In this talk we briefly review how the unitarization of Chiral Perturbation Theory with dispersion relations can successfully describe the meson-meson scattering data and generate light resonances, whose mass, width and nature can be related to QCD parameters like quark masses and the number of colors.
We calculate the scattering amplitudes of Goldstone bosons off the pseudoscalar D-mesons in unitarized heavy meson chiral approach. The low energy constants appearing in $\mathcal{O}(p^2)$ chiral Lagrangian are determined by fitting lattice simulations on $S$-wave scattering lengths. $D_{s0}^{*}(2317)$ is obtained as a bound state in $(S,I)=(1,0)$ $DK$ channel. Possible bound states or resonance states in other channels are investigated as well. The quark mass dependence of the mass and binding energy of $D_{s0}^{*}(2317)$ is also investigated, which indicates predominately $DK$ molecular natu…
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…
One-loop unitarized Chiral Perturbation Theory (UChPT) calculations, suggest a different Nc behaviour for the sigma or f_0(600) and rho(770) mesons: while the rho meson becomes narrower with Nc, as is expected for a q-qbar meson, the sigma becomes broader, and its contribution to the total cross section is less and less important. On the other hand, local duality requires a cancellation between the sigma and rho amplitudes, but if there is a different Nc behaviour for them, there is a possible contradiction between the Inverse Amplitude Method (IAM) and local duality for large Nc. However, nex…
We review the unitarization of Chiral Perturbation Theory with dispersion relations and how it describes meson-meson scattering data, generating light resonances whose mass, width and nature can be related to QCD parameters like quark masses and the number of colors.
For several decades, the $σ/f_0(500)$ and $κ/K_0^*(700)$ resonances have been subject to long-standing debate. Both their existence and properties were controversial until very recently. In this tutorial review we compare model-independent dispersive and analytic techniques versus unitarized Chiral Perturbation Theory, when applied to the lightest scalar mesons $σ/f_0(500)$ and $κ/K_0^*(700)$. Generically, the former have settled the long-standing controversy about the existence of these states, providing a precise determination of their parameters, whereas unitarization of chiral effective th…
We study the pion mass dependence of the rho(770) and f_0(600) masses and widths from one and two-loop unitarized Chiral Perturbation Theory. We show the consistency of one-loop calculations with lattice results for the M_rho, f_pi and the isospin 2 scattering length a_20.Then, we develop and apply the modified Inverse Amplitude Method formalism for two-loop ChPT. In contrast to the f_0(600), the rho(770) is rather sensitive to the two-loop ChPT parameters --our main source of systematic uncertainty. We thus provide two-loop unitarized fits constrained by lattice information on M_rho, f_pi, by…
We study the dependence of the pion-pion scattering phase shifts on the light quark mass in both standard and unitarized SU(2) Chiral Perturbation Theory (ChPT) to one and two loops. We then use unitarized SU(3) ChPT to study the elastic f_0(600), kappa(800), rho(770) and K*(892) resonances. The quark masses are varied up to values of interest for lattice studies. We find a very soft dependence on the light quark mass of the pion-pion phase shifts at one loop and slightly stronger at two loops and a good agreement with lattice results. The SU(3) analysis shows that the properties of the rho(77…
We review our work on the rho and sigma resonances derived from the Inverse Amplitude Method. In particular, we study the leading 1/N_c behavior of the resonances masses and widths and their evolution with changing m_pi. The 1/N_c expansion gives a clear definition of quark-antiquark states, which is neatly satisfied by the rho but not by the sigma, showing that its dominant component is not quark-antiquark. The m_pi dependence of the resonance properties is relevant to connect with lattice studies. We show that our predictions compare well with some lattice results and we find that the rho-pi…
In this work, a color structure dependent flip-flop potential is developed for the two quarks and two antiquarks system. Then, this potential is applied to a microscopic quark model which, by integrating the internal degrees of freedom, is transformed into a model of mesons with non-local interactions. With this, the T matrix for the system is constructed and meson-meson scattering is studied. Tetraquarks states, interpreted as poles of of the T matrix, both bound states and resonances, are found. Special emphasis is given to the truly exotic $qq\bar{Q}\bar{Q}$ system, but some results for the…
We present a comprehensive analysis of form factors for two light pseudoscalar mesons induced by scalar, vector, and tensor quark operators. The theoretical framework is based on a combination of unitarized chiral perturbation theory and dispersion relations. The low-energy constants in chiral perturbation theory are fixed by a global fit to the available data of the two-meson scattering phase shifts. Each form factor derived from unitarized chiral perturbation theory is improved by iteratively applying a dispersion relation. This study updates the existing results in the literature and explor…
Chiral potentials are derived for the interactions between Goldstone bosons and pseudoscalar charmed mesons up to next-to-next-to-leading order in a covariant chiral effective field theory with explicit vector charmed-meson degrees of freedom. Using the extended-on-mass-shell scheme, we demonstrate that the ultraviolet divergences and the so-called power counting breaking terms can be properly absorbed by the low-energy constants of the chiral Lagrangians. We calculate the scattering lengths by unitarizing the one-loop potentials and fit them to the data extracted from lattice QCD. The obtaine…
We review our studies on the rho and sigma resonances properties derived from the Inverse Amplitude Method. In particular, we study the leading $1/N_c$ behavior of the resonances masses and widths and their evolution with changing $m_π$. The $1/N_c$ expansion gives a clear definition of $\bar qq$ states, which is neatly satisfied by the $ρ$ but not by the sigma, showing that its dominant component is not $\bar qq$. The $m_π$ dependence of the resonance properties is relevant to connect with lattice studies. We show that our predictions compare well with some lattice results and we find that th…
We develop a scheme for the extraction of the properties of the scalar mesons f0(600), f0(980), and a0(980) from lattice QCD data. This scheme is based on a two-channel chiral unitary approach with fully relativistic propagators in a finite volume. In order to discuss the feasibility of finding the mass and width of the scalar resonances, we analyze synthetic lattice data with a fixed error assigned, and show that the framework can be indeed used for an accurate determination of resonance pole positions in the multi-channel scattering.
