Isoscalar ππ, KK¯, ηη scattering and the

Raúl A. Briceño

¹

,

Jozef J. Dudek

²

,

Robert G. Edwards

³

et al.

Abstract

We present the first lattice QCD study of coupled isoscalar ππ; KK; ηη S-and D-wave scattering extracted from discrete finite-volume spectra computed on lattices which have a value of the light quark mass corresponding to m π ∼ 391 MeV. In the J P ¼ 0 þ sector we find analogues of the experimental σ and f 0 ð980Þ states, where the σ appears as a stable bound-state below ππ threshold, and, similar to what is seen in experiment, the f 0 ð980Þ manifests itself as a dip in the ππ cross section in the vicinity of the KK threshold. For J P ¼ 2 þ we find two states resembling the f 2 ð1270Þ and f 0 2 ð1525Þ, observed as narrow peaks, with the lighter state dominantly decaying to ππ and the heavier state to KK. The presence of all these states is determined rigorously by finding the pole singularity content of scattering amplitudes, and their couplings to decay channels are established using the residues of the poles.

Lattice QCD and neutrino-nucleus scattering

“…The theoretical framework for understanding the transition to multihadron states from Euclidean-space lattice QCD calculations have been further developed over the past several years. Notably, the formalism has been extended both to inelastic scattering [127][128][129][130][131] with several two-body channels, and to three-body scattering [132][133][134][135][136][137], and there have now been several computational applications of these advances [138][139][140][141].…”

Pion scattering in the isospin I=2 channel from elongated lattices

“…The isoscalar sector is particularly interesting because of the presence of the broad f 0 (500) "σ" resonance. Only recently, phaseshifts in this channel have been calculated [21][22][23] (for calculations of the scattering lengths, see, e.g., Refs. [24,25]).…”

Quark-Mass Dependence of Elastic πK Scattering from QCD

“…Roy-Steiner equations, which account for the known singularities due to cross-channel physics. In the current case, an input to such a calculation would be information about ππ → KK in several partial waves, which can be obtained in a lattice calculation using the generalization of the Lüscher formalism for coupled-channels [46,48].…”