In string models, the production of charged particles can be described by the convolution of the Schwinger mechanism with string tension fluctuations, usually modeled as a Gaussian distribution. However, by incorporating $q$-Gaussian string tension fluctuations, we can fully describe the $p_T$-spectrum of charged particles produced in pp collisions obtaining Tricomi’s function, which captures both asymptotic behaviors at low and high $p_T$ values. We prove that heavy-tailed distributions describing string tension fluctuations are necessary to produce high $p_T$ particles (rare events involving intense color interactions). Consequently, the system created in the collision departs from the thermal description, where temperature fluctuations are a local property occurring in a small part of the system.