tion cross section; the largest individual channel is $\tilde{\chi}_1^+\tilde{\chi}_1^- \to Zh$ contributing 14%. Nonetheless $\tilde{\chi}_1^0\tilde{\chi}_1^\pm$ (13%) and $\tilde{\chi}_2^0\tilde{\chi}_1^\pm$ (12%) co-annihilations are also important. $\tilde{\chi}_1^0\tilde{\chi}_2^0$ co-annihilation contributes about 4%. The decay modes determining the collider signatures are as follows:

<table><thead><tr><th>mass</th><th>decays</th></tr></thead><tbody><tr><td>703 GeV</td><td>$\tilde{\chi}_3^\pm \to \tilde{\chi}_1^\pm Z$ (78%), $\tilde{\chi}_1^\pm h$ (16%), $\tilde{\chi}_{3,4}^0 W^\pm$ (6%)</td></tr><tr><td>670 GeV</td><td>$\tilde{\chi}_6^0 \to \tilde{\chi}_4^0 Z$ (45%), $\tilde{\chi}_1^\pm W^\pm$ (36%), $\tilde{\chi}_3^0 h$ (18%)</td></tr><tr><td>669 GeV</td><td>$\tilde{\chi}_5^0 \to \tilde{\chi}_3^0 Z$ (46%), $\tilde{\chi}_1^\pm W^\pm$ (35%), $\tilde{\chi}_4^0 h$ (18%)</td></tr><tr><td>620 GeV</td><td>$\tilde{\chi}_2^\pm \to \tilde{\chi}_3^0 W^\pm$ (50%), $\tilde{\chi}_4^0 W^\pm$ (50%)</td></tr><tr><td>434 GeV</td><td>$\tilde{\chi}_4^0 \to \tilde{\chi}_1^\pm W^*$ (99%)</td></tr><tr><td>433 GeV</td><td>$\tilde{\chi}_3^0 \to \tilde{\chi}_1^\pm W^*$ (99%)</td></tr><tr><td>399 GeV</td><td>$\tilde{\chi}_1^\pm \to \tilde{\chi}_2^0 W^*$ (58%), $\tilde{\chi}_1^0 W^*$ (42%)</td></tr><tr><td>388 GeV</td><td>$\tilde{\chi}_2^0 \to \tilde{\chi}_1^0 \gamma$ (100%); $\Gamma_{\text{tot}} = 4.1 \times 10^{-16}$ GeV ($c\tau \approx 0.5$ m)</td></tr><tr><td>388 GeV</td><td>$\tilde{\chi}_1^0$, stable</td></tr></tbody></table>

The $\tilde{\chi}_i^+\tilde{\chi}_j^-$ and $\tilde{\chi}_i^\pm\tilde{\chi}_k^0$ ($i, j = 1, 2, 3$; $k = 3...6$) production cross sections are 27 fb and 55 fb at the 13 TeV LHC, respectively, but again no relevant constraints can be obtained from re-interpretation of the current SUSY searches.

For the design of dedicated analyses it is relevant to note that $\tilde{\chi}_{2,3}^\pm\tilde{\chi}_{5,6}^0$ production would give signatures like $2W2Z + E_T^{\text{miss}}$ or $3W1Z + E_T^{\text{miss}}$, etc., accompanied by additional jets and/or leptons from intermediate $\tilde{\chi}_{3,4}^0 \to \tilde{\chi}_1^\pm W^*$ decays appearing in the cascade.

We also note that the $\tilde{\chi}_2^0$ is long-lived with a mean decay length of about 0.5 m. However, given the tiny mass difference to the $\tilde{\chi}_1^0$ of 180 MeV, the displaced photon from the $\tilde{\chi}_2^0 \to \tilde{\chi}_1^0 \gamma$ transition will be extremely soft and thus hard, if not impossible, to detect.

**Point 6 (SPhenoDiracGauginos_11321)** is a higgsino DM point with $m_{\tilde{\chi}_1^0} \simeq 1.1$ TeV and a rather large mass splitting between the higgsino-like states, $m_{\tilde{\chi}_2^0} - m_{\tilde{\chi}_1^0} \simeq 4$ GeV and $m_{\tilde{\chi}_1^\pm} - m_{\tilde{\chi}_1^0} \simeq 6$ GeV. Here, $\Omega h^2 = 0.112$ results mainly from $\tilde{\chi}_1^0\tilde{\chi}_2^0$ and $\tilde{\chi}_{1,2}^0\tilde{\chi}_1^\pm$ co-annihilations. The main decay modes of the heavy EW-ino spectrum are:

<table><thead><tr><th>mass</th><th>decays</th></tr></thead><tbody><tr><td>1529 GeV</td><td>$\tilde{\chi}_3^\pm \to \tilde{\chi}_1^\pm Z$ (90%), $\tilde{\chi}_1^\pm h$ (8%)</td></tr><tr><td>1528 GeV</td><td>$\tilde{\chi}_6^0 \to \tilde{\chi}_1^0 Z$ (83%), $\tilde{\chi}_2^0 h$ (6%), $\tilde{\chi}_1^\pm W^\mp$ (7%), $\tilde{\chi}_2^0 Z$ (4%)</td></tr><tr><td>1527 GeV</td><td>$\tilde{\chi}_5^0 \to \tilde{\chi}_1^0 Z$ (62%), $\tilde{\chi}_2^0 Z$ (22%), $\tilde{\chi}_1^\pm W^\mp$ (8%), $\tilde{\chi}_2^0 h$ (6%)</td></tr><tr><td>1526 GeV</td><td>$\tilde{\chi}_2^\pm \to \tilde{\chi}_1^\pm Z^\pm$ (60%), $\tilde{\chi}_1^0 W^\pm$ (17%), $\tilde{\chi}_2^0 W^\pm$ (17%), $\tilde{\chi}_1^\pm h$ (6%)</td></tr><tr><td>1474 GeV</td><td>$\tilde{\chi}_4^0 \to \tilde{\chi}_1^0 Z$ (69%), $\tilde{\chi}_2^0 Z$ (15%), $\tilde{\chi}_1^\pm W^\mp$ (8%), $\tilde{\chi}_2^0 h$ (7%)</td></tr><tr><td>1470 GeV</td><td>$\tilde{\chi}_3^0 \to \tilde{\chi}_2^0 Z$ (79%), $\tilde{\chi}_1^\pm W^\mp$ (9%), $\tilde{\chi}_1^0 h$ (8%), $\tilde{\chi}_1^0 Z$ (5%)</td></tr><tr><td>1081 GeV</td><td>$\tilde{\chi}_1^\pm \to \tilde{\chi}_1^0 W^*$ (100%)</td></tr><tr><td>1079 GeV</td><td>$\tilde{\chi}_2^0 \to \tilde{\chi}_1^0 Z^*$ (89%), $\tilde{\chi}_1^0 \gamma$ (11%); $\Gamma_{\text{tot}} = 9.9 \times 10^{-10}$ GeV (prompt)</td></tr><tr><td>1075 GeV</td><td>$\tilde{\chi}_1^0$, stable</td></tr></tbody></table>

The LHC production cross sections are however very low for such heavy EW-inos, below 1 fb at 13–14 TeV. This is clearly a case for the high luminosity (HL) LHC, or a higher-energy machine.

**Point 7 (SPhenoDiracGauginos_37)** is another higgsino DM point with $m_{\tilde{\chi}_1^0} \simeq 1.1$ TeV but small, sub-GeV mass splittings between the higgsino-like states, $m_{\tilde{\chi}_2^0} - m_{\tilde{\chi}_1^0} \simeq 120$ MeV and $m_{\tilde{\chi}_1^\pm} - m_{\tilde{\chi}_1^0} \simeq 400$ MeV. Co-annihilations between $\tilde{\chi}_1^0$, $\tilde{\chi}_2^0$ and $\tilde{\chi}_1^\pm$ result in $\Omega h^2 = 0.124$. The main decay modes are:
756

<table><thead><tr><th>mass</th><th>decays</th></tr></thead><tbody><tr><td>1957 GeV</td><td>χ̃<sub>6</sub><sup>0</sup> → χ̃<sub>1</sub><sup>±</sup>W<sup>∓</sup> (33%), χ̃<sub>1,2</sub><sup>0</sup>Z (33%), χ̃<sub>1,2</sub><sup>0</sup>h (31%)</td></tr><tr><td>1951 GeV</td><td>χ̃<sub>5</sub><sup>0</sup> → χ̃<sub>1</sub><sup>±</sup>W<sup>∓</sup> (33%), χ̃<sub>1,2</sub><sup>0</sup>Z (32%), χ̃<sub>1,2</sub><sup>0</sup>h (32%)</td></tr><tr><td>1300 GeV</td><td>χ̃<sub>3</sub><sup>±</sup> → χ̃<sub>1</sub><sup>±</sup>Z (55%), χ̃<sub>1</sub><sup>±</sup>h (40%), χ̃<sub>1,2</sub><sup>0</sup>W<sup>∓</sup> (5%)</td></tr><tr><td>1296 GeV</td><td>χ̃<sub>3,4</sub><sup>0</sup> → χ̃<sub>1</sub><sup>±</sup>W<sup>∓</sup> (44%), χ̃<sub>1,2</sub><sup>0</sup>Z (31%), χ̃<sub>1,2</sub><sup>0</sup>h (25%)</td></tr><tr><td>1292 GeV</td><td>χ̃<sub>2</sub><sup>±</sup> → χ̃<sub>1</sub><sup>0</sup>W<sup>∓</sup> (49%), χ̃<sub>2</sub><sup>0</sup>W<sup>∓</sup> (50%)</td></tr><tr><td>1159 GeV</td><td>χ̃<sub>1</sub><sup>±</sup> → χ̃<sub>1</sub><sup>0</sup>π<sup>±</sup> (69%), χ̃<sub>2</sub><sup>0</sup>π<sup>±</sup> (21%); Γ<sub>tot</sub> = 3.4 × 10<sup>-14</sup> GeV (cτ ≈ 6 mm)<br>χ̃<sub>2</sub><sup>0</sup> → χ̃<sub>1</sub><sup>0</sup>γ (100%); Γ<sub>tot</sub> = 2.1 × 10<sup>-15</sup> GeV (cτ ≈ 92 mm)</td></tr><tr><td>1159 GeV</td><td>χ̃<sub>1</sub><sup>0</sup>, stable</td></tr></tbody></table>

757

758

759

760

761

762

763

764

The high degree of compression of the higgsino states causes both the $\tilde{\chi}_2^0$ and the $\tilde{\chi}_1^±$ to be long-lived with mean decay lengths of 92 mm and 6 mm, respectively. While the $\tilde{\chi}_2^0$ likely appears as invisible co-LSP production of $\tilde{\chi}_1^±$ (either directly or through decays of heavier EW-inos) can lead to short tracks in the detector. Overall this gives a mix of prompt and displaced signatures as discussed in more detail for Points 9 and 10. Again, cross sections are below 1 fb in pp collisions at 13–14 TeV.

