The boundary effect of QGP droplets and the self-similarity effect of hadrons on QGP-hadron phase transition

We investigate the boundary effect of quark-gluon plasma (QGP) droplets and the self-similarity effect of hadrons on QGP-hadron phase transition. In intermediate- or low-energy collisions, when the transverse momentum is below quantum chromodynamics (QCD) scale, QGP cannot be produced. However, if the transverse momentum changes to a relatively large value, a small-scale QGP droplet is produced. The modified MIT bag model with the multiple reflection expansion method is employed to study the QGP droplet with the curved boundary effect. It is found that the energy density, entropy density and pressure of QGP with the influence are smaller than those without the influence. In the hadron phase, we propose the two-body fractal model (TBFM) to study the self-similarity structure, arising from resonance, quantum correlation and interaction effects. It is observed that the energy density, entropy density and pressure increase due to the self-similarity structure. We calculate the transverse momentum spectra of pions with the self-similarity structure influence, which show good agreement with experimental data. Considering both boundary effect and self-similarity structure influence, our model predicts an increase in the transition temperature compared to the scenarios without these two effects in the High Intensity heavy-ion Accelerator Facility (HIAF) energy region, 2.2 GeV to approximately 4.5 GeV.