We review how the use of recent precise data on kaon decays together with forward dispersion relations (FDR) and Roy's equations allow us to determine the sigma resonance pole position very precisely, by using only experimental input. In addition, we present preliminary results for a modified set of Roy-like equations with only one subtraction, that show a remarkable improvement in the precision around the sigma resonance region. For practical applications, these results are shown to be very well approximated by a very simple conformal expansion.
We show how the new precise data on kaon decays together with forward dispersion relations, sum rules and once- and twice-subtracted Roy's equations allow for a precise determination of the sigma meson pole position. We present a comparison and a study of the different sources of uncertainties when using either once- or twice-subtracted Roy's equations to analyze the data. Finally we present a preliminary determination of the sigma pole from the constrained dispersive data analysis.
We review how the use of recent precise data on kaon decays together with forward dispersion relations (FDR) and Roy's equations allow us to determine the sigma resonance pole position very precisely, by using only experimental input. In addition, we present preliminary results for a modified set of Roy-like equations with only one subtraction, that show a remarkable improvement in the precision around the sigma region. We also improve the matching between the parametrizations at low and intermediate energy of the S0 wave, and show that the effect of this on the sigma pole position is negligib…
BES data on the sigma pole are refitted taking into account new information on coupling of sigma to KK and eta-eta. The fit also includes Cern-Munich data on pi-pi elastic phases shifts and Ke4 data, and gives a pole position of 500 +- 30 - i(264 +- 30) MeV. However, there is a clear discrepancy with the sigma pole position recently predicted by Caprini et al. using the Roy equation. This discrepancy may be explained naturally by uncertainties arising from inelasticity in KK and eta-eta channels and mixing between sigma and f0(980). Adding freedom to accomodate these uncertainties gives an opt…
We study how we can understand the change of the spectral function and the pole location of the correlation function for sigma at finite temperature, which were previously obtained in the linear sigma model with a resummation technique called optimized perturbation theory. There are two relevant poles in the sigma channel. One pole is the original sigma pole which shows up as a broad peak at zero temperature and becomes lighter as the temperature increases. The behavior is understood from the decreasing of the sigma condensate, which is consistent with the Brown-Rho scaling. The other pole cha…
We investigate the determination of the $σ$ pole from $ππ$ scattering data below the $K\bar{K}$ threshold, including the new precise results obtained from $K_{e4}$ decay by NA48/2 Collaboration. We discuss also the experimental status of the threshold parameters $a_0^0$ and $b_0^0$ and the phase shift $δ_0^0$. In order to reduce the theoretical bias, we use a large class of analytic parametrizations of the isoscalar $S$-wave, based on expansions in powers of conformal variables. The $σ$ pole obtained with this method is consistent with the prediction based on ChPT and Roy equations. However, t…
We use our latest dispersive analysis of pion-pion scattering data and the very recent Kl4 experimental results to obtain the mass, width and couplings of the two lightest scalar-isoscalar resonances. These parameters are defined from their associated poles in the complex plane. The analytic continuation to the complex plane is made in a model independent way by means of once and twice subtracted dispersion relations for the partial waves, without any other theoretical assumption. We find the f0(600) pole at (457^{+14}_{-13})-i(279^{+11}_{-7}) MeV and that of the f0(980) at (996\pm7)-i(25^{+10…
We show how the Regge trajectory of a resonance can be obtained from its pole in a scattering process and analytic constraints in the complex angular momentum plane. The method is suited for resonances that dominate an elastic scattering amplitude. In particular, from the rho(770) resonance pole in pion-pion scattering, we obtain its linear Regge trajectory, characteristic of ordinary quark-antiquark states. In contrast, the f0(500) pole -the sigma meson- which dominates scalar isoscalar pion-pion scattering, yields a non-linear trajectory with a much smaller slope at the f0(500) mass. Convers…
The first part of this report reviews recent developments at the interface between lattice work on QCD with light dynamical quarks, effective field theory and low energy precision experiments. Then I discuss how dispersion theory can be used to analyze the low energy structure of the $ππ$ scattering amplitude in a model independent manner. This leads to an exact formula for the mass and width of the lowest few resonances, in terms of observable quantities. As an application, I consider the pole position of the $σ$, paying particular to error propagation in the numerical analysis. The report is…
