Fully coupled-channel study of $K^-pp$ resonance in a chiral SU(3)-based $K^{bar}N$ potential
Akinobu Doté, Takashi Inoue, Takayuki Myo
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11 pages, 4 figures, 1 table, A plenary talk given at the 13th International Conference on Hypernuclear and Strange Particle Physics, June 24-29, 2018, Portsmouth, VA
Nuclear system with antikaons, so-called kaonic nuclei, has been a longstanding issue in strange nuclear physics and hadron physics, because they might have exotic nature; In particular, they could be a doorway to the dense matter due to the strong attraction between antikaon and nucleon. Among kaonic nuclei, the three-body system composed of two protons and a single $K^-$ meson, $K^-pp$, is the most essential. In this article, we will report on the recent situation of $K^-pp$ studies in both theoretical and experimental sides. Afterwards, we will explain our latest study of the $K^-pp$ with a fully coupled-channel complex scaling method (Full ccCSM) using a chiral SU(3)-based $\bar{K}N$(-$πY$) potential. In Full ccCSM, the $K^-pp$ is completely treated as a resonant state of a $\bar{K}NN$-$πΣN$-$πΛN$ coupled-channel system. The energy dependence involved in the chiral potential is handled with a self-consistent calculation in which two extreme ansatzes are examined: field picture and particle picture. With our chiral SU(3)-based potential constrained by the precise data of kaonic hydrogen atom (SIDDHARTA experiment), the $K^-pp$ resonance is obtained as a shallowly bound state measured from the $\bar{K}NN$ threshold with a narrow width, if the field picture is employed in the calculation: the binding energy is $14-28$ MeV and half value of the mesonic decay width are $8-15$ MeV. On the other hand, if the particle picture is employed, it is found that the binding energy could be as large as about 50 MeV, even though such a chiral potential is used. Based on these results of Full ccCSM calculation, we have discussed on the possibility for kaonic nuclei to form a dense matter and on the latest experimental result reported by J-PARC E15 collaboration.
Recent chiral EFT calculations of nucleon polarizabilities reveal a problem in the current empirical determination of proton's electromagnetic polarizabilities. We also report on the progress in the empirical determination of the $Δ$(1232)-resonance magnetic moment in the process of $γp \to p π^0 γ'$ measured at MAMI.
We report the chiral quark model approach for the study of baryon resonances in meson photoproduction and meson-nucleon scattering processes. Focussing on the $πN$ and $K N$ scatterings, we show that the cross sections near threshold can be well accounted for by the chiral quark model with only few parameters. The $S$-wave dominance in both $π^- p\to ηn$ and $K^- p\to Σ^0π^0$ can be well understood in the quark model framework. In particular, the quark model provides a constraint on the relative signs for resonance coupling form factors, which seems to be consistent with results from isobaric …
We probe nuclear multipole resonances in the framework of the random-phase approximation by using the interaction obtained from the chiral effective field theory. The three-nucleon force is included in a form of the in-medium two-nucleon interaction which was derived from the chiral three-nucleon force. The isoscalar monopole, isoscalar dipole, isovector dipole and isoscalar quadrupole resonances of the closed-shell $^{56,68,78}$Ni have been investigated. The calculations reasonably reproduce the experimental multipole resonances of $^{56,68}$Ni, and well describe the pygmy dipole resonance an…
We discuss baryon resonances which are dynamically generated in hadron dynamics based on chiral coupled channels approach. With the dynamical description of the baryon resonance, we discuss the origin of the resonance pole, finding that for the description of N(1535) some other components than meson and baryon are necessary. Since the chiral unitary model provides a microscopic description in terms of constituent hadrons, it is straightforward to calculate transition amplitudes and form factors of resonances without introducing further parameters. Finally we briefly discuss few-body nuclear ka…
We analyze s-wave pion-nucleon scattering in a unitarized chiral effective Lagrangian including all dimension two contact terms. We find that both the S11(1535) and the S11(1650) are dynamically generated, but the S31(1620) is not. We further discuss the structure of these dynamically generated resonances.
