New open cluster Cepheids in the VVV survey tightly constrain
  near-infrared period--luminosity relations
  Classical Cepheids are among the most useful Galactic and nearby
extragalactic distance tracers because of their well-defined period--luminosity
relations (PLRs). Open cluster (OC) Cepheids are important objects to
independently calibrate these PLRs. Based on Data Release 1 of the {\sl VISTA}
Variables in the V\'ia L\'actea survey, we have discovered four new, faint and
heavily reddened OC Cepheids, including the longest-period OC Cepheid known,
ASAS J180342$-$2211.0 in Teutsch 14a. The other OC--Cepheid pairs include NGC
6334 and V0470 Sco, Majaess 170 and ASAS J160125$-$5150.3, and Teutsch 77 and
BB Cen. ASAS J180342$-$2211.0, with a period of $\log P = 1.623$ [days] is
important to constrain the slope of the PLR. The currently most complete
$JHK_{\rm s}$ Galactic Cepheid PLRs are obtained based on a significantly
increased sample of 31 OC Cepheids, with associated uncertainties that are
improved by 40 per cent compared with previous determinations (in the $J$
band). The NIR PLRs are in good agreement with previous PLRs determined based
on other methods.
