ππscattering

Abstract

We demonstrate that, together with the available experimental information, chiral symmetry determines the low energy behaviour of the $\pi \pi$ scattering amplitude to within very small uncertainties. In particular, the threshold parameters of the S-, P-, D- and F-waves are predicted, as well as the mass and width of the $\rho$ and of the broad bump in the S-wave. The implications for the coupling constants that occur in the effective Lagrangian beyond leading order and also show up in other processes, are discussed. Also, we analyze the dependence of various observables on the mass of the two lightest quarks in some detail, in view of the extrapolations required to reach the small physical masses on the lattice. The analysis relies on the standard hypothesis, according to which the quark condensate is the leading order parameter of the spontaneously broken symmetry. Our results provide the basis for an experimental test of this hypothesis, in particular in the framework of the ongoing DIRAC experiment: The prediction for the lifetime of the ground state of a ${\pi }^{+}{\pi }^{-}$ atom reads $\tau =(2.90\pm 0.10)10^{-15}sec$.

61 pages (LaTex), 11 figures

References in corpus (1)

• Quark Masses on the Lattice: Light and Heavy

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• Determination of SU(2) Chiral Perturbation Theory low energy constants from a precise description of pion-pion scattering threshold parameters
• Proximity of $f_0(1500)$ and $f_0(1710)$ to the scalar glueball
• Further remarks on $\pi \pi$ scattering dispersion relations
• $K\to \pi {\ell }^{+}{\ell }^{-}$ form factor in the Large-N${}_c$ and cut-off regularization method
• Ordinary and exotic mesons in the extended Linear Sigma Model
• Dispersive treatment of $K_S\to \gamma \gamma$ and $K_S\to \gamma {\ell }^{+}{\ell }^{-}$
• Can parameters of f_0-mesons be determined correctly analyzing only pion-pion scattering?
• Model independent bounds on the modulus of the pion form factor on the unitarity cut below the $\omega \pi$ threshold
• Light and strange vector resonances from lattice QCD at physical quark masses
• Theoretical status of ${\epsilon }^{\prime }/\epsilon$
• Closing in on the radiative weak chiral couplings
• Scales in nuclear matter: Chiral dynamics with pion nucleon form factors
• Probing SUSY effects in $K_S^0\to {\mu }^{+}{\mu }^{-}$
• Masses and widths of scalar-isoscalar multi-channel resonances from data analysis
• Density of States of a Coupled-Channel System
• Isospin 0 and 2 two-pion scattering at physical pion mass using all-to-all propagators with periodic boundary conditions in lattice QCD
• Event generators for $\eta /{\eta }^{\prime }$ decays at BESIII
• Isotropic and Anisotropic Lattice Spacing Corrections for I=2 pi-pi Scattering from Effective Field Theory
• Froissart Bound on Inelastic Cross Section Without Unknown Constants
• Constraining the low energy Pion electromagnetic form factor with space-like and phase of time-like data
• I=2 pion-pion scattering phase shift in the continuum limit calculated with two-flavor full QCD
• Measurement of the decay ${\eta }^{\prime }\to {\pi }^0{\pi }^0\eta$ at MAMI
• The $\pi f_0(500)$ decay of the $a_1(1260)$
• Is $J^{PC}=3^{-+}$ molecule possible?
• A Simple Parametrisation of the Pion Form Factor
• QCD inequalities for hadron interactions
• Bootstrapping gauge theories
• Relations at Order $p^6$ in Chiral Perturbation Theory
• Low-energy pion-pion scattering in the $pp\to pp{\pi }^{+}{\pi }^{-}$ and $p\bar{p}\to p\bar{p}{\pi }^{+}{\pi }^{-}$ reactions
• Overview and Perspectives in Nuclear Physics
• Chiral Nonet Mixing in $\pi K$ Scattering
