A new set of the next-to-leading order (NLO) and the next-to-next-to-leading order (NNLO) low-energy constants $L_i^r$ and $C_i^r$ in chiral perturbation theory is obtained. These values are computed using the new experimental data with a new calculation method. This method combines the traditional global fit and Monte Carlo method together. The higher order contributions are estimated with this method. The theoretical values of the observables provide good convergence at each chiral dimension, except for the NNLO values of the $πK$ scattering lengths $a_0^{3/2}$ and $a_0^{1/2}$. The fitted values for $L_i^r$ at NLO are close to their results with the new method at NNLO; i.e., these $L_i^r$ are nearly order-independent in this method. The estimated ranges for $C_i^r$ are consistent with those in the literature, and their possible upper or/and lower boundaries are given. The values of some linear combinations of $C_i^r$ are also given, and they are more reliable. If one knows a more exact value $C_i^r$, another $C_i^r$ can be obtained by these values.
It is shown that the chiral nonanalytic terms generated by $Δ_{33}$ resonance in the nucleon self-energy is reproduced in chiral perturbation theory by perturbing appropriate local operators contained in the pion-nucleon effective Lagrangian itself.
Spontaneous breaking of chiral symmetry in QCD has traditionally been inferred indirectly through low-energy theorems and comparison with experiments. Thanks to the understanding of an unexpected connection between chiral Random Matrix Theory and chiral Perturbation Theory, the spontaneous breaking of chiral symmetry in QCD can now be shown unequivocally from first principles and lattice simulations. In these lectures I give an introduction to the subject, starting with an elementary discussion of spontaneous breaking of global symmetries.
We evaluate the branching ratios for the decays $K\rightarrow πππeν$ at leading order in chiral perturbation theory and give an isospin relation for the decay rates.
The basic ideas and some recent developments of the chiral perturbation theory approach to hadron dynamics at low-energies are reviewed. (Invited talk at the HADRON'93 Conference Como, Italy June 1993.)
Calculations of eta->pi^0 pi^0 gamma gamma decay in generalized chiral perturbation theory are presented. Tree level and some of next-to-leading corrections are involved. Sensitivity to the deviations from the standard chiral perturbation theory is discussed.
The basic ideas and power counting rules of chiral perturbation theory are discussed. The formalism of velocity dependent fields for baryons, and for hadrons containing a heavy quark, is explained. (Invited Talk, 1993 QCD Rencontres de Moriond)
This talk is an overview of Chiral Perturbation Theory for Kaon physics as far as not covered by other speakers. It includes a short introduction to the strengths and weaknesses of Chiral Perturbation Theory and its applications to semileptonic Kaon decays and $K\toππ(π)$.
Based on an effective chiral theory the 10 coefficients of ChPT are predicted. There is no new parameter. The current quark masses, m_η, f_{K}, and f_η are determined too.
We investigate omega-phi meson mixing to leading order in chiral perturbation theory utilizing the antisymmetric tensor field formulation. We update the quark mass ratio R from rho-omega mixing, R = 42 \pm 4.
An introduction to the basic ideas and methods of Chiral Perturbation Theory is presented. Several phenomenological applications of the effective Lagrangian technique to strong, electromagnetic and weak interactions are discussed.
An introduction to the basic ideas and methods of Chiral Perturbation Theory is presented. Several phenomenological applications of the effective Lagrangian technique to strong, electromagnetic and weak interactions are discussed.
I : Chiral Perturbation Theory is introduced and its applications to semileptonic and nonleptonic kaon decays are discussed. II: The method of large $N_c$ is used to calculate $K\toππ$ nonleptonic matrix elements, in particular the matching procedure between long and short-distance evolution that takes all scheme dependence correctly into account is discussed. Numerical results reproduce the $ΔI=1/2$ rule without the introduction of any free parameters.
We express the two-massless-flavor Gell-Mann--Oakes--Renner ratio in terms of low-energy pi-pi observables, including the O(p^6) double chiral logarithms of generalized chiral perturbation theory. Their contribution is sizeable and tends to compensate the one from the single chiral logarithms. However it is not large enough to spoil the convergence of the chiral expansion. As a signal of reduced theoretical uncertainty, we find that the scale dependence from the one-loop single logarithms is almost completely canceled by the one from the two-loop double logarithms.