We investigate the effect of resonance decays on the three-particle correlator charge separation observable in search for the chiral magnetic effect, using a simple simulation with realistic inputs. We find that resonance decays can largely account for the measured signal. We suppress the elliptic flow ($v_2$) background by using zero event-by-event $v_2$ (or via the mixed-event technique). We find that the background is suppressed, but not eliminated as naively anticipated. We identify the reason to be the non-identicalness of the resonance and final-state particle's $v_2$ and the induced cor…
We have investigated the most essential kaonic nucleus "$K^-pp$" as a resonant state of the $\bar{K}NN$-$πΣN$-$πΛN$ coupled channel system using a chiral SU(3)-based $\bar{K}N$ potential. We treat the "$K^-pp$" resonance adequately with a fully coupled-channel complex scaling method (full ccCSM). Self-consistency needs to be considered for the energy dependence of the chiral SU(3)-based potential. In the present study, we propose a simple prescription for the treatment of self-consistency, considering the {\it averaged threshold} and {\it averaged binding energy of mesons}. With this prescript…
The Chiral Magnetic Effect (CME) refers to charge separation along a strong magnetic field, due to topological charge fluctuations in QCD. Charge correlation ($Δγ$) signals consistent with CME have been first observed almost a decade ago. It has also been known since then that the $Δγ$ is contaminated by a major background from resonance decays coupled with elliptic flow. In this contribution, we propose differential $Δγ$ measurements as function of the pair invariant mass ($m_{\rm inv}$). The $Δγ$ in the high $m_{\rm inv}$ region is essentially free of resonance backgrounds. In the low $m_{\r…
We review the important role played by the chiral SU(3) symmetry in predicting the properties of antikaons and hyperon resonances in cold nuclear matter. Objects of crucial importance are the meson-baryon scattering amplitudes obtained within the chiral coupled-channel effective field theory. The formation of baryon resonances as implied by chiral coupled-channel dynamics is discussed. Results for antikaon and hyperon-resonance spectral functions are presented for isospin symmetric and asymmetric matter.
We study the formation of resonances in terms of the chiral SU(3) Lagrangian. At leading order parameter-free predictions are obtained for the scattering of Goldstone bosons off any hadron once we insist on approximate crossing symmetry of the unitarized scattering amplitude. A wealth of empirically established resonances are recovered and so far unseen resonances are predicted. Here we review in some detail the properties of light axial-vector mesons.
I discuss the problem of formulating the baryon chiral perturbation theory ($χ$PT) in the presence of a light resonance, such as the $Δ(1232)$, the lightest nucleon resonance. It is shown how to extend the power counting of $χ$PT to correctly account for the resonant contributions. Recent applications of the resulting chiral effective-field theory to the description of pion production reactions in $Δ$-resonance region are briefly reviewed.
The processes involving low energy $\bar{K}N$ and $Yπ$ interactions (where $Y= Σ$ or $Λ$) are studied in the framework of heavy baryon chiral perturbation theory with the $Λ$(1405) resonance appearing as an independent field. The leading and next-to-leading terms in the chiral expansion are taken into account. We show that an approach which explicitly includes the $Λ$(1405) resonance as an elementary quantum field gives reasonable descriptions of both the threshold branching ratios and the energy dependence of total cross sections.
There is an important connection between the low energy theorems of QCD and the energy dependence of the Delta resonance in pi-N scattering, as well as the closely related gamma^{*} N -> pi N reaction. The resonance shape is due not only to the strong pi-N interaction in the p wave but the small interaction in the s wave; the latter is due to spontaneous chiral symmetry breaking in QCD (i.e. the Nambu-Goldstone nature of the pion). A brief overview of experimental tests of chiral perturbation theory and chiral based models is presented
The linear $\s$-model is used to study the effects of chiral symmetry in unitarized amplitudes incorporating scalar resonances. When just a single resonance is present, we show that the iteration of a chiral tree amplitude by means of regularized two-pion loops preserves the smallness of $\p\p$ interaction at low energies and estimate the importance of pion off-shell contributions. The inclusion of a second resonance is performed by means of a chiral extension of the linear $\s$-model lagrangian. The new $\p\p$ ampitude at tree level complies with low-energy theorems, depends on a mixing angle…
The extension of chiral theories to the description of resonances, via the incorporation of unitarity in coupled channels, has provided us with a new theoretical perspective on the nature of some of the observed excited hadrons. In this contribution some of the early achievements in the field of baryonic resonances are reviewed, the recent evidence of the two-pole nature of the Lambda(1405) is discussed and results on charmed baryon resonances are presented.
