tree-level S-matrix. It turns out that the on-shell constructibility of the full extended DBI remains valid, even if its DBI sub-theory is modified in such a way to preserve its own on-shell constructibility. We thus propose a slight generalization of the DBI sub-theory, which we call 2-scale DBI theory. Gluing it back to the rest of the extended DBI theory gives a new set of on-shell reconstructible theories -- the 2-scale extended DBI theory and its descendants. The uniqueness of the parent theory is confirmed by the bottom-up approach that uses on-shell amplitude methods exclusively., Comment: 52 pages, 6 figures, 3 appendices. v2: minor changes, matches accepted version in JHEP

We use the amplitude soft bootstrap method to explore the space of effective field theories (EFT) of massless vectors and scalars. It is known that demanding vanishing soft limits fixes uniquely a special class of EFTs: non-linear sigma model, scalar Galileon and Born-Infeld theories. Based on the amplitudes analysis, we conjecture no-go theorems for higher-derivative vector theories and theories with coupled vectors and scalars. We then allow for more general soft theorems where the non-trivial part of the soft limit of the (n+1)-pt amplitude is equal to a linear combination of n-pt amplitudes. We derive the form of these soft theorems for general power-counting and spins of particles and use it as an input into the soft bootstrap method in the case of Galileon power-counting and coupled scalar-vector theories. We show that this unifies the description of existing Galileon theories and leads us to the discovery of a new exceptional theory: Special scalar-vector Galileon., Comment: 40 pages, 4 figures; v2: minor changes, published version

The current state of knowledge of the order parameters of the spontaneously broken chiral symmetry, the quark condensate and the pseudoscalar decay constant in the chiral limit, is briefly reviewed, based on available phenomenological fits and lattice QCD calculations. We argue that while the theory is pretty well understood in the two-flavour case, there is still a gap in the knowledge of the characteristics of the QCD vacuum in the three-flavour one. Our constraints for the three-flavour parameters obtained by a Bayesian statistical analysis of the decays of eta to three pions are presented. Possible implications of a new analysis of subthreshold parameters of pion-pion scattering is outlined., Comment: Presented at ICHEP2020, Prague, July 31, 2020. 6 pages, 2 tables, 1 figure

In this paper, we initiate the study of multi-flavor Galileon theories using the methods of scattering amplitudes. We explore this topic from different perspectives and extend the techniques employed so far mainly in the single-flavor case. This includes soft theorems, generalized soft theorems with non-trivial right-hand side, Galileon dualities, soft bootstrap and bonus relations. We demonstrate new properties on two examples, the multi-flavor U(N) Galileon and the three-flavor U(2)/U(1) Galileon., Comment: 42 pages, 2 figures

In this paper we investigate the high-energy behavior of two-point and three-point Green functions of the QCD chiral currents and densities using the framework of the operator product expansion in the chiral limit. In detail, we study the contributions of the quark, gluon, quark-gluon and four-quark condensates to all the relevant non-vanishing three-point correlators.

We present and develop a general dispersive framework allowing us to construct representations of the amplitudes for the processes $P\pi\to\pi\pi$, $P=K,\eta$, valid at the two-loop level in the low-energy expansion. The construction proceeds through a two-step iteration, starting from the tree-level amplitudes and their S and P partial-wave projections. The one-loop amplitudes are obtained for all possible configurations of pion masses. The second iteration is presented in detail in the cases where either all masses of charged and neutral pions are equal, or for the decay into three neutral pions. Issues related to analyticity properties of the amplitudes and of their lowest partial-wave projections are given particular attention. This study is introduced by a brief survey of the situation, for both experimental and theoretical aspects, of the decay modes into three pions of charged and neutral kaons and of the eta meson., Comment: 38 pages, 11 figures; minor reformulations for clarification, 4 references added

In this letter we discuss new soft theorems for the Goldstone boson amplitudes with non-vanishing soft limits. The standard argument is that the non-linearly realized shift symmetry leads to the vanishing of scattering amplitudes in the soft limit, known as the Alder zero. This statement involves certain assumptions of the absence of cubic vertices and the absence of linear terms in the transformations of fields. For theories which fail to satisfy these conditions, we derive a new soft theorem which involves certain linear combinations of lower point amplitudes, generalizing the Adler zero statement. We provide an explicit example of $SU(N)/SU(N-1)$ sigma model which was also recently studied in the context of $U(1)$ fibrated models. The soft theorem can be then used as an input into the modified soft recursion relations for the reconstruction of all tree-level amplitudes., Comment: 5 pages, 2 figures

