A new regularization of loop integral, no divergence, no hierarchy problem

TL;DR

The paper introduces a novel regularization method for loop integrals based on discrete virtual particle energies and Riemann zeta function regulation, eliminating divergences and hierarchy problem in quantum field theory.

Contribution

A new regularization scheme inspired by Bose-Einstein condensation that removes divergences and hierarchy issues without relying on dimensional regularization.

Findings

Divergences in loop integrals are eliminated.

Hierarchy problem in scalar mass corrections is resolved.

Results align with Dimensional Regularization and extend beyond it.

Abstract

We find a new regularization scheme which is motivated by the Bose-Einstein condensation. The energy of the virtual particle is considered as discrete. Summing them and regulating the summation by the Riemann $\zeta$ function can give the result of loop integral. All the divergences vanish, we can get almost the same results as Dimensional Regularization. The prediction beyond Dimensional Regularization is also shown in the QED. The hierarchy problem of the radiative correction of scalar mass completely vanish.