Ultraperipheral production of very small number of particles in ultrarelativistic heavy ion collisions \*

Ultrarelativistic collisions of heavy ions provide a nice oportunity to study γγ collisions. An enhancement of the cross section for the reactions of this type compared to proton-proton or e+e− collisions which is caused by large charges of the colliding ions is expected. In this type of reactions virtual (almost real) photons couple to the nucleus as a whole. Naively the enhancement of the cross section is proportional to Z1Z 2 2 which is a huge factor. We have discussed that the inclusion of realistic charge distributions and realistic nucleus charge form factor reflects in a cross section smaller than those obtained by other models using naive predictions, usually found in literature.


Introduction
Ultrarelativistic collisions of heavy ions provide a nice oportunity to study γγ collisions.An enhancement of the cross section for the reactions of this type compared to proton-proton or e + e − collisions which is caused by large charges of the colliding ions is expected.In this type of reactions virtual (almost real) photons couple to the nucleus as a whole.Naively the enhancement of the cross section is proportional to Z 2  1 Z 2 2 which is a huge factor.We have discussed that the inclusion of realistic charge distributions and realistic nucleus charge form factor reflects in a cross section smaller than those obtained by other models using naive predictions, usually found in literature.

Equivalent Photon Approximation
The Equivalent Photon Approximation [1] is a standard semi-classical alternative to the Feynman rules for calculating cross sections of electromagnetic interactions.The method is based on the observation that the electric and magnetic fields of a fast-moving charged particle are nearly transverse to the direction of motion (see figure 1).The total cross section is calculated by the convolution: where X 1 and X 2 are leptons, quarks or mesons, S 2 abs (b is the absorption factor (ultraperipheral collisions), N(ω, b) the photon flux, ω is the energy of photon and Y X 1 X 2 = 1 2 (y X 1 +y X 2 ) rapidity of the outgoing X 1 X 2 system.3 Exclusive production of µ + µ − pairs Elementary cross section for charged leptons can be calculated within Quantum Electrodynamics.In Ref. [2] we have presented several distributions for exclusive muon-pair production in nucleusnucleus collisions.Realistic (Fourier transform of charged density) charge form factors of nuclei are used and the corresponding results are compared with the cross sections calculated with monopole form factor often used in the literature.It was discussed in the literature that higher-order are not important for the presented distributions [3].

Exclusive production of cc and b b
We have calculated also cross sections for exclusive production of charm-anticharm and bottomantibottom pairs, for the Q Qg and Q Qq q final state, as well as for the single-resolved components in the high-energy peripheral lead-lead collisions for the LHC energy √ s NN = 5.5 TeV.In figure 3 we compare the contributions of different mechanisms discussed in Ref. [4].Large cross sections have been found in the case of charm quarks production.In table 1 we show partial contribution of different subprocesses discussed in our paper.

EPJ Web of Conferences
04028-p.2  5 Double J/Ψ production In Ref. [5] we have calculated the cross section for the γγ → J/ΨJ/Ψ process.Two mechanisms are considered: box (two-loop) diagrams (dashed line) of the order of O(α 2 em α 2 s ) and two-gluon exchange (dotted line) of the order of O(α 2 em α 4 s ).The first mechanism is calculated in the heavy-quark nonrelativistic approximation while in the second case we also include the effects of quantum motion of quarks in the bound state.6 ρ 0 ρ 0 and ππ pair production In Ref. [6][7][8] we have calculated, for the first time, differential distributions for two ρ 0 mesons and for pion-pion production in exclusive, ultraperipheral, ultrarelativistic collisions.In figure 5 we show theoretical distribution for the full phase space (upper solid lines) and with extra cuts on z = cos θ.
At lower energies the result does not depend on the angulat cuts.the big differences start in the region where the elementary cross section can be understood in terms of the BL pQCD and handbag mechanisms.The peaks reflect complicated energy dependence of the elementary γγ → ππ cross section [8]. [GeV]

2 bFigure 1 .
Figure 1.Left panel -The method.Right panel -The quantities used in the impact parameter calculations.

Figure 3 .
Figure 3. Nuclear cross section as a function of γγ subsystem energy W γγ for the PbPb → PbPbcc (left panel) and for the PbPb → PbPbb b (right panel).

Table 1 .
Partial contributions of different mechanisms at √ s NN = 5.5 TeV.