The puzzling properties of the Helium White Dwarf orbiting the millisecond pulsar PSR J1911$-$5958A in NGC 6752

We have used phase-resolved high-resolution images and low resolution spectra taken at the ESO Very Large Telescope, to study the properties of the low-mass Helium White Dwarf companion to the millisecond pulsar (hereafter COM~J1911$-$5958A), in the halo of the Galactic Globular Cluster NGC 6752. The radial velocity curve confirms that com is orbiting the pulsar and allows to derive a systemic velocity of the binary system nicely in agreement with that of NGC 6752. This strongly indicates that the system is a member of the cluster, despite its very offset position ($sim 74$ core radii) with respect to the core. Constraints on the orbital inclination ($gapp 70^circ$) and pulsar mass ($1.2-1.5~{rm M_odot}$) are derived from the mass ratio $M_{PSR}/M_{COM}= 7.49pm0.64$ and photometric properties of COM~J1911$-$5958A. The light curve in B-band shows two phases of unequal brightening ($Delta$mag$sim 0.3$ and $0.2$, respectively) located close to quadratures and superimposed on an almost steady baseline emission: this feature is quite surprising and needs to be further investigated.