New method for the spin determination of dark matter

We construct a new kinematical variable that is able to fully reconstruct the absolute value, and partially reconstruct the sign, of the angular distribution in the center of momentum system of a decaying particle in certain cases where the center of momentum system is only known up to a twofold ambiguity. After making contact with Drell-Yan production at the Large Hadron Collider, we apply this method to the pair production of dark matter in association with two charged leptons at the International Linear Collider and show that for a small intermediate width, perfect agreement is found with the true angular distribution in the absence of initial state radiation. In the presence of initial state radiation, we find that the modification to the angular distributions is small for most angles and that different spin combination classes should still be distinguishable. This enables us to determine the spin of the mother particle and the dark-matter particle in certain cases.

Figure 1

Decay of $B$ into $L$ and $D$ where $L$ is an observed SM particle, $D$ is the missing dark-matter particle and $B$ is the parent of this decay.

Figure 2

The Drell-Yan process $\overline{u}d\to {\ell }^{-}{\nu }_{\ell }$, where $R^{-}$ is some general charged resonance.

Figure 3

The c.m. angular distributions using the large solution [Eq. (40)] and reconstructing as outlined in the text. The three curves are solid black for the true c.m. angular distribution, dashed blue for the reconstructed large solution when the width is 0.1% of the mass and dotted red when the width is 1% of the mass. From top to bottom the three plots are for a scalar, vector and tensor $R$.

Figure 4

An antler diagram for the pair production of two $B$ fields which then each decay to $L$ and $D$. The energy of each $D$ is known in this case as described in the text.

Figure 5

Pair production of $B$ followed by its decay to a muon and $D$ at the ILC.

Figure 6

The c.m. angular distributions described in the text. The solid green lines come from the analytic formulas given in Table 2, the solid black lines come from the true simulated c.m. angular distributions, the dashed blue lines come from the large solution given in Eq. (3), and the dotted red lines come from dividing the dashed blue lines in half and taking the mirror image on the $\cos {\theta }_{\ell B}>0$ side. We used $\sqrt{s}=500$, $M_B=200$ and $M_D=50\mathrm{GeV}$ for this figure.

Figure 7

Class iii and iv c.m. angular distributions for the values $\sqrt{s}=1\mathrm{TeV}$, $M_B=200\mathrm{GeV}$ and $M_D=70\mathrm{GeV}$. In the case of iii, the solid black line is for class iiia, the blue dashed line is for class iiib, the red dot-dashed line is for class iiic and the orange dotted line is for class iiid. In the case of iv, the solid black line is for case iva while the dashed blue line is for case ivb.

Figure 8

The effect of a finite width on the c.m. angular distributions. The solid green lines come from the on-shell angular distributions given by the analytic formulas in Table 2, the solid black and dashed blue lines come from the large solution given in Eq. (3) where the width of $B$ is taken to be 1% and 5%, respectively. The collision energy and masses are the same as in Fig. 6.

Figure 9

The effect of ISR and beamstrahlung on the c.m. angular distributions. The solid green lines come from the analytic formulas given in Table 2, the solid black lines comes from the large solution given in Eq. (3) where the ISR and beamstrahlung is turned on and the dashed blue lines, additionally, have the cuts in Eqs. (45) through (47) applied. The collision energy and masses are the same as in Fig. 6.

Figure 10

Diagram of a scattering process dominated by an on-shell $B$ which decays to $L$ and $D$.

Figure 11

Pair production of $B^{+}$ and $B^{-}$ followed by the decay of $B^{-}$ to ${\mu }^{-}D$.