I present a quick overview of the current status of Chiral perturbation theory in the meson sector. To illustrate the successes and some problems in the description of the phenomenology, I focus on a few selected examples that are relevant for DAFNE.
In the context of chiral SU(2) perturbation theory, pion-kaon scattering is analysed near the threshold to fourth chiral order. The scattering amplitude is calculated both in the relativistic framework and by using an approach similar to heavy baryon chiral perturbation theory. Both methods lead to equivalent results. We obtain relations between threshold parameters, valid to fourth chiral order, where all those combinations of low-energy constants which are not associated with chiral-symmetry breaking terms drop out. The remaining low-energy constants can be estimated using chiral SU(3) symme…
We calculate the pion-pion elastic scattering phase shifts for pion masses from the chiral limit to values of interest for lattice studies. At low energies, we use the standard Chiral Perturbation Theory expressions to one and two loops. In addition, we study the phase shifts mass dependence in the resonance region by means of dispersion theory in the form of unitarized Chiral Perturbation Theory and the Inverse Amplitude Method. We pay particular attention to the case when resonances are close to threshold, illustrating the different behavior between scalar and vector resonances. We also prov…
The renormalization of chiral perturbation theory is carried out to next-to-next-to-leading order in the meson sector. We calculate the divergent part of the generating functional of Green functions of quark currents to O(p^6) for chiral SU(n), involving one- and two-loop diagrams. The renormalization group equations for the renormalized low-energy constants of O(p^6) are derived. We compare our results with previous two-loop calculations in chiral perturbation theory.
The inverse-amplitude method is applied to the one-loop chiral expansion of the pion, kaon, and $K_{l3}$ form factors. Since these form factors are determined by the same chiral low-energy constants, it is possible to obtain finite predictions for the inverse-amplitude method. It is shown that this method clearly improves one-loop chiral perturbation theory, and a very good agreement between the inverse-amplitude method and the experimental information is obtained. This suggests that the inverse-amplitude method is a rather systematic way of improving chiral perturbation theory.
We calculate the scattering lengths of Nambu-Goldstone bosons interacting with $D$ mesons in a covariant formulation of chiral perturbation theory, which satisfies heavy-quark spin symmetry and analytical properties of loop amplitudes. We compare our results with previous studies performed using heavy meson chiral perturbation theory and show that recoil corrections are sizable in most cases.
The status of chiral perturbation theory in the meson sector is reviewed. The main emphasis is on recent developments in pion pion scattering, in semileptonic decays and in nonleptonic kaon decays. A few other selected topics are also discussed.
We construct the general pion-nucleon SU(2) Lagrangian including both virtual photons and leptons for relativistic baryon chiral perturbation theory up to fourth order. We include the light leptons as explicit dynamical degrees of freedom by introducing new building blocks which represent these leptons.
A review of chiral perturbation theory and that of recent developments on the comparison of its predictions with experiment is presented. Some interesting topics with scope for further elaboration are touched upon.
An introduction to Chiral Perturbation Theory is given including a discussion of power counting, the Wess-Zumino term, the values of the coupling constants and the inclusion of the effects of other resonances.
We calculate the weak nonleptonic decay of the Omega^- baryon to octet final states in heavy baryon chiral perturbation theory (HBChPT). We include the one-loop leading logarithmic effects and show that this improves the universality of the HBChPT constants.
We establish exact relations between relativistic form factors and amplitudes for single-baryon processes and the corresponding quantities calculated in the framework of heavy baryon chiral perturbation theory. A crucial ingredient for the proper matching is the first complete treatment of baryon wave function renormalization in heavy baryon chiral perturbation theory.
We demonstrate how heavy mass methods, previously applied to chiral perturbation theory calculations involving the interactions of nucleons and pions, can be generalized to include interactions with the $Δ(1232)$ in a systematic formalism which we call the "small scale expansion."
We compute nonanalytical pion-loop corrections to baryon masses in a combined expansion in chiral symmetry breaking and 1/N_c, where N_c is the number of colors. Specifically, we compute flavor-27 baryon mass splittings at leading order in chiral perturbation theory. Our results, at the physical value N_c=3, are compared with the expressions obtained in heavy baryon chiral perturbation theory with no 1/N_c expansion.
