Helioseismology and p+p $\to$ d + e${}^{+}$ + ${\nu }_e$ in the sun

By using a phenomenological field theory of nucleon-nucleon interactions, Oberhummer et al. found a cross section of p+p $\to$ d + e${}^{+}$ + ${\nu }_e$ about 2.9 times that given by the potential approach and adopted in Standard Solar Model calculations. We show that a solar model with $S=2.9S_{SSM}$ is inconsistent with helioseismic data, the difference between model predictions and helioseismic determinations being typically a factor ten larger than estimated uncertainties. We also show that, according to helioseismology, $\text{Sppzero}$ cannot differ from $S_{SSM}$ by more than 15%.