Exclusive electromagnetic production of pion pairs in lead-lead collisions at LHC ?

Abstract. The cross section for π+π− and π0π0 meson pairs production in peripheral ultrarelativistic heavy-ion collisions is calculated in the impact parameter space equivalent photon approximation. The cross section is calculated at the energy available at the CERN Large Hadron Collider, √ sNN = 3.5 TeV. For the first time the world data for γγ → ππ are described, both for the total cross section and for the angular distribution. This is obtained simultaneously for γγ → π+π− and γγ → π0π0 at all experimentally available energies.

In figure 1 we show the basic mechanism of the exclusive production of π + π − and π 0 π 0 meson pairs.To calculate nuclear cross section, we have to take into account the correct form of the elementary cross section.We discuss γγ → ππ reactions at low, intermediate and high sub-energies.

Elementary cross section
The γγ → ππ reaction is rather complicated.Different mechanisms contribute in general.We try to understand both γγ → π + π − and γγ → π 0 π 0 processes simultaneously, starting from the twopion threshold (W = 2m π ) up to the maximal experimentally available energy W γγ ≈ 6 GeV.We include both soft (figure 2), hard continuum (right panel of figure 3 -pQCD mechanisms proposed by Brodsky and Lepage [7] and the handbag mechanism proposed by Diehl, Kroll and Vogt [8]) as well as s-channel resonances (left panel of figure 3).We show that for a correct description of the low-energy experimental data we have to include also pion-pion rescattering (figure 4), which leads to a coupling between the π + π − and π 0 π 0 channels.In figure 5 we show our model results against world data for γγ → ππ.We get a good agreement with all available data for the first time in such a large range of energies.This make our model for EPJ Web of Conferences 04014-p.2photoproduction of pions well suited for the predictions of the cross sections for nucleus-nucleus collisions.
In figure 6 we present a ratio of the neutral and charged pion pair cross sections as a function of γγ energy.The upper line represents the handbag model result, which is independent of z = cos θ and of the collision energy.Our result, which includes the BL pQCD and handbag contribution, describes the experimental data measured by the Belle Collaboration. [GeV]

Nuclear cross section
The nuclear cross section has been calculated with the help of b-space equivalent photon approximation (EPA).This approach allows to separate peripheral collisions of nuclei (b > R 1 + R 2 ≈ 14 fm).A compact formula for calculating the total cross section takes the form: The details of its derivation can be found in our papers [2,6].
Table 1.Cross section for different lower cuts on pion transverse momenta at the LHC energy.
In table 1 the total cross sections for √ s NN = 3.5 TeV are reported for both π + π − and π 0 π 0 channels and for different lower cuts on pion transverse momentum.

Conclusions
We have shown that in order to describe the word data for γγ → π + π − and γγ → π 0 π 0 reactions, one should consider several different mechanisms: soft two-pion continuum, several resonanses, pionpion rescattering, pQCD mechanisms proposed by Brodsky and Lepage, as well as the hand-bag mechanism proposed by Diehl, Kroll and Vogt.The energy-dependent cross sections for these two sub-processes have been used next in EPA in the impact parameter space to calculate for the first time corresponding production rate in ultraperipheral ultrarelativistic heavy-ion reactions.In this calculation we have taken into account realistic charge distributions in colliding nuclei.
The γγ → π + π − sub-process constitutes a background to the exclusive AA → Aρ 0 (→ π + π − )A process, initiated by photon-pomeron or pomeron-photon sub-processes.We have found [9] that only a part of the dipion invariant mass spectrum associated with γγ-collisions can be potentially visible as the cross section for the AA → Aρ 0 A reaction is very large.

Figure 1 .
Figure 1.The diagram illustrating the formation of the pion pair.For the LHC the A 1 and A 2 letters denote the 208 Pb nuclei.