In this work, we present an updated study about the interactions of quarkonia with surrounding hadronic medium. The meson-meson interactions are described with a chiral effective Lagrangian within the framework of unitarized coupled channel amplitudes. In particular, we extend a previous work performed in the charmonium sector by calculating the cross-sections for $Υ$ scattering by light pseudoscalar mesons ($π, K, η$) and vector mesons ($ρ, K^\ast, ω$). We evaluate the relevant channels and compare the results with existing literature. The analysis is completed by including the finite-tempera…
We study the hadronic $η^{\prime}\toηππ$ decays within the framework of $U(3)_{L}\otimes U(3)_{R}$ Chiral Perturbation Theory including resonance states and the complete one-loop corrections. The amplitude is projected in partial waves and unitarized by means of the $N/D$ method resumming both the important $S$-and $D$-wave $ππ$ and the subleading $S$-wave $πη$ final-state interactions. The participating scalar multiplet mass and coupling strengths are determined from fits to the Dalitz plot experimental data recently released by the A2 collaboration. As a byproduct of our analysis, the associ…
We study the strange and non-strange quark mass dependence of the parameters of the f_0(600), kappa(800), rho(770) and K*(892) resonances generated from elastic meson-meson scattering using unitarized one-loop Chiral Perturbation Theory. We fit simultaneously all experimental scattering data up to 0.8-1 GeV together with lattice results on decay constants and scattering lengths up to a pion mass of 440 MeV. Then, the strange and non-strange quark masses are varied from the chiral limit up to values of interest for lattice studies. In these amplitudes, the mass and width of the rho(770) and K*(…
$S=-1$ Meson-Baryon Unitarized Coupled Channel Chiral Perturbation Theory and the $S_{01}-$ $Λ$(1405) and $- Λ$(1670) Resonances
在考虑手征对称性的Bethe-Salpeter耦合道模型中,分析了奇异性$S=-1$和同位旋I=0扇区的$s-$波介子-重子散射.已考虑了四个通道:$πΣ$、$\bar K N$、$ηΛ$和$K Ξ$。求解Bethe-Salpeter方程所需的输入取自相对论形式的最低阶手征微扰理论。有出现未确定的低能量常数,作为重整化的振幅,这是从拟合的$πΣ\toπΣ$质谱,弹性$\bar K N \to \bar K N$和$ \bar K N\to πΣ$ $t$ -矩阵和$ K^- p \to ηΛ$横截面数据。在散射振幅的第二个黎曼面中的复极点的位置和留数决定了$S_{01}-$ $Λ$(1405)和$-Λ$(1670)共振的质量、宽度和分支比,与实验合理地一致。一个很好的整体描述的数据,从$πΣ$阈值高达1.75 GeV,实现尽管三体通道没有明确包括在内的事实。
We study the light quark mass dependence of the f_0(600), kappa(800), rho(770) and K*(892) resonance parameters generated from elastic meson-meson scattering using unitarized one-loop Chiral Perturbation Theory. First, we show that it is possible to fit simultaneously all experimental scattering data up to 0.8-1 GeV together with lattice results on decay constants and scattering lengths up to a pion mass of 400 MeV, using chiral parameters compatible with existing determinations. Then, the strange and non-strange quark masses are varied from the chiral limit up to values of interest for lattic…
In the present work we study the production of vector resonances at the LHC by means of the vector boson scattering $WZ \to WZ$ and explore the sensitivities to these resonances for the expected future LHC luminosities. We are assuming that these vector resonances are generated dynamically from the self interactions of the longitudinal gauge bosons, $W_L$ and $Z_L$, and work under the framework of the electroweak chiral Lagrangian to describe in a model independent way the supposedly strong dynamics of these modes. The properties of the vector resonances, mass, width and couplings to the $W$ a…