We report here our results on how to obtain the Regge trajectory of a resonance from its pole in a scattering process by imposing analytic constraints in the complex angular momentum plane. The method, suited for resonances that dominate an elastic scattering amplitude, has been applied to the ρ(770) and the f_0(500) resonances. Whereas for the former we obtain a linear Regge trajectory, characteristic of ordinary quark-antiquark states, for the latter we find a non-linear trajectory with a much smaller slope at the resonance mass. This provides a strong indication of the non-ordinary nature o…
The K^- p --> pi^0 pi^0 Sigma^0 reaction is studied within a chiral unitary model. The distribution of pi^0 Sigma^0 states forming the Lambda(1405) shows, in agreement with a recent experiment, a peak at 1420 MeV and a relatively narrow width of 38 MeV. This reaction gives maximal possible weight to the second Lambda(1405) state found in chiral unitary theories, which is narrow and of higher energy than the nominal Lambda(1405). In contrast, the pi^- p --> K^0 pi Sigma reaction gives more weight to the pole at lower energy and with a larger width. The data of these two experiments, together wi…
We estimate the di-photon coupling of $f_0(600)$, $f_0(980)$ and $f_2(1270)$ resonances in a coupled channel dispersive approach. The $f_0(600)$ di-photon coupling is also reinvestigated using a single channel $T$ matrix for $ππ$ scattering with better analyticity property, and it is found to be significantly smaller than that of a $\bar qq$ state. Especially we also estimate the di-photon coupling of the third sheet pole located near $\bar KK$ threshold, denoted as $f_0^{III}(980)$. It is argued that this third sheet pole may be originated from a coupled channel Breit-Wigner description of th…
We review the use of new and precise dispersive equations, which also implement crossing symmetry, in order to shed further light on the long-standing puzzle in the parameters of the f0(500), as well as the f0(980). This puzzle is finally being settled thanks to several analyses carried out during the last years. In this talk we show how our very recent dispersive data analysis allowed for a precise and model independent determination of the amplitudes for the S,P,D and F waves. In particular, we show how the analytic continuation of once subtracted dispersion relations for the S0 wave to the …
We study the effect of thermal width of $π$ on the spectral function of $σ$ applying a resummation technique called optimized perturbation theory at finite temperature ($T$) to ${\cal O}(4)$ linear sigma model. In order to take into account finite thermal width of $π$, we replace the internal pion mass in the self-energy of $σ$ with that of complex pole found in a previous paper. The obtained spectral function for $T\aplg 100 {\rm MeV}$ turns out to possess two broad peaks. Although a sharp peak at $σ\toππ$ threshold was observed in the one-loop calculation without pion thermal width, the peak…
We study the effect of the thermal width of $π$ on the spectral function of $σ$. In order to take into account a finite thermal width of $π$, we replace the internal pion mass in the self-energy of $σ$ with that of the complex pole found in a previous paper. The obtained spectral function for $T\aplg 100 {\rm MeV}$ turns out to possess two broad peaks. Although a sharp peak at $σ\toππ$ threshold was observed in the one-loop calculation without the pion thermal width, the peak is shown to be smeared out. We also search for the poles of the $σ$ propagator and analyze the behavior of the spectral…
Based on the recently proposed Roy-Steiner equations for pion-nucleon scattering, we derive a system of coupled integral equations for the pi pi --> N-bar N and K-bar K --> N-bar N S-waves. These equations take the form of a two-channel Muskhelishvili-Omnes problem, whose solution in the presence of a finite matching point is discussed. We use these results to update the dispersive analysis of the scalar form factor of the nucleon fully including K-bar K intermediate states. In particular, we determine the correction Delta_sigma=sigma(2M_pi^2)-sigma_{pi N}, which is needed for the extraction o…
The available data on the a0(980), f0(980), f0(1300) and K*0(1430) mesons are fitted as a distorted 0++ nonet using only 6 parameters and a very general model. This includes all light two-pseudoscalar thresholds, constraints from Adler zeroes, flavour symmetric couplings, unitarity and physically acceptable analyticity. One finds that with the large overall coupling there can appear two physical resonance poles from only one q bar q state. Thus the f0(980) and f0(1300) resonance poles are two manifestations of the same s bar s state. On the other hand, the u bar u state, when unitarized and st…
In the framework of the dispersion relation N/D-method we restore the low-energy pi-pi (IJ^{PC}=00^{++})-wave amplitude sewing it with the previously obtained K-matrix solution for the region 450--1900 MeV [V.V. Anisovich, Yu.D. Prokoshkin and A.V. Sarantsev, Phys. Lett. B389, 388 (1996)]. The restored N/D-amplitude has a pole on the second sheet of the complex-s plane, near the pi-pi threshold. We discuss the hypothesis that this low-mass pole, or the low-mass sigma-meson, corresponds to the dynamical state related to the confinement forces, that is the eyewitness of confinement.
