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We investigate the origin of the scaling corrections in ballistic depositionmodels in high dimensions using the method proposed by Alves \textit{et al}.[Phys Rev. E \textbf{90}, 052405 (20014)] in $d=2+1$ dimensions, where theintrinsic width associated with the fluctuations of the height incrementsduring the deposition processes is explicitly taken into account. In thepresent work, we show that this concept holds for $d=3+1$ and 4+1 dimensions.We have found that growth and roughness exponents and dimensionless cumulantratios are in agreement with other models, presenting small finite-timecorrections to the scaling, that in principle belong to the Kardar-Parisi-Zhang(KPZ) universality class in both $d=3+1$ and 4+1. Our results constitute a newevidence that the upper critical dimension of the KPZ class, if it exists, islarger than 4.

Scaling, cumulant ratios and height distribution of the ballistic deposition in 3+1 and 4+1 dimensions