Hojman-Rosenbaum-Ryan-Shepley torsion theory and Eötvös-Dicke-Braginsky experiments

Considering a modified form of local gauge invariance and minimal coupling, Hajman, Rosenbaum, Ryan, and Shepley obtained a dynamic torsion theory which allows propagation of torsion in vacuo. In this theory, the torsion is determined by the gradient of a scalar field $\phi$. For the Sun, $\phi =0.67\mathrm{}\times {10}^{-4\mathrm{}}U$ where $U$ is the Newtonian potential. In this field, test bodies with different electromagnetic energy contents behave differently. For aluminum and gold (or platinum), the gravitational accelerations would differ by $2\times {10}^{-7\mathrm{}}{\overrightarrow{\nabla }}^U$. This implication disagrees with the null experiments of precisions ${10}^{-11\mathrm{}}{\overrightarrow{\nabla }}^U$ and ${10}^{-12\mathrm{}}{\overrightarrow{\nabla }}^U$ performed respectively by Roll, Krotkov, and Dicke and by Braginsky and Panov.