We present a complete one-loop renormalization of the Special Galileon $S-$matrix. Especially we give a complete list of the higher derivative operators which are necessary for one-loop on-shell renormalization and prove the invariance of the one-loop on-shell effective action with respect to the Special Galileon symmetry. This enables us to enlarge the validity of the enhanced $O(p^3)$ soft behavior of the scattering amplitudes to the one-loop level. As an illustration we discuss explicitly the four-point and five-point one-loop scattering amplitudes and comment on some conjectures appearing in the existing literature., Comment: 28 pages

We give a proof of the equivalence of the electric-magnetic duality on one side and helicity conservation of the tree level amplitudes on the other side within general models of nonlinear electrodynamics. Using modified Feynman rules derived from generalized normal ordered Lagrangian we discuss the interrelation of the above two properties of the theory also at higher loops. As an illustration we present two explicit examples, namely we find the generalized normal ordered Lagrangian for the Born-Infeld theory and derive a semi-closed expression for the Lagrangian of the Bossard-Nicolai model (in terms of the weak field expansion with explicitly known coefficients) from its normal ordered form., Comment: 31 pages

In this study, we revisit and complete the full next-to-leading order corrections to pseudoscalar double-Dalitz decays within the soft-photon approximation. Comparing to the previous study, we find small differences, which are nevertheless relevant for extracting information about the pseudoscalar transition form factors. Concerning the latter, these processes could offer the opportunity to test them-for the first time-in their double-virtual regime, Comment: 22 pages, 9 figures; minor changes added (results unchanged). Matches the published version in PRD. Results in Mathematica notebooks added as ancillary files

We present a bottom-up construction of vector effective field theories using the infrared structure of scattering amplitudes. Our results employ two distinct probes of soft kinematics: multiple soft limits and single soft limits after dimensional reduction, applicable in four and general dimensions, respectively. Both approaches uniquely specify the Born-Infeld (BI) model as the only theory of vectors completely fixed by certain infrared conditions which generalize the Adler zero for pions. These soft properties imply new recursion relations for on-shell scattering amplitudes in BI theory and suggest the existence of a wider class of vector effective field theories., Comment: 6 pages, 2 figures

We provide the complete set of radiative corrections to the Dalitz decays $\eta^{(\prime)}\to \ell^+\ell^-\gamma$ beyond the soft-photon approximation, i.e. over the whole range of the Dalitz plot and with no restrictions on the energy of a radiative photon. The corrections inevitably depend on the $\eta^{(\prime)}\to\gamma^*\gamma^{(*)}$ transition form factors. For the singly virtual transition form factor appearing e.g. in the bremsstrahlung correction, recent dispersive calculations are used. For the one-photon-irreducible contribution at the one-loop level (for the doubly virtual form factor), we use a vector-meson-dominance-inspired model while taking into account the $\eta$-$\eta^\prime$ mixing., Comment: 30 pages, 8 figures, 12 tables; v2: hadronic vacuum polarization contribution, spectral function fit and ancillary files containing data points added, minor corrections; v3: accepted version for publication in Phys. Rev. D., extended results section and end of Section IV, corrected values in Tables III-VI, Figs. 5a and 5b and ancillary files updated, other minor corrections and improvemets

The $\eta \to 3\pi$ decays are a valuable source of information on low energy QCD. Yet they were not used for an extraction of the three flavor chiral symmetry breaking order parameters until now. We use a Bayesian approach in the framework of resummed chiral perturbation theory to obtain constraints on the quark condensate and pseudoscalar decay constant in the chiral limit. We compare our results with recent CHPT and lattice QCD fits and find some tension, as the $\eta \to 3\pi$ data seem to prefer a larger ratio of the chiral order parameters. The results also disfavor a very large value of the pseudoscalar decay constant in the chiral limit, which was found by some recent works. In addition, we present results of a combined analysis including $\eta \to 3\pi$ decays and $\pi\pi$ scattering and though the picture does not changed appreciably, we find some tension between the data we use. We also try to extract information on the mass difference of the light quarks, but the uncertainties prove to be large., Comment: 23 pages, 8 figures