The structure of baryon resonance in coupled-channel meson-baryon scattering is studied from the viewpoint of chiral dynamics. The meson-baryon scattering amplitude can be successfully described together with the properties of the resonance in the scattering, by implementing the unitarity condition for the amplitude whose low energy structure is constrained by chiral theorem. Recently, there have been a major progress in the study of the structure of the resonance in chiral dynamics. We review the methods to clarify the structure of the resonance by focusing on the Lambda(1405) resonance.
The magnetic moments of the low-lying spin-parity $J^P=$ $1/2^-$, $3/2^-$ $Λ$ resonances, like, for example, $Λ(1405)$ $1/2^-$, $Λ(1520)$ $3/2^-$, as well as their transition magnetic moments, are calculated using the chiral quark model. The results found are compared with those obtained from the nonrelativistic quark model and those of unitary chiral theories, where some of these states are generated through the dynamics of two hadron coupled channels and their unitarization.
A nonlinear chiral SU(3) approach including the spin 3/2 decuplet is developed to describe dense matter. The coupling constants of the baryon resonances to the scalar mesons are determined from the decuplet vacuum masses and SU(3) symmetry relations. Different methods of mass generation show significant differences in the properties of the spin-3/2 particles and in the nuclear equation of state.
We study meson resonances with quantum numbers J^P=1^+ in terms of the chiral SU(3) Lagrangian. At leading order a parameter-free prediction is obtained for the scattering of Goldstone bosons off vector mesons with J^P=1^- once we insist on approximate crossing symmetry of the unitarized scattering amplitude. A resonance spectrum arises that is remarkably close to the empirical pattern. In particular, we find that the strangeness-zero resonances h_1(1380), f_(1285) and b_1(1235) are formed due to strong K \bar K_μand \bar K K_μchannels. This leads to large coupling constants of those resonance…
We study J^P=(3/2)^- baryon resonances as generated by chiral coupled-channel dynamics. Parameter free results are obtained in terms of the Weinberg-Tomozawa term predicting the leading s-wave interaction strength of Goldstone bosons with baryon-decuplet states. In the 'heavy' SU(3) limit with m_π= m_K \sim 500 MeV the resonances turn into bound states forming a decuplet and octet representation of the SU(3) group. Using physical masses the mass splitting are remarkably close to the empirical pattern.
We calculate the magnetic moments of the N(1535) resonance using the chiral unitary model, where the resonance is dynamically generated in the scatterings of the lowest-lying mesons and baryons. We obtain the magnetic moments of the resonance as +1.1 and -0.25 for p(1535) and n(1535), respectively, in units of the nuclear magneton. We discuss the origin of these numbers within the chiral unitary model, then we compare the present results with those of the quark model and the chiral doublet model. The possibility to observe the magnetic moments in experiments is also investigated.
The mass spectra of nucleon resonances with spin 1/2, 3/2, and 5/2 are systematically studied in the constituent quark model with meson-quark coupling, which is inspired by the spontaneous breaking of chiral symmetry of QCD. The meson-quark coupling gives rise not only to the one-meson-exchange potential between quarks but also to the self-energy of baryon resonances due to the existence of meson-baryon decay channels. The two contributions are consistently taken into account in the calculation. The gross properties of the nucleon resonance spectra are reproduced fairly well although the predi…
The nature of baryon resonances is studied in the dynamical chiral coupled-channel approach for meson-baryon scattering. In general, origin of resonances in two-body scattering can be classified into two categories: dynamically generated states and genuine elementary particles. We demonstrate that the genuine contribution in the loop function can be excluded by adopting a natural renormalization scheme. The origin of resonances can be studied by looking at the effective interaction in the natural renormalization scheme, which is deduced from the phenomenological amplitude fitted to experimenta…
Using a chiral unitary model in which the negative parity nucleon resonance $N^\ast \equiv N^\ast(1535)$ is generated dynamically by means of the Bethe Salpeter equation with coupled meson baryon channels in the $S = 0$ sector, we have obtained the $π^0 N^\ast N^\ast$ and $ηN^\ast N^\ast$ couplings. The $π^0 N^\ast N^\ast$ coupling has smaller strength and the same sign as the $π^0 N N$ coupling. This rules out the mirror assignment of chiral symmetry where the ground state nucleon $N$ and the negative parity resonance $N^\ast$ are envisaged as chiral partners in the baryon sector.
