0000000000262746
AUTHOR
E. Ruiz Arriola
Improved unitarized Heavy Baryon Chiral Perturbation Theory for π N scattering
We show how the unitarized description of pion nucleon scattering within Heavy Baryon Chiral Perturbation Theory can be considerably improved, by a suitable reordering of the expansion over the nucleon mass. Within this framework, the $\Delta$ resonance and its associated pole can be recovered from the chiral parameters obtained from low-energy determinations. In addition, we can obtain a good description of the six $S$ and $P$ wave phase shifts in terms of chiral parameters with a natural size and compatible with the Resonance Saturation Hypothesis.
Large-NCproperties of theρandf0(600)mesons from unitary resonance chiral dynamics
We construct $\ensuremath{\pi}\ensuremath{\pi}$ amplitudes that fulfill exact elastic unitarity, account for one-loop chiral perturbation theory contributions and include all $1/{N}_{C}$ leading terms, with the only limitation of considering just the lowest-lying nonet of exchanged resonances. Within such a scheme, the ${N}_{C}$ dependence of $\ensuremath{\sigma}$ and $\ensuremath{\rho}$ masses and widths is discussed. Robust conclusions are drawn in the case of the $\ensuremath{\rho}$ resonance, confirming that it is a stable meson in the limit of a large number of QCD colors, ${N}_{C}$. Less definitive conclusions are reached in the scalar-isoscalar sector. With the present quality of dat…
S=−1meson-baryon unitarized coupled channel chiral perturbation theory and theS01resonances Λ(1405) and -Λ(1670)
The $s-$wave meson-baryon scattering is analyzed for the strangeness $S=-1$ and isospin I=0 sector in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry. Four channels have been considered: $\pi \Sigma$, $\bar K N$, $\eta \Lambda$ and $K \Xi$. The required input to solve the Bethe-Salpeter equation is taken from lowest order Chiral Perturbation Theory in a relativistic formalism. There appear undetermined low energy constants, as a consequence of the renormalization of the amplitudes, which are obtained from fits to the $\pi\Sigma\to\pi\Sigma$ mass-spectrum, to the elastic $\bar K N \to \bar K N$ and $ \bar K N\to \pi \Sigma$ $t$--matrices and to the $ K^- p \to \eta \…
Large-Nc Properties of the rho and f0(600) Mesons from Unitary Resonance Chiral Dynamics
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, we cannot firmly conclude whether or not the Nc=3 f0(600) resonance completely disappears at larg…
Couplings in coupled channels versus wave functions: Application to theX(3872)resonance
We perform an analytical study of the scattering matrix and bound states in problems with many physical coupled channels. We establish the relationship of the couplings of the states to the different channels, obtained from the residues of the scattering matrix at the poles, with the wave functions for the different channels. The couplings basically reflect the value of the wave functions around the origin in coordinate space. In the concrete case of the $X(3872)$ resonance, understood as a bound state of ${D}^{0}{\overline{D}}^{*0}$ and ${D}^{+}{D}^{*\ensuremath{-}}$ (and $c.c.$ From now on, when we refer to ${D}^{0}{\overline{D}}^{*0}$ , ${D}^{+}{D}^{*\ensuremath{-}}$, or $D{\overline{D}}…
S=--1 Meson-Baryon Scattering in Coupled Channel Unitarized Chiral Perturbation Theory
The $s-$wave meson-baryon scattering amplitude is analyzed for the strangeness $S=-1$ and isospin I=0 sector in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry. Four two-body channels have been considered: $\bar K N$, $\pi \Sigma $, $\eta \Lambda $, $ K \Xi$. The needed two particle irreducible matrix amplitude is taken from lowest order Chiral Perturbation Theory in a relativistic formalism. Off-shell behaviour is parameterized in terms of low energy constants, which outnumber those assumed in previous works and provide a better fit to the data. The position of the complex poles in the second Riemann sheet of the scattering amplitude determine masses and widths of …
Meson Resonances at large Nc: Complex Poles vs Breit-Wigner Masses
The rigorous quantum mechanical definition of a resonance requires determining the pole position in the second Riemann sheet of the analytically continued partial wave scattering amplitude in the complex Mandelstam s variable plane. For meson resonances we investigate the alternative Breit–Wigner (BW) definition within the large NC expansion. By assuming that the pole position is View the MathML source and exploiting unitarity, we show that the BW determination of the resonance mass differs from the pole position by View the MathML source terms, which can be extracted from ππ scattering data. For the case of the σ (f0(600)) pole, the BW scalar mass is predicted to occur at not, vert, simila…
THE X(3872) AND OTHER X,Y,Z RESONANCES AS HIDDEN CHARM MESON-MESON MOLECULES
We report on some ideas concerning the nature of the X(3872) resonance and the need for approximately equal charged and neutral components of $D \bar{D}^* +cc$. Then we discuss how some hidden charm states are obtained from the interaction between vector mesons with charm and can be associated to some of the charmonium-like X,Y,Z states. Finally we discuss how the nature of these states could be investigated through different types of radiative decay.