Theory known as Special Galileon has recently attracted considerable interest due to its peculiar properties. It has been shown that it represents an extremal member of the set of effective field theories with enhanced soft limit. This property makes its tree-level S-matrix fully on-shell reconstructible and representable by means of the Cachazo-He-Yuan representation. The enhanced soft limit is a consequence of new hidden symmetry of the Special Galileon action, however, until now, the origin of this peculiar symmetry has remained unclear. In this paper we interpret this symmetry as a special transformation of the coset space $GAL(D,1)/SO(1,D-1)$ and show, that there exists a three-parametric family of invariant Galileon actions. The latter family is closed under duality which appears as a natural generalization of the above mentioned symmetry. We also present a geometric construction of the Special Galileon action using $D$-dimensional brane propagating in $2D$-dimensional flat pseudo-riemannian space. Within such framework, the Special Galileon symmetry emerges as an $U(1,D-1)$ symmetry of the target space, which can be treated as a $D$-dimensional K\"ahler manifold. Such a treatment allows for classification of the higher order invariant Lagrangians needed as counterterms on the quantum level. We also briefly comment on relation between such higher order Lagrangians and the Lagrangians invariant with respect to the polynomial shift symmetry., Comment: 42 pages, 8 figures

We systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local S-matrix. To do so we define an EFT classification based on four parameters characterizing 1) the number of derivatives per interaction, 2) the soft properties of amplitudes, 3) the leading valency of the interactions, and 4) the spacetime dimension. Carving out the allowed space of EFTs, we prove that exceptional EFTs like the non-linear sigma model, Dirac-Born-Infeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Using on-shell momentum shifts and recursion relations, we prove that EFTs with arbitrarily soft behavior are forbidden and EFTs with leading valency much greater than the spacetime dimension cannot have enhanced soft behavior. We then enumerate all single scalar EFTs in d<6 and verify that they correspond to known theories in the literature. Our results suggest that the exceptional theories are the natural EFT analogs of gauge theory and gravity because they are one-parameter theories whose interactions are strictly dictated by properties of the S-matrix., Comment: 54 pages, 4 figures, 2 tables; v3 matched to JHEP version

Even today, the convergence of the decay widths and some of the Dalitz plot parameters of the $\eta $$\,\rightarrow $$3\pi$ decays seems problematic in low energy QCD. We provide an overview of the current experimental and theoretical situation with historical background and summarize our recent results, which explore the question of compatibility of experimental data with a reasonable convergence of a carefully defined chiral series in the framework of resummed chiral perturbation theory., Comment: Presented at "QCD 16", Montpellier, France, July 6, 2016. 5 pages, 2 figures

Theoretical efforts to describe and explain the $\eta\to 3\pi$ decays reach far back in time. Even today, the convergence of the decay widths and some of the Dalitz plot parameters seems problematic in low energy QCD. In the framework of resummed CHPT, we explore the question of compatibility of experimental data with a reasonable convergence of a carefully defined chiral series, where NNLO remainders are assumed to be small. By treating the uncertainties in the higher orders statistically, we numerically generate a large set of theoretical predictions, which are then confronted with experimental information. In the case of the decay widths, the experimental values can be reconstructed for a reasonable range of the free parameters and thus no tension is observed, in spite of what some of the traditional calculations suggest. The Dalitz plot parameters $a$ and $d$ can be described very well too. When the parameters $b$ and $\alpha$ are concerned, we find a mild tension for the whole range of the free parameters, at less than 2$\sigma$ C.L. This can be interpreted in two ways - either some of the higher order corrections are indeed unexpectedly large or there is a specific configuration of the remainders, which is, however, not completely improbable. Also, the distribution of the theoretical uncertainties is found to be significantly non-gaussian, so the consistency cannot be simply judged by the 1$\sigma$ error bars., Comment: 57 pages, 5 figures

We derive the first ever on-shell recursion relations for amplitudes in effective field theories. Based solely on factorization and the soft behavior of amplitudes, these recursion relations employ a new rescaling momentum shift to construct all tree-level scattering amplitudes in theories like the non- linear sigma model, Dirac-Born-Infeld theory, and the Galileon. Our results prove that all theories with enhanced soft behavior are on-shell constructible., Comment: 5 pages

