Dynamical generation of hadronic resonances

One type of dynamical generation consists in the formation of multiple hadronic resonances from single seed states by incorporating hadronic loop contributions on the level of $s$-wave propagators. Along this line, we study the propagator poles within two models of scalar resonances and report on the status of our work: (i) Using a simple quantum field theory describing the decay of $f_{0}(500)$ into two pions, we may obtain a second, additional pole on the first Riemann sheet below the pion-pion threshold (i.e., a stable state can emerge). (ii) We perform a numerical study of the pole(s) of $a_{0}(1450)$ by using as an input the results obtained in the extended Linear Sigma Model (eLSM). Here, we do not find any additional pole besides the original one, thus we cannot obtain $a_{0}(980)$ as an emerging state. (iii) We finally demonstrate that, although the coupling constants in typical effective models might be large, the next-to-leading-order contribution to the decay amplitude is usually small and can be neglected.Comment: 6 pages, 1 figure, 1 table, prepared for proceedings of the workshop "EEF70 - Workshop on Unquenched Hadron Spectroscopy: Non-Perturbative Models and Methods of QCD vs. Experiment", Coimbra, Portugal, September 1-5, 201

The lightest scalar meson in a simple approach

We study basic properties of scalar hadronic resonances within a quantum field theoretical toy model. In particular, we focus on the spectral function, the mass and the decay width of the resonance $f_{0}(500)$. In this work, this meson is understood as a seed state in an effective Lagrangian which couples to pions. With such a setup we use the position of the pole on the second Riemann sheet in order to obtain its spectral function. We confirm that $f_{0}(500)$ cannot be described by an ordinary Breit--Wigner function, and that a more complicated structure is needed.Comment: 5 pages, 1 figure, 1 table; prepared for proceedings of the conference "Excited QCD 2013", 3-9 February, Bjelasnica Mountain, Sarajev

The role of the next-to-leading order triangle-shaped diagram in two-body hadronic decays

The next-to-leading-order contribution to the amplitude of a two-body decay process is a triangle-shaped diagram in which the unstable state is exchanged by the emitted particles. In this work we calculate this diagram in the framework of a scalar quantum field theory and we estimate its role in hadronic physics, i.e., we apply our results to the well-known scalar-isoscalar resonances $f_{0}(500)$, $f_{0}(980)$, $f_{0}(1370)$, $f_{0}(1500)$, $f_{0}(1710)$ and the scalar-isovector resonance $a_{0}(1450)$. It turns out that, with the exception of the broad resonance $f_{0}(500)$, the next-to-leading-order contribution is small and can be neglected.Comment: 18 pages, 6 figures, 1 tabl

K0∗(800)K_{0}^{\ast}(800) as a companion pole of K0∗(1430)K_{0}^{\ast}(1430)

We study the light scalar sector up to $1.8$ GeV by using a quantum field theoretical approach which includes a single kaonic state in a Lagrangian with both derivative and non-derivative interactions. By performing a fit to $\pi K$ phase shift data in the $I=1/2,$ $J=0$ channel, we show that $K_{0}^{\ast}(800)$ (or $\kappa$) emerges as a dynamically generated companion pole of $K_{0}^{\ast }(1430)$. This is a result of investigating quantum fluctuations with one kaon and one pion circulating in the loops dressing $K_{0}^{\ast}(1430)$. We determine the position of the poles on the complex plane in the context of our approach: for $K_{0}^{\ast}(1430)$ we get $(1.413\pm0.002)-i{0.02cm}(0.127\pm0.003)$ (in GeV), while for $\kappa$ we get $(0.746\pm0.019)-i{0.02cm}(0.262\pm0.014)$ (in GeV). The model-dependence of these results and related uncertainties are discussed in the paper. A large-$N_{c}$ study confirms that $K_{0}^{\ast}(1430)$ is predominantly a quarkonium and that $K_{0}^{\ast}(800)$ is a molecular-like dynamically generated state.Comment: 7 pages, 5 figures, 2 table

Propagator poles and an emergent stable state below threshold: general discussion and the E(38) state

In the framework of a simple quantum field theory describing the decay of a scalar state into two (pseudo)scalar ones we study the pole(s) motion(s) of its propagator: besides the expected pole on the second Riemann sheet, we find -- for a large enough coupling constant -- a second, additional pole on the first Riemann sheet below threshold, which corresponds to a stable state. We then perform a numerical study for a hadronic system in which a scalar particle couples to pions. We investigate under which conditions a stable state below the two-pion threshold can emerge. In particular, we study the case in which this stable state has a mass of 38 MeV, which corresponds to the recently claimed novel scalar state E(38). Moreover, we also show that the resonance $f_{0}(500)$ and the stable state E(38) could be two different manifestation of the same `object'. Finally, we also estimate the order of magnitude of its coupling to photons.Comment: 9 pages, 4 figure