Calculation of the Cross Section γ∗ → e+e− at Next to Leading Order Using Implicit Regularization

We illustrate a new way to calculate the process γ∗ → e+e− at higher energies beyond the leading order, at one loop to approximation using Im- plicit Regularization, in this context we calculate in the physical dimension (four dimensions) the virtual contribution, this is with the diagram at tree level and diagrams with loop momentum, also the real contribution with external particles, for this regularization we isolate the Ultraviolet (UV) divergences using a simple mathematical identity and representing the UV divergences in terms of momentum loop integrals, these divergences are removed by the renormalization, the cross section of the virtual contribu- tion remains Infrared divergences, also the real contribution has Infrared divergences, these divergences are dependent on a fictitious mass, in the total cross section these divergences are canceled, and finally we have the same result for the same process as if we had used Dimensional Regular- ization, but without the problems that Dimensional regularization could generate like extra dimensions, changes in the Lagrangian, new Feynman diagrams, and others problems that could appear, therefore we calcu- late the process γ∗ → e+e− in a physical framework, without alter the Lagrangian neither any kind of inconsistency due to regularization frame- work at one loop, and preserving the symmetries of the theory that the Implicit Regularization satisfy.