765

766

767

768

769

770

771

772

**Point 8 (SPhenoDiracGauginos_100)** is the one wino LSP point that our MCMC found (within the parameter space of $m_{DY}$, $m_{D2}$, $\mu < 2$ TeV), where the $\tilde{\chi}_1^0$ accounts for all the DM. Three of the wino-like states, $\tilde{\chi}_{1,2}^0$ and $\tilde{\chi}_1^±$, are quasi-degenerate at a mass of 1327 GeV, with the fourth one, $\tilde{\chi}_2^±$, being 5 GeV heavier. The relic density is $\Omega h^2 = 0.11$ as a result of co-annihilations between all four winos. What is special regarding collider signatures is that the $\tilde{\chi}_2^±$ decays into $\tilde{\chi}_1^± + \gamma$, while the $\tilde{\chi}_1^±$ is quasi-stable on collider scales. Chargino-pair and chargino-neutralino production is thus characterised by 1–2 HSCP tracks, in part accompanied by prompt photons. In more detail, the spectrum of decays is:

773

<table><thead><tr><th>mass</th><th>decays</th></tr></thead><tbody><tr><td>2078 GeV</td><td>χ̃<sub>6</sub><sup>0</sup> → χ̃<sub>4</sub><sup>0</sup>Z (28%), χ̃<sub>3</sub><sup>0</sup>h (21%), χ̃<sub>2</sub><sup>0</sup>h (18%), χ̃<sub>1</sub><sup>0</sup>Z (14%), χ̃<sub>2</sub><sup>±</sup>W<sup>∓</sup> (10%)</td></tr><tr><td>2076 GeV</td><td>χ̃<sub>5</sub><sup>0</sup> → χ̃<sub>4</sub><sup>0</sup>h (24%), χ̃<sub>3</sub><sup>0</sup>Z (24%), χ̃<sub>2</sub><sup>0</sup>Z (21%), χ̃<sub>1</sub><sup>0</sup>h (12%), χ̃<sub>2</sub><sup>±</sup>W<sup>∓</sup> (11%)</td></tr><tr><td>2059 GeV</td><td>χ̃<sub>3</sub><sup>±</sup> → χ̃<sub>3</sub><sup>0</sup>W<sup>∓</sup> (41%), χ̃<sub>4</sub><sup>0</sup>W<sup>∓</sup> (37%) χ̃<sub>1</sub><sup>±</sup>Z (9%), χ̃<sub>1</sub><sup>±</sup>h (9%)</td></tr><tr><td>1356</td><td>χ̃<sub>4</sub><sup>0</sup> → χ̃<sub>1</sub><sup>±</sup>W<sup>*</sup> (81%), χ̃<sub>2</sub><sup>±</sup>W<sup>*</sup> (19%)</td></tr><tr><td>1346</td><td>χ̃<sub>3</sub><sup>0</sup> → χ̃<sub>1</sub><sup>±</sup>W<sup>*</sup> (65%), χ̃<sub>2</sub><sup>±</sup>W<sup>*</sup> (35%)</td></tr><tr><td>1332 GeV</td><td>χ̃<sub>2</sub><sup>±</sup> → χ̃<sub>1</sub><sup>±</sup>γ (100%)</td></tr><tr><td>1327 GeV</td><td>χ̃<sub>1</sub><sup>±</sup> → χ̃<sub>1</sub><sup>0</sup>e<sup>±</sup>ν (100%); Γ<sub>tot</sub> = 2.3 × 10<sup>-18</sup> GeV (cτ ≈ 84 m)<br>χ̃<sub>2</sub><sup>0</sup> → χ̃<sub>1</sub><sup>0</sup>γ (100%); Γ<sub>tot</sub> = 1.6 × 10<sup>-16</sup> GeV (cτ ≈ 1.2 m)</td></tr><tr><td>1327 GeV</td><td>χ̃<sub>1</sub><sup>0</sup>, stable</td></tr></tbody></table>

774

775

776

777

778

Like for Points 6 and 7, the LHC cross sections are very low for such a heavy spectrum. Nonetheless SModelS gives $r_{max} = 0.28$ from HSCP searches; from the Pythia-based recasting we compute $1 - \text{CL}_s = 0.38$. We hence expect that this point will be testable at Run 3 of the LHC.

779

780

781

782

783

784

**Point 9 (SPhenoDiracGauginos_625)** is an example for higgsino-like LSPs at lower mass, around 600 GeV, where the $\tilde{\chi}_1^0$ is underabundant, constituting about 30% of the DM in the standard freeze-out picture. The higgsino-like states are highly compressed, $m_{\tilde{\chi}_1^±} - m_{\tilde{\chi}_1^0} \simeq 230$ MeV and $m_{\tilde{\chi}_2^0} - m_{\tilde{\chi}_1^0} \simeq 435$ MeV, which renders the $\tilde{\chi}_1^±$ long-lived with a mean decay length of 55 mm. Direct $\tilde{\chi}_1^±$ production has a cross section of about 10 fb at the 13 TeV LHC; more concretely $\sigma(pp \to \chi_1^±\chi_{1,2}^0) \simeq 8$ fb and $\sigma(pp \to \chi_1^+\chi_2^-) \simeq 2$ fb. The $\tilde{\chi}_1^±$ can also be produced
756

<table><thead><tr><th>mass</th><th>decays</th></tr></thead><tbody><tr><td>1957 GeV</td><td>χ̃<sub>6</sub><sup>0</sup> → χ̃<sub>1</sub><sup>±</sup>W<sup>∓</sup> (33%), χ̃<sub>1,2</sub><sup>0</sup>Z (33%), χ̃<sub>1,2</sub><sup>0</sup>h (31%)</td></tr><tr><td>1951 GeV</td><td>χ̃<sub>5</sub><sup>0</sup> → χ̃<sub>1</sub><sup>±</sup>W<sup>∓</sup> (33%), χ̃<sub>1,2</sub><sup>0</sup>Z (32%), χ̃<sub>1,2</sub><sup>0</sup>h (32%)</td></tr><tr><td>1300 GeV</td><td>χ̃<sub>3</sub><sup>±</sup> → χ̃<sub>1</sub><sup>±</sup>Z (55%), χ̃<sub>1</sub><sup>±</sup>h (40%), χ̃<sub>1,2</sub><sup>0</sup>W<sup>∓</sup> (5%)</td></tr><tr><td>1296 GeV</td><td>χ̃<sub>3,4</sub><sup>0</sup> → χ̃<sub>1</sub><sup>±</sup>W<sup>∓</sup> (44%), χ̃<sub>1,2</sub><sup>0</sup>Z (31%), χ̃<sub>1,2</sub><sup>0</sup>h (25%)</td></tr><tr><td>1292 GeV</td><td>χ̃<sub>2</sub><sup>±</sup> → χ̃<sub>1</sub><sup>0</sup>W<sup>∓</sup> (49%), χ̃<sub>2</sub><sup>0</sup>W<sup>∓</sup> (50%)</td></tr><tr><td>1159 GeV</td><td>χ̃<sub>1</sub><sup>±</sup> → χ̃<sub>1</sub><sup>0</sup>π<sup>±</sup> (69%), χ̃<sub>2</sub><sup>0</sup>π<sup>±</sup> (21%); Γ<sub>tot</sub> = 3.4 × 10<sup>-14</sup> GeV (cτ ≈ 6 mm)<br>χ̃<sub>2</sub><sup>0</sup> → χ̃<sub>1</sub><sup>0</sup>γ (100%); Γ<sub>tot</sub> = 2.1 × 10<sup>-15</sup> GeV (cτ ≈ 92 mm)</td></tr><tr><td>1159 GeV</td><td>χ̃<sub>1</sub><sup>0</sup>, stable</td></tr></tbody></table>

757

758

759

760

761

762

763

764

The high degree of compression of the higgsino states causes both the $\tilde{\chi}_2^0$ and the $\tilde{\chi}_1^±$ to be long-lived with mean decay lengths of 92 mm and 6 mm, respectively. While the $\tilde{\chi}_2^0$ likely appears as invisible co-LSP production of $\tilde{\chi}_1^±$ (either directly or through decays of heavier EW-inos) can lead to short tracks in the detector. Overall this gives a mix of prompt and displaced signatures as discussed in more detail for Points 9 and 10. Again, cross sections are below 1 fb in pp collisions at 13–14 TeV.

