Chiral dynamics in form factors, spectral-function sum rules, meson-meson scattering and semilocal duality

Abstract

In this work, we perform the one-loop calculation of the scalar and pseudoscalar form factors in the framework of Uð3Þ chiral perturbation theory with explicit tree level exchanges of resonances. The mesonmeson scattering calculation from Guo and Oller [Phys. Rev. D 84, 034005 (2011)] is extended as well. The spectral functions of the nonet scalar-scalar (SS) and pseudoscalar-pseudoscalar (PP) correlators are constructed by using the corresponding form factors. After fitting the unknown parameters to the scattering data, we discuss the resonance content of the resulting scattering amplitudes. We also study spectral-function sum rules in the SS À SS, PP À PP, and SS À PP sectors as well as semilocal duality from scattering. The former relate the scalar and pseudoscalar spectra between themselves while the latter mainly connects the scalar spectrum with the vector one. Finally we investigate these items as a function of N C for N C > 3. All these results pose strong constraints on the scalar dynamics and spectroscopy that are discussed. They are successfully fulfilled by our meson-meson scattering amplitudes and spectral functions.

τ − →K − η (′) ν τ decays in Chiral Perturbation Theory with resonances

“…[76][77][78] (for the strangeness-changing form factors) 7 and [95,96] (for the strangeness-conserving ones) unitarizing SU (3) and U (3) (respectively) χP T with explicit exchange of resonances [97]. However, given the large errors of the τ − → K − ην τ decay spectra measured by the BaBar [42] and Belle [41] Collaborations and the absence of data on the K − η channel we consider that it is not timely to perform such a cumbersome numerical analysis in the absence of enough experimental guidance 8 .…”

Interesting features of scalar and pseudoscalar spectral function sum rules within aU(3) chiral framework

“…We refer to Refs. [7,9] for details. We only include the single-particle exchange contributions from either pseudo-Goldstone bosons or pseudoscalar resonances to calculate the pseudoscalar spectral functions…”

“…However, χPT, whose success is based on momentum and light quark mass perturbative expansions, is not valid any more in the energy region where resonance states appear. A sophisticated approach, unitarized χPT that inherits the chiral symmetry and also extends the applicable energy region of χPT by resumming the unitarity cut, is then brought up and has been demonstrated useful in many processes [4][5][6][7][8][9][10]. Therefore, unitarized χPT can provide us another reliable way to calculate the spectral functions.…”

“…In this note, we briefly review our main results on the spectral functions obtained in Refs. [7][8][9][10]. …”

“…In our recent works, Refs. [7][8][9][10], we first fit the free parameters in our theory to meson-meson scattering data and then scalar and pseudoscalar spectral functions calculated within the framework of unitarized U(3) χPT with explicit exchanges of resonances are predicted. In this note, we briefly review our main results on the spectral functions obtained in Refs.…”