Can Y(4140) be a c cbar s sbar tetraquark ?

In this exploratory study the spectrum of tetraquarks of type c \bar{c} s \bar{s} is calculated within a simple quark model with chromomagnetic interaction and effective quark masses extracted from meson and baryon spectra. It is tempting to see if this spectrum can accommodate the resonance Y(4140), observed by the CDF Collaboration, but not yet confirmed. The results seem to favor the JPC = 1++ sector where the coupling to the VV channel is nearly as small as that of X(3872), when described as a c \bar{c} q \bar{q} tetraquark. This suggests that Y(4140) could possibly be the strange partner of X(3872) in a tetraquark interpretation. However, the sector JPC = 0++ cannot entirely be excluded. This work questions the practice of extracting effective quark masses containing spin-independent contributions, from mesons and baryons, to be used in multiquark systems as well.