Comment on the Prediction of Two-loop Standard Chiral Perturbation Theory for Low-Energy ππScattering

Abstract

Four of the six parameters defining the two-loop ππscattering amplitude have been determined using Roy dispersion relations. Combining this information with the Standard χPT expressions, we obtain the threshold parameters, low-energy phases and the O(p^4) constants $l_1^r,l_2^r$. The result $l_2^r(M_{\rho })=(1.6\pm 0.4\pm 0.9)\times 10^{-3}({\bar{l}}_2=4.17\pm 0.19\pm 0.43$) reproduces the correct D-waves but it is incompatible with existing Standard χPT analyses of $K_{l4}$ form factors beyond one loop.

arXiv comment14 pages, Latex209, 2 figures

References in corpus (18)

• Elastic $\pi \pi$ scattering to two loops
• Generalized Dimensional Analysis
• The Low Energy $\pi \pi$ Amplitude to One and Two Loops
• Dispersive analysis of the decay eta -> 3 pi
• Simple Description of Pion-Pion Scattering to 1 GeV
• What $\pi -\pi$ Scattering Tells Us About Chiral Perturbation Theory
• $K_{l4}$ - Decays Beyond One Loop
• Consistency of the Chiral Pion-Pion Scattering Amplitudes with Axiomatic Constraints
• Photon-Photon Scattering, Pion Polarizability and Chiral Symmetry
• The Chiral Lagrangian parameters, ${\overline{\ell }}_1$, ${\overline{\ell }}_2$, are determined by the $\rho$--resonance
• Exploring $\pp$ scattering in the $\1N$ picture
• Determination of Two-Loop $\pi \pi$ Scattering Amplitude Parameters
• The Reaction $\gamma \gamma \to {\pi }^0{\pi }^0$ in Generalized Chiral Perturbation Theory
• The Chiral Coupling Constants $\lb{1}$ and $\lb{2}$ from \pipi Phase Shifts
• Effective Chiral Lagrangian from Dual Resonance Models
• Low Energy Sum Rules For Pion-Pion Scattering and Threshold Parameters
• Scattering Lengths and Medium and High Energy $\pi \pi$ Scattering
• Standard vs. Generalized Chiral Perturbation Theory : the Chell-Olsson test

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• Experimental status of the $\pi \pi$ isoscalar S wave at low energy: $f_0(600)$ pole and scattering length
• On the size of the sigma meson and its nature
• $K_{\ell 4}$ Form-Factors and $\pi$-$\pi$ Scattering
• S-matrix Bootstrap for Effective Field Theories: Massless Pions
• Chiral extrapolation of light resonances from one and two-loop unitarized Chiral Perturbation Theory versus lattice results
• The Inverse Amplitude Method in $\pi \pi$ Scattering in Chiral Perturbation Theory to Two Loops
• Bootstrapping Pions at Large $N$
• Generalized positivity bounds on chiral perturbation theory
• Scalar Form Factors in SU(3) Chiral Perturbation Theory
• Decay widths and energy shifts of pi pi and pi K atoms
• Error estimates for pi-pi scattering threshold parameters in Chiral Perturbation Theory to two loops
• Chiral extrapolation of pion-pion scattering phase shifts within standard and unitarized Chiral Perturbation Theory
• The pionium lifetime in generalized chiral perturbation theory
• Low-energy photon-photon fusion into three pions in Generalized Chiral Perturbation Theory
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• Measuring the quark condensate from the decays tau -> 3 pi + nu(tau)
• Double chiral logarithms of Generalized Chiral Perturbation Theory for low-energy pi-pi scattering
• Pion-pion and pion-nucleon interactions in chiral perturbation theory