We have recalculated the Mikaelian and Smith radiative corrections to the Dalitz decay $\pi^0\to e^+e^-\gamma$ beyond the soft-photon approximation, i.e. over the whole range of the Dalitz plot and with no restrictions on the radiative photon. In contrast to the previous calculations, we did not neglect the terms of order higher than $\mathcal{O}(m^2)$ and also included the one-photon-irreducible contribution at one-loop level and the virtual muon loop contribution. The results can then be used also for heavier particles in the final state., Comment: 15 pages, 5 figures, 1 table and 3 ancillary files (C++ code); v2: accepted version for publication in Phys. Rev. D.; extended discussion, one table and muon loop contribution added, C++ code updated

We derive scalar effective field theories - Lagrangians, symmetries, and all - from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galileons. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist., Comment: 5 pages

The eta to 3 pion decays are a valuable source of information on low energy QCD. Yet they were not used for an extraction of the chiral symmetry breaking order parameters until now. We use a bayesian approach in the framework of resummed chiral perturbation theory to obtain constraints on the quark condensate and pseudoscalar decay constant in the chiral limit, as well as the mass difference of light quarks. We compare our results with recent CHPT and lattice QCD fits and find some tension, as the eta to 3pi data seem to prefer a larger ratio of the chiral order parameters. The results also seem to exclude a large value of the chiral decay constant, which was found by some recent works., Comment: Presented at "QCD 14", Montpellier, France, July 1st, 2014. This is a significant update of our initial report (arXiv:1308.3061). 4 pages, 2 figures

The preceding experimental and theoretical results on the rare decay $\pi^0 \to e^+e^-$ are briefly summarized. Already computed two-loop QED corrections are reviewed and the bremsstrahlung contribution beyond the soft-photon approximation is analytically calculated. The possible further contribution of QCD loop corrections is estimated using the leading logarithm approximation. The complete result can be used to fit the value of the contact interaction coupling $\chi^r$ to the recent KTeV experiment with the result $\chi^r(M_\rho) = 4.5 \pm 1.0$., Comment: 10 pages, 9 figures, 1 table

We study dualities of the general Galileon theory in d dimensions in terms of coordinate transformations on the coset space corresponding to the spontaneously broken Galileon group. The most general duality transformation is found to be determined uniquely up to four free parameters and under compositions these transformations form a group which can be identified with GL(2,R). This group represents a unified framework for all the up to now known Galileon dualities. We discuss a representation of this group on the Galileon theory space and using concrete examples we illustrate its applicability both on the classical and quantum level., Comment: 73 pages, 5 figures, 1 table; Accepted for publication in JHEP, a revised and enlarged version, discussion of superluminal propagation included

Quark condensate and pseudoscalar decay constant in the chiral limit are the principal order parameters of spontaneous chiral symmetry breaking in QCD. Yet their three flavor values are still only weakly constrained by analyses using experimental data. We try to obtain such constraints by statistical methods from the decay width of the eta to pi+pi-pi0 decay in the framework of resummed chiral perturbation theory. We rely on recent estimates of the isospin violating parameter R, which is proportional to the difference of the u and d quark masses. Alternatively, we relax the assumption and try to extract information on R as well., Comment: Presented at "Hadron Structure 2013", Tatransk\'e Matliare, Slovakia, June 30, 2013. 4 pages, 2 figures

We study in detail the general structure and further properties of the tree-level amplitudes in the SU(N) nonlinear sigma model. We construct the flavor-ordered Feynman rules for various parameterizations of the SU(N) fields U(x), write down the Berends-Giele relations for the semi-on-shell currents and discuss their efficiency for the amplitude calculation in comparison with those of renormalizable theories. We also present an explicit form of the partial amplitudes up to ten external particles. It is well known that the standard BCFW recursive relations cannot be used for reconstruction of the the on-shell amplitudes of effective theories like the SU(N) nonlinear sigma model because of the inappropriate behavior of the deformed on-shell amplitudes at infinity. We discuss possible generalization of the BCFW approach introducing "BCFW formula with subtractions" and with help of Berends-Giele relations we prove particular scaling properties of the semi-on-shell amplitudes of the SU(N) nonlinear sigma model under specific shifts of the external momenta. These results allow us to define alternative deformation of the semi-on-shell amplitudes and derive BCFW-like recursion relations. These provide a systematic and effective tool for calculation of Goldstone bosons scattering amplitudes and it also shows the possible applicability of on-shell methods to effective field theories. We also use these BCFW-like relations for the investigation of the Adler zeroes and double soft limit of the semi-on-shell amplitudes., Comment: 57 pages, 14 figures