Improved unitarized heavy baryon chiral perturbation theory for πN scattering to fourth order
We extend our previous analysis of the unitarized pion-nucleon scattering amplitude including up to fourth order terms in heavy baryon chiral perturbation theory. We pay special attention to the stability of the generated Delta(1232) resonance, the convergence problems, and the power counting of the chiral parameters.
Bethe-Salpeter approach for unitarized chiral perturbation theory
The Bethe-Salpeter equation restores exact elastic unitarity in the $s-$ channel by summing up an infinite set of chiral loops. We use this equation to show how a chiral expansion can be undertaken in the two particle irreducible amplitude and the propagators accomplishing exact elastic unitarity at any step. Renormalizability of the amplitudes can be achieved by allowing for an infinite set of counter-terms as it is the case in ordinary Chiral Perturbation Theory. Crossing constraints can be imposed on the parameters to a given order. Within this framework, we calculate the leading and next-to-leading contributions to the elastic $\pi \pi$ scattering amplitudes, for all isospin channels, a…
Inverse amplitude method in pi pi scattering in chiral perturbation theory to two loops
The inverse amplitude method is used to unitarize the two loop $\pi\pi$ scattering amplitudes of SU(2) Chiral Perturbation Theory in the $I=0,J=0$, $I=1,J=1$ and $I=2,J=0$ channels. An error analysis in terms of the low energy one-loop parameters $\bar l_{1,2,3,4,}$ and existing experimental data is undertaken. A comparison to standard resonance saturation values for the two loop coefficients $\bar b_{1,2,3,4,5,6} $ is also carried out. Crossing violations are quantified and the convergence of the expansion is discussed.
Large-$N_c$ naturalness in coupled-channel meson-meson scattering
The analysis of hadronic interactions with effective field theory techniques is complicated by the appearance of a large number of low-energy constants, which are usually fitted to data. On the other hand, the large-$N_c$ limit imposes natural short-distance constraints on these low-energy constants, providing a parameter reduction. A Bayesian interpretation of the expected $1/N_c$ accuracy allows for an easy and efficient implementation of these constraints, using an augmented $\chi^2$. We apply this approach to the analysis of meson-meson scattering, in conjunction with chiral perturbation theory to one loop and coupled-channel unitarity, and show that it helps to largely reduce the many …
Isospin breaking effects in the dynamical generation of the X(3872)
We have studied isospin breaking effects in the X(3872) resonance and found a natural explanation for the branching fraction of the X decaying to $J/\psi$ with two and three pions being close to unit. Within our framework the X(3872) is a dynamically generated resonance in coupled channels. We also study the relationship between the couplings of the resonance to the coupled channels with its wave function, which further helps us to understand the isospin structure of the resonance.
Meson-Baryon Interactions in Unitarized Chiral Perturbation Theory
Meson-Baryon Interactions can be successfully described using both Chiral Symmetry and Unitarity. The $s-$wave meson-baryon scattering amplitude is analyzed in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry in the potential. Two body coupled channel unitarity is exactly preserved. The needed two particle irreducible matrix amplitude is taken from lowest order Chiral Perturbation Theory in a relativistic formalism. Off-shell behavior is parameterized in terms of low energy constants. The relation to the heavy baryon limit is discussed. The position of the complex poles in the second Riemann sheet of the scattering amplitude determine masses and widths baryonic reson…
Couplings in coupled channels versus wave functions: application to the X(3872) resonance
We perform an analytical study of the scattering matrix and bound states in problems with many physical coupled channels. We establish the relationship of the couplings of the states to the different channels, obtained from the residues of the scattering matrix at the poles, with the wave functions for the different channels. The couplings basically reflect the value of the wave functions around the origin in coordinate space. In the concrete case of the X(3872) resonance, understood as a bound state of D-0(D) over bar*(0) and D+D*(-) (and c.c. From now on, when we refer to D-0(D) over bar*(0), D+D*(-), or D (D) over bar* we are actually referring to the combination of these states with the…
Error estimates for pi-pi scattering threshold parameters in Chiral Perturbation Theory to two loops
Using the analysis of ChPT to two loops, we perform an error analysis of the threshold and low energy parameters, based on the uncertainties for the one loop low energy parameters and the resonance saturation mechanism. Different sets of one loop low energy constants have been considered.Thus, the predictive power of the effective field theory is quantified on the basis of the present experimental uncertainties.
The S01 − Λ(1405) and − Λ(1670) resonances in meson-baryon unitarized coupled channel chiral perturbation theory
Abstract The s-wave meson-baryon system with strangeness S = −1 and isospin I = 0 is studied using the Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry. The needed two particle irreducible potential is taken from lowest order Chiral Perturbation Theory in a relativistic formalism. The K N, πΣ, νΛ , and KΞ two-body channels have been included. Off-shell behavior is parameterized in terms of low energy constants, which outnumber those assumed in previous works and provide a better fit to the data. The masses, widths and branching ratios of the Λ(1405) and Λ(1670) resonances are determined. In our model, we find no one but two resonances in the Λ(1405) region.