An analysis of electromagnetic corrections to the (dominant) octet K -> pi pi hamiltonian using chiral perturbation theory is carried out. Relative shifts in amplitudes at the several per cent level are found.
A survey is made of semileptonic and nonleptonic kaon decays in the framework of chiral perturbation theory. The emphasis is on what has been done rather than how it was done. The theoretical predictions are compared with available experimental results.
We calculate the width of the delta resonance at leading two-loop order in baryon chiral perturbation theory. This gives a correlation between the leading pion-nucleon-delta and pion-delta couplings, which is relevant for the analysis of pion-nucleon scattering and other processes.
We include the eta-prime in chiral perturbation theory without employing 1/N_c counting rules. The method is illustrated by calculating the masses and decay constants of the Goldstone boson octet (pions, kaons, eta) and the singlet eta-prime up to one-loop order. The effective Lagrangian describing the interactions of the eta-prime with the Goldstone boson octet is presented up to fourth chiral order and the loop integrals are evaluated using infrared regularization, which preserves Lorentz and chiral symmetry.
We analyse the extension of Chiral Perturbation Theory to describe a meson gas out of thermal equilibrium. For that purpose, we let the pion decay constant be a time-dependent function and work within the Schwinger-Keldysh contour technique. A useful connection with curved space-time QFT allows to consistently renormalise the model, introducing two new low-energy constants in the chiral limit. We discuss the applicability of our approach within a Relativistic Heavy-Ion Collision environment. In particular, we investigate the formation of Disoriented Chiral Condensate domains in this model, via…
Hadronic (Pi+Pi-) atom is studied in the relativistic perturbative approach based on the Bethe-Salpeter equation. The general expression for the atom lifetime is derived. Lowest-order corrections to the relativistic Deser-type formula for the atom lifetime are evaluated within the Chiral Perturbation Theory.
The contributions of the lightest tensor-meson resonances to the low-energy coupling constants of second order chiral perturbation theory with two flavours are evaluated and compared with the available phenomenological information as well as with similar results for other resonances.
I discuss recent progress in our understanding of the pi pi scattering amplitude at low energy thanks to the combined use of chiral perturbation theory and dispersion relations. I also comment on the criticism raised by Pelaez and Yndurain on this work.
A brief introduction to the subject of chiral perturbation theory ($χ$pt) is presented, including a discussion of effective field theory and applications of $χ$pt in the arena of purely mesonic interactions as well as in the $πN$ sector.
Pionium lifetime corrections to the nonrelativistic formula are calculated in the framework of the quasipotential-constraint theory approach. The calculation extends an earlier evaluation, made in the scheme of standard chiral perturbation theory, to the scheme of generalized chiral perturbation theory, in which the quark condensate is left as a free parameter. The pionium lifetime is calculated as a function of the combination $(a_0^0-a_0^2)$ of the $ππ$ S-wave scattering lengths with isospin I=0,2.
The chiral Lagrangian for baryons is formulated in an expansion in 1/N_c. The chiral Lagrangian implements the contracted spin-flavor symmetry of large-N_c baryons as well as nonet symmetry of the leading planar diagrams. Large-N_c consistency conditions ensure that chiral loop corrections are suppressed in 1/N_c through exact cancellation of chiral loop graphs to fixed orders in 1/N_c. Application of 1/N_c baryon chiral perturbation theory to the flavor-27 baryon mass splittings and the baryon axial vector currents are considered as examples.
Heavy baryon chiral perturbation theory for pentaquarks is applied beyond leading order. The mass splitting in the pentaquark anti-decuplet is calculated up to NNLO. An expansion in the coupling of pentaquarks to non-exotic baryons simplifies calculations and makes the pentaquark masses insensitive to the pentaquark-nucleon mass difference. The possibility of determining coupling constants in the chiral Lagrangian on the lattice is discussed. Both positive and negative parities are considered.
QCD sum rules are useful tools for studying the spectral properties of hadrons; however, assumptions underlying standard sum-rule analyses can lead to inconsistencies with known results of chiral perturbation theory. This possibility is demonstrated with QCD sum-rule extractions of the nucleon mass and $σ$ term. In both cases, inconsistent chiral behavior leads to an uncertainty in the sum-rule predictions of $\sim 100\,\text{MeV}$.
