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We study the Horizon Wave Function (HWF) description of a generalizeduncertainty principle (GUP) black hole in the presence of two natural cutoffsas a minimal length and a maximal momentum. This is motivated by a metric whichallows the existence of sub-Planckian black holes, where the black hole mass$m$ is replaced by$M=m\Big(1+\frac{\beta^{2}}{2}\frac{M_{pl}^{2}}{m^{2}}-\beta\frac{M_{pl}}{m}\Big)$.Considering a wave-packet with a Gaussian profile, we evaluate the HWF and theprobability that the source might be a (quantum) black hole. By decreasing thefree parameter the general form of probability distribution,${\mathcal{P}}_{BH}$, is preserved , but this resulted in reducing theprobability for the particle to be a black hole accordingly. The probabilityfor the particle to be a black hole grows when the mass is increasing slowlyfor larger positive $\beta$, and for a minimum mass value it reaches to $0$. Ineffect, for larger $\beta$ the magnitude of $M$ and $r_{H}$ increases, matchingwith our intuition that either the particle ought to be more localized or moremassive to be a black hole. The scenario undergoes a change for some values of$\beta$ significantly, where there is a minimum in ${\mathcal{P}}_{BH}$ , sothis expresses that every particle can have some probability of decaying to ablack hole. In addition, for sufficiently large $\beta$ we find that everyparticle could be fundamentally a quantum black hole.

Black Hole Production in the Presence of a Maximal Momentum in Horizon Wave Function Formalism