765

766

767

768

769

770

771

772

**Point 8 (SPhenoDiracGauginos_100)** is the one wino LSP point that our MCMC found (within the parameter space of $m_{DY}$, $m_{D2}$, $\mu < 2$ TeV), where the $\tilde{\chi}_1^0$ accounts for all the DM. Three of the wino-like states, $\tilde{\chi}_{1,2}^0$ and $\tilde{\chi}_1^±$, are quasi-degenerate at a mass of 1327 GeV, with the fourth one, $\tilde{\chi}_2^±$, being 5 GeV heavier. The relic density is $\Omega h^2 = 0.11$ as a result of co-annihilations between all four winos. What is special regarding collider signatures is that the $\tilde{\chi}_2^±$ decays into $\tilde{\chi}_1^± + \gamma$, while the $\tilde{\chi}_1^±$ is quasi-stable on collider scales. Chargino-pair and chargino-neutralino production is thus characterised by 1–2 HSCP tracks, in part accompanied by prompt photons. In more detail, the spectrum of decays is:

773

<table><thead><tr><th>mass</th><th>decays</th></tr></thead><tbody><tr><td>2078 GeV</td><td>χ̃<sub>6</sub><sup>0</sup> → χ̃<sub>4</sub><sup>0</sup>Z (28%), χ̃<sub>3</sub><sup>0</sup>h (21%), χ̃<sub>2</sub><sup>0</sup>h (18%), χ̃<sub>1</sub><sup>0</sup>Z (14%), χ̃<sub>2</sub><sup>±</sup>W<sup>∓</sup> (10%)</td></tr><tr><td>2076 GeV</td><td>χ̃<sub>5</sub><sup>0</sup> → χ̃<sub>4</sub><sup>0</sup>h (24%), χ̃<sub>3</sub><sup>0</sup>Z (24%), χ̃<sub>2</sub><sup>0</sup>Z (21%), χ̃<sub>1</sub><sup>0</sup>h (12%), χ̃<sub>2</sub><sup>±</sup>W<sup>∓</sup> (11%)</td></tr><tr><td>2059 GeV</td><td>χ̃<sub>3</sub><sup>±</sup> → χ̃<sub>3</sub><sup>0</sup>W<sup>∓</sup> (41%), χ̃<sub>4</sub><sup>0</sup>W<sup>∓</sup> (37%) χ̃<sub>1</sub><sup>±</sup>Z (9%), χ̃<sub>1</sub><sup>±</sup>h (9%)</td></tr><tr><td>1356</td><td>χ̃<sub>4</sub><sup>0</sup> → χ̃<sub>1</sub><sup>±</sup>W<sup>*</sup> (81%), χ̃<sub>2</sub><sup>±</sup>W<sup>*</sup> (19%)</td></tr><tr><td>1346</td><td>χ̃<sub>3</sub><sup>0</sup> → χ̃<sub>1</sub><sup>±</sup>W<sup>*</sup> (65%), χ̃<sub>2</sub><sup>±</sup>W<sup>*</sup> (35%)</td></tr><tr><td>1332 GeV</td><td>χ̃<sub>2</sub><sup>±</sup> → χ̃<sub>1</sub><sup>±</sup>γ (100%)</td></tr><tr><td>1327 GeV</td><td>χ̃<sub>1</sub><sup>±</sup> → χ̃<sub>1</sub><sup>0</sup>e<sup>±</sup>ν (100%); Γ<sub>tot</sub> = 2.3 × 10<sup>-18</sup> GeV (cτ ≈ 84 m)<br>χ̃<sub>2</sub><sup>0</sup> → χ̃<sub>1</sub><sup>0</sup>γ (100%); Γ<sub>tot</sub> = 1.6 × 10<sup>-16</sup> GeV (cτ ≈ 1.2 m)</td></tr><tr><td>1327 GeV</td><td>χ̃<sub>1</sub><sup>0</sup>, stable</td></tr></tbody></table>

774

775

776

777

778

Like for Points 6 and 7, the LHC cross sections are very low for such a heavy spectrum. Nonetheless SModelS gives $r_{max} = 0.28$ from HSCP searches; from the Pythia-based recasting we compute $1 - \text{CL}_s = 0.38$. We hence expect that this point will be testable at Run 3 of the LHC.

779

780

781

782

783

784

**Point 9 (SPhenoDiracGauginos_625)** is an example for higgsino-like LSPs at lower mass, around 600 GeV, where the $\tilde{\chi}_1^0$ is underabundant, constituting about 30% of the DM in the standard freeze-out picture. The higgsino-like states are highly compressed, $m_{\tilde{\chi}_1^±} - m_{\tilde{\chi}_1^0} \approx 230$ MeV and $m_{\tilde{\chi}_2^0} - m_{\tilde{\chi}_1^0} \approx 435$ MeV, which renders the $\tilde{\chi}_1^±$ long-lived with a mean decay length of 55 mm. Direct $\tilde{\chi}_1^±$ production has a cross section of about 10 fb at the 13 TeV LHC; more concretely $\sigma(pp \to \chi_1^±\chi_{1,2}^0) \approx 8$ fb and $\sigma(pp \to \chi_1^+\chi_2^-) \approx 2$ fb. The $\tilde{\chi}_1^±$ can also be produced
in decays of heavier EW-inos, in particular of the wino-like $\tilde{\chi}_{3,4}^0$ and $\tilde{\chi}_{2,3}^{\pm}$, which have masses around 900 GeV. This gives rise to WZ, WH and WW events (with or without $E_T^{\text{miss}}$) accompanied by short disappearing tracks with a cross section of about 2 fb at 13 TeV. The classic, prompt WZ, WH, WW + $E_T^{\text{miss}}$ signatures also have a cross section of the same order (about 2 fb). While all this is below Run 2 sensitivity, it shows an interesting potential for searches at high luminosity. The detailed spectrum of decays is:

<table><thead><tr><th>mass</th><th>decays</th></tr></thead><tbody><tr><td>1383 GeV</td><td>$\tilde{\chi}_6^0 \to \tilde{\chi}_1^\pm W^\mp$ (35%), $\tilde{\chi}_{1,2}^0 Z$ (33%), $\tilde{\chi}_{1,2}^0 h$ (31%)</td></tr><tr><td>1381 GeV</td><td>$\tilde{\chi}_5^0 \to \tilde{\chi}_1^\pm W^\mp$ (34%), $\tilde{\chi}_{1,2}^0 Z$ (33%), $\tilde{\chi}_{1,2}^0 h$ (32%)</td></tr><tr><td>904 GeV</td><td>$\tilde{\chi}_3^\pm \to \tilde{\chi}_1^\pm Z$ (49%), $\tilde{\chi}_1^\pm h$ (44%), $\tilde{\chi}_{1,2}^0 W^\pm$ (7%)</td></tr><tr><td>901 GeV</td><td>$\tilde{\chi}_4^0 \to \tilde{\chi}_{1,2}^0 Z$ (37%), $\tilde{\chi}_{1,2}^0 h$ (31%), $\tilde{\chi}_1^\pm W^\mp$ (33%)</td></tr><tr><td></td><td>$\tilde{\chi}_3^0 \to \tilde{\chi}_1^\pm W^\mp$ (34%), $\tilde{\chi}_{1,2}^0 Z$ (33%), $\tilde{\chi}_{1,2}^0 h$ (32%)</td></tr><tr><td>898 GeV</td><td>$\tilde{\chi}_2^\pm \to \tilde{\chi}_{1,2}^0 W^\pm$ (94%), $\tilde{\chi}_1^\pm h$ (3%), $\tilde{\chi}_1^\pm Z$ (3%)</td></tr><tr><td>606 GeV</td><td>$\tilde{\chi}_2^0 \to \tilde{\chi}_1^0 \gamma$ (87%), $\tilde{\chi}_1^0 \pi^0$ (11%); $\Gamma_{\text{tot}} = 2.5 \times 10^{-13}$ GeV ($c\tau \lesssim 1$ mm)</td></tr><tr><td></td><td>$\tilde{\chi}_1^\pm \to \tilde{\chi}_1^0 \pi^\pm$ (96%), $\tilde{\chi}_1^0 l^\pm \nu$ (4%); $\Gamma_{\text{tot}} = 3.6 \times 10^{-15}$ GeV ($c\tau \approx 55$ mm)</td></tr><tr><td>605 GeV</td><td>$\tilde{\chi}_1^0$, stable</td></tr></tbody></table>

**Point 10 (SPhenoDiracGauginos_236)** is another example of a low-mass higgsino LSP point with long-lived charginos. The peculiarity of this point is that the whole EW-ino spectrum lies below 1 TeV: the higgsino-, wino- and bino-like states have masses around 250, 500 and 800 GeV, respectively. The $\tilde{\chi}_1^0$ is highly underabundant in this case, providing only 5% of the DM relic density. Nonetheless the point is interesting from the collider perspective, as it has light masses that escape current limits. Moreover, with a mean decay length of the $\tilde{\chi}_1^\pm$ of about 13 mm, it gives rise to both prompt and DT signatures. Indeed, SModelS reports $r_{\text{max}} = 0.39$ for the prompt part of the signal, concretely for $WZ + E_T^{\text{miss}}$ from ATLAS-SUSY-2017-03 ($\sigma = 17.51$ fb compared to the 95% CL limit of $\sigma_{95} = 44.97$ fb). The cross section for one or two DTs is estimated as 0.4 pb by SModelS, however the short tracks caused by $\tilde{\chi}_1^\pm$ decays are outside the range of the DT search results considered in section 4.2.2. Last but not least, DTs with additional gauge or Higgs bosons have a cross section of about 50 fb.<fnref n="15" /> Recasting with MadAnalysis 5 gives $1-\text{CL}_s = 0.73$ (corresponding to $r = 0.6$) from the ATLAS-SUSY-2019-08 [107] analysis. The decay patterns of Point 10 are as follows:

<table><thead><tr><th>mass</th><th>decays</th></tr></thead><tbody><tr><td>822 GeV</td><td>$\tilde{\chi}_6^0 \to \tilde{\chi}_1^\pm W^\mp$ (35%), $\tilde{\chi}_{1,2}^0 Z$ (34%), $\tilde{\chi}_{1,2}^0 h$ (29%)</td></tr><tr><td></td><td>$\tilde{\chi}_5^0 \to \tilde{\chi}_1^\pm W^\mp$ (35%), $\tilde{\chi}_{1,2}^0 Z$ (33%), $\tilde{\chi}_{1,2}^0 h$ (30%)</td></tr><tr><td>491 GeV</td><td>$\tilde{\chi}_3^\pm \to \tilde{\chi}_1^\pm Z$ (50%), $\tilde{\chi}_1^\pm h$ (34%), $\tilde{\chi}_{1,2}^0 W^\pm$ (15%)</td></tr><tr><td>486 GeV</td><td>$\tilde{\chi}_4^0 \to \tilde{\chi}_{1,2}^0 Z$ (37%), $\tilde{\chi}_1^\pm W^\mp$ (35%), $\tilde{\chi}_{1,2}^0 h$ (28%)</td></tr><tr><td>485 GeV</td><td>$\tilde{\chi}_3^0 \to \tilde{\chi}_{1,2}^0 Z$ (44%), $\tilde{\chi}_1^\pm W^\mp$ (33%), $\tilde{\chi}_{1,2}^0 h$ (22%)</td></tr><tr><td>480 GeV</td><td>$\tilde{\chi}_2^\pm \to \tilde{\chi}_{1,2}^0 W^\pm$ (90%), $\tilde{\chi}_1^\pm h$ (5%), $\tilde{\chi}_1^\pm Z$ (5%)</td></tr><tr><td>247 GeV</td><td>$\tilde{\chi}_1^\pm \to \tilde{\chi}_1^0 \pi^\pm$ (92%), $\tilde{\chi}_1^0 l^\pm \nu$ (8%); $\Gamma_{\text{tot}} = 1.5 \times 10^{-14}$ GeV ($c\tau \approx 13$ mm)</td></tr><tr><td></td><td>$\tilde{\chi}_2^0 \to \tilde{\chi}_1^0 \gamma$ (95%), $\tilde{\chi}_1^0 \pi^0$ (5%); $\Gamma_{\text{tot}} = 1.2 \times 10^{-13}$ GeV ($c\tau \approx 2$ mm)</td></tr><tr><td>247 GeV</td><td>$\tilde{\chi}_1^0$, stable</td></tr></tbody></table>

**The SLHA files for these 10 points**, which can be used as input for MadGraph, micrOMEGAs or SModelS are available via Zenodo [135]. The main difference between the SLHA files

<footnote n="15">¹⁵See [104, 125] for details on the computation of the prompt and displaced signal fractions in SModelS.</footnote>
in decays of heavier EW-inos, in particular of the wino-like $\tilde{\chi}_{3,4}^0$ and $\tilde{\chi}_{2,3}^{\pm}$, which have masses around 900 GeV. This gives rise to WZ, WH and WW events (with or without $E_T^{\text{miss}}$) accompanied by short disappearing tracks with a cross section of about 2 fb at 13 TeV. The classic, prompt WZ, WH, WW + $E_T^{\text{miss}}$ signatures also have a cross section of the same order (about 2 fb). While all this is below Run 2 sensitivity, it shows an interesting potential for searches at high luminosity. The detailed spectrum of decays is:

<table><thead><tr><th>mass</th><th>decays</th></tr></thead><tbody><tr><td>1383 GeV</td><td>$\tilde{\chi}_6^0 \rightarrow \tilde{\chi}_1^\pm W^\mp$ (35%), $\tilde{\chi}_{1,2}^0 Z$ (33%), $\tilde{\chi}_{1,2}^0 h$ (31%)</td></tr><tr><td>1381 GeV</td><td>$\tilde{\chi}_5^0 \rightarrow \tilde{\chi}_1^\pm W^\mp$ (34%), $\tilde{\chi}_{1,2}^0 Z$ (33%), $\tilde{\chi}_{1,2}^0 h$ (32%)</td></tr><tr><td>904 GeV</td><td>$\tilde{\chi}_3^\pm \rightarrow \tilde{\chi}_1^\pm Z$ (49%), $\tilde{\chi}_1^\pm h$ (44%), $\tilde{\chi}_{1,2}^0 W^\pm$ (7%)</td></tr><tr><td>901 GeV</td><td>$\tilde{\chi}_4^0 \rightarrow \tilde{\chi}_{1,2}^0 Z$ (37%), $\tilde{\chi}_{1,2}^0 h$ (31%), $\tilde{\chi}_1^\pm W^\mp$ (33%)</td></tr><tr><td></td><td>$\tilde{\chi}_3^0 \rightarrow \tilde{\chi}_1^\pm W^\mp$ (34%), $\tilde{\chi}_{1,2}^0 Z$ (33%), $\tilde{\chi}_{1,2}^0 h$ (32%)</td></tr><tr><td>898 GeV</td><td>$\tilde{\chi}_2^\pm \rightarrow \tilde{\chi}_{1,2}^0 W^\pm$ (94%), $\tilde{\chi}_1^\pm h$ (3%), $\tilde{\chi}_1^\pm Z$ (3%)</td></tr><tr><td>606 GeV</td><td>$\tilde{\chi}_2^0 \rightarrow \tilde{\chi}_1^0 \gamma$ (87%), $\tilde{\chi}_1^0 \pi^0$ (11%); $\Gamma_{\text{tot}} = 2.5 \times 10^{-13}$ GeV ($c\tau \lesssim 1$ mm)</td></tr><tr><td></td><td>$\tilde{\chi}_1^\pm \rightarrow \tilde{\chi}_1^0 \pi^\pm$ (96%), $\tilde{\chi}_1^0 l^\pm \nu$ (4%); $\Gamma_{\text{tot}} = 3.6 \times 10^{-15}$ GeV ($c\tau \approx 55$ mm)</td></tr><tr><td>605 GeV</td><td>$\tilde{\chi}_1^0$, stable</td></tr></tbody></table>

**Point 10 (SPhenoDiracGauginos_236)** is another example of a low-mass higgsino LSP point with long-lived charginos. The peculiarity of this point is that the whole EW-ino spectrum lies below 1 TeV: the higgsino-, wino- and bino-like states have masses around 250, 500 and 800 GeV, respectively. The $\tilde{\chi}_1^0$ is highly underabundant in this case, providing only 5% of the DM relic density. Nonetheless the point is interesting from the collider perspective, as it has light masses that escape current limits. Moreover, with a mean decay length of the $\tilde{\chi}_1^\pm$ of about 13 mm, it gives rise to both prompt and DT signatures. Indeed, SModelS reports $r_{\text{max}} = 0.39$ for the prompt part of the signal, concretely for $WZ + E_T^{\text{miss}}$ from ATLAS-SUSY-2017-03 ($\sigma = 17.51$ fb compared to the 95% CL limit of $\sigma_{95} = 44.97$ fb). The cross section for one or two DTs is estimated as 0.4 pb by SModelS, however the short tracks caused by $\tilde{\chi}_1^\pm$ decays are outside the range of the DT search results considered in section 4.2.2. Last but not least, DTs with additional gauge or Higgs bosons have a cross section of about 50 fb.<fnref n="15" /> Recasting with MadAnalysis 5 gives $1-\text{CL}_s = 0.73$ (corresponding to $r = 0.6$) from the ATLAS-SUSY-2019-08 [107] analysis. The decay patterns of Point 10 are as follows:

<table><thead><tr><th>mass</th><th>decays</th></tr></thead><tbody><tr><td>822 GeV</td><td>$\tilde{\chi}_6^0 \rightarrow \tilde{\chi}_1^\pm W^\mp$ (35%), $\tilde{\chi}_{1,2}^0 Z$ (34%), $\tilde{\chi}_{1,2}^0 h$ (29%)</td></tr><tr><td></td><td>$\tilde{\chi}_5^0 \rightarrow \tilde{\chi}_1^\pm W^\mp$ (35%), $\tilde{\chi}_{1,2}^0 Z$ (33%), $\tilde{\chi}_{1,2}^0 h$ (30%)</td></tr><tr><td>491 GeV</td><td>$\tilde{\chi}_3^\pm \rightarrow \tilde{\chi}_1^\pm Z$ (50%), $\tilde{\chi}_1^\pm h$ (34%), $\tilde{\chi}_{1,2}^0 W^\pm$ (15%)</td></tr><tr><td>486 GeV</td><td>$\tilde{\chi}_4^0 \rightarrow \tilde{\chi}_{1,2}^0 Z$ (37%), $\tilde{\chi}_1^\pm W^\mp$ (35%), $\tilde{\chi}_{1,2}^0 h$ (28%)</td></tr><tr><td>485 GeV</td><td>$\tilde{\chi}_3^0 \rightarrow \tilde{\chi}_{1,2}^0 Z$ (44%), $\tilde{\chi}_1^\pm W^\mp$ (33%), $\tilde{\chi}_{1,2}^0 h$ (22%)</td></tr><tr><td>480 GeV</td><td>$\tilde{\chi}_2^\pm \rightarrow \tilde{\chi}_{1,2}^0 W^\pm$ (90%), $\tilde{\chi}_1^\pm h$ (5%), $\tilde{\chi}_1^\pm Z$ (5%)</td></tr><tr><td>247 GeV</td><td>$\tilde{\chi}_1^\pm \rightarrow \tilde{\chi}_1^0 \pi^\pm$ (92%), $\tilde{\chi}_1^0 l^\pm \nu$ (8%); $\Gamma_{\text{tot}} = 1.5 \times 10^{-14}$ GeV ($c\tau \approx 13$ mm)</td></tr><tr><td></td><td>$\tilde{\chi}_2^0 \rightarrow \tilde{\chi}_1^0 \gamma$ (95%), $\tilde{\chi}_1^0 \pi^0$ (5%); $\Gamma_{\text{tot}} = 1.2 \times 10^{-13}$ GeV ($c\tau \approx 2$ mm)</td></tr><tr><td>247 GeV</td><td>$\tilde{\chi}_1^0$, stable</td></tr></tbody></table>

**The SLHA files for these 10 points**, which can be used as input for MadGraph, micrOMEGAs or SModelS are available via Zenodo [135]. The main difference between the SLHA files

<footnote n="15">¹⁵See [104, 125] for details on the computation of the prompt and displaced signal fractions in SModelS.</footnote>
for MadGraph5_aMC@NLO or micrOMEGAs is that the MadGraph5_aMC@NLO ones have complex mixing matrices, while the micrOMEGAs ones have real mixing matrices and thus neutralino masses can have negative sign. The SModelS input files consist of masses, decay tables and cross sections in SLHA format but don't include mixing matrices. The CalcHEP model files for micrOMEGAs are also provided at [135]. The UFO model for MadGraph5_aMC@NLO is available at [84], and the SPheno code at [96].

