  We present the calculation of the spectral function of an unstable scalar
boson coupled to fermions as resulting from the resummation of the one loop
diagrams in the scalar particle self energy. We work with a large but finite
high-energy cutoff: in this way, the spectral function of the scalar field is
always correctly normalized to unity, independently on the value of the cutoff.
We show that this high energy cutoff affects the Breit-Wigner width of the
unstable particle: the larger the cutoff, the smaller is the width at fixed
coupling. Thus, the existence of a high energy cutoff (alias minimal length),
and for instance the possible opening of new degrees of freedom beyond that
energy scale, could then be in principle proven by measuring, at lower energy
scales, the line shape of the unstable scalar state. Although the Lagrangian
here considered represents only a toy-model, we discuss possible future
extensions of our work which could be relevant for particle physics
phenomenology.
