${\pi }^{+}{\pi }^{-}$ and ${\pi }^0{\pi }^0$ pair production in photon-photon and in ultraperipheral ultrarelativistic heavy ion collisions

Abstract

We discuss $\gamma \gamma \to \pi \pi$ reactions, starting from the two-pion threshold up to about $\sqrt{s_{\gamma \gamma }}$ = 6 GeV. 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 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 $f_0(1710)$ as well as the tensor resonances $f_2^{\prime }(1525)$, $f_2(1565)$ and $f_2(1950)$. 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 ${\Gamma }_{f_4\to \gamma \gamma }\approx$ 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. 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 $\sqrt{s_{NN}}=$ 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 $AA\to A{\rho }^0(\to {\pi }^{+}{\pi }^{-})A$ process.

Comments: 29 pages, 22 figures, two references added