Pion pion scattering is studied in a generalized linear sigma model which contains two scalar nonets (one of quark-antiquark type and the other of diquark-antidiquark type) and two corresponding pseudoscalar nonets. An interesting feature concerns the mixing of the four isosinglet scalar mesons which yield poles in the scattering amplitude. Some realism is introduced by enforcing exact unitarity via the K-matrix method. It is shown that a reasonable agreement with experimental data is obtained up to about 1 GeV. The poles in the unitarized scattering amplitude are studied in some detail. The l…
We discuss how the lightest scalars, in particular the broad sigma resonance, can be understood as unitarized (qbar q) states within a unitarized quark model (UQM). The bare (qbar q) scalars are strongly distorted by hadronic mass shifts, and the (ubar u+ dbar d) state becomes a very broad resonance, with its pole at 470-i250 MeV. This is the sigma meson required by models for spontaneous breaking of chiral symmetry. We also discuss the less well known phenomenon that with a large coupling there can appear two physical resonance poles on the second sheet although only one bare quark-antiquark …
We review our recent dispersive and model independent determination of the lightest two scalars, in terms of poles and residues - or mass, width and coupling- by means of once and twice subtracted Roy equations, using as input constrained fits to data, including the most recent ones from Kl4 decays. We find the f0(600) pole at (457+14-13)-i(279+11-7) MeV and that of the f0(980) at (996+-7)-i(25+10-6) MeV, whereas their respective couplings to two pions are 3.59+0.11-0.13 GeV and 2.3+-0.2 GeV.
We present a coupled system of integral equations for the pi pi --> Nbar N and Kbar K --> Nbar N S-waves derived from Roy-Steiner equations for pion-nucleon scattering. We discuss the solution of the corresponding two-channel Muskhelishvili-Omnes problem and apply the results to a dispersive analysis of the scalar form factor of the nucleon fully including Kbar K intermediate states. In particular, we determine the corrections Delta_sigma and Delta_D, which are needed for the extraction of the pion-nucleon sigma term from pi N scattering, and show that the difference Delta_D - Delta_sigma=(-1.…
Model independent amplitude analyses of $π^- p_\uparrow \to π^- π^+ n$ on polarized target at 17.2 GeV/c reveal resonant structure of S-wave transversity amplitudes $|\bar S|^2Σ$ and $|S|^2Σ$ near 750 MeV. Simultaneous fit to $|\bar S|^2Σ$ and $|S|^2Σ$ with a single $σ$ pole yields $m_σ= 775 \pm 17$ MeV and $Γ_σ= 147 \pm 33$ MeV. Simultaneous fit with two common $σ$ poles yields a lower $χ^2/dpt$. Their resonance parameters are $m_σ= 786 \pm 24$ MeV, $Γ_σ= 130 \pm 47$ MeV and $m_{σ^\prime} = 670 \pm 30$ MeV, $Γ_{σ^\prime} = 59 \pm 58$ MeV.
