Scalar-involved three-point Green functions and their phenomenology

Abstract

We analyse within the framework of resonance chiral theory the SA µ A ν and SV µ V ν three-point Green functions, where S, A µ and V µ 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. *

Lepton-flavour violation in hadronic tau decays and μ-τ conversion in nuclei

“…As it is well known, the identification of those multiplets with the experimentally determined resonances in the PDG [82] is clear in all cases except for the scalars; see ref. [83] and references therein.…”

Two and three pseudoscalar production in e+e− annihilation and their contributions to (g − 2)μ

“…One may use experimental data to obtain information of the couplings. Meanwhile, there is one theoretical tool that has proven efficient in this task: one can extract information on the coupling constants by matching the perturbative Green functions of QCD currents, using the operator product expansion (OPE) at leading order, with those constructed in the RχT framework [10][11][12][13][14][15][16]. Actually, RχT can also match, by construction, with χPT by integrating out the resonances in the Lagrangian [4,17], allowing to relate their coupling constants, too.…”

“…The coupling constants of the interaction terms of L V−GB could be extracted from the phenomenology involving those states. As commented in the introduction the matching between the leading order in the OPE expansion of specific Green functions of QCD and their expressions within RχT is also a useful tool that has been employed in the bibliography [10][11][12][13][14][15][16]. We will implement this procedure as far as it helps in our task.…”

Study of $\tau^- \to\nu_{\tau} \pi^{-}\pi^{0}\ell^{+}\ell^{-}$ decays in the framework of Resonance Chiral Theory

“…) get modified when including three-point Green functions in both intrinsic parity sectors [4,[28][29][30][31][32][33][34][35][36][37][38][39][40][41]. The consistent set of relations in this more general case includes = √ 3 [42] that -through the appropriate asymptotic behaviour of the spin-one correlatorsimplies, = / √ 3 and = √ 2 .…”