It is well-known that the standard BCFW construction cannot be used for on-shell amplitudes in effective field theories due to bad behavior for large shifts. We show how to solve this problem in the case of the SU(N) non-linear sigma model, i.e. non-renormalizable model with infinite number of interaction vertices, using scaling properties of the semi-on-shell currents, and we present new on-shell recursion relations for all on-shell tree-level amplitudes in this theory., Comment: 4 pages, 2 figures

This paper is devoted to the two-loop QED radiative corrections to the decay pi0 -> e+ e-. We compute the virtual corrections without using any approximation and we take into account all the relevant graphs with the inclusion of those omitted in the previous approximative calculations. The bremsstrahlung is then treated within the soft photon approximation. We concentrate on the technical aspects of the calculation and discuss in detail the UV renormalization and the treatment of IR divergences within the dimensional regularization. As a result we obtain the O(alpha^3 p^2) contribution in closed analytic form. We compare the exact two-loop results with existing approximative calculations of QED corrections and find significant disagreement in the kinematical region relevant for the KTeV experiment., Comment: 48 pages plus 4 appendices (72 pages total), 26 figures; v3: new chapter 9 with phenomenological discussion added, references added, minor typos corrected; coincides with the journal version

Using the large N_C approximation we have constructed the most general chiral resonance Lagrangian in the odd-intrinsic parity sector that can generate low energy chiral constants up to O(p^6). Integrating out the resonance fields these O(p^6) constants are expressed in terms of resonance couplings and masses. The role of eta' is discussed and its contribution is explicitly factorized. Using the resonance basis we have also calculated two QCD Green functions of currents: and and found, imposing high energy constraints, additional relations for resonance couplings. We have studied several phenomenological implications based on these correlators from which let us mention here our prediction for the pi0-pole contribution to the muon g-2 factor: $a_\mu^{\pi^0} = 65.8(1.2)\times 10^{-11}$., Comment: 42 pages, 3 figures

Because of their small electromagnetic corrections, the isospin-breaking decays $\eta\to3\pi$ seem to be good candidates for extracting isospin-breaking parameters $ (m_d-m_u)$. This task is unfortunately complicated by large chiral corrections and the discrepancy between the experimentally measured values of the Dalitz parameters describing the energy dependence of the amplitudes of these decays and those predicted from chiral perturbation theory. We present two methods based on an analytic dispersive representation that use the information from the NNLO chiral result and the one from the measurement of the charged $\eta\to3\pi$ decay by KLOE together in a harmonized way in order to determine the value of the quark mass ratio $R$. Our final result is $R=37.7\pm 2.2$. This value supplemented by values of $m_s/\hat{m}$ or even $\hat{m}$ and $m_s$ from other methods (as sum-rules or lattice) enables us to obtain further quark mass characteristics. For instance the recent lattice value for $m_s/\hat{m}~27.5$ leads to $Q= 23.1\pm0.7$. We also quote the corresponding values of the current masses $m_u$ and $m_d$., Comment: 40 pages, 4 figures

We study in detail various aspects of the renormalization of the spin-1 resonance propagator in the effective field theory framework. First, we briefly review the formalisms for the description of spin-1 resonances in the path integral formulation with the stress on the issue of propagating degrees of freedom. Then we calculate the one-loop 1-- meson self-energy within the Resonance chiral theory in the chiral limit using different methods for the description of spin-one particles, namely the Proca field, antisymmetric tensor field and the first order formalisms. We discuss in detail technical aspects of the renormalization procedure which are inherent to the power-counting non-renormalizable theory and give a formal prescription for the organization of both the counterterms and one-particle irreducible graphs. We also construct the corresponding propagators and investigate their properties. We show that the additional poles corresponding to the additional one-particle states are generated by loop corrections, some of which are negative norm ghosts or tachyons. We count the number of such additional poles and briefly discuss their physical meaning., Comment: 65 pages, 12 figures

We study various aspects of the renormalization of the Resonance Chiral Theory at the one-loop level using a spin-one resonance propagator as a concrete example. We calculate explicitly the one-loop self-energy within the antisymmetric tensor field formalism, briefly discuss the general structure of the corresponding propagator obtained by means of the Dyson re-summation and give a classification of the propagating degrees of freedom. We find that additional pathological poles (negative norm ghosts or tachyons) are unavoidably generated and various scenarios according to their position are possible. We also briefly comment on the eventual dynamical generation of the opposite parity resonances which are frozen at the tree level and discuss the role of appropriate symmetry which could prevent such a scenario., Comment: 8 pages, 3 figures, to appear in Proceedings of the conference EFT 09, Valencia, 2-6 February 2009

