Production of Scalar Unparticle Pairs in Electron-positron Collisions

In this work, we study the phenomenology of unparticle physics via the production of scalar unparticle pairs in electron-positron collisions ( ) at high-energy colliders. Using numerical analysis methods, we perform a detailed investigation into the dependence of both the differential and total cross-sections on the characteristic model parameters ( , ), the center-of-mass energy ( ), and specifically the energy of the produced unparticles ( ). The numerical results reveal that the differential cross-section exhibits a strong angular dependence, peaking in directions parallel and anti-parallel to the incident beam. More importantly, the cross-section is significantly enhanced in the low  region and diminishes as  increases. This indicates that the energy loss of the initial  beam is substantial in the low-energy regime, corresponding to the dominant emission of energetic unparticles. Regarding the total cross-section, our calculations show a rapid suppression as the center-of-mass energy  and the energy scale  increase. Furthermore, the cross-section demonstrates critical sensitivity to the scaling dimension ; as  increases from 1.1 to 1.9, the magnitude of the cross-section decreases by approximately 8 to 9 orders of magnitude. These findings suggest that experimental signatures of scalar unparticle production are most prominent in the low-energy regime and for models characterized by small scaling dimensions .