We study basic properties of scalar hadronic resonances within the so-called extended Linear Sigma Model (eLSM), which is an effective model of QCD based on chiral symmetry and dilatation invariance. In particular, we focus on the mass and decay width of the scalar isovector state $a_{0}(1450)$ and perform a numerical study of the propagator pole(s) on the unphysical Riemann sheets. In this work, this meson is understood as a seed state explicitly included in the eLSM. Our results show that the inclusion of hadronic loops does not modify much the previously obtained tree-level results. Moreove…
We discuss how the a_0(980), f_0(980), K^*_0(1430) and particularly the broad sigma resonance can be understood within a coupled channel framework, which includes all light two-pseudoscalar thresholds together with constraints from Adler zeroes, flavour symmetric couplings, unitarity and physically acceptable analyticity. All (qbar q) scalars are, when unitarized, strongly distorted by hadronic mass shifts, and the nonstrange isoscalar state becomes a very broad resonance, with its pole at 470-i250 MeV. We believe this is the sigma meson required by models for spontaneous breaking of chiral sy…
The properties of $σ$(600) meson are studied using the QCD sum rules (QSR) for the tetraquark operators. In the SU(3) chiral limit, we investigate separately SU(3) singlet and octet tetraquark states as constituents of the $σ$ meson, and discuss their roles for the classification of the light scalar nonets, $σ, f_0, a_0$, and $κ$, as candidates of tetraquark states. All our analyses are performed in the the suitable Borel window which is indispensable to avoid the {\it pseudo peak} artifacts outside of the Borel window. The acceptably wide Borel window originates after preparing the favorable …
We analyze the $f_0(500)$ state generated as a pole of $ππ$ scattering within unitarized low-energy effective theories at finite temperature. First, we report on the $σ$ self-energy in the LSM, which is used as a benchmark in order to test the hypotheses carried out. The relation of that thermal pole with the scalar susceptibility is studied within a scalar saturation approach, which yields results complying with lattice data. The robustness and predictability of this method are studied in terms of the low-energy constants involved and the unitarization method. Our analysis highlights the impo…
The K^- p --> pi^0 pi^0 Sigma^0 reaction is studied within a chiral unitary model. The distribution of pi^0 Sigma^0 states forming the Lambda(1405) shows, in agreement with a recent experiment, a peak at 1420 MeV and a relatively narrow width of Gamma = 38 MeV. The mechanism for the reaction is largely dominated by the emission of a pi^0 prior to the K^- p interaction leading to the Lambda(1405). This ensures the coupling of the Lambda(1405) to the K^- p channel, thus maximizing the contribution of the second state found in chiral unitary theories, which is narrow and of higher energy than the…
I present a short review of the current understanding of the scalar meson sector, with special attention to the problem of the low-mass $σ$. The dispersion relation $N/D$-method used for the restoration of the low-energy $ππ$ $(IJ^{PC}=00^{++})$-wave amplitude is discussed. The low-energy $ππ$ amplitude was determined from the data in the energy region 280--500 MeV and it was sewn with the previously found $K$-matrix solution for the region 450--1950 MeV. The $N/D$-amplitude has a pole on the second sheet of the complex-$s$ plane, near the $ππ$ threshold at $\sqrt s \simeq 430-i325$ MeV, that …
Complex mass poles, or ghost poles, are present in the Hartree-Fock solution of the Schwinger-Dyson equation for the nucleon propagator in renormalizable models with Yukawa-type meson-nucleon couplings, as shown many years ago by Brown, Puff, and Wilets (BPW). These ghosts violate basic theorems of quantum field theory and their origin is related to the ultraviolet behavior of the model interactions. Recently, Krein et.al, proved that the ghosts disappear when vertex corrections are included in a self-consistent way, softening the interaction sufficiently in the ultraviolet region. In previous…
We apply a recently developed dispersive formalism to calculate the Regge trajectories of the $f_2(1270)$ and $f_2'(1525)$ mesons. Trajectories are calculated, not fitted to a family of resonances. Assuming that these spin-2 resonances can be treated in the elastic approximation the only input are the pole position and residue of the resonances. In both cases, the predicted Regge trajectories are almost real and linear, with slopes in agreement with the universal value of order 1 GeV$^{-2}$.