• Physical-mass calculation of $\rho (770)$ and $K^{\ast }(892)$ resonance parameters via $\pi \pi$ and $K\pi$ scattering amplitudes from lattice QCD
• Chiral perturbation theory, dispersion relations and final state interactions in K -> pi pi
• Theory of Scalars
• Cross sections for inelastic meson-meson scattering
• Recent progress in applying lattice QCD to kaon physics
• Comment on evidence for new interference phenomena in the decay D+ -> K- pi+ mu+ nu
• Quantum Chromodynamics, Antiferromagnets and XY Models from a Unified Point of View
• $\Delta I=3/2$ and $\Delta I=1/2$ channels of $K\to \pi \pi$ decay at the physical point with periodic boundary conditions
• Scalar resonances: scattering and production amplitudes
• Pseudoscalar mesons in a finite cubic volume with twisted boundary conditions
• Measurement of Direct Emission in the KL->pi+pi-gamma Decay Mode
• Update on ${\epsilon }_K$ with lattice QCD inputs
• Pion scalar form factor and model independent values of $f_0(500)$ and $f_0(980)$ meson parameters
• Radiative corrections in $K_{e4}$ decay
• Chiral Perturbation Theory Reflections on Effective Theories of the Standard Model
• Temperature-dependent cross sections for meson-meson nonresonant reactions in hadronic matter
• New dispersion relations in the description of $\pi \pi$ scattering amplitudes
• Connections between chiral Lagrangians and QCD sum-rules
• Strong Interactions at Low Energy
• Exclusive photon-fusion production of even-spin resonances and exotic QED atoms in high-energy hadron collisions
• On-shell Delta I = 3/2 kaon weak matrix elements with non-zero total momentum
• Revisiting $O(N)$ $\sigma$ model at unphysical pion masses and high temperatures
• On the effective lagrangian at nonzero isospin chemical potential
• New constraints on the Pion EM form factor using Pi'(-Q^2)
• S-wave and P-wave pion-pion and kaon-pion contributions to three-body decay processes in the Resonance-Spectrum Expansion
• Nucleons and nuclei in the context of low-energy QCD
• Matching effective chiral Lagrangians with dimensional and lattice regularization
• Light Meson Masses using AdS/QCD modified Soft Wall Model
• Hadronic light-by-light contribution to $(g-2{)}_{\mu }$: a dispersive approach
• Analytical dispersive parameterization for elastic scattering of spinless particles
• The isospin symmetry breaking effects in $K_{e4}$ decays
• A unitarity analysis on the I=0 $d$ wave $\pi \pi$ scattering amplitude
• Scalar radius of the pion in the Kroll-Lee-Zumino renormalizable theory
• A study on the correlation between poles and cuts in $\pi \pi$ scattering
• Evaluation of the Axial Vector Commutator Sum Rule for Pion-Pion Scattering
• First measurement of a long-lived ${\pi }^{+}{\pi }^{-}$ atom lifetime
• Central hadron production in crossing of dedicated hadronic beams
• Investigating the pion emission source in pp collisions using the AMPT model with sub-nucleon structure
• Chiral Nonet Mixing in $\pi \eta$ Scattering
• Photon radiation in $e^{+}{e}^{-}\to$ hadrons at low energies with CARLOMAT 3.1
• Quark flavor physics and lattice QCD
• Model-independent constraint on the pion scalar form factor and light quark masses
• The electromagnetic effects in $K_{e4}$ decay
• QCD in the delta-Regime
• Current status of ${\epsilon }_K$ in lattice QCD
• On concise hypotheses for the interpretation of a wide scalar resonance as gauge boson binary in QCD - some new analyses
• Cross Sections for Inelastic 2-to-2 Meson-Meson Scattering in Hadronic Matter
• Correlations of $C$ and $CP$ violation in $\eta \to {\pi }^0{\ell }^{+}{\ell }^{-}$ and ${\eta }^{\prime }\to \eta {\ell }^{+}{\ell }^{-}$
• Final state interaction in kaons decays
• The Observed Correlations for the Strange Multibaryon States in Systems with $\Lambda$-Hyperon from pa Collision at Momentum of 10 Gev/$c$