We discuss the renormalization of the $1^{--}$ vector meson propagator within Resonance chiral theory at one loop. Using the particular form of the interaction Lagrangian we show that additional poles of the renormalized propagator corresponding to $1^{+-}$ degrees of freedom can be generated. We give a concrete example of such an effect., Comment: 4 pages, 1 figure, to appear in Proceedings of the conference QCD 08, Montpellier, 7-12 July 2008

The NA48/2 collaboration has shown clear experimental evidence for a cusp in the data for K -> pi pi^0 pi^0. This effect can be used to extract information on the pi-pi scattering lengths. We address this issue using a two-loop dispersive construction of pi pi -> pi pi and K -> pi pi pi amplitudes in the presence of isospin breaking., Comment: 4 pages, 1 figure, to appear in Proceedings of the conference QCD 08, Montpellier, 7-12 July 2008

We study the problems related to the renormalization of propagators in Resonance Chiral Theory, concentrating on the case of vector $1^{--}$ resonances in the antisymmetric tensor formalism. We have found that renormalization of the divergences of the self-energy graphs needs new type of kinetic counterterms with two derivatives which are not present in the original leading order Lagrangian. The general form of the propagator for antisymmetric tensor fields could then contain not only poles corresponding to the original $1^{--}$ resonance states but also to the additional states with opposite parity which decouple in the free field limit. In some cases, these dynamically generated additional states might be negative norm ghosts or tachyons., Comment: 7 pages, presented by J.T. at Hadron structure 07, Slovakia

We study two general approaches how to describe spin one particles, using vector and antisymmetric tensor fields within RChT. In this paper we focus on the question of an equivalence of both ways. The appearing problems lead us to the introduction of a new type of the description - the first order formalism which naturally connects both traditional formalisms. Moreover, it gives a more general result on the level of the effective chiral Lagrangian that contain all terms from effective chiral Lagrangians in vector and antisymmetric tensor formulations., Comment: 7 pages, presented by J.T. at Petrov School, Kazan, Russia

The main idea of the first order formalism is demonstrated on a toy example of spin-0 particle. The full formalism for spin-1 is applied to the vector formfactor of the pion and its high-energy behaviour is studied., Comment: 6 pages, 1 figure; presented by K.K. at Final Euridice Meeting

We study the relation of vector Proca field formalism and antisymmetric tensor field formalism for spin-one resonances in the context of the large N_C inspired chiral resonance Lagrangian systematically up to the order O(p6) and give a transparent prescription for the transition from vector to antisymmetric tensor Lagrangian and vice versa. We also discuss the possibility to describe the spin-one resonances using an alternative "mixed" first order formalism, which includes both types of fields simultaneously, and compare this one with the former two. We also briefly comment on the compatibility of the above lagrangian formalisms with the high-energy constraints for concrete VVP correlator., Comment: 34 pages, 3 figures

The amplitude of the Dalitz decay pi0 -> e+ e gamma is studied and its model-independent properties are discussed in detail. A calculation of radiative corrections is performed within the framework of two-flavour chiral perturbation theory, enlarged by virtual photons and leptons. The lowest meson dominance approximation, motivated by large N\_C considerations, is used for the description of the pi0 - gamma* - gamma* transition form factor and for the estimate of the NLO low energy constants involved in the analysis. The two photon reducible contributions is included and discussed. Previous calculations are extended to the whole kinematical range of the soft-photon approximation, thus allowing for the possibility to consider various experimental situations and observables.

The \pi^0\gamma\gamma vertex is used as an explicit example of the subtleties connected with the application of equation of motion within Chiral Perturbation Theory at the order O(p^6)., Comment: 7 pages, 2 figures; presented at Int. Conf. Renormalization Group 2002, Slovakia, March 2002

As an illustration of general principles, the $W$-boson loop contribution to the amplitude for the decay $H\to \gamma \gamma$ is calculated within a specific model for the effective lagrangian describing the anomalous gauge boson couplings. Different approaches to the dependence of the result on the scale of new physics $\Lambda$ are briefly discussed., Comment: 17 pages, 2 figures, accepted for publication in Czechoslovak Journal of Physics