We discuss the determination of the $f_0(500)$ (or $σ$) resonance by analytic continuation through Padé approximants of the $ππ$-scattering amplitude from the physical region to the pole in the complex energy plane. The aim is to analyze the uncertainties of the method, having in view the fact that analytic continuation is an ill-posed problem in the sense of Hadamard. Using as input a class of admissible parameterizations of the scalar-isoscalar $ππ$ partial wave, which satisfy with great accuracy the same set of dispersive constraints, we find that the Roy-type integral representations lead …
The lightest QCD resonance, the sigma, has been recently fixed in the pi-pi scattering amplitude. The nature of this state remains nowadays one of the most intriguing and difficult issues in particle physics. Its coupling to photons is crucial to discriminate its structure. We propose a new method that fixes this coupling using only available precise experimental data on the proton electromagnetic polarizabilities together with analyticity and unitarity. Taking into account the uncertainties in the analysis and in the parameter values, our result is Gamma_{pole}(sigma -> gamma gamma) = (1.2 +-…
In this paper, we present a data-driven analysis of the $γγ\to D^+D^-$ and $γγ\to D^0\bar{D}^0$ reactions from threshold up to 4.0 GeV in the $D\bar{D}$ invariant mass. For the $S$-wave contribution, we adopt a partial-wave dispersive representation, which is solved using the $N/D$ ansatz. The left-hand cuts are accounted for using the model-independent conformal expansion. The $D$-wave $χ_{c2}(3930)$ state is described as a Breit-Wigner resonance. The resulting fits are consistent with the data on the invariant mass distribution of the $e^+e^- \to J/ψD\bar{D}$ process. Performing an analytic …
A Kbar N-pi Sigma-pi Lambda coupled-channel potential is constructed on the basis of chiral SU(3) dynamics. Several matching conditions are introduced to formulate an equivalent local potential that reproduces the coupled-channel scattering amplitudes resulting from chiral SU(3)_L times SU(3)_R meson-baryon effective field theory. In contrast to a previously constructed effective single-channel Kbar N potential, the explicit treatment of the pi Sigma channel yields a natural description of the low-mass pole as part of the two-pole structure of the Lambda(1405) resonance. The energy dependence …
Complex poles of the unitarized pi-pi scattering amplitude in nuclear matter are studied. Partial restoration of chiral symmetry is modeled by the decrease of in-medium pion decay constant f*_{pi}. For large chiral restoration (f*_{pi}/f_{pi} << 1), 2nd sheet poles in the scalar (sigma) and the vector (rho) mesons are both dictated by the Lambert W function and show universal softening as f*_{pi} decreases. In-medium pi-pi cross section receives substantial contribution from the soft mode and exhibits a large enhancement in low-energy region. Fate of this universality for small chiral restorat…
Chiral first order phase transition at finite baryon density and zero temperature from self-consistent pole masses in the linear sigma model with quarks
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Departamento de Física, Universidade Federal de São Paulo（圣保罗联邦大学物理系）；Instituto de Física Teórica, Universidade Estadual Paulista（圣保罗州立大学理论物理研究所）
It is shown from a very general model and an analysis of data on the lightest 0++ meson nonet that the f0(980) and f0(1200) resonance poles are two manifestations of the same ss state. Similarily the a0(980) and the a0(1450) are likely to be two manifestations of the same qq state. On the other hand, the uu+dd state, when unitarized and strongly distorted by hadronic mass shifts, becomes an extremely broad Breit-Wigner-like background, m=860 MeV, Gamma=880 MeV, with its pole at s=(0.158-i0.235) GeV^2. This we identify with the sigma meson required by models for spontaneous breaking of chiral s…
Neuro-dispersive extractions of light-meson resonances
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of California, Berkeley（加州大学伯克利分校）；The College of William & Mary（威廉与玛丽学院）；Università degli Studi di Messina（墨西拿大学）；Thomas Jefferson National Accelerator Facility（托马斯·杰斐逊国家加速器设施）；Old Dominion University（老道明大学）；Universidad Nacional de Educación a Distancia (UNED)（西班牙国立远程教育大学）；INFN Sezione di Catania（意大利国家核物理研究所卡塔尼亚分部）
