\pi^+ \pi^- and \pi^0 \pi^0 pair production in photon-photon scattering and ultraperipheral ultrarelativistic heavy-ion collisions
M. Kłusek-Gawenda and A. Szczurek
Accepted
We discuss $\gamma \gamma \to \pi \pi$ reactions, starting from the two-pion threshold up to about \mbox{$\sqrt{s_{\gamma\gamma}}$ = 6 GeV}. Several reaction mechanisms are identified. We include the dipion continuum due to pion exchange (for $\pi^+\pi^-$) and $\rho^\pm$ exchange (for $\pi^0\pi^0$) as well as the pronounced dipion $\sigma(600)$, $f_0(980)$ and $f_2(1270)$ s-channel resonances. We discuss also a possible contribution of less pronounced scalar resonances $f_0(1500)$ and $f_0(1710)$ being glueball candidates, as well as the tensor the resonances $f'_2(1525)$, $f_2(1565)$ and $f_2(1950)$. While the contribution of $f'_2(1525)$ is rather small, the contribution of $f_2(1565)$ changes the spectrum around the resonance position. We find that the inclusion of the spin-four $f_4(2050)$ resonant state improves the situation at $\sqrt{s_{\gamma\gamma}} \approx$ 2 GeV. We estimate the relevant diphoton partial decay width to be \mbox{$\Gamma_{f_4 \to \gamma \gamma} \approx$ 0.7 keV}. At higher energies, Brodsky-Lepage and hand-bag mechanisms are included in addition. We nicely describe the world data for $\gamma \gamma \to \pi \pi$ for the first time both for the total cross section and angular distributions for $\gamma \gamma \to \pi^+ \pi^-$ and $\gamma \gamma \to \pi^0 \pi^0$ reactions simultaneously at all experimentally available energies. The cross section for the production of two-pions in ultraperipheral ultrarelativistic heavy ion collisions is calculated in the impact parameter space Equivalent Photon Approximation (EPA). We obtain the nuclear cross section of 46.7 mb for $\pi^+\pi^-$ and 8.7 mb for $\pi^0\pi^0$ at the LHC energy \mbox{$\sqrt{s_{NN}} =$ 3.5 TeV} and minimal cut on pion transverse momentum $p_t>$ 0.2 GeV. Differential distributions in impact parameter, dipion invariant mass, single pion and dipion rapidity, pion transverse momentum as well as pion pseudorapidity are shown. The $\gamma \gamma \to \pi^+ \pi^-$ subprocess constitutes a background to the exclusive $A A \to A \rho^0 (\to \pi^+ \pi^-) A$ process, initiated by photon-pomeron or pomeron-photon subprocesses. We find that only a part of the dipion invariant mass spectrum associated with $\gamma\gamma$-collisions can be potentially visible as the cross section for the $A A \to A \rho^0 A$ reaction is very large.