A new scalar resonance at 750 GeV: Towards a proof of concept in favor of strongly interacting theories

Abstract: We interpret the recently observed excess in diphoton invariant mass as a new spin-0 resonant particle. On the theoretical ground, an interesting question is whether this new scalar resonance belongs to a strongly coupled sector or a well-defined weakly coupled theory. A possible UV-completion that has been widely considered in literature is based on the existence of new vector-like fermions whose loop contributions---Yukawa-coupled to the new resonance---explain the observed signal rate. The large total width preliminarily suggested by data seems to favor a large Yukawa coupling, at the border of a healthy perturbative definition. This potential problem can be fixed by introducing multiple vector-like fermions or large electric charges, bringing back the theory to a weakly coupled regime. However, this solution risks to be only a low-energy mirage: Large multiplicity or electric charge can dangerously reintroduce the strong regime by modifying the renormalization group running of the dimensionless couplings. This issue is also tightly related to the (in)stability of the scalar potential. First, we study---in the theoretical setup described above---the parametric behavior of the diphoton signal rate, total width, and one-loop $\beta$ functions. Then, we numerically solve the renormalization group equations, taking into account the observed diphoton signal rate and total width, to investigate the fate of the weakly coupled theory. We find that---with the only exception of few fine-tuned directions---weakly coupled interpretations of the excess are brought back to a strongly coupled regime if the running is taken into account.