Scalar-involved three-point Green functions and their phenomenology

Abstract

We analyse within the framework of resonance chiral theory the $⟨S{A}_{\mu }{A}_{\nu }⟩$ and $⟨S{V}_{\mu }{V}_{\nu }⟩$ three-point Green functions, where $S$, $A_{\mu }$ and $V_{\mu }$ are short for scalar, axial-vector and vector $SU(3)$ hadronic currents. We construct the necessary Lagrangian such that the Green functions fulfill the asymptotic constraints, at large momenta, imposed by QCD at leading order. We study the implications of our results on the spectrum of scalars in the large-$N_C$ limit, and analyse their decays.

30 pages, 5 figures. v2: Typos in Eqs. (B.4) and (B.6) of the appendices in the published version are corrected

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• Two and Three Pseudoscalar Production in $e^{+}{e}^{-}$ annihilation and their contributions to $(g-2{)}_{\mu }$
• Scalar resonances in the hadronic light-by-light contribution to the muon $(g-2)$
• Two body final states production in electron-positron annihilation and their contributions to $(g-2{)}_{\mu }$
• Tension between $e^{+}{e}^{-}\to \eta {\pi }^{-}{\pi }^{+}$ and ${\tau }^{-}\to \eta {\pi }^{-}{\pi }^0{\nu }_{\tau }$ data and non-standard interactions
• Lepton-pair production in di-pion $\tau$ lepton decays
• OPE of Green Functions of Chiral Currents
• Vector and Scalar Mesons' Mixing from QCD Sum Rules
• Nature of $X(2370)$
• Tensor Meson Pole contributions to the HLbL piece of $a_{\mu }$ within R$\chi$T
• Hadronic contributions to $a_{\mu }$ within Resonance Chiral Theory