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RESEARCH PRODUCT

One-Loop Two and Three-Point Functions

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In this chapter we present a few relevant calculations of one-loop, one and two-point (scalar, vector and tensor) functions. IR and UV divergences are extensively treated. One example of IR-pole cancellation is presented. The two and three-body phase space integrals in D dimensions, needed for the calculation of IR divergent cross sections are also given. Last, the usage of the generic parametrization ( 6.27) for non-integer powers of propagators (which appear when one needs to integrate over the four-momentum, logarithmic functions that depend on the four-momentum) is shown with a simple two-loop example. With the tools given here, the reader should find straightforward to construct any higher order scalar or tensor integral for any N-point function at one-loop level.