  Among the sample of Galactic transient X-ray binaries (SXTs) discovered to
date, about 70 have been proposed as likely candidates to host a black hole.
Yet, only 19 have been dynamically confirmed. Such a reliable confirmation
requires phase-resolved spectroscopy of their companion stars, which is
generally feasible when the system is in a quiescent state. However, since most
of the SXT population lies in the galactic plane, which is strongly affected by
interstellar extinction, their optical brightness during quiescence usually
falls beyond the capabilities of the current instrumentation ($R\gtrsim22$). To
overcome these limitations and thereby increase the number of confirmed
Galactic black holes, a correlation between the full-width at half maximum
(FWHM) of the H$\alpha$ line and the semi-amplitude of the donor's radial
velocity curve ($K_2$) was presented in the past. Here, we extend the
FWHM-$K_2$ correlation to the near-infrared (NIR), exploiting disc lines such
as He I $\lambda$10830, Pa$\gamma$, and Br$\gamma$, in a sample of dynamically
confirmed black-hole SXTs. We obtain $K_2 = 0.22(3) ~\textrm{FWHM}$, in good
agreement with the optical correlation derived using H$\alpha$. The similarity
of the two correlations seems to imply that the widths of H$\alpha$ and the NIR
lines are consistent in quiescence. When combined with information on orbital
periods, the NIR correlation allows us to constrain the mass of the compact
object of systems in quiescence by using single-epoch spectroscopy. We
anticipate that this new correlation will give access to highly reddened
black-hole SXTs, which cannot be otherwise studied at optical wavelengths.