## 6 Conclusions

Supersymmetric models with Dirac instead of Majorana gaugino masses have distinct phenomenological features. In this paper, we investigated the electroweakino sector of the Minimal Dirac Gaugino Supersymmetric Standard Model. The MDGSSM can be defined as the minimal Dirac gaugino extension of the MSSM: to introduce DG masses, one adjoint chiral superfield is added for each gauge group, but nothing else. The model has an underlying R-symmetry that is explicitly broken in the Higgs sector through a (small) $B_μ$ term, and new superpotential couplings $λ_S$ and $λ_T$ of the singlet and triplet fields with the Higgs. The resulting EW-ino sector thus comprises two bino, four wino and three higgsino states, which mix to form six neutralino and three chargino mass eigenstates (as compared to four and two, respectively, in the MSSM) with naturally small mass splittings induced by $λ_S$ and $λ_T$.

All this has interesting consequences for dark matter and collider phenomenology. We explored the parameter space where the $\tilde{\chi}_1^0$ is a good DM candidate in agreement with relic density and direct detection constraints, updating previous such studies. The collider phenomenology of the emerging DM-motivated scenarios is characterised by the richer EW-ino spectrum as compared to the MSSM, naturally small mass splittings as mentioned above, and the frequent presence of long-lived charginos and/or neutralinos.

We worked out the current LHC constraints on these scenarios by re-interpreting SUSY and LLP searches from ATLAS and CMS, in both a simplified model approach and full recasting using Monte Carlo event simulation. While HSCP and disappearing track searches give quite powerful limits on scenarios with charged LLPs, scenarios with mostly $E_T^{miss}$ signatures remain poorly constrained. Indeed, the prompt SUSY searches only allow the exclusion of (certain) points with an LSP below 200 GeV, which drops to about 100 GeV when the winos are heavy. This is a stark contrast to the picture for constraints on colourful sparticles, and indicates that this sector of the theory is likely most promising for future work. We provided a set of 10 benchmark points to this end.

We also demonstrated the usefulness of a simplified models approach for EW-inos, in comparing it to a full recasting. While cross section upper limits have the in-built shortcoming of not being able to properly account for complex spectra (where several signals overlap), the results are close enough to give a good estimate of the excluded region. This is particularly true since it is a much faster method of obtaining constraints, and the implementation of new results is much more straightforward (and hence more complete and up-to-date). Moreover, the constraining power could easily be improved if more efficiency maps and likelihood information were available and implemented. This holds for both prompt and LLP searches.

We note in this context that, while this study was finalised, ATLAS made pyhf likelihood files for the $1l+H(\to b\bar{b})+E_T^{miss}$ EW-ino search [107] available on HEPData [136] in addition to digitised acceptance and efficiency maps. We appreciate this very much and are looking forward to using this data in future studies. To go a step further, it would be very interesting if the assumption $m_{\tilde{\chi}_1^\pm} = m_{\tilde{\chi}_2^0}$ could be lifted in the simplified model interpretations.

Furthermore, the implementation in other recasting tools of more analyses with the full $\approx 140 \text{ fb}^{-1}$ integrated luminosity from Run 2 would be of high utility in constraining the
for MadGraph5_aMC@NLO or micrOMEGAs is that the MadGraph5_aMC@NLO ones have complex mixing matrices, while the micrOMEGAs ones have real mixing matrices and thus neutralino masses can have negative sign. The SModelS input files consist of masses, decay tables and cross sections in SLHA format but don't include mixing matrices. The CalcHEP model files for micrOMEGAs are also provided at [135]. The UFO model for MadGraph5_aMC@NLO is available at [84], and the SPheno code at [96].

## 6 Conclusions

Supersymmetric models with Dirac instead of Majorana gaugino masses have distinct phenomenological features. In this paper, we investigated the electroweakino sector of the Minimal Dirac Gaugino Supersymmetric Standard Model. The MDGSSM can be defined as the minimal Dirac gaugino extension of the MSSM: to introduce DG masses, one adjoint chiral superfield is added for each gauge group, but nothing else. The model has an underlying R-symmetry that is explicitly broken in the Higgs sector through a (small) $B_μ$ term, and new superpotential couplings $λ_S$ and $λ_T$ of the singlet and triplet fields with the Higgs. The resulting EW-ino sector thus comprises two bino, four wino and three higgsino states, which mix to form six neutralino and three chargino mass eigenstates (as compared to four and two, respectively, in the MSSM) with naturally small mass splittings induced by $λ_S$ and $λ_T$.

All this has interesting consequences for dark matter and collider phenomenology. We explored the parameter space where the $\tilde{\chi}_1^0$ is a good DM candidate in agreement with relic density and direct detection constraints, updating previous such studies. The collider phenomenology of the emerging DM-motivated scenarios is characterised by the richer EW-ino spectrum as compared to the MSSM, naturally small mass splittings as mentioned above, and the frequent presence of long-lived charginos and/or neutralinos.

We worked out the current LHC constraints on these scenarios by re-interpreting SUSY and LLP searches from ATLAS and CMS, in both a simplified model approach and full recasting using Monte Carlo event simulation. While HSCP and disappearing track searches give quite powerful limits on scenarios with charged LLPs, scenarios with mostly $E_T^{\text{miss}}$ signatures remain poorly constrained. Indeed, the prompt SUSY searches only allow the exclusion of (certain) points with an LSP below 200 GeV, which drops to about 100 GeV when the winos are heavy. This is a stark contrast to the picture for constraints on colourful sparticles, and indicates that this sector of the theory is likely most promising for future work. We provided a set of 10 benchmark points to this end.

We also demonstrated the usefulness of a simplified models approach for EW-inos, in comparing it to a full recasting. While cross section upper limits have the in-built shortcoming of not being able to properly account for complex spectra (where several signals overlap), the results are close enough to give a good estimate of the excluded region. This is particularly true since it is a much faster method of obtaining constraints, and the implementation of new results is much more straightforward (and hence more complete and up-to-date). Moreover, the constraining power could easily be improved if more efficiency maps and likelihood information were available and implemented. This holds for both prompt and LLP searches.

We note in this context that, while this study was finalised, ATLAS made pyhf likelihood files for the $1l+H(\to b\bar{b})+E_T^{\text{miss}}$ EW-ino search [107] available on HEPData [136] in addition to digitised acceptance and efficiency maps. We appreciate this very much and are looking forward to using this data in future studies. To go a step further, it would be very interesting if the assumption $m_{\tilde{\chi}_1^\pm} = m_{\tilde{\chi}_2^0}$ could be lifted in the simplified model interpretations.

Furthermore, the implementation in other recasting tools of more analyses with the full $\approx 140 \text{ fb}^{-1}$ integrated luminosity from Run 2 would be of high utility in constraining the
EW-ino sector. Here, the recasting of LLP searches is also a high priority, as theories with such particles are very easily constrained, with the limits reaching much higher masses than for searches for promptly decaying particles. A review of available tools for reinterpretation and detailed recommendations for the presentation of results from new physics searches are available in [137].

Last but not least, we note that the automation of the calculation of particle decays when there is little phase space will also be a fruitful avenue for future work.

## Acknowledgements

We thank Geneviève Belanger, Benjamin Fuks, Andre Lessa, Sasha Pukhov, and Wolfgang Wal-tenberger for helpful discussions related to the tools used in this study. Moreover, we thank Pat Scott for sharing a pre-release version of ColliderBit Solo, and apologise for in the end not using it in this study. MDG would also like to thank his children for stimulating discussions during the lockdown.

**Funding information** This work was supported in part by the IN2P3 through the projects "Théorie – LHCiTools" (2019) and "Théorie – BSMGA" (2020). This work has also been done within the Labex ILP (reference ANR-10-LABX-63) part of the Idex SUPER, and received fi-nancial state aid managed by the Agence Nationale de la Recherche, as part of the programme Investissements d'avenir under the reference ANR-11-IDEX-0004-02, and the Labex "Institut Lagrange de Paris" (ANR-11-IDEX-0004-02, ANR-10-LABX-63) which in particular funded the scholarship of SLW. SLW has also been supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under grant 396021762 - TRR 257. MDG acknowledges the support of the Agence Nationale de Recherche grant ANR-15-CE31-0002 "HiggsAutoma-tor." HRG is funded by the Consejo Nacional de Ciencia y Tecnología, CONACYT, scholarship no. 291169.

## A Appendices

### A.1 Electroweakinos in the MRSSM

In this appendix we provide a review of the EW-ino sector of the MRSSM in our notation, to contrast with the phenomenology of the MDGSSM.

The MRSSM [19] is characterised by preserving a $U(1)$ R-symmetry even after EWSB. To allow the Higgs fields to obtain vacuum expectation values, they must have vanishing R-charges, and we therefore need to add additional partner fields $R_{u,d}$ so that the higgsinos can obtain a mass (analogous to the $\mu$-term in the MSSM).

