Simultaneous production of lepton pairs in ultraperipheral relativistic heavy ion collisions

We calculate the total cross sections and probabilities of electromagnetic productions of electron, muon, and tauon pairs simultaneously. At the CERN Large Hadron Collider (LHC), the available electromagnetic energy is sufficient to produce all kinds of leptons coherently. The masses of muons and tauons are large, so their Compton wavelengths are small enough to interact with the colliding nuclei. Therefore, the realistic nuclear form factors are included in the calculations of electromagnetic pair productions. The cross section calculations show that, at LHC energies, the probabilities of simultaneous productions of all kinds of leptons are increased significantly compared to energies available at the BNL Relativistic Heavy Ion Collider (RHIC) . Experimentally, observing this simultaneous production can give us important information about strong QED.

Figure 1

Relativistic collision of two heavy ion is illustrated as schematic diagram. Impact parameter between the ions is $b$, and the Lorentz contracted electric field is also shown.

Figure 2

Second-order Feynman diagrams for simultaneous (a) electron and muon pair production, (b) electron and tauon pair production, (c) muon and tauon pair production, and (d) electron, muon, and tauon pair production.

Figure 3

The electromagnetic form factor for gold. The solid line is the analytic form of the Woods-Saxon distribution and the starred line is the numerical calculation of the same equation.

Figure 4

Impact parameter dependent cross section for lepton pairs produced by Au+Au ion collisions at (a) 100 GeV and (b) 3400 GeV.

Figure 5

(a) The behaviors of the probability values are shown depending on impact parameter $b$ for two of the $e^{\pm }\text{−}{\mu }^{\pm }\text{−}{\tau }^{\pm }$ pairs produced at the same time by Au+Au collisions at (a) 100 GeV and (b) at 3400 GeV.

Figure 6

The probability of lepton pairs being produced at the same time by Au+Au collisions at 100 and 3400 GeV is shown depending on impact parameter $b$.