Universal Three-Body Parameter of Heavy-Heavy-Light systems with negative intraspecies scattering length

we investigate the dependence of Three-body Parameter on the intraspecies interaction in heteronuclear atomic systems. Through calculating the $|a^{\scriptscriptstyle(1)}_{-}|$ for ten mass imbalanced systems, we predict the universal dependence of $|a^{\scriptscriptstyle(1)}_{-}|$ on the background scattering length $a_{\scriptscriptstyle HH}$. We find that the $|a_-^{\scriptscriptstyle(1)}|$ have a dramatically strong dependence on the background scattering length $a_{\scriptscriptstyle HH}$ for the mass less-imbalanced systems, and for the strong mass imbalanced systems, the interspecies interaction plays less important role in determining the value of $|a_-^{\scriptscriptstyle(1)}|$. Specially, when the homonuclear atoms are in resonance, the $a^{\scriptscriptstyle (1)}_{-}$ is nearly a constant expressed in terms of the van der Waals length $r_{\scriptscriptstyle vdW,HL}$: $a^{\scriptscriptstyle (1)}_{-} = -(6.3 \pm 15\%) r_{\scriptscriptstyle vdW,HL}$.