Chiral extrapolation of light resonances from one and two-loop unitarized chiral perturbation theory versus lattice results

Abstract

We study the pion mass dependence of the ð770Þ and f 0 ð600Þ masses and widths from one and twoloop unitarized chiral perturbation theory (ChPT). We show the consistency of one-loop calculations with lattice results for the M , f , and the isospin-2 scattering length a 20 . Then, we develop and apply the modified inverse amplitude method formalism for two-loop ChPT. In contrast to the f 0 ð600Þ, the ð770Þ is rather sensitive to the two-loop ChPT parameters-our main source of systematic uncertainty. We thus provide two-loop unitarized fits constrained by lattice information on M , f , by the q " q leading 1=N c behavior of the and by existing estimates of low-energy constants. These fits yield relatively stable predictions up to m ' 300-350 MeV for the coupling and width as well as for all the f 0 ð600Þ parameters. We confirm, to two loops, the weak m dependence of the coupling and the KawarabayashiSuzuki-Riazuddin-Fayyazuddin relation, and the existence of two virtual f 0 ð600Þ poles for sufficiently high m . At two loops one of these poles becomes a bound state when m is somewhat larger than 300 MeV.

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

“…[41] and extended in Refs. [42][43][44][45][46][47][48]. The O(p 2 ) chiral Lagrangian [49,50] qualitatively leads to the generation of the scalar resonances, while, as shown in Ref.…”

Dispersion relation for hadronic light-by-light scattering: two-pion contributions

“…-45 - This form of the IAM thus correctly describes the low-energy phase shifts as well as resonance properties, and has indeed been used in recent years to determine the quark-mass dependence of σ and ρ resonances [122,123]. For our purposes, the single-channel IAM for ππ scattering conveniently separates the ππ channel from its mixing toKK in the vicinity of the f 0 (980) and defines a reasonable continuation to high energies, without compromising the low-energy physics.…”

“…We use the 1-loop IAM with low-energy constants as specified in [123], which produces the phase shifts shown in figure 13. As expected, there is good agreement throughout, apart from the fact that the IAM I = 0 phase shift avoids the rise related to the f 0 (980) and the coupling to theKK channel.…”

Chiral behavior of vector meson self-energies

“…Such ideas are more than fifty years old [30,31] and have been revived some time ago employing "Unitarized ChPT" in [32][33][34][35][36]. In [37][38][39][40], the quark mass dependence of the ρ and σ resonance masses was studied within such an approach. It would be very nice to see a consistent picture emerge when comparing the chiral Lagrangian framework to such non-perturbative approaches.…”