The mean-field scaling function of the universality class of absorbing phase transitions with a conserved field

We consider two mean-field like models which belong to the universality class of absorbing phase transitions with a conserved field. In both cases we analytically derive the order parameter as a function of the control parameter and of an external field conjugated to the order parameter. This allows us to calculate the universal scaling function of the mean-field behaviour. The obtained universal function is in perfect agreement with recently obtained numerical data of the corresponding five- and six-dimensional models, showing that four is the upper critical dimension of this particular universality class.