The relevant field content is summarised in Table 4. The superpotential of the MRSSM is

$$W^{\text{MRSSM}} = \mu_u \mathbf{R}_u \cdot \mathbf{H}_u + \mu_d \mathbf{R}_d \cdot \mathbf{H}_d + \lambda_{S_u} \mathbf{S} \mathbf{R}_u \cdot \mathbf{H}_u + \lambda_{S_d} \mathbf{S} \mathbf{R}_d \cdot \mathbf{H}_d + 2\lambda_{T_u} \mathbf{R}_u \cdot \mathbf{TH}_u + 2\lambda_{T_d} \mathbf{R}_d \cdot \mathbf{TH}_d. \quad (19)$$

Here we define the triplet as

$$\mathbf{T} \equiv \frac{1}{2} \mathbf{T}^a \sigma^a = \frac{1}{2} \begin{pmatrix} \mathbf{T}_0 & \sqrt{2}\mathbf{T}_+ \\ \sqrt{2}\mathbf{T}_- & -\mathbf{T}_0 \end{pmatrix}. \quad (20)$$

Notably the model has an $N = 2$ supersymmetry if

$$\lambda_{S_u} = g_Y/\sqrt{2}, \quad \lambda_{S_d} = -g_Y/\sqrt{2}, \quad \lambda_{T_u} = g_2/\sqrt{2}, \quad \lambda_{T_d} = g_2/\sqrt{2}. \quad (21)$$
EW-ino sector. Here, the recasting of LLP searches is also a high priority, as theories with such particles are very easily constrained, with the limits reaching much higher masses than for searches for promptly decaying particles. A review of available tools for reinterpretation and detailed recommendations for the presentation of results from new physics searches are available in [137].

Last but not least, we note that the automation of the calculation of particle decays when there is little phase space will also be a fruitful avenue for future work.

## Acknowledgements

We thank Geneviève Belanger, Benjamin Fuks, Andre Lessa, Sasha Pukhov, and Wolfgang Wal-tenberger for helpful discussions related to the tools used in this study. Moreover, we thank Pat Scott for sharing a pre-release version of ColliderBit Solo, and apologise for in the end not using it in this study. MDG would also like to thank his children for stimulating discussions during the lockdown.

**Funding information** This work was supported in part by the IN2P3 through the projects "Théorie – LHCiTools" (2019) and "Théorie – BSMGA" (2020). This work has also been done within the Labex ILP (reference ANR-10-LABX-63) part of the Idex SUPER, and received fi-nancial state aid managed by the Agence Nationale de la Recherche, as part of the programme Investissements d'avenir under the reference ANR-11-IDEX-0004-02, and the Labex "Institut Lagrange de Paris" (ANR-11-IDEX-0004-02, ANR-10-LABX-63) which in particular funded the scholarship of SLW. SLW has also been supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under grant 396021762 - TRR 257. MDG acknowledges the support of the Agence Nationale de Recherche grant ANR-15-CE31-0002 "HiggsAutoma-tor." HRG is funded by the Consejo Nacional de Ciencia y Tecnología, CONACYT, scholarship no. 291169.

## A Appendices

### A.1 Electroweakinos in the MRSSM

In this appendix we provide a review of the EW-ino sector of the MRSSM in our notation, to contrast with the phenomenology of the MDGSSM.

The MRSSM [19] is characterised by preserving a $U(1)$ R-symmetry even after EWSB. To allow the Higgs fields to obtain vacuum expectation values, they must have vanishing R-charges, and we therefore need to add additional partner fields $R_{u,d}$ so that the higgsinos can obtain a mass (analogous to the $\mu$-term in the MSSM).

The relevant field content is summarised in Table 4. The superpotential of the MRSSM is

$$W^{\text{MRSSM}} = \mu_u \mathbf{R}_u \cdot \mathbf{H}_u + \mu_d \mathbf{R}_d \cdot \mathbf{H}_d + \lambda_{S_u} \mathbf{S} \mathbf{R}_u \cdot \mathbf{H}_u + \lambda_{S_d} \mathbf{S} \mathbf{R}_d \cdot \mathbf{H}_d + 2\lambda_{T_u} \mathbf{R}_u \cdot \mathbf{TH}_u + 2\lambda_{T_d} \mathbf{R}_d \cdot \mathbf{TH}_d. \quad (19)$$

Here we define the triplet as

$$\mathbf{T} \equiv \frac{1}{2} \mathbf{T}^a \sigma^a = \frac{1}{2} \begin{pmatrix} \mathbf{T}_0 & \sqrt{2}\mathbf{T}_+ \\ \sqrt{2}\mathbf{T}_- & -\mathbf{T}_0 \end{pmatrix}. \quad (20)$$

Notably the model has an $N = 2$ supersymmetry if

$$\lambda_{S_u} = g_Y / \sqrt{2}, \quad \lambda_{S_d} = -g_Y / \sqrt{2}, \quad \lambda_{T_u} = g_2 / \sqrt{2}, \quad \lambda_{T_d} = g_2 / \sqrt{2}. \quad (21)$$
<table><caption>Table 4: Chiral and gauge supermultiplets in the MRSSM, in addition to the quarks and leptons.</caption><thead><tr><th>Names</th><th>Spin 0, R = 0</th><th>Spin 1/2, R = -1</th><th></th><th>SU(3), SU(2), U(1)<sub>Y</sub></th></tr></thead><tbody><tr><td rowspan="2">Higgs</td><td>H<sub>u</sub></td><td>(H<sup>+</sup><sub>u</sub>, H<sup>0</sup><sub>u</sub>)</td><td>(H̃<sup>+</sup><sub>u</sub>, H̃<sup>0</sup><sub>u</sub>)</td><td>(1, 2, 1/2)</td></tr><tr><td>H<sub>d</sub></td><td>(H<sup>0</sup><sub>d</sub>, H̃<sup>-</sup><sub>d</sub>)</td><td>(H̃<sup>0</sup><sub>d</sub>, H̃<sup>-</sup><sub>d</sub>)</td><td>(1, 2, -1/2)</td></tr><tr><td>DG-octet</td><td>O</td><td>O</td><td>χ<sub>O</sub></td><td>(8, 1, 0)</td></tr><tr><td>DG-triplet</td><td>T</td><td>{T<sup>0</sup>, T<sup>±</sup>}</td><td>{χ<sup>±</sup><sub>T</sub>, χ<sup>0</sup><sub>T</sub>}</td><td>(1, 3, 0)</td></tr><tr><td>DG-singlet</td><td>S</td><td>S</td><td>χ<sub>S</sub></td><td>(1, 1, 0)</td></tr></tbody></table><table><thead><tr><th>Names</th><th>Spin 0, R = 2</th><th>Spin 1/2, R = 1</th><th>Spin 1, R = 0</th><th>SU(3), SU(2), U(1)<sub>Y</sub></th></tr></thead><tbody><tr><td>Gluons</td><td>W<sub>3α</sub></td><td>g̃<sub>α</sub></td><td>g</td><td>(8, 1, 0)</td></tr><tr><td>W</td><td>W<sub>2α</sub></td><td>W̃<sup>±</sup>, W̃<sup>0</sup></td><td>W<sup>±</sup>, W<sup>0</sup></td><td>(1, 3, 0)</td></tr><tr><td>B</td><td>W<sub>1α</sub></td><td>B̃</td><td>B</td><td>(1, 1, 0)</td></tr><tr><td rowspan="2">R-Higgs</td><td>R<sub>d</sub></td><td>(R<sup>+</sup><sub>d</sub>, R<sup>0</sup><sub>d</sub>)</td><td>(R̃<sup>+</sup><sub>d</sub>, R̃<sup>0</sup><sub>d</sub>)</td><td>(1, 2, 1/2)</td></tr><tr><td>R<sub>u</sub></td><td>(R<sup>0</sup><sub>u</sub>, R̃<sup>-</sup><sub>u</sub>)</td><td>(R̃<sup>0</sup><sub>u</sub>, R̃<sup>-</sup><sub>u</sub>)</td><td>(1, 2, -1/2)</td></tr></tbody></table>

The above definitions are common to e.g. [38, 59, 75] and can be translated to the notation of [50] via

$$ \lambda_{S_u} \equiv \lambda_u, \quad \lambda_{S_d} \equiv \lambda_d, \quad \lambda_{T_u} \equiv \frac{1}{\sqrt{2}} \Lambda_u, \quad \lambda_{T_d} \equiv \frac{1}{\sqrt{2}} \Lambda_d. \qquad (22) $$

The Higgs fields as well as the triplet and singlet scalars have R-charges 0, so their fermionic partners all have R-charge -1. The $R_{u,d}$ fields have R-charges 2, so the R-higgsinos have R-charge 1. Together with the “conventional” bino and wino fields, which also have R-charge 1, this gives 2 × four Dirac spinors with opposite R-charges. After EWSB, the EW gauginos and (R-)higgsinos thus form four Dirac neutralinos with mass-matrix

$$ \mathcal{L}_{\text{MRSSM}} \supset -(\tilde{B}, \tilde{W}^0, \tilde{R}_d^0, \tilde{R}_u^0) \begin{pmatrix} m_{DY} & 0 & -\frac{1}{2}g_Y v_d & \frac{1}{2}g_Y v_u \\ 0 & m_{D2} & \frac{1}{2}g_2 v_d & -\frac{1}{2}g_2 v_u \\ -\frac{1}{2}\lambda_{S_d} v_d & -\frac{1}{2}\lambda_{T_d} v_d & -\mu_d^{\text{eff,+}} & 0 \\ \frac{1}{2}\lambda_{S_u} v_u & -\frac{1}{2}\lambda_{T_u} v_u & 0 & \mu_u^{\text{eff,-}} \end{pmatrix} \begin{pmatrix} \chi_S^0 \\ \chi_T^0 \\ \tilde{H}_d^0 \\ \tilde{H}_u^0 \end{pmatrix}, \quad (23) $$

where

$$ \mu_{u,d}^{\text{eff,±}} \equiv \mu_{u,d} + \frac{1}{\sqrt{2}} \lambda_{S_{u,d}} v_S \pm \frac{1}{\sqrt{2}} \lambda_{T_{u,d}} v_T. \qquad (24) $$

The above mass matrix looks very similar to that of the MSSM in the case of $N = 2$ supersymmetry!

