Abstract
The lepton pair production in ultraperipheral collisions is studied in the classical field approximation. We derive a general form of the cross section in terms of photon distributions that depend on the transverse momentum and coordinate based on the wave packet form of nuclear wave functions. Such a general form of the cross section in the classical field approximation contains the results of the generalized equivalent photon approximation (EPA) as well as the corrections beyond EPA in the Born approximation. By rewriting the general form of the cross section in light-cone coordinates, we find a good connection with the transverse momentum dependent distribution factorization formalism in the Born approximation. Our numerical results are consistent with current experimental data.
Highlights
Strong electromagnetic fields are produced in the relativistic heavy ion collisions [1,2,3,4,5,6,7,8,9]
By rewriting the general form of the cross section in light-cone coordinates, we find a good connection with the transverse momentum dependent distribution factorization formalism in the Born approximation
The wave functions of two colliding nuclei moving in the Æz direction are assumed to be in the form of wave packets that allow a rigorous description of ultraperipheral collisions
Summary
Strong electromagnetic fields are produced in the relativistic heavy ion collisions [1,2,3,4,5,6,7,8,9]. The azimuthal asymmetry in the lepton pair from linearly polarized photons in UPC has been studied in the transverse momentum dependent (TMD) factorization formalism [80,81] similar to polarized gluons [82,83,84] In this formalism, the photon Wigner functions are introduced into the cross section which depends on the transverse momentum and coordinate [85,86]. The numerical results of the cross section in the general form are given in Sec. VI, and a comparison is made with experimental data as well as the results of (g)EPA and the TMD formalism. The inner product of two vectors in light-cone coordinates is a · b 1⁄4 a−bþ þ aþb− − aT · bT
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