Diphoton and dark matter from cascade decay

We propose a simplified model to study the possible new heavy diphoton resonance from the cascade decay of a heavier particle at colliders, which may be related to dark matter or other new physics beyond the Standard Model. Model-independent constraints and predictions on the allowed couplings for generating the observed diphoton data are studied in detail. We demonstrate that this scenario can be tested by the possible four-photon signal or the $WW/ZZ/Z\gamma$ resonances. Meanwhile, this cascade decay scenario also provides us with dark matter candidates, which is consistent with the observed dark matter relic density.

Figure 1

The Feynman diagram for the production of the 750 GeV diphoton excess.

Figure 2

The Feynman diagram for the production of the 1.6 TeV diphoton excess.

Figure 3

The MET distribution in the $R\to (S\to AA)(S\to \gamma \gamma )$ channel. The three figures correspond to (a) $M_R=1600\mathrm{GeV}$, $M_S=750\mathrm{GeV}$, and $\mathrm{\Gamma }(S)=50\mathrm{GeV}$; (b) $M_R=1540\mathrm{GeV}$, $M_S=765\mathrm{GeV}$, and $\mathrm{\Gamma }(S)=10\mathrm{GeV}$; and (c) $M_R=1530.1\mathrm{GeV}$, $M_S=765\mathrm{GeV}$, and $\mathrm{\Gamma }(S)=1\mathrm{GeV}$.

Figure 4

The constraints for $N_S^A$ and $B_R^g$ when fixing $c_{Rgg}$. In order to generate a diphoton excess with a $10\pm 3\mathrm{fb}$ cross section, $c_{Rgg}$ need to be between 0.2 and 0.5 for different benchmark points. The colored bands stand for the cross section of diphoton excess which is smaller than 7 fb when fixing different $c_{Rgg}$, respectively.

Figure 5

The contour plot for $c_{Rgg}$ and $B_R^g$, assuming a diphoton excess larger than 7 fb. The purple, wheat, and green regions denote that the diphoton excess is smaller than 7 fb, when fixing $N_S^A=1$, 5, and 10, respectively. The orange region stands for ${\mathrm{\Gamma }}_R>100\mathrm{GeV}$, and the blue region means ${\sigma }_{\text{dijet}}>100\mathrm{fb}$. The white region stands for the allowed parameter space.

Figure 6

The allowed parameter spaces for $c_{RB}$ and $c_{RW}$ from $WW$, $ZZ$, and $Z\gamma$ experiment data at the 8 and 13 TeV LHC.

Figure 7

The predicted $gg\to R\to 2\gamma$ cross section, where we use benchmark 1 in (a), benchmark 4 in (b), and benchmark 5 in (c). The constraints mainly come from the fact that we require the cross section $gg\to R\to SS\to 2\gamma 2A$ to be about $10\pm 3\mathrm{fb}$. Other constraints on the couplings discussed above are also included.

Figure 8

The $5\sigma$ discovery (a) and $3\sigma$ exclusion (b) parameter spaces for $gg\to R\to 2\gamma$ in the $\mathcal{L}-c_{R\gamma \gamma }$ plane. Different colors stand for choosing different $B_R^g$ and $N_S^A$ benchmark points and the corresponding $c_{Rgg}$, which satisfy the fact that 750 GeV diphoton cross section is 10 fb in each benchmark point.

Figure 9

The Feynman diagram for dark matter annihilation channel $AA\to \gamma \gamma$.

Figure 10

The constraints for $M_A$ and $c_{S\gamma \gamma }^2{c}_{SAA}^2$. The pink region stands for the parameter spaces satisfying the observed DM relic density $\mathrm{\Omega }{h}^2<(0.1186\pm 0.0020)$ [60], when the DM is composed of more than one species of particles. The green, blue, and purple bands are allowed parameter spaces for $10\mathrm{GeV}<\mathrm{\Gamma }(S)<50\mathrm{GeV}$ with $N_S^A=1$, 5, and 10, respectively. So the overlapping regions between the pink and green (blue, purple) ones are the allowed parameter spaces for $N_S^A=1$ (5, 10).

