$\sin ^{2}\theta _{W}$ estimate and neutrino electromagnetic properties from low-energy solar data

We report new values of weak-mixing angle ($\sin ^{2}\theta _{W}$)$,$ neutrino effective magnetic moment and the charge radius using the lowest-energy (to-date) solar neutrino data of pp, $^{7}$Be and pep spectra from phase-I and phase-II runs of Borexino experiment. The best-fit values are $\sin ^{2}\theta _{W}=$0.235$\pm $0.019 with a precision comparable to that of the combined reactor and accelerator very short-baseline experiments and $\mu _{\nu }^{eff}\leq 8.7\times 10^{-12}\mu _{B}$ at 90% C.L. with a factor of 3 improvement than the previous bounds. This leads to the improvement of all the related magnetic moment matrix elements for the Majorana-type and Dirac-type in mass basis and also improvement on bounds on the flavor magnetic moment states. The bounds on the neutrino charged radii turn out to be $-0.82\times 10^{-32}$cm$^{2}\leq \left \langle r_{\nu _{e}}^{2}\right \rangle \ \leq 1.27\times 10^{-32}$ cm$^{2}\ $and $-9\times 10^{-32}$cm$^{2}\leq \left \langle r_{\nu _{\mu },\nu _{\tau }}^{2}\right \rangle \ \leq 3.1\times 10^{-31}$ cm$^{2}\ $ at 90% C.L..