Scalar one-loop 4-point integral with one massless vertex in loop regularization

Abstract

The scalar one-loop 4-point function with one massless vertex is evaluated analytically by employing the loop regularization method. According to the method a characteristic scale ${\mu }_s$ is introduced to regularize the divergent integrals. The infrared divergent parts, which take the form of ${\ln }^2({\lambda }^2/{\mu }_s^2)$ and $\ln ({\lambda }^2/{\mu }_s^2)$ as ${\mu }_s\to 0$ where $\lambda$ is a constant and expressed in terms of masses and Mandelstam variables, and the infrared stable parts are well separated. The result is shown explicitly via $44$ dilogarithms in the kinematic sector in which our evaluation is valid.

arXiv comment31 pages, 1 figure

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