Isospin-1/2 Dπ scattering and the lightest $$ {D}_0^{\ast } $$ resonance from lattice QCD

Isospin-1/2 Dπ scattering amplitudes are computed using lattice QCD, working in a single volume of approximately (3.6 fm)3 and with a light quark mass corresponding to mπ ≈ 239 MeV. The spectrum of the elastic Dπ energy region is computed yielding 20 energy levels. Using the Lüscher finite-volume quantisation condition, these energies are translated into constraints on the infinite-volume scattering amplitudes and hence enable us to map out the energy dependence of elastic Dπ scattering. By analytically continuing a range of scattering amplitudes, a $$ {D}_0^{\ast } $$ D 0 ∗ resonance pole is consistently found strongly coupled to the S-wave Dπ channel, with a mass m ≈ 2200 MeV and a width Γ ≈ 400 MeV. Combined with earlier work investigating the $$ {D}_{s0}^{\ast } $$ D s 0 ∗ , and $$ {D}_0^{\ast } $$ D 0 ∗ with heavier light quarks, similar couplings between each of these scalar states and their relevant meson-meson scattering channels are determined. The mass of the $$ {D}_0^{\ast } $$ D 0 ∗ is consistently found well below that of the $$ {D}_{s0}^{\ast } $$ D s 0 ∗ , in contrast to the currently reported experimental result.

NEW PARAMETERIZATION OF THE RESONANT PRODUCTION AMPLITUDES NEAR AN INELASTIC THRESHOLD

New formulae for the resonant scattering and the production amplitudes near an inelastic threshold are derived. It is shown that the Flatté formula, frequently used in experimental analyses, is not sufficiently accurate. Its application to data analysis can lead to a substantial distortion of the effective mass spectra and of the resonance pole positions. A unitary parameterization, satisfying a generalized Watson theorem for the production amplitudes, is proposed. It can be easily applied to study production processes, multichannel meson-meson interactions and the resonance properties, including among others the scalar resonances a0(980) and f0(980).

PRECISE DISPERSIVE DATA ANALYSIS OF THE f0(600) POLE

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 σ 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 negligible.

Non-adiabatic dynamics in the α+6He scattering and the nuclear breakup of 10Be

The α+6 He low-energy reactions and the structural changes of 10 Be in the microscopic α+α+N+N model are studied by the generalized two-center cluster model with the Kohn-Hulthén-Kato variation method. It is found that, in the inelastic scattering to the [Formula: see text] channel, characteristic enhancements are expected as the results of the parity-dependent non-adiabatic dynamics. In the positive parity state, the enhancement originates from the excited eigenstate generated by the resonance pole of the final channel, while that in the negative parity state is induced by the Landau-Zener level-crossing. The reaction mechanism in breakup of 10 Be into the 5 He +5 He and α+6 He continuums is also studied. The strong enhancement in the breakup of [Formula: see text] is discussed in connection with the non-adiabatic dynamics.

Resonances of a λ-rational Sturm–Liouville problem

We consider a family of self-adjoint 2 × 2-block operator matrices Ãϑ in the space L2(0, 1) ⊕ L2(0, 1), depending on the real parameter ϑ. If Ã0 has an eigenvalue that is embedded in the essential spectrum, then it is shown that for ϑ ≠ 0 this eigenvalue in general disappears, but the resolvent of Ãϑ has a pole on the unphysical sheet of the Riemann surface. Such a pole is called a resonance pole. The unphysical sheet arises from analytic continuation from the upper half-plane ℂ+ across the essential spectrum. Furthermore, the asymptotic behaviour of this resonance pole for small ϑ is investigated. The results are proved by considering a certain λ-rational Sturm-Liouville problem and its Titchmarsh–Weyl coefficient.