On the other hand, for the charginos, although there are eight Weyl spinors, these organise into four Dirac spinors, and again into two pairs with opposite R-charges. So we have

$$ \mathcal{L}_{\text{MRSSM}} \supset -(\chi_T^-, \tilde{H}_d^-) \begin{pmatrix} g_2 v_T + m_{D2} & \lambda_{T_d} v_d \\ \frac{1}{\sqrt{2}} g_2 v_d & \mu_d^{\text{eff},-} \end{pmatrix} \begin{pmatrix} \tilde{W}^+ \\ \tilde{R}_d^+ \end{pmatrix} \\ -(\tilde{W}^-, \tilde{R}_u^-) \begin{pmatrix} -g_2 v_T + m_{D2} & \frac{1}{\sqrt{2}} g_2 v_u \\ -\lambda_{T_u} v_u & -\mu_u^{\text{eff,+}} \end{pmatrix} \begin{pmatrix} \chi_T^+ \\ \tilde{H}_u^+ \end{pmatrix} + \text{h.c.} \qquad (25) $$

The MRSSM therefore does not entail naturally small splittings between EW-ino states. However, if the R-symmetry is broken by a small parameter, then this situation is reversed: small mass splittings would appear between each of the Dirac states.
<table><caption>Table 4: Chiral and gauge supermultiplets in the MRSSM, in addition to the quarks and leptons.</caption><thead><tr><th>Names</th><th>Spin 0, R = 0</th><th>Spin 1/2, R = -1</th><th></th><th>SU(3), SU(2), U(1)<sub>Y</sub></th></tr></thead><tbody><tr><td rowspan="2">Higgs</td><td>H<sub>u</sub></td><td>(H<sup>+</sup><sub>u</sub>, H<sup>0</sup><sub>u</sub>)</td><td>(H̃<sup>+</sup><sub>u</sub>, H̃<sup>0</sup><sub>u</sub>)</td><td>(1, 2, 1/2)</td></tr><tr><td>H<sub>d</sub></td><td>(H<sup>0</sup><sub>d</sub>, H̃<sup>-</sup><sub>d</sub>)</td><td>(H̃<sup>0</sup><sub>d</sub>, H̃<sup>-</sup><sub>d</sub>)</td><td>(1, 2, -1/2)</td></tr><tr><td>DG-octet</td><td>O</td><td>O</td><td>χ<sub>O</sub></td><td>(8, 1, 0)</td></tr><tr><td>DG-triplet</td><td>T</td><td>{T<sup>0</sup>, T<sup>±</sup>}</td><td>{χ<sup>±</sup><sub>T</sub>, χ<sup>0</sup><sub>T</sub>}</td><td>(1, 3, 0)</td></tr><tr><td>DG-singlet</td><td>S</td><td>S</td><td>χ<sub>S</sub></td><td>(1, 1, 0)</td></tr></tbody></table><table><thead><tr><th>Names</th><th>Spin 0, R = 2</th><th>Spin 1/2, R = 1</th><th>Spin 1, R = 0</th><th>SU(3), SU(2), U(1)<sub>Y</sub></th></tr></thead><tbody><tr><td>Gluons</td><td>W<sub>3α</sub></td><td>g̃<sub>α</sub></td><td>g</td><td>(8, 1, 0)</td></tr><tr><td>W</td><td>W<sub>2α</sub></td><td>W̃<sup>±</sup>, W̃<sup>0</sup></td><td>W<sup>±</sup>, W<sup>0</sup></td><td>(1, 3, 0)</td></tr><tr><td>B</td><td>W<sub>1α</sub></td><td>B̃</td><td>B</td><td>(1, 1, 0)</td></tr><tr><td rowspan="2">R-Higgs</td><td>R<sub>d</sub></td><td>(R<sup>+</sup><sub>d</sub>, R<sup>0</sup><sub>d</sub>)</td><td>(R̃<sup>+</sup><sub>d</sub>, R̃<sup>0</sup><sub>d</sub>)</td><td>(1, 2, 1/2)</td></tr><tr><td>R<sub>u</sub></td><td>(R<sup>0</sup><sub>u</sub>, R̃<sup>-</sup><sub>u</sub>)</td><td>(R̃<sup>0</sup><sub>u</sub>, R̃<sup>-</sup><sub>u</sub>)</td><td>(1, 2, -1/2)</td></tr></tbody></table>

The above definitions are common to e.g. [38, 59, 75] and can be translated to the notation of [50] via

$$ \lambda_{S_u} \equiv \lambda_u, \quad \lambda_{S_d} \equiv \lambda_d, \quad \lambda_{T_u} \equiv \frac{1}{\sqrt{2}} \Lambda_u, \quad \lambda_{T_d} \equiv \frac{1}{\sqrt{2}} \Lambda_d. \qquad (22) $$

The Higgs fields as well as the triplet and singlet scalars have R-charges 0, so their fermionic partners all have R-charge -1. The $R_{u,d}$ fields have R-charges 2, so the R-higgsinos have R-charge 1. Together with the “conventional” bino and wino fields, which also have R-charge 1, this gives 2 × four Dirac spinors with opposite R-charges. After EWSB, the EW gauginos and (R-)higgsinos thus form four Dirac neutralinos with mass-matrix

$$ \mathcal{L}_{\text{MRSSM}} \supset -(\tilde{B}, \tilde{W}^0, \tilde{R}_d^0, \tilde{R}_u^0) \begin{pmatrix} m_{DY} & 0 & -\frac{1}{2}g_Y v_d & \frac{1}{2}g_Y v_u \\ 0 & m_{D2} & \frac{1}{2}g_2 v_d & -\frac{1}{2}g_2 v_u \\ -\frac{1}{2}\lambda_{S_d} v_d & -\frac{1}{2}\lambda_{T_d} v_d & -\mu_d^{\text{eff,+}} & 0 \\ \frac{1}{2}\lambda_{S_u} v_u & -\frac{1}{2}\lambda_{T_u} v_u & 0 & \mu_u^{\text{eff,-}} \end{pmatrix} \begin{pmatrix} \chi_S^0 \\ \chi_T^0 \\ \tilde{H}_d^0 \\ \tilde{H}_u^0 \end{pmatrix}, \quad (23) $$

where

$$ \mu_{u,d}^{\text{eff},\pm} \equiv \mu_{u,d} + \frac{1}{\sqrt{2}} \lambda_{S_{u,d}} v_S \pm \frac{1}{\sqrt{2}} \lambda_{T_{u,d}} v_T. \qquad (24) $$

The above mass matrix looks very similar to that of the MSSM in the case of $N = 2$ supersymmetry!

On the other hand, for the charginos, although there are eight Weyl spinors, these organise into four Dirac spinors, and again into two pairs with opposite R-charges. So we have

$$ \mathcal{L}_{\text{MRSSM}} \supset -(\chi_T^-, \tilde{H}_d^-) \begin{pmatrix} g_2 v_T + m_{D2} & \lambda_{T_d} v_d \\ \frac{1}{\sqrt{2}} g_2 v_d & \mu_d^{\text{eff},-} \end{pmatrix} \begin{pmatrix} \tilde{W}^+ \\ \tilde{R}_d^+ \end{pmatrix} \\ -(\tilde{W}^-, \tilde{R}_u^-) \begin{pmatrix} -g_2 v_T + m_{D2} & \frac{1}{\sqrt{2}} g_2 v_u \\ -\lambda_{T_u} v_u & -\mu_u^{\text{eff,+}} \end{pmatrix} \begin{pmatrix} \chi_T^+ \\ \tilde{H}_u^+ \end{pmatrix} + \text{h.c.} \qquad (25) $$

The MRSSM therefore does not entail naturally small splittings between EW-ino states. However, if the R-symmetry is broken by a small parameter, then this situation is reversed: small mass splittings would appear between each of the Dirac states.
## A.2 MCMC scan: steps of the implementation

The algorithm starts from a random uniformly drawn point, computes $-\log(L)$ denoted as $-\log(L)_{old}$, then a new point is drawn from a Gaussian distribution around the previous point, from which $-\log(L)$, denoted as $-\log(L)_{new}$, is computed. If $pp \times \log(L)_{new} \le \log(L)_{old}$, where $pp$ is a random number between 0 and 1, the old point is replaced by the new one and $-\log(L)_{old}=-\log(L)_{new}$. The next points will be drawn from a Gaussian distribution around the point that corresponds to $-\log(L)_{old}$. The steps of the implementation are the following:

1. Draw a starting point from a random uniform distribution.

2. If point lies within allowed scan range, eq. (6), compute spectrum with SPheno. If the computation fails, go back to step 1 (or 9).

3. Check if $120 < m_h < 130$ GeV. If not, go back to step 1 (or 9).

4. Call micrOMEGAs, check if the point is excluded by LEP mass limits or invisible Z decays, or if the LSP is charged. If yes to any, go back to step 1 (or 9).

5. Compute the relic density and $p_{X1T}$ with micrOMEGAs.

6. If relic density below $\Omega h^2_{Planck} + 10\% = 0.132$, save point.

7. Compute $\chi^2_{\Omega h^2}$ for relic density.

8. Compute $-\log(L)_{old} = \chi^2_{\Omega h^2} - \log(p_{X1T}) + \log(m_{LSP})$.

9. Draw a new point from a Gaussian distribution around the old one.

10. Repeat steps 2 to 7.

11. Compute $-\log(L)_{new}$.

12. Run the Metropolis-Hastings algorithm:

pp(random(uniform(0,1.))

If $pp \times \log(L)_{new} \le \log(L)_{old}$:

$\log(L)_{old} = \log(L)_{new}$

13. Iteration++. While iteration<n<iterations: repeat steps 9 to 13.

This algorithm was run several times, starting from a different random point each time, to explore the whole parameter space defined by eq. (6).