After a general introduction to the structure of effective field theories, the main ingredients of chiral perturbation theory are reviewed. Applications include the light quark mass ratios and pion-pion scattering to two-loop accuracy. In the pion-nucleon system, the linear sigma model is contrasted with chiral perturbation theory. The heavy-nucleon expansion is used to construct the effective pion-nucleon Lagrangian to third order in the low-energy expansion, with applications to nucleon Compton scattering.
We have performed a theoretical study of the axial Nucleon to Delta(1232) ($N\toΔ$) transition form factors up to one-loop order in covariant baryon chiral perturbation theory within a formalism in which the unphysical spin-1/2 components of the $Δ$ fields are decoupled.
We review our recent work on unitarization and chiral perturbation theory both in the $ππ$ and the $πN$ sectors. We pay particular attention to the Bethe-Salpeter and Inverse Amplitude unitarization methods and their recent applications to $ππ$ and $πN$ scattering.
We report on a search of relations valid at order $p^6$ in Chiral Perturbation Theory. We have found relations between $ππ$, $πK$ scattering, $K_{\ell4}$ decays, masses and decay constants and scalar and vector form factors. In this paper we give the relations and a first numerical check of them.
We investigate eta-eta' mixing in infrared regularized U(3) chiral perturbation theory by calculating the eta and eta' masses up to one-loop order. From this analysis it becomes obvious that even at leading order eta-eta' mixing does not obey the usually assumed one-mixing angle scheme if large N_c counting rules are not employed.
The Generalized Chiral Perturbation Theory enlarges the framework of the standard $χ$PT, relaxing certain assumptions which do not necessarily follow from QCD or from experiment, and which are crucial for the usual formulation of the low energy expansion. In this way, experimental tests of the foundations of the standard $χ$PT become possible. Emphasis is put on physical aspects rather than on formal developements of G$χ$PT.
Baryon chiral perturbation theory as conventionally applied using dimensional regularization has a well-known problem with the convergence of the SU(3) chiral expansion. One can reformulate the theory equally rigorously using a momentum-space cutoff and we show that the convergence is thereby greatly improved for reasonable values of the cutoff. In effect, this is accomplished because the cutoff formalism removes the spurious physics of propagation at distance scales much smaller than the baryon size.
Charm and bottom mesons and baryons are incorporated into a low energy chiral Lagrangian. Interactions of the heavy hadrons with light octet Goldstone bosons are studied in a framework which represents a synthesis of chiral perturbation theory and the heavy quark effective theory. The differential decay rate for the semileptonic process $\LBzero \to Σ_c^{++} + e^- + \barν_e + π^-$ is calculated at the zero recoil point using this hybrid formalism.
We calculate the amplitude of pi-eta scattering in generalized chiral perturbation theory at the order O(p^4) and present preliminary results of the numerical analysis of the S-wave scattering length, which seems to be particularly sensitive to the deviations from the standard case.
We explore the extension of chiral perturbation theory out of thermal equilibrium. The pion decay constant becomes then a time-dependent function and we work within the Schwinger-Keldysh contour technique. A useful connection with curved space-time QFT allows to renormalise the model. We discuss the applicability of our approach within a relativistic heavy-ion collision environment.
We study the kaon polarizabilities in the framework of Chiral Perturbation Theory to order $p^4$. For the neutral kaon we find that them vanish and they have the first non-zero contribution to order $p^6$. We also emphasize the theoretical potential of an eventual measuremnet of the kaon polarizabilities, in particular of the neutral kaon ones.
We analize the most general low-energy effective lagrangian including local parity violating terms parametrized by an axial chemical potential $μ_5$. This result is obtained following the external source method, up to $\mathcal{O}(p^4)$ order in the chiral expansion for two light flavours. We show that the $\mathcal{O}(p^4)$ lagrangian includes new terms proportional to $μ_5^2$ and new low-energy constants. Finally, the $μ_5$ and temperature dependences of several observables related to the vacuum energy density are studied.
Neutral current single pion production induced by neutrinos and antineutrinos on nucleon targets has been investigated in manifestly relativistic baryon chiral perturbation theory with explicit $Δ(1232)$ degrees of freedom up to $\mathcal{O}(p^3)$. At low energies, where chiral perturbation theory is applicable, the total cross sections for the different reaction channels exhibit a sizable non-resonant contribution, which is not present in event generators of broad use in neutrino oscillation and cross section experiments such as GENIE and NuWro.
