Publication: Chiral extrapolation of light resonances from one and two-loop unitarized chiral perturbation theory versus lattice results
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2010-11-01
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Rios, G.
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Amer Physical Soc
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We study the pion mass dependence of the ρ(770) and f_0(600) masses and widths from one and two-loop unitarized chiral perturbation theory ( ChPT). We show the consistency of one-loop calculations with lattice results for the M_ρ, f_π 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 ρ(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_ρ, f_π, by the q q̅ leading 1/N_c behavior of the ρ and by existing estimates of low-energy constants. These fits yield relatively stable predictions up to m_π ̴̲ 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_π dependence of the rho coupling and the Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin relation, and the existence of two virtual f_0(600) poles for sufficiently high m_π. At two loops one of these poles becomes a bound state when m_π is somewhat larger than 300 MeV.
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©2010 The American Physical Society.
We thank C. Hanhart for useful discussions. Work partially supported by Spanish Ministerio de Educación y Ciencia research Contract Nos. FPA2007-29115-E, FPA2008-00592, and FIS2006- 03438, U. Complutense/ Banco Santander Grant Nos. PR34/07-15875-BSCH and UCM-BSCH GR58/08 910309. We acknowledge the support of the European Community-Research Infrastructure Integrating Activity Study of Strongly Interacting Matter (acronym HadronPhysics2, Grant Agreement No. 227431) under the Seventh Framework Programme of EU.
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