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 rho(770) and f_0(600) masses and widths from one and two-loop unitarized Chiral Perturbation Theory. We show the consistency of one-loop calculations with lattice results for the M_rho, f_pi 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(600), the rho(770) 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_rho, f_pi, by the qqbar leading 1/N_c behavior of the rho and by existing estimates of low energy constants. These fits yield relatively stable predictions up to m_pi\simeq 300-350 MeV for the rho coupling and width as well as for all the f_0(600) parameters. We confirm, to two-loops, the weak m_pi dependence of the rho coupling and the KSRF relation, and the existence of two virtual f_0(600) poles for sufficiently high m_pi. At two loops one of these poles becomes a bound state when m_pi is somewhat larger than 300 MeV.

15 pages, to appear in Phys. Rev. D

References in corpus (19)

• Nature of the f_0(600) from its N_c dependence at two loops in unitarized Chiral Perturbation Theory
• The K^*_0(800) scalar resonance from Roy-Steiner representations of pi K scattering
• Quark mass dependence of the rho and sigma from dispersion relations and Chiral Perturbation Theory
• Chiral Perturbation Theory Beyond One Loop
• Precise Determination of the I=2 pipi Scattering Length from Mixed-Action Lattice QCD
• Scalar Mesons a0(1450) and sigma(600) from Lattice QCD
• Lattice study of light scalar tetraquarks with I=0,2,1/2,3/2: are sigma and kappa tetraquarks?
• Experimental status of the $\pi \pi$ isoscalar S wave at low energy: $f_0(600)$ pole and scattering length
• The Inverse Amplitude Method and Adler Zeros
• Infrared regularization for spin-1 fields
• Gluonium nature of the sigma/f_0(600) from its coupling to KK
• Model independent determination of the sigma pole
• Pion scattering poles and chiral symmetry restoration
• The low-lying Scalar Mesons and Related Topics
• Chiral extrapolation of the sigma and rho mesons from dispersion relations and Chiral Perturbation Theory
• Dispersive chiral approach to Meson-meson dynamics: Spectroscopy results for light scalars and precision studies
• Light meson spectrum with $N_f=2$ dynamical overlap fermions
• Scalar mesons from Unitarized Chiral Perturbation Theory: N_c and quark mass dependences
• Chiral Extrapolations of light resonances from dispersion relations and Chiral Perturbation Theory