We obtained 16 VLT/X-shooter observations of GX 339 - 4 in quiescence in the period May – September 2016 and detected absorption lines from the donor star in its NIR spectrum .
This allows us to measure the radial velocity curve and projected rotational velocity of the donor for the first time .
We confirm the 1.76 day orbital period and we find that K _ { 2 } = 219 \pm 3 km s ^ { -1 } , \gamma = 26 \pm 2 km s ^ { -1 } and v \sin i = 64 \pm 8 km s ^ { -1 } .
From these values we compute a mass function f ( M ) = 1.91 \pm 0.08 ~ { } M _ { \odot } , a factor \sim 3 lower than previously reported , and a mass ratio q = 0.18 \pm 0.05 .
We confirm the donor is a K-type star and estimate that it contributes \sim 45 - 50 \% of the light in the J - and H -band .
We constrain the binary inclination to 37 ^ { \circ } < i < 78 ^ { \circ } and the black hole mass to 2.3 ~ { } M _ { \odot } < M _ { \mathrm { BH } } < 9.5 ~ { } M _ { \odot } .
GX 339 - 4 may therefore be the first black hole to fall in the ‘ mass-gap ’ of 2 - 5 M _ { \odot } .