Figure 11

The Feynman diagram for the production of the four-photon signal at 1.6 TeV.

Figure 12

The predicted $gg\to 4\gamma$ cross section in the $N_S^A\text{−}{B}_R^g$ plane with $c_{Rgg}=0.16$, 0.2, and 0.24, respectively. The cross section for $gg\to R\to SS\to 2\gamma 2A$ is required to be between 7 and 13 fb. Other constraints from the width of $S$ and $R$ and dijet resonances searching are also included.

Figure 13

The constraint of $c_{S\gamma \gamma }$ and $N_S^A$ from the width of $S$, where we assume that the $S$ width is between 10 and 50 GeV. The white region corresponds to allowed parameter spaces. (a) $S$ couple only with $\gamma \gamma$. (b) Including the contribution from the interaction of $SZZ$ and $SZ\gamma$ with $c_{SW}=0$. (c) Including the contribution from the interaction of $SZZ$ and $SWW$ with $c_{SW}=c_{SB}$.

Figure 14

The constraints for $N_S^A$ and $B_R^g$ when fixing $c_{Rgg}$. The meaning of the colored region is similar to Fig. 4, but we include the contribution from the interaction of $SZZ$ and $SZ\gamma$ of case II in (a) and the interaction of $SZZ$ and $SWW$ of case III in (b).

Figure 15

The Feynman diagram for diboson production, where $V_1{V}_2=ZZ/Z\gamma /\gamma \gamma$ in case II and $V_1{V}_2=WW/ZZ/\gamma \gamma$ in case III.

Figure 16

The $5\sigma$ discovery potential for $gg\to R\to SS\to Z\gamma AA/ZZAA/WWAA$ in the $c_{SB}-c_{SW}$ plane with $100{\mathrm{fb}}^{-1}$ at the 13 TeV LHC. The parameter spaces are consistent with the diphoton excess cross section, i.e., ${\sigma }_{\gamma \gamma AA}=10\mathrm{fb}$. The pink regions stand for the fact that the width of $S$ is larger than 40 GeV. The white regions in three figures are where the signal can be observed over the level of $5\sigma$. The plots (a), (b) and (c) stand for the process $gg\to R\to ZZ\gamma \gamma$, $gg\to R\to ZZAA$ and $gg\to R\to WWAA$, respectively.

Figure 17

The Feynman diagram for dark matter annihilation channel $AA\to V_1{V}_2$, where $V_1{V}_2=\gamma \gamma$, $Z\gamma ZZ$, $Z\gamma$, $ZZ$, and $WW$. In case II, $V_1{V}_2=\gamma \gamma$, and $ZZ$ $Z\gamma$; in case III, $V_1{V}_2=\gamma \gamma$, $ZZ$, and $WW$.

Figure 18

The constraints for $M_A$ and $c_{S\gamma \gamma }^2{c}_{SAA}^2$ including the constraints of the DM relic density. The meaning of the colored region is similar to Fig. 10, but we include the contribution from the interaction of $SZZ$ and $SZ\gamma$ of case II in (a) and the interaction of $SZZ$ and $SWW$ of case III in (b).

Figure 19

The predicted $gg\to 4\gamma$ cross section in the $N_S^A\text{−}{B}_R^g$ plane with $c_{Rgg}=0.16$, 0.20, and 0.24 for case II and $c_{Rgg}=0.24$, 0.30, and 0.34 for case III. The cross section for $gg\to R\to SS\to 2\gamma 2A$ is required to be between 7 and 13 fb. Other constraints from the width of $S$ and $R$ and dijet resonances searching are also included. These figures are similar to Fig. 12, but we include the contribution from the interaction of $SZZ$ and $SZ\gamma$ of case II in (a)–(c) and the interaction of $SZZ$ and $SWW$ of case III in (d)–(f).