Isoscalar ππ Scattering and the σ Meson Resonance from QCD

Abstract

We present for the first time a determination of the energy dependence of the isoscalar ππ elastic scattering phase-shift within a first-principles numerical lattice approach to QCD. Hadronic correlation functions are computed including all required quark propagation diagrams, and from these the discrete spectrum of states in the finite volume defined by the lattice boundary is extracted. From the volume dependence of the spectrum we obtain the S-wave phase-shift up to the KK threshold. Calculations are performed at two values of the u, d quark mass corresponding to mπ = 236, 391 MeV and the resulting amplitudes are described in terms of a σ meson which evolves from a bound-state below ππ threshold at the heavier quark mass, to a broad resonance at the lighter quark mass.

Statistics of baryon correlation functions in lattice QCD

“…34 can be compared with the σ-meson mass extracted from mesonic sector calculations to test the heuristic arguments above that lighter excitations will make volumesuppressed contributions. Calculations of the σ-meson face a severe StN problem, particularly at light quark masses where the σ-meson describes a broad ππ isoscalar resonance rather than a compact QCD bound state, but a recent calculation by the Hadron Spectrum collaboration has precisely determined M σ = 758(4) MeV at m π ∼ 391 MeV where the σ-meson is weakly bound [45]. Similarly precise results at slightly higher quark masses are not available for interpolation to m π ∼ 450 MeV, but a crude extrapolation can be made using the Hadron Spectrum result and the (real part of the) physical position of the σ-meson pole obtained from dispersive analysis of experimental data: M σ = 457(14) MeV [46,47].…”

Coupled-channel Dπ, Dη and D s K ¯ $$ {D}_s\overline{K} $$ scattering from lattice QCD

“…In particular, the Lüscher method and its extensions for relating finite-volume spectra to scattering amplitudes are now well established for elastic [5][6][7][8][9][10][11][12][13][14] and coupled-channel [15][16][17][18][19] hadron-hadron scattering. These methods have been demonstrated in a number of applications, notably for the ρ-resonance seen in P -wave ππ scattering [20][21][22][23][24][25][26][27][28][29], and for the σ resonance seen in S-wave ππ scattering [30]. It has also recently been shown that, with sufficiently extensive and precise spectra, information on coupled-channel hadron-hadron scattering amplitudes can be obtained [26,[31][32][33] -this is crucial for understanding highly excited states that are typically kinematically permitted to decay into several channels.…”

Isospin-0 ππ s-wave scattering length from twisted mass lattice QCD

“…The authors of Ref. [14] on the other hand extracted many energy eigenstates in the corresponding channel and obtained the scattering amplitudes for two values of pion mass -236 MeV and 391 MeV. The information about the σ meson is deduced from the pole structure Ref.…”

“…For the isospin-0 channel the situation is more complicated mainly due to the fermionic disconnected diagrams contributing here, which are challenging to compute in lattice QCD. To date there are only two full lattice QCD computations dedicated to this channel [11,14]. In Ref.…”