We present a detailed analysis of S-wave Kpi scattering up to 2 GeV, making use of the resonance chiral Lagrangian predictions together with a suitable unitarisation method. Our approach incorporates known theoretical constraints at low and high energies. The present experimental status, with partly conflicting data from different experiments, is discussed. Our analysis allows to resolve some experimental ambiguities, but better data are needed in order to determine the cross-section in the higher-energy range. Our best fits are used to determine the masses and widths of the relevant scalar re…
We stress, on theoretical and phenomenological grounds, the importance of the $Δ(1232)$-resonance in a chiral effective field theory approach applied to the study of $πN$ scattering. We show how its inclusion as a dynamical degree of freedom allow us to obtain reliably valuable information from $πN$ scattering data.
We study the phase diagram of a generalized chiral SU(3)-flavor model in mean-field approximation. In particular, the influence of the baryon resonances, and their couplings to the scalar and vector fields, on the characteristics of the chiral phase transition as a function of temperature and baryon-chemical potential is investigated. Present and future finite-density lattice calculations might constrain the couplings of the fields to the baryons. The results are compared to recent lattice QCD calculations and it is shown that it is non-trivial to obtain, simultaneously, stable cold nuclear ma…
Both scalar and vector light resonances can be generated from the unitarization of one-loop chiral perturbation theory. This amounts to using in a dispersion relation the chiral expansion, which incorporates the correct QCD quark mass dependence. We can thus predict the quark mass dependence of the poles associated to those light resonances. Our results compare well with some recent lattice results for the rho(770) mass and can be used as a benchmark for future lattice results on the rho(770) or the f0(600) also known as the sigma.
Heavy baryon chiral perturbation theory is briefly reviewed, paying particular attention to the role of the spin 3/2 delta resonances. The concept of resonance saturation for the baryonic sector is critically discussed. Starting from a relativistic formulation of the pion-nucleon-delta system, the heavy baryon chiral lagrangian including spin 3/2 resonances is constructed by means of a 1/m-expansion. The effective theory obtained admits a systematic expansion in terms of soft momenta, the pion mass $M_π$ and the delta-nucleon mass difference $Δ$.
We study the resonance properties within chiral perturbation theory by explicitly taking into account the U_A(1) anomaly effect. This assures we have the appropriate degrees of freedom of low energy QCD in the large Nc limit. We calculate the various resonance properties, such as mass, width and residues, for the physical case, i.e. Nc=3. Then we extrapolate the values of Nc to study the trajectories of resonance poles.
The properties of giant and pygmy resonances are calculated starting from chiral two-and three-nucleon interactions. The aim is to assess the predictive power of modern Hamiltonians and especially the role of the three-nucleon force. Methods based on the random-phase approximation (RPA) provide an optimal description of the modes of interest with minimal computational requirements. Here we discuss the giant resonances (GRs) of 40,48Ca isotopes and their low-energy dipole response. A comparison with previous results obtained with a transformed Argonne V18 two-nucleon potential points to certain…
In this talk we review the important role played by chiral SU(3) symmetry in hadron physics. Exciting new results on the formation of baryon resonances as implied by chiral coupled-channel dynamics are presented and discussed. The results are the consequence of progress made in formulating a consistent effective field theory for the meson-baryon scattering processes in the resonance region. Strangeness channels are found to play a decisive role in the formation of resonances. As a further application of chiral coupled-channel dynamics the properties of antikaons and hyperon resonances in cold …
Chiral quark models with Polyakov loop at finite temperature have been often used to describe the phase transition. We show how the transition to a hadron resonance gas is realized based on the quantum and local nature of the Polyakov loop.
