[Paper Review] Reactions gamma gamma -> pi pi and gamma gamma -> K \bar K: the (IJ^{PC}=00^{++})-wave spectra at E_{gamma gamma}^{(c.m.)} = 300- 1900 MeV

A. V. Anisovich, V.V. Anisovich|arXiv (Cornell University)|Jun 22, 1999

Quantum Chromodynamics and Particle Interactions9 references4 citations

TL;DR

This study calculates the $00^{++}$-wave two-meson spectra in $\gamma\gamma \to \pi\pi$ and $\gamma\gamma \to K\bar{K}$ processes using a $K$-matrix analysis of $00^{++}$ amplitudes and a newly developed method for computing $f_0(q\bar{q}) \to \gamma\gamma$ decay amplitudes. The key finding is that $f_0(980)$ and $f_0(1500)$ appear as dips in the $\pi^+\pi^-$ and $\pi^0\pi^0$ spectra, suggesting their scalar isoscalar nature in $\gamma\gamma$ transitions.

ABSTRACT

We calculate the $00^{++}$-wave two-meson spectra for the reactions $\gamma\gamma o\pi^0\pi^0$, $\gamma\gamma o\pi^+\pi^-$, $\gamma\gamma o K^0\bar K^0$ and $\gamma\gamma o K^+ K^-$ on the basis of: (i) the results of the $K$-matrix analysis of the $00^{++}$ amplitudes for the reactions $\pi\pi o \pi\pi$, $K\bar K$, $\eta\eta$, $\eta\eta'$, $\pi\pi\pi\pi $, and (ii) recently developed method for calculation of the decay amplitudes $f_0(1^3P_0q\bar q) o \gamma\gamma$, $f_0(2^3P_0q\bar q) o \gamma\gamma$. The reconstructed $\pi\pi $ and $K\bar K$ spectra can be used as a guide for the extraction of partial widths of scalar/isoscalar resonances $f_0(980) o \gamma\gamma$, $f_0(1300) o \gamma\gamma$, $f_0(1500) o \gamma\gamma$, $f_0(1750) o \gamma\gamma$. As follows from our calculations, the resonances $f_0(980)$ and $f_0(1500)$ in the $\pi^+\pi^-$ and $\pi^0\pi^0$ spectra reveal themselves as dips.

Motivation & Objective

• To determine the $00^{++}$-wave two-meson spectra in $\gamma\gamma \to \pi^+\pi^-$, $\gamma\gamma \to \pi^0\pi^0$, $\gamma\gamma \to K^0\bar{K}^0$, and $\gamma\gamma \to K^+K^-$ processes.
• To provide a theoretical guide for extracting partial widths of scalar isoscalar resonances $f_0(980)$, $f_0(1300)$, $f_0(1500)$, and $f_0(1750)$ in $\gamma\gamma$ decays.
• To investigate the visibility of $f_0(980)$ and $f_0(1500)$ resonances in $\pi\pi$ spectra via their $\gamma\gamma$ decay behavior.

Proposed method

• Utilizes a $K$-matrix analysis of $00^{++}$ amplitudes from $\pi\pi$, $K\bar{K}$, $\eta\eta$, $\eta\eta'$, and $\pi\pi\pi\pi$ final states to model the $00^{++}$-wave amplitudes.
• Applies a recently developed method for calculating the decay amplitudes $f_0(n^3P_0 q\bar{q}) \to \gamma\gamma$ for scalar resonances with $n=1,2$.
• Constructs the $\gamma\gamma \to \pi\pi$ and $\gamma\gamma \to K\bar{K}$ spectra by combining the $K$-matrix amplitudes with the $f_0 \to \gamma\gamma$ decay amplitudes.
• Performs a unitary and coupled-channel analysis to ensure consistency with the $\pi\pi$, $K\bar{K}$, and other meson scattering data.

Experimental results

Research questions

• RQ1 How do the $\gamma\gamma \to \pi^+\pi^-$ and $\gamma\gamma \to \pi^0\pi^0$ spectra manifest the $f_0(980)$ and $f_0(1500)$ resonances in the $300-1900$ MeV center-of-mass energy range?
• RQ2 What is the role of the $K$-matrix formalism in describing the $00^{++}$-wave dynamics of $\pi\pi$ and $K\bar{K}$ final states?
• RQ3 Why do $f_0(980)$ and $f_0(1500)$ appear as dips rather than peaks in the $\pi\pi$ spectra?
• RQ4 How do the $f_0 \to \gamma\gamma$ decay amplitudes influence the reconstructed $\gamma\gamma \to \pi\pi$ and $\gamma\gamma \to K\bar{K}$ spectra?

Key findings

• The $\pi^+\pi^-$ and $\pi^0\pi^0$ spectra reconstructed from the $K$-matrix and $f_0 \to \gamma\gamma$ decay amplitudes show clear dips at the masses of $f_0(980)$ and $f_0(1500)$.
• The $f_0(980)$ resonance is visible as a dip in both $\pi^+\pi^-$ and $\pi^0\pi^0$ spectra, indicating a suppression in its $\gamma\gamma$ decay width.
• The $f_0(1500)$ resonance also appears as a dip in the $\pi^+\pi^-$ and $\pi^0\pi^0$ spectra, suggesting a similar suppression in its coupling to photons.
• The reconstructed $K\bar{K}$ spectra provide a guide for extracting the partial widths of $f_0(1300)$ and $f_0(1750)$ in $\gamma\gamma$ decays.
• The results suggest that $f_0(980)$ and $f_0(1500)$ are not prominent peaks in $\gamma\gamma \to \pi\pi$ but rather appear as dips due to interference or suppressed coupling.