Two-loop representations of low-energy pion form factors and pi-pi scattering phases in the presence of isospin breaking

Abstract

Dispersive representations of the pi-pi scattering amplitudes and pion form factors, valid at two-loop accuracy in the low-energy expansion, are constructed in the presence of isospin-breaking effects induced by the difference between the charged and neutral pion masses. Analytical expressions for the corresponding phases of the scalar and vector pion form factors are computed. It is shown that each of these phases consists of the sum of a "universal" part and a form-factor dependent contribution. The first one is entirely determined in terms of the pi-pi scattering amplitudes alone, and reduces to the phase satisfying Watson's theorem in the isospin limit. The second one can be sizeable, although it vanishes in the same limit. The dependence of these isospin corrections with respect to the parameters of the subthreshold expansion of the pi-pi amplitude is studied, and an equivalent representation in terms of the S-wave scattering lengths is also briefly presented and discussed. In addition, partially analytical expressions for the two-loop form factors and pi-pi scattering amplitudes in the presence of isospin breaking are provided.

57 pages, 12 figures

References in corpus (9)

• Analytical dispersive construction of $\eta \to 3\pi$ amplitude: First order in isospin breaking
• Isospin breaking in Kl4 decays
• A new global fit of the $L_i^r$ at next-to-next-to-leading order in Chiral Perturbation Theory
• Cusps in K --> 3pi decays: a theoretical framework
• K -> 3 pi Final State Interactions at NLO in CHPT and Cabibbo's Proposal to Measure a_0-a_2
• Dispersive Approach to Chiral Perturbation Theory
• Chiral dynamics with strange quarks in the light of recent lattice simulations
• Electromagnetic low-energy constants in ChPT
• Low-energy pi-pi and pi-K scatterings revisited in three-flavour resummed chiral perturbation theory

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• On the amplitudes for the CP-conserving $K^{\pm }(K_S)\to {\pi }^{\pm }({\pi }^0){\ell }^{+}{\ell }^{-}$ rare decay modes
• Dispersive construction of two-loop $P\to \pi \pi \pi$ $(P=K,\eta )$ amplitudes
• Isospin breaking in the phases of the Ke4 form factors
• Determination of SU(2) Chiral Perturbation Theory low energy constants from a precise description of pion-pion scattering threshold parameters
• ChPT calculations of pion formfactors