Loop functions

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We used for the calculation of the one-loop self energies and the one-loop corrections to the tadpoles in -scheme the scalar functions defined in . The basic integrals are

with the renormalization scale . The integrals are regularized by integrating in dimensions. The result for is

where . The function has the analytic expression


and . All the other, necessary functions can be expressed by and . For instance,


Furthermore, for the vector boson self-energies it is useful to define

See also