We present a dispersive representation of the $γN\rightarrow πN$ partial-wave amplitude based on unitarity and analyticity. In this representation, the right-hand-cut contribution responsible for $πN$ final-state-interaction effect are taken into account via an Omnés formalism with elastic $πN$ phase shifts as inputs, while the left-hand-cut contribution is estimated by invoking chiral perturbation theory. Numerical fits are performed in order to pin down the involved subtraction constants. It is found that good fit quality can be achieved with only one free parameter and the experimental data…
We describe the meson-meson data for the ($IJ^{PC}=00^{++}$) wave at $280\leq\sqrt s\leq 1900$ MeV in two approaches: (i) the K-matrix approach and (ii) the dispersion relation D-matrix method. With a good description of low energy data (at $280\leq\sqrt s\leq 900$ MeV) as well as the data of two-meson transition amplitudes and antiproton-proton annihilation into three pseudoscalar meson states (at $450\leq\sqrt s\leq 1950$ MeV) we have found the positions of the resonance poles: (i) for the $σ$ meson pole: $M_σ= (390\pm 35)-i(235\pm 50)$ MeV; (ii) two poles for the $f_0(980)$, on the second s…
We present a data-driven analysis of the resonant S-wave $ππ\to ππ$ and $πK \to πK$ reactions using the partial-wave dispersion relation. The contributions from the left-hand cuts are accounted for using the Taylor expansion in a suitably constructed conformal variable. The fits are performed to experimental and lattice data as well as Roy analyses. For the $ππ$ scattering we present both a single- and coupled-channel analysis by including additionally the $K\bar{K}$ channel. For the latter the central result is the Omnès matrix, which is consistent with the most recent Roy and Roy-Steiner res…
The existence and properties of the sigma meson have been controversial for almost six decades, despite playing a central role in the spontaneous chiral symmetry of QCD or in the nucleon-nucleon attraction. This controversy has also been fed by the strong indications that it is not an ordinary quark-antiquark meson. Here we review both the recent and old experimental data and the model independent dispersive formalisms which have provided precise determinations of its mass and width, finally settling the controversy and leading to its new name: $f_0(500)$. We then provide a rather conservative…
We present a data-driven analysis of the S-wave $ππ\to ππ\,(I=0,2)$ and $πK \to πK\,(I=1/2, 3/2)$ reactions using the partial-wave dispersion relation. The contributions from the left-hand cuts are parametrized using the expansion in a suitably constructed conformal variable, which accounts for its analytical structure. The partial-wave dispersion relation is solved numerically using the $N/D$ method. The fits to the experimental data supplemented with the constraints from chiral perturbation theory at threshold and Adler zero give the results consistent with Roy-like (Roy-Steiner) analyses. F…
We study the Landau-gauge Gribov ghost form-factor sigma(p^2) for SU(N) Yang-Mills theories in the d-dimensional case. We find a qualitatively different behavior for d=3,4 w.r.t. d=2. In particular, considering any (sufficiently regular) gluon propagator D(p^2) and the one-loop-corrected ghost propagator G(p^2), we prove in the 2d case that sigma(p^2) blows up in the infrared limit p -> 0 as -D(0)\ln(p^2). Thus, for d=2, the no-pole condition σ(p^2) < 1 (for p^2 > 0) can be satisfied only if D(0) = 0. On the contrary, in d=3 and 4, sigma(p^2) is finite also if D(0) > 0. The same results are ob…
We review our recent study of the pion mass dependence of the rho and sigma resonances, generated from one-loop SU(2) Chiral Perturbation Theory (ChPT) with the Inverse Amplitude Method (IAM). In order to properly account for the Adler zero region, we also review the recently obtained modified version of the IAM; which is based on analyticity, elastic unitarity and ChPT at low energies, thus yielding the correct pion mass dependence of the resonance pole positions up to next-to-leading order in ChPT. As main results we find that the rho-pi-pi coupling constant is almost pion mass independent a…
In this work we present a precise and model-independent dispersive determination from data of the existence and parameters of the lightest strange resonance $κ/K_0^*(700)$. We use both subtracted and unsubtracted partial-wave hyperbolic and fixed-$t$ dispersion relations as constraints on combined fits to $πK\rightarrowπK$ and $ππ\rightarrow K\bar K$ data. We then use the hyperbolic equations for the analytic continuation of the isospin $I=1/2$ scalar partial wave to the complex plane, in order to determine the $κ/K_0^*(700)$ and $K^*(892)$ associated pole parameters and residues.