## A.3 Higgs mass classifier

A common drawback for the efficiency of phenomenological parameter scans, is finding the subset of the parameter space where the Higgs mass $m_h$ is around the experimentally measured value. Our case is not the exception, as $m_h$ depends on all the input variables considered in our study. This is clear for $\mu$, the mass term in the scalar potential, and $\tan\beta$, the ratio between the vevs. For the soft terms, the dependence becomes apparent when one realises that in DG models, the Higgs quartic coupling receives corrections of the form

$$ \delta\lambda \sim \mathcal{O}\left(\frac{g_Y m_{DY}}{m_{SR}}\right)^2 + \mathcal{O}\left(\frac{\sqrt{2}\lambda_S m_{DY}}{m_{SR}}\right)^2 + \mathcal{O}\left(\frac{g_2 m_{D2}}{m_{TP}}\right)^2 + \mathcal{O}\left(\frac{\sqrt{2}\lambda_T m_{D2}}{m_{TP}}\right)^2, \quad (26) $$
## A.2 MCMC scan: steps of the implementation

The algorithm starts from a random uniformly drawn point, computes $-\log(L)$ denoted as $-\log(L)_{old}$, then a new point is drawn from a Gaussian distribution around the previous point, from which $-\log(L)$, denoted as $-\log(L)_{new}$, is computed. If $pp \times \log(L)_{new} \le \log(L)_{old}$, where $pp$ is a random number between 0 and 1, the old point is replaced by the new one and $-\log(L)_{old}=-\log(L)_{new}$. The next points will be drawn from a Gaussian distribution around the point that corresponds to $-\log(L)_{old}$. The steps of the implementation are the following:

1. Draw a starting point from a random uniform distribution.

2. If point lies within allowed scan range, eq. (6), compute spectrum with SPheno. If the computation fails, go back to step 1 (or 9).

3. Check if $120 < m_h < 130$ GeV. If not, go back to step 1 (or 9).

4. Call micrOMEGAs, check if the point is excluded by LEP mass limits or invisible Z decays, or if the LSP is charged. If yes to any, go back to step 1 (or 9).

5. Compute the relic density and $p_{X1T}$ with micrOMEGAs.

6. If relic density below $\Omega h^2_{Planck} + 10\% = 0.132$, save point.

7. Compute $\chi^2_{\Omega h^2}$ for relic density.

8. Compute $-\log(L)_{old} = \chi^2_{\Omega h^2} - \log(p_{X1T}) + \log(m_{LSP})$.

9. Draw a new point from a Gaussian distribution around the old one.

10. Repeat steps 2 to 7.

11. Compute $-\log(L)_{new}$.

12. Run the Metropolis-Hastings algorithm:

pp(random(uniform(0,1.))

If $pp \times \log(L)_{new} \le \log(L)_{old}$:

$\log(L)_{old} = \log(L)_{new}$

13. Iteration++. While $\text{iteration} < n_{\text{iterations}}$: repeat steps 9 to 13.

This algorithm was run several times, starting from a different random point each time, to explore the whole parameter space defined by eq. (6).

## A.3 Higgs mass classifier

A common drawback for the efficiency of phenomenological parameter scans, is finding the subset of the parameter space where the Higgs mass $m_h$ is around the experimentally measured value. Our case is not the exception, as $m_h$ depends on all the input variables considered in our study. This is clear for $\mu$, the mass term in the scalar potential, and $\tan\beta$, the ratio between the vevs. For the soft terms, the dependence becomes apparent when one realises that in DG models, the Higgs quartic coupling receives corrections of the form

$$ \delta\lambda \sim \mathcal{O}\left(\frac{g_Y m_{DY}}{m_{SR}}\right)^2 + \mathcal{O}\left(\frac{\sqrt{2}\lambda_S m_{DY}}{m_{SR}}\right)^2 + \mathcal{O}\left(\frac{g_2 m_{D2}}{m_{TP}}\right)^2 + \mathcal{O}\left(\frac{\sqrt{2}\lambda_T m_{D2}}{m_{TP}}\right)^2, \quad (26) $$
<table><caption>Table 5: Number of events expected in each signal region in [107] (columns labelled “ATLAS”) against result from recasting in MadAnalysis 5 (columns labelled “MA”) for different parameter points. The quoted error bands are Monte Carlo uncertainties, but the cross-section uncertainties can also reach 10% for some regions.</caption><thead><tr><th rowspan="2">m(χ̃<sub>1</sub><sup>±</sup>, χ̃<sub>1</sub><sup>0</sup>)[GeV]</th><th rowspan="2">Region</th><th colspan="2">m<sub>CT</sub> ∈ [180, 230]</th><th colspan="2">m<sub>CT</sub> ∈ [230, 280]</th><th colspan="2">m<sub>CT</sub> > 230</th></tr><tr><th>ATLAS</th><th>MA</th><th>ATLAS</th><th>MA</th><th>ATLAS</th><th>MA</th></tr></thead><tbody><tr><td>(300, 75)</td><td>LM</td><td>6</td><td>7.1 ±2.2</td><td>11</td><td>8.5 ±2.5</td><td>11</td><td>12.8 ±3.0</td></tr><tr><td>(500, 0)</td><td>MM</td><td>2.5</td><td>1.6 ±0.4</td><td>3.5</td><td>2.6 ±0.5</td><td>5.5</td><td>4.8 ±0.7</td></tr><tr><td>(750, 100)</td><td>HM</td><td>2</td><td>2.0 ±0.2</td><td>2.5</td><td>2.7 ±0.2</td><td>6</td><td>5.4 ±0.3</td></tr></tbody></table>

of a chargino and a heavy neutralino, where the neutralino decays by emitting an on-shell Higgs, and the chargino decays by emitting a W-boson, i.e. $WH + E_T^{\text{miss}}$. The Higgs is identified by looking for two b-jets with an invariant mass in the window [100, 140] GeV, while the W-boson is identified through leptonic decays by requiring one signal lepton. Cuts also require $E_T^{\text{miss}} > 240$ GeV and minimum values of the transverse mass (defined from the lepton transverse momentum and missing transverse momentum). The signal regions are divided into “Low Mass” (LM), “Medium Mass” (MM) and “High Mass” (HM), with four regions for each defined according to the values of the transverse mass and binned according to the con- transverse mass of the two b-jets

$$m_{\text{CT}} \equiv \sqrt{2p_T^{b_1} p_T^{b_2} (1 + \cos \Delta\phi_{bb})},$$

where there are three bins for exclusion limits ($m_{CT} \in [180, 230]$, $m_{CT} \in [230, 280]$, $m_{CT} > 230$) and a “discovery” (disc.) region defined for each $m_T$ region (effectively the sum of the three $m_{CT}$ bins), making twelve signal regions in all.

This search should be particularly effective when other supersymmetric particles (such as sleptons and additional Higgs fields) are heavy. Given constraints on heavy Higgs sectors and colourful particles, it is rather model independent and difficult to evade in a minimal model. The ATLAS collaboration made available substantial additional data via HEPData at [136], in particular including detailed cutflows and tables for the exclusion curves, which are essential for validating our recast code.

The implementation in MadAnalysis 5 follows the cuts of [107] and implements the lepton isolation and a jet/lepton removal procedure as described in that paper directly in the analysis. Jet reconstruction is performed using fastjet [138] in Delphes 3 [122], where b-tagging and lepton/jet reconstruction efficiencies are taken from a standard ATLAS Delphes 3 card used in other recasting analyses [139–142]. The analysis was validated by comparing signals generated for the same MSSM simplified scenario as in [107]: this consists of a degenerate wino-like chargino and heavy neutralino, together with a light bino-like neutralino. The analysis requires two or three signal jets, two of which must be b-jets (to target the Higgs decay); the signal is simulated by a hard process of

$$p, p \rightarrow \tilde{\chi}_1^+, \tilde{\chi}_2^0 + n \text{ jets}, \quad n \le 2.$$

In the validation, up to 2 hard jets are simulated at leading order in MadGraph5_aMC@NLO, the parton shower is performed in Pythia 8.2, and the jet merging is performed by the MLM algorithm using MadGraph5_aMC@NLO defaults. In addition, to select only leptonic decays of the W-boson, and b-quark decays of the Higgs, the branching ratios are modified in the SLHA file (with care that Pythia does not override them with the SM values) and the signal cross-sections weighted accordingly: this improves the efficiency of the simulation by a factor
<table><caption>Table 5: Number of events expected in each signal region in [107] (columns labelled “ATLAS”) against result from recasting in MadAnalysis 5 (columns labelled “MA”) for different parameter points. The quoted error bands are Monte Carlo uncertainties, but the cross-section uncertainties can also reach 10% for some regions.</caption><thead><tr><th rowspan="2">m(χ̃<sub>1</sub><sup>±</sup>, χ̃<sub>1</sub><sup>0</sup>)[GeV]</th><th rowspan="2">Region</th><th colspan="2">m<sub>CT</sub> ∈ [180, 230]</th><th colspan="2">m<sub>CT</sub> ∈ [230, 280]</th><th colspan="2">m<sub>CT</sub> > 230</th></tr><tr><th>ATLAS</th><th>MA</th><th>ATLAS</th><th>MA</th><th>ATLAS</th><th>MA</th></tr></thead><tbody><tr><td>(300, 75)</td><td>LM</td><td>6</td><td>7.1 ±2.2</td><td>11</td><td>8.5 ±2.5</td><td>11</td><td>12.8 ±3.0</td></tr><tr><td>(500, 0)</td><td>MM</td><td>2.5</td><td>1.6 ±0.4</td><td>3.5</td><td>2.6 ±0.5</td><td>5.5</td><td>4.8 ±0.7</td></tr><tr><td>(750, 100)</td><td>HM</td><td>2</td><td>2.0 ±0.2</td><td>2.5</td><td>2.7 ±0.2</td><td>6</td><td>5.4 ±0.3</td></tr></tbody></table>

of a chargino and a heavy neutralino, where the neutralino decays by emitting an on-shell Higgs, and the chargino decays by emitting a W-boson, i.e. $WH + E_T^{\text{miss}}$