Futility of high-precision SO(10) calculations

In grand unified models, there are a large number of scalar bosons with masses of the order of the unification scale. Since the masses could be an order of magnitude or so above or below the vectorboson masses, they will affect the beta functions and thus low-energy predictions; the lack of knowledge of the masses translates into an uncertainty in these predictions. Although the effect is very small for a single scalar field, SO(10) models have hundreds of such fields, leading to very large uncertainties. We analyze this effect in SO(10) models with intermediate scales, and show that all such models have an additional uncertainty which can be as large as 4 orders of magnitude in the proton lifetime and as large as a factor of 0.02 in ${{sin}^2\theta }_w$. In models with 210-dimensional representations, the weak mixing angle is uncertain by as much as 0.06. As a result, we argue that precise calculations in SO(10) models with intermediate scales may not be possible.