Chiral extrapolation of light resonances from one and two-loop unitarized Chiral Perturbation Theory versus lattice results

TL;DR

This paper investigates how the masses and widths of light resonances, specifically the rho(770) and f_0(600), depend on pion mass using unitarized Chiral Perturbation Theory at one and two loops, comparing results with lattice data.

Contribution

It develops a two-loop unitarized Chiral Perturbation Theory approach and applies it to analyze light resonance properties, incorporating lattice constraints and systematic uncertainties.

Findings

Two-loop fits provide stable predictions for resonance parameters up to m_pi≈350 MeV.

The rho coupling remains weakly dependent on m_pi, confirming the KSRF relation.

The f_0(600) exhibits two virtual poles, with one becoming a bound state at higher m_pi.

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.