Double Chiral Logs

Abstract

We determine the full structure of the leading (double-pole) divergences of O(p^6) in the meson sector of chiral perturbation theory. The field theoretic basis for this calculation is described. We then use an extension of this result to determine the p^6 contributions containing double chiral logarithms (L^2), single logarithms times p^4 constants (L x L_i^r) and products of two p^4 constants (L_i^r x L_j^r) for F_π, F_K/F_π, K_{l3} and K_{e4} form factors. Numerical results are presented for these quantities.

Latex, 13 pages, 1 figure

References in corpus (2)

• Pion-pion scattering at low energy
• Two-loop Analysis of Axialvector Current Propagators in Chiral Perturbation Theory

Cited by in corpus (40)

• Review of lattice results concerning low energy particle physics
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• $K_{\ell 3}$ decays in Chiral Perturbation Theory
• Pion and Kaon Electromagnetic Form Factors
• Two-point Functions at Two Loops in Three Flavour Chiral Perturbation Theory
• Chiral Perturbation Theory Beyond One Loop
• The < S P P > Green function and SU(3) breaking in K_{l3} decays
• $K_{\ell 4}$ Form-Factors and $\pi$-$\pi$ Scattering
• Chiral expansions of the pi0 lifetime
• $\pi K$ Scattering in Three Flavour ChPT
• The nucleon axial-vector coupling beyond one loop
• f_K/f_pi in Full QCD with Domain Wall Valence Quarks
• Renormalization group equations for effective field theories
• Towards a determination of the chiral couplings at NLO in 1/N(C): L_8(mu) and C_38(mu)
• Vector form factor in K_l3 semileptonic decay with two flavors of dynamical domain-wall quarks
• Low Energy Constants from Kl4 Form-Factors
• Leading Logarithms in the Massive O(N) Nonlinear Sigma Model
• The Massive O(N) Non-linear Sigma Model at High Orders
• A Parametrization for $K^{+}\to {\pi }^{+}{\pi }^{-}{e}^{+}\nu$
• Leading logarithms in N-flavour mesonic Chiral Perturbation Theory
• Radiative Ke3 decays revisited
• Chiral extrapolation and determination of low-energy constants from lattice data
• The expansion by regions in pi K scattering
• Approximating chiral SU(3) amplitudes
• Contributions of order $\mathcal{O}(m_{\mathrm{quark}}^2)$ to $K_{\ell 3}$ form factors and unitarity of the CKM matrix
• Leading logarithms for the nucleon mass
• The chiral logs of the K -> pi pi amplitude
• Chiral Perturbation Theory Reflections on Effective Theories of the Standard Model
• The leading two loop counterterm in the nonleptonic weak sector of CHPT
• Leading Logarithms of the Two Point Function in Massless O(N) and SU(N) Models to any Order from Analyticity and Unitarity
• Analysis of the vector form factors $f_{K\pi }^{+}(Q^2)$ and $f_{K\pi }^{-}(Q^2)$ with light-cone QCD sum rules
• K_{l3} and pi_{e3} decays: radiative corrections and CKM unitarity
• Leading Chiral Logarithms of $K_S\to \gamma \gamma$ and $K_S\to \gamma l^{+}{l}^{-}$ at two Loops
• Chiral extrapolation of SU(3) amplitudes
• Scalar form factors $f_{\pi \pi }(Q^2)$ and $f_{KK}(Q^2)$ with light-cone QCD sum rules
• Leading logarithms for mesons and nucleons
• A Symmetric Approach to the Massive Nonlinear Sigma Model
• Double chiral logarithms of Generalized Chiral Perturbation Theory for low-energy pi-pi scattering
• Analytic Approximations for the Extrapolation of Lattice Data