• Pion polarizabilities: Theory vs Experiment
• News on PHOTOS Monte Carlo: gamma^* -> pi^+ pi^-(gamma) and K^\pm -> pi^+ pi^- e^\pm nu (gamma)
• Kaon-antikaon nuclear optical potentials and the kappa meson in the nuclear medium
• ${\pi }_{e3}$ form factor $f_{-}$ near the mass shell
• CP-violation and unitarity triangle test of the Standard Model
• The Relativistic Cornell-type Mechanism of Exotic Scalar Resonances
• On the low energy end of the QCD spectrum
• Review of chiral perturbation theory
• Quark mass dependence of on-shell and half off-shell scattering amplitudes from Bethe-Salpeter wave function inside the interaction range
• Strong correlation of the neutron star core-crust transition density with the $\sigma$-meson mass via vacuum polarization
• Vector meson decays from the Extended Chiral Quark Model
• Cross sections for 2-to-3 meson-meson scattering
• QCD Sum Rules study of meson-baryon sigma terms
• Unitarity and Unitarization
• Topics in Lattice QCD and Effective Field Theory
• Compton Scattering by the Nucleon
• Chiral dynamics and pion properties at finite temperature and isospin chemical potential
• The reactions $\pi \pi \to \pi \pi$ and $\gamma \gamma \to \pi \pi$ in $\chi$PT with an isosinglet scalar resonance
• Radiative corrections to neutral pion-pair production
• In memory of Paco Yndurain: A precise determination of pion-pion scattering from experiment and dispersion relations
• New method for fitting the low-energy constants in chiral perturbation theory
• Investigation of meson-meson interaction
• {\bar p}p-annihilation processes in the tree approximation of SU(3) chiral effective theory
• Introduction to chiral symmetry in QCD
• Vector Meson Dominance as the first order of a sequence of Pade Approximants
• $\sigma (600)$ and background in $\pi \pi$ scattering
• Low-energy QCD and hadronic structure
• Dispersive determination of resonances from $\pi \pi$ scattering data
• From QCD to Physical Resonances
• The pion mass in finite volume to two loops
• Bayesian method for fitting the low-energy constants in chiral perturbation theory
• Pion propagation in real time field theory at finite temperature
• Low Energy Pion-Pion Elastic Scattering in Sakai-Sugimoto Model
• Vector exchanges in production of light meson pairs and elementary atoms
• $\Lambda (1405)$ and $\bar{\Lambda }(1405)$ in $J/\psi$ four-body decays
• Role of the strange quark in the rho(770) meson
• Selected challenges in low-energy QCD and hadron physics
• Assessing the role of threshold conditions in the determination of uncertainties in pole extractions using Padé approximants
• Formation of $\pi \mu$ atoms in $K_{μ4} decay
• On the role of final-state interactions in Dalitz plot studies
• $\pi \pi$ scattering from a similarity renormalization group perspective
• Non-Strange Meson Production with Hadronic Probes
• Role of electromagnetic corrections in the $\pi \pi$ distributions of ${\psi }^{\prime }\to J/\psi \pi \pi$
• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$
• Subthreshold parameters of $\pi \pi$ scattering revisited
• Understanding large localized CP violation in $B^{\pm }\to K^{\pm }{\pi }^{+}{\pi }^{-}$ using dispersive methods
• Radiative corrections to the charged pion-pair production process {\boldmath${\pi }^{-}\gamma \to {\pi }^{+}{\pi }^{-}{\pi }^{-}$} at low energies
• Three-body final state interactions in $B^{+}\to D\bar{D}{K}^{+}$ decays
• CP-violation in K_{S,L}->π^{+}π^{-}γand K_{S,L}->π^{+}π^{-}e^{+}e^{-} decays
• Meson-Meson Interactions and Resonances in the 't Hooft Model
• Chiral Effective Field Theory in the Delta-resonance region
• Three-pion scattering: From the chiral Lagrangian to the lattice