I= 1 and I= 2 π–π scattering phase shifts from Nf= 2 + 1 lattice QCD

Abstract

The I = 1 p-wave and I = 2 s-wave elastic π-π scattering amplitudes are calculated from a first-principles lattice QCD simulation using a single ensemble of gauge field configurations with N f = 2 + 1 dynamical flavors of anisotropic clover-improved Wilson fermions. This ensemble has a large spatial volume V = (3.7fm) 3 , pion mass m π = 230MeV, and spatial lattice spacing a s = 0.11fm. Calculation of the necessary temporal correlation matrices is efficiently performed using the stochastic LapH method, while the large volume enables an improved energy resolution compared to previous work. For this single ensemble we obtain m ρ /m π = 3.350(24), g ρππ = 5.99(26), and a clear signal for the I = 2 s-wave. The success of the stochastic LapH method in this proof-of-principle large-volume calculation paves the way for quantitative study of the lattice spacing effects and quark mass dependence of scattering amplitudes using state-of-the-art ensembles.

Chiral extrapolations of the ρ(770) meson in Nf=2+1 lattice QCD simulations

“…The extrapolated phase shifts for the Wilson15 [26] and Bulava16 [28] data are on top of the experimental data as Fig. 1 shows.…”

“…In addition, we have also shown that the KK channel can be effectively included in the ππ → ππ interaction. [26,28,30,34] are highlighted in red. The extrapolation to the physical point in comparison to the experimental data (blue) [58] is shown in the bottom figure.…”

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.…”

Recent results on the meson and baryon spectrum from lattice QCD

“…After a pioneering study by the CP-PACS collaboration [9], multiple groups provided proof of principle calculations demonstrating the feasibility of lattice resonance studies [10][11][12]. In the meantime a number of further studies exist [13][14][15][16][17][18]. Figure 4 shows an example of a state-of-the-art calculation by the Hadron Spectrum Collaboration [15].…”

“…The large number of lattice data points results from using all lattice irreps for multiple center-of-mass momenta, and multiple lattice volumes. Figure 5 shows the current world data for g ρππ from the lattice determinations [10][11][12][13][14][15][16][17][18]. While there is in general a good agreement among the lattice data, the uncertainties in the plot are (in most cases) statistical only and there is no calculation demonstrating a full control of systematic uncertainties.…”