We report on the latests developments in the field of baryonic resonances generated from the meson-baryon interaction in coupled channels using a chiral unitary approach. The collection of resonances found in different strangeness and isospin sectors can be classified into SU(3) multiplets. The Lambda(1405) emerges as containing the effect of two poles of the scattering amplitude and various reactions that might preferentially select one or the other pole are discussed.
In these lectures I make an introduction to chiral unitary theory applied to the meson baryon interaction and show how several well known resonances are dynamically generated, and others are predicted. Two very recent experiments are analyzed, one of them showing the existence of two $Λ(1405)$ states and the other one providing support for the $Λ(1520)$ resonance as a quasibound state of $Σ(1385) π$. The use of chiral Lagrangians to account for the hadronic interaction at the elementary level introduces a new approach to deal with the modification of meson and baryon properties in a nuclear me…
The internal structure of the resonant Lambda(1405) state is investigated based on meson-baryon coupled-channels chiral dynamics. We evaluate Lambda(1405) form factors which are extracted from current-coupled scattering amplitudes in meson-baryon degrees of freedom. Using several probe currents and channel decomposition, we find that the resonant Lambda(1405) state is dominantly composed of widely spread Kbar around N, with escaping pi Sigma component.
We present an ongoing project to assess the importance of D-waves and the $Δ(1232)$ resonance for descriptions of neutral pion photoproduction in Heavy Baryon Chiral Perturbation Theory. This research has been motivated by data published by the A2 and CB-TAPS collaborations at MAMI [1]. This data has reached unprecedented levels of accuracy from threshold through to the $Δ$ resonance. Accompanying the experimental work, there has also been a series of publications studying the theory that show that, to go beyond an energy of $E_γ=170$ MeV, it is necessary to include other aspects, in particula…
Baryon resonances with even and odd parity are collectively investigated from the viewpoint of chiral symmetry(ChS). We propose a quartet scheme where Delta's and N^*'s with even and odd parity form a chiral multiplet. This scheme gives parameter-free constraints on the baryon masses in the quartet, which are consistent with observed masses with spin 1/2, 3/2, 5/2. The scheme also gives selection rules in the one-pion decay: The absence of the parity non-changing decay N(1720) -> pi Delta(1232) is a typical example which should be confirmed experimentally to unravel the role of ChS in baryon r…
We consider the electromagnetic transition form factors of the Roper resonance in the framework of an effective field theory of pions, nucleons and delta and Roper resonances as explicit degrees of freedom. Due to the lack experimental data in the region of applicability of low energy effective field theory we fit available free coupling constants and compare obtained results compare to the predictions of a theoretical model.
By means of a coupled channel non-perturbative unitary approach, it is possible to extend the strong constrains of Chiral Perturbation Theory to higher energies. In particular, it is possible to reproduce the lowest lying resonances in meson-meson scattering up to 1.2 GeV using the parameters of the O(p^2) and O(p^4) Chiral Lagrangian. The meson baryon sector can also be tackled along similar lines. We report on an update of these results showing some examples of photon induced reactions where the techniques have been recently applied.
We perform a relativistic chiral effective field theory calculation of the radiative pion photoproduction ($γp \to π^0 p γ'$) in the $Δ$-resonance region, to next-to-leading order in the ``delta-expansion''. This work is aimed at a model-independent extraction of the $Δ^+$ magnetic moment from new precise measurements of this reaction. It also predicts the chiral behavior of $Δ$'s magnetic moment, which can be used to extrapolate the recent lattice QCD results to the physical point.
Several conceptual points concerning the inclusion of the $Δ$(1232) resonance in the framework of chiral effective-field theory are discussed, with an emphasis on the problem of power counting in the baryon sector in general. I also formulate a new dispersion relation in the pion-mass squared (or, the quark mass) and make a link between the power counting and the analytic properties of chiral expansion. A controversy regarding the determination of the proton's magnetic polarizability from Compton-scattering data is stressed here as well.
