Is two-pole’s $$\varLambda (1405)$$ one state or two?

To understand the nature of two poles for the $$\varLambda (1405)$$ Λ ( 1405 ) state, we revisit the interactions of $${\bar{K}}N$$ K ¯ N and $$\pi \Sigma $$ π Σ with their coupled channels, where two-pole structure is found in the second Riemann sheet. We also dynamically generate two poles in the single channel interaction of $${\bar{K}}N$$ K ¯ N and $$\pi \Sigma $$ π Σ , respectively. Moreover, we make a further study of two poles’ properties by evaluating the couplings, the compositeness, the wave functions, and the radii for the interactions of four coupled channels, two coupled channels and the single channel. Our results show that the nature of two poles is unique. The higher-mass pole is a pure $${\bar{K}} N$$ K ¯ N molecule, and the lower-mass one is a composite state of mainly $$\pi \Sigma $$ π Σ with tiny component $${\bar{K}} N$$ K ¯ N . From our results, one can conclude that the $$\varLambda (1405)$$ Λ ( 1405 ) state may be overlapped with two different states of the same quantum numbers.

Theoretical analysis of the γγ(*) → π0η process

The theoretical analysis of the γγ → π0η process is presented within the energy range up to 1.4 GeV. The S -wave resonance a0(980) is described involving the coupled channel dispersive framework and the D-wave a2(1320) is approximated as a Breit-Wigner resonance. For the a0(980) the pole is found on the IV Riemann sheet resulting in a two-photon decay width of Γa0 → γγ = 0.27(4) keV. The first dispersive prediction is provided for the single-virtual γγ*(Q2) → π0η process in the spacelike region up to Q2 = 1 GeV2.

Resonances in the two-center Coulomb systems

We investigate the existence of resonances for two-center Coulomb systems with arbitrary charges in two dimensions, defining them in terms of generalized complex eigenvalues of a non-selfadjoint deformation of the two-center Schrödinger operator. We construct the resolvent kernels of the operators and prove that they can be extended analytically to the second Riemann sheet. The resonances are then analyzed by means of perturbation theory and numerical methods.

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 f0(500) and the stable state E(38) could be two different manifestations of the same "object". Finally, we also estimate the order of magnitude of its coupling to photons.

Hyperasymptotics for nonlinear ODEs I. A Riccati equation

We illustrate how one can obtain hyperasymptotic expansions for solutions of nonlinear ordinary differential equations. The example is a Riccati equation. The main tools that we need are transseries expansions and the Riemann sheet structure of the Borel transform of the divergent asymptotic expansions. Hyperasymptotic expansions determine the solutions uniquely. A numerical illustration is included.