Form factors of the isovector scalar current and the scattering phase shifts

M. Albaladejo; B. Moussallam

doi:10.1140/epjc/s10052-015-3715-z

EPJ

a
b
c
d
e
ap
st
h
plus
ds
pv
ti
qt
am
n

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2015) 75: 488
https://doi.org/10.1140/epjc/s10052-015-3715-z

Regular Article - Theoretical Physics

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

M. Albaladejo¹^,2 and B. Moussallam¹^*

¹ Groupe de Physique Théorique, IPN (UMR8608), Université Paris-Sud 11, Orsay, France
² Instituto de Física Corpuscular (IFIC), Centro Mixto CSIC-Universidad de Valencia, Valencia, Spain

^* e-mail: moussall@ipno.in2p3.fr

Received: 20 July 2015
Accepted: 2 October 2015
Published online: 13 October 2015

Abstract

A model for S-wave $\eta \pi$ scattering is proposed which could be realistic in an energy range from threshold up to above 1 GeV, where inelasticity is dominated by the $K{\bar{K}}$ channel. The T-matrix, satisfying two-channel unitarity, is given in a form which matches the chiral expansion results at order $$p^4$$ exactly for the $\eta \pi \rightarrow \eta \pi$ , $\eta \pi \rightarrow K{\bar{K}}$ amplitudes and approximately for $K{\bar{K}}\rightarrow K{\bar{K}}$ . 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 $\eta \pi$ and $K{\bar{K}}$ form factor matrix elements of the $$I=1$$ scalar current from the T-matrix. The phenomenological parameters are determined such as to reproduce the experimental properties of the $$a_0(980)$$ , $$a_0(1450)$$ resonances, as well as the chiral results of the $\eta \pi$ and $K{\bar{K}}$ scalar radii, which are predicted to be remarkably small at $$O(p^4)$$ . This T-matrix model could be used for a unified treatment of the $\eta \pi$ final-state interaction problem in processes such as $\eta '\rightarrow \eta \pi \pi$ , $\phi \rightarrow \eta \pi \gamma$ , or the $\eta \pi$ initial-state interaction in $\eta \rightarrow 3\pi$ .