Form factors of the isovector scalar current and the $$\eta \pi $$ η π scattering phase shifts

Abstract

A model for S-wave scattering is proposed which could be realistic in an energy range from threshold up to above 1 GeV, where inelasticity is dominated by the channel. The T-matrix, satisfying two-channel unitarity, is given in a form which matches the chiral expansion results at order exactly for the , amplitudes and approximately for . It contains six phenomenological parameters. Asymptotic conditions are imposed which ensure a minimal solution of the Muskhelishvili–Omnès problem, thus allowing one to compute the and form factor matrix elements of the scalar current from the T-matrix. The phenomenological parameters are determined such as to reproduce the experimental properties of the , resonances, as well as the chiral results of the and scalar radii, which are predicted to be remarkably small at . This T-matrix model could be used for a unified treatment of the final-state interaction problem in processes such as , , or the initial-state interaction in .

Theoretical analysis of the γγ→π0η process

“…In all these cases, a 0 (980) shows up as a sharp (cusplike) peak exactly at the two kaon threshold. This behavior of the hadronic cross section is somewhat different from the recent K-matrix analysis [37] which takes as an input the pole on the second Riemann sheet from [41,42]. In Fig.…”

“…In the two-channel case there are four Riemann sheets, which correspond to different signs of the imaginary parts of the center of mass momenta [28]. In the neighborhood of the pole, the t-matrix elements can be written as [21] compared to the K-matrix [29], inverse amplitude method (IAM) [30] and χPT [30,31] analyses. For the latter we show the spread between the LO and NLO results (with the NLO low-energy constants taken from [30]).…”

“…We note that though the location of the pole is not too far away from the KK threshold, its precise determination may require taking into account higher order effects in the left-hand cuts of the dispersive approach [21], or fitting the corresponding conformal expansion coefficients C k directly to future experimental data. A number of theoretical efforts were devoted to understanding the properties of the a 0 (980) resonance [30,[33][34][35][36][37]. Recently, the first analysis of the πη scattering was performed by lattice QCD in Refs.…”

Extended chiral Khuri–Treiman formalism for $$\eta \rightarrow 3\pi $$ η → 3 π and the role of the $$a_0(980)$$ a 0 ( 980 ) , $$f_0(980)$$ f 0 ( 980 ) resonances

“…We will rely here on the chiral Kmatrix model proposed in Ref. [50] which provides a simple interpolation between certain known properties of the prominent I = 1 scalar resonances a 0 (980) and a 0 (1450) and the low-energy properties constrained by chiral symmetry. The T -matrix reproduces, by construction, the ηπ → ηπ and ηπ → KK chiral amplitudes at NLO (and more approximately the amplitude KK → KK ).…”

$${\bar{B}}^0$$ B ¯ 0 , $$B^{-}$$ B - and $${\bar{B}}^0_s$$ B ¯ s 0 decays into $$J/\psi $$ J / ψ and $$K {\bar{K}}$$ K K ¯ or $$\pi \eta $$ π η

“…Some work along these lines has been recently done in Ref. [21]. The chiral unitary approach for mesons [22][23][24][25][26][27] is particularly suited for this purpose and has been used in many processes where the f 0 (500), f 0 (980), a 0 (980), κ(800) are produced, including some related to D and B weak decays [28,29].…”