Resonance effects in pion and kaon decay constants

Abstract

In this article we study impact of the lightest vector and scalar resonance multiplets in the pion and kaon decay constants up to next-to-leading order in the $1/N_C$ expansion, i.e., up to the one-loop level. The $F_{\pi }$ and $F_K$ predictions obtained within the framework of Resonance Chiral Theory are confronted with lattice simulation data. The vector loops (and the $\rho -\pi \pi$ coupling $G_V$ in particular) are found to play a crucial role in the determination of the Chiral Perturbation Theory couplings $L_4$ and $L_5$ at next-to-leading order in $1/N_C$. Puzzling, values of $G_V<40$ MeV seem to be necessary to agree with current phenomenological results for $L_4$ and $L_5$. Conversely, a value of $G_V>60$ MeV compatible with standard $\rho -\pi \pi$ determinations turns these chiral couplings negative. However, in spite of the strong anti-correlation with $L_4$, the $SU(3)$ chiral coupling $F_0$ remains stable all the time and stays within the range $78\sim 86$ MeV when $G_V$ is varied in a wide range, from $40$ up to $70$ MeV. Finally, we would like to remark that the leading order expressions used in this article for the $\eta -{\eta }^{\prime }$ mixing, mass splitting of the vector multiplet masses and the quark mass dependence of the $\rho (770)$ mass are found in reasonable agreement with the lattice data.

48 pages, 9 eps figures. Further commments on additional operators with the ${\eta }_1$ field, the impact of a second scalar nonet and the KSRF relation have been incorporated. References added. Minor typos corrected. Phys. Rev. D 89, 094024 (2014) published version

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• Unified study of $J/\psi \to PV$, $P{\gamma }^{(\ast )}$ and light hadron radiative processes
• Improved ${\pi }^0,\eta ,{\eta }^{\prime }$ transition form factors in resonance chiral theory and their $a_{\mu }^{\mathrm{HLbL}}$ contribution
• Radiative transition processes of light vector resonances in a chiral framework
• On the chiral expansion of vector meson masses
• Renormalisation of the low-energy constants of chiral perturbation theory from loops with dynamical vector mesons
• On pion and kaon decay constants and chiral SU(3) extrapolations
• Improved description of di-lepton production in ${\tau }^{-}\to {\nu }_{\tau }{P}^{-}$ decays
• Momentum-dependence of $\rho -\omega$ mixing in the pion vector form factor and its effect on $(g-2{)}_{\mu }$