QFT without infinities and hierarchy problem

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The standard way to do computations in Quantum Field Theory (QFT) often results in the requirement of dramatic cancellations between contributions induced by a “heavy” sector into the physical observables of the “light” (or low energy) sector – the phenomenon known as “technical hierarchy problem”. This procedure uses divergent multi-loop Feynman diagrams, their regularisation to handle the UV divergences, and then renormalisation to remove them. At the same time, the ultimate outcome of the renormalisation is the mapping of several finite parameters defining the renormalisable field theory into different observables (e.g. all kinds of particle cross-sections). In this paper, we first demonstrate how to relate the parameters of the theory to observables without running into intermediate UV divergences. Then we go one step further: we show how in theories with different mass scales, all physics of the “light” sector can be computed in a way that does not require dramatic cancellations induced by the physics of the “heavy” sector. The existence of such a technique suggests that the “hierarchy problem” in renormalisable theories is not really physical, but rather an artefact of the conventional procedure to compute correlation functions. If the QFT is defined by the “divergencies-free” method all fine-tunings in theories with well-separated energy scales may be avoided.