We present the first direct $$N_f=2$$
N
f
=
2
lattice QCD computation of two- and three-$$\pi ^+$$
π
+
scattering quantities that includes an ensemble at the physical point. We study the quark mass dependence of the two-pion phase shift, and the three-particle interaction parameters. We also compare to phenomenology and chiral perturbation theory (ChPT). In the two-particle sector, we observe good agreement to the phenomenological fits in s- and d-wave, and obtain $$M_\pi a_0 = -0.0481(86)$$
M
π
a
0
=
-
0.0481
(
86
)
at the physical point from a direct computation. In the three-particle sector, we observe reasonable agreement at threshold to the leading order chiral expansion, i.e. a mildly attractive three-particle contact term. In contrast, we observe that the energy-dependent part of the three-particle quasilocal scattering quantity is not well described by leading order ChPT.
We present an investigation of the ρ-meson from N f = 2 + 1 + 1 flavour lattice QCD.The calculation is performed based on gauge configuration ensembles produced by the ETM collaboration with three lattice spacing values and pion masses ranging from 230 MeV to 500 MeV. Applying the Lüscher method phase shift curves are determined for all ensembles separately. Assuming a Breit-Wigner form, the ρ-meson mass and width are determined by a fit to these phase shift curves. Mass and width combined are then extrapolated to the chiral limit, while lattice artefacts are not detectable within our statistical uncertainties. For the ρmeson mass extrapolated to the physical point we find good agreement with experiment. The corresponding decay width differs by about two standard deviations from the experimental value.
We discuss the relation of a variety of different methods to determine energy levels in lattice QCD simulations: the generalised eigenvalue, the Prony, the generalised pencil of function and the Gardner methods. All three former methods can be understood as special cases of a generalised eigenvalue problem. We show analytically that the leading corrections to an energy $$E_l$$
E
l
in all three methods due to unresolved states decay asymptotically exponentially like $$\exp (-(E_{n}-E_l)t)$$
exp
(
-
(
E
n
-
E
l
)
t
)
. Using synthetic data we show that these corrections behave as expected also in practice. We propose a novel combination of the generalised eigenvalue and the Prony method, denoted as GEVM/PGEVM, which helps to increase the energy gap $$E_{n}-E_l$$
E
n
-
E
l
. We illustrate its usage and performance using lattice QCD examples. The Gardner method on the other hand is found less applicable to realistic noisy data.
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