The theoretical analysis of the $γγ\to π^0η$ process is presented within the energy range up to 1.4 GeV. The $S$-wave resonance $a_0(980)$ is described involving the coupled channel dispersive framework and the $D$-wave $a_2(1320)$ is approximated as a Breit-Wigner resonance. For the $a_0(980)$ the pole is found on the IV Riemann sheet resulting in a two-photon decay width of $Γ_{a_0\toγγ}=0.27(4)$ keV. The first dispersive prediction is provided for the single-virtual $γγ^*(Q^2)\toπ^0η$ process in the spacelike region up to $Q^2=1$ GeV$^2$.
Our results on obtaining the Regge trajectory of a resonance from its pole in a scattering process and from analytic constraints in the complex angular momentum plane are presented. The method, suited for resonances that dominate an elastic scattering amplitude, has been applied to the $ρ(770)$, $f_2(1270)$, $f_2'(1525)$ and $f_0(500)$ resonances. Whereas for the first three we obtain linear Regge trajectories, characteristic of ordinary quark-antiquark states, for the latter we find a non-linear trajectory with a much smaller slope at the resonance mass. We also show that if a linear trajecto…
The chiral limit of the rho and sigma masses and widths is discussed. We work within the inverse amplitude method to one loop in SU(2) ChPT and analyze the consequences that all chiral logarithms cancel out in the rho-channel, while they do not cancel for the sigma case, and how they strongly influence the properties of this latter resonance. Our results confirm and explain the different behavior of the sigma and rho poles for NC not far from 3, but we extend the analysis to very large NC, where the behavior of these two resonances is re-analyzed. We note that the rather natural requirement of…
We extract the pole positions, hadronic and gamma-gamma widths of sigma and f_0(980, from pi-pi and gamma-gamma scattering data using an improved analytic K-matrix model. Our results favour a large gluon component for the sigma and a \bar ss or/and gluon component for the f_0(980) but neither a large four-quark nor a molecule component. Gluonium sigma_B production from J/psi, phi radiative and D_s semi-leptonic decays are also discussed.
A pole in the D-pi S-wave analogous to the sigma and kappa is predicted at 2098 +- 40 - i(260 +- 40) MeV. The main objective of this paper is to provide formulae for fitting it to data.
The variation of the resonance poles, i.e., the mass and width, originating from changing the values of $N_C$, the number of the QCD colors, provide an intuitive theoretical method to discriminate the interior constituents of hadrons. Many different approaches, including unitarized chiral amplitudes, dispersive methods, quark models, linear-sigma-model-like framework, etc., have been widely used to determine the $N_C$ trajectories of the various resonance pole positions. We focus on the discussions of the light-flavor meson resonances in this work.
We report our recent effort for the extraction of resonance parameters (complex pole mass and residues etc.) associated with Lambda* and Sigma* hyperons. This was accomplished via a comprehensive partial-wave analysis of the data for K^- p --> barK N, pi Sigma, pi Lambda, eta Lambda, K Xi reactions from the thresholds up to W=2.1 GeV within a dynamical coupled-channels approach. The results suggest a possible existence of new narrow J^P=3/2^+ Λresonance with pole mass 1671^{+2}_{-8} -i(5^{+11}_{-2}) MeV, located close to the eta Lambda threshold. This resonance is found to be responsible for r…
A local coupled-channels Kbar N-pi Sigma-pi Lambda potential is constructed, equivalently reproducing the scattering amplitude in chiral SU(3) dynamics. By analyzing the wave function of the Lambda(1405), we show the Kbar N dominance of the upper pole within the two-pole structure of the Lambda(1405). The resulting potential will be useful for investigating Kbar few-nucleon systems including their coupled channels.
The potential of performing a combined analysis of the strangeness-changing decays $τ^{-}\to K_{S}π^{-}ν_τ$ and $τ^{-}\to K^{-}ην_τ$ for unveiling the $K^{*}(1410)$ resonance pole parameters is illustrated. Our study is carried out within the framework of Chiral Perturbation Theory, including resonances as explicit degrees of freedom. Resummation of final state interactions are considered through a dispersive parameterization of the required form factors. A considerable improvement in the determination of the pole position with mass $M_{K^{*}(1410)}=1304\pm17$ MeV and width $Γ_{K^{*}(1410)}=17…
