  The list of two dimensional Dirac systems with a tilt in their Dirac cone
spectrum is expanding, and now in addition to organic system
$\alpha$(BEDT-TTF)$_2$I$_3$ includes the two dimensional $8Pmmn$-borophene
sheet, which allows for controlled doping by the gate voltage. We analytically
calculate the polarization function of tilted Dirac cone for arbitrary tilt
parameter, $0\le \eta <1$, and arbitrary doping. This enables us to find two
interesting plasmonic effects solely caused by the tilt: (i) In addition to the
standard plasmon oscillations, strong enough tilt, induces an additional
linearly dispersing overdamped branch of plasmons, which is strongly Landau
damped due to overlap with a large density of intra-band free particle-hole
(PH) excitations. (ii) There appears a kink in the plasmon dispersion for any
non-zero tilt parameter. The kink appears when the plasmon branch enters the
inter-band continuum of PH excitations. This kink becomes most manifest for
wave vectors perpendicular to the tilt direction and fades away by approaching
the tilt direction. Experimental measurement of the wave vector and energy of
the plasmonic kink, when combined with our analytic formula for the kink energy
scale, allows for a direct experimental measurement of the tilt parameter.
