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 (55)

• ππscattering
• Chiral symmetry amplitudes in the s-wave isoscalar and isovector channels and the $\sigma ,f_0(980),a_0(980)$ scalar mesons
• Chiral Symmetry Amplitudes in the S-Wave Isoscalar and Isovector Channels and the σ, f_0(980), a_0(980) Scalar Mesons
• Meson-Meson interaction in a non-perturbative chiral approach
• Mass and width of the lowest resonance in QCD
• Evidence that the a0(980) and f0(980) are not elementary particles
• The QCD spectrum with three quark flavors
• Non-perturbative Approach to effective chiral Lagrangians and Meson Interactions
• Couplings in coupled channels versus wave functions: application to the X(3872) resonance
• The inverse amplitude method in Chiral Perturbation Theory
• On the nature of light scalar mesons from their large $N_c$ behavior
• Meson-meson scattering within one loop Chiral Perturbation Theory and its unitarization
• Insight into the Scalar Mesons from a Lattice Calculation
• A new analysis of $\pi K$ scattering from Roy and Steiner type equations
• Nature of the f_0(600) from its N_c dependence at two loops in unitarized Chiral Perturbation Theory
• Dynamical Twisted Mass Fermions with Light Quarks
• A global fit of $\pi \pi$ and $\pi K$ elastic scattering in ChPT with dispersion relations
• QCD Isospin Breaking in Meson Masses, Decay Constants and Quark Mass Ratios
• A new measurement of K+(e4) decay and the s-wave pi-pi-scattering length a00
• The K^*_0(800) scalar resonance from Roy-Steiner representations of pi K scattering
• Lattice QCD Calculation of the $\rho$ Meson Decay Width
• Quark mass dependence of the rho and sigma from dispersion relations and Chiral Perturbation Theory
• Chiral Perturbation Theory Beyond One Loop
• The pion-pion scattering amplitude
• Light scalars as tetraquarks or two-meson states from large Nc and unitarized Chiral Perturbation Theory
• 2+1 flavor domain wall QCD on a (2 fm)^3 lattice: light meson spectroscopy with Ls = 16
• Precise Determination of the I=2 pipi Scattering Length from Mixed-Action Lattice QCD
• KK bar scattering amplitude to one loop in chiral perturbation theory, its unitarization and pion form factors
• The pi+ pi+ scattering length from maximally twisted mass lattice QCD
• Bethe-Salpeter Approach for Meson-Meson Scattering in Chiral Perturbation Theory
• Scalar Particles in Lattice QCD
• Strange and non-strange quark mass dependence of elastic light resonances from SU(3) Unitarized Chiral Perturbation Theory to one loop
• 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?
• Pion-pion scattering at low energy
• 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
• The Mixing Angle of the Lightest Scalar Nonet
• Chiral and Continuum Extrapolation of Partially-Quenched Lattice Results
• The Inverse Amplitude Method in $\pi \pi$ Scattering in Chiral Perturbation Theory to Two Loops
• Gluonium nature of the sigma/f_0(600) from its coupling to KK
• Model independent determination of the sigma pole
• Comment on the Prediction of Two-loop Standard Chiral Perturbation Theory for Low-Energy ππScattering
• Pion scattering poles and chiral symmetry restoration
• Second sheet $\sigma$ pole and the threshold enhancement of the spectral function in the scalar-isoscalar meson-sector
• Properties of light resonances from unitarized Chiral perturbation theory: Nc behavior and quark mass dependence
• Chiral extrapolation of the sigma and rho mesons from dispersion relations and Chiral Perturbation Theory
• The low-lying Scalar Mesons and Related Topics
• Unitarized Chiral Perturbation Theory and the meson spectrum
• Light meson spectrum with $N_f=2$ dynamical overlap fermions
• Dispersive chiral approach to Meson-meson dynamics: Spectroscopy results for light scalars and precision studies
• Spectroscopy of light tetraquark states
• 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

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• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
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• Nucleon resonance parameters from Roy-Steiner equations
• Quark mass dependence of $\pi \pi$ scattering in isospin 0, 1, and 2 from lattice QCD
• Data-driven dispersive analysis of the $\pi \pi$ and $\pi K$ scattering
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• QCD with two light dynamical chirally improved quarks: Mesons
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• Review on recent progress in the study of the $N^{\ast }(920)$ subthreshold singularity and the $\sigma /f_0(500)$ meson
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