We have recently completed the one loop calculation of meson-meson scattering within Chiral Perturbation Theory. Once unitarized, these amplitudes provide simultaneously a remarkable description of the resonance region up to 1.2 GeV as well as the low energy region, respecting the chiral symmetry expansion. The position of the poles in these amplitudes is related to the mass and width of the associated resonances that are generated without being explicitly included in the Lagrangian. The spectroscopic nature of these states can then be deduced by studying the behavior of these poles, through t…
The Lambda(1405) resonance is studied by a chiral unitary approach, in which the resonance is dynamically generated in coupled-channel meson-baryon scattering. Investigating the analytic structure of the scattering amplitudes obtained by the chiral unitary approach, we find two poles around the energies of the Lambda(1405) coupling differently to the meson-baryon states. We reach the conclusion that the Lambda(1405) resonance seen in experiments is not just one single resonance, but a superposition of these two states.
We show the results for the scattering poles associated to the rho, f0, a0, K*, sigma and kappa resonances in meson-meson scattering. Our amplitudes are obtained from the complete one-loop meson-meson scattering amplitudes from Chiral Perturbation Theory. Once unitarized with the Inverse Amplitude Method, they describe remarkably well the data simultaneously in the low energy and resonance regions up to 1.2 GeV, using low energy parameters compatible with present determinations.
We report on our recent progress in the generation of resonant behavior in unitarized meson-meson scattering amplitudes obtained from Chiral Perturbation Theory. These amplitudes provide simultaneously a remarkable description of the resonance region up to 1.2 GeV as well as the low energy region, since they respect the chiral symmetry expansion. By studying the position of the poles in these amplitudes it is possible to determine the mass and width of the associated resonances, as well as to get a hint on possible classification schemes, that could be of interest for the spectroscopy of the s…
By means of a coupled channel non-perturbative unitary approach, it is possible to extend the strong constrains of Chiral Perturbation Theory to higher energies. In particular, it is possible to reproduce the lowest lying resonances in meson-meson scattering up to 1.2 GeV using the parameters of the O(p^2) and O(p^4) Chiral Lagrangian. We report on an update of these results examining their possible relevance for meson spectroscopy.
We study the origin of the resonances associated with pole singularities of the scattering amplitude in the chiral unitary approach. We propose a "natural renormalization" scheme using the low-energy interaction and the general principle of the scattering theory. We develop a method to distinguish dynamically generated resonances from genuine quark states [Castillejo-Dalitz-Dyson (CDD) poles] using the natural renormalization scheme and phenomenological fitting. Analyzing physical meson-baryon scatterings, we find that the Lambda(1405) resonance is largely dominated by the meson-baryon molecul…
The s-wave meson-baryon interaction is studied using the lowest-order chiral Lagrangian in a unitary coupled-channels Bethe-Salpeter equation. In the strangeness $S=-1$ sector the low-energy $K^- p$ dynamics leads to the dynamical generation of the $Λ(1405)$ as a ${\bar K}N$ state, along with a good description of the $K^- p$ scattering observables. At higher energies, the $Λ(1670)$ is also found to be generated dynamically as a $K Ξ$ quasibound state for the first time. For strangeness S=0, it is the $S_{11}(1535)$ resonance that emerges from the coupled-channels equations, leading to a satis…
We analyze recent results on isoscalar $ππ$ scattering from a $N_f=2+1$ lattice simulation by the HadronSpectrum collaboration by re-summing the two-flavor chiral scattering amplitude of the next-to-leading order in the so-called inverse amplitude method. The lattice data can be well extrapolated to the physical pion mass. We also find that both $I=0$ and $I=1$ lattice data can be described simultaneously for pion masses up to $M_π=236$ MeV.
The nature of the Lambda(1405) is discussed based on the unitarised coupled-channels approach with chiral dynamics (chiral unitary model). This approach describes the Kbar N scattering cross sections and the Lambda(1405) spectra phenomenologically very well. With this successful description of Lambda(1405), it is found that the Lambda(1405) is composed by two resonance states having different coupling nature to the meson-baryon states. As a consequence, the resonance position in the pi Sigma invariant mass spectrum depends on the initial channel of the Lambda(1405) production. To observe the L…
In this work we address the question of how well the chiral crossover transition can be understood in terms of a noninteracting hadron resonance gas model. Using the latest results on the variation of hadron masses as a function of the pion mass from lattice quantum chromodynamics, we study the temperature dependence of the renormalized chiral condensate in 2+1 flavor QCD. Furthermore, we suggest a better criterion to estimate of the pseudocritical temperature, which gives $T_c = 161.2 \pm 1.7$ MeV, which is much improved compared to all the earlier results within the hadron resonance gas mode…
We calculate hyperon-nucleon and hyperon-hyperon interactions at next-to-leading order in SU(3) baryon chiral perturbation theory extending earlier work by the Bonn-Juelich group. The constructed potentials in momentum space include all one- and two-meson exchange terms generated by the SU(3) chiral Lagrangian. Effects from intermediate decuplet baryons are considered as well. These chiral baryon-baryon potentials, together with appropriate contact terms, provide a new basis for systematic studies of hyperon-nucleon scattering and light hypernuclei.
We study nuclear multipole resonances in the framework of the random phase approximation using the chiral potential NNLO$_{\text{sat}}$. This potential includes two- and three-body terms that has been simultaneously optimized to low-energy nucleon-nucleon scattering data and selected nuclear structure data. Our main foci have been the isoscalar monopole, isovector dipole, and isoscalar quadrupole resonances of the closed-shell nuclei, $^4$He, $^{16,22,24}$O, and $^{40,48}$Ca. These resonance modes have been widely observed in experiment. In addition, we use a renormalized chiral potential $V_{…
The $SU(3)$ chiral effective lagrangian at next-to-leading order is applied to the S-wave meson-baryon interaction in the energy range around the $ηN$ threshold. Potentials are derived from this lagrangian and used in a coupled channel calculation of the $πN$, $ηN$, $K Λ$, $K Σ$ system in the isospin-$1/2$, $l=0$ partial wave. Using the same parameters as obtained from a fit to the low energy $\overline{K} N$ data it is found that a quasi-bound $K Σ$-state is formed, with properties remarkably similar to the $S_{11}(1535)$ nucleon resonance. In particular, we find a large partial decay width i…
As the pion mass approaches a critical value $m_π^\star$ from below, an $S$-wave resonance crosses pion-baryon threshold and becomes a bound state with arbitrarily small binding energy, thus driving the scattering length to diverge. I explore the consequences of chiral symmetry for the values of $m_π$ close to $m_π^\star$. It turns out that chiral symmetry is crucial for an $S$-wave resonance to be able to stand very near threshold and in the meantime to remain narrow, provided that the mass splitting is reasonably small. The effective range of pion-baryon scattering is unexpectedly large, pro…
We construct pi-pi amplitudes that fulfill exact elastic unitarity, account for one loop Chiral Perturbation Theory contributions and include all 1/Nc leading terms, with the only limitation of considering just the lowest-lying nonet of exchanged resonances. Within such scheme, the Nc dependence of sigma and rho masses and widths is discussed. Robust conclusions are drawn in the case of the rho resonance, confirming that it is a stable meson in the limit of a large number of QCD colors, Nc. Less definitive conclusions are reached in the scalar-isoscalar sector. With the present quality of data…
Based on the recent phenomenological analysis done by M. Mojzis, Eur. Phys. Jour. {\bf C2} (1998) 182, of $πN $ scattering within the framework of Heavy Baryon Chiral Perturbation Theory we predict, after a suitable unitarization of the amplitude, the $Δ$ resonance at $\sqrt{s} = M_Δ= 1238 \er{22}{18}{\rm MeV} $ and with a width of $ Γ_Δ= 150 \er{43}{31} {\rm MeV} $ in excellent agreement with the experimental numbers. The error bars reflect only the uncertainties in the low energy parameters as determined from an extrapolation to threshold of experimental data. We also describe satisfactorily…
The dimensionless parameter $ξ= M_π^2/(16 π^2 F_π^2)$, where $F_π$ is the pion decay constant and $M_π$ is the pion mass, is expected to control the convergence of chiral perturbation theory applicable to QCD. Here we demonstrate that a strongly coupled lattice gauge theory model with the same symmetries as two-flavor QCD but with a much lighter $σ$-resonance is different. Our model allows us to study efficiently the convergence of chiral perturbation theory as a function of $ξ$. We first confirm that the leading low energy constants appearing in the chiral Lagrangian are the same when calcula…
