Induced Violation of Weak Equivalence Principle in the Brans-Dicke Theory

A quantum correction to the Brans-Dicke theory due to interactions among matter fields is calculated, resulting in violation of WEP, hence giving a constraint on the parameter $\omega$ far more stringent than accepted so far. The tentative estimate gives the lower bounds $\text{gsim}{10}^6$ and $\text{gsim}{10}^8$ for the assumed force-range $\text{gsim}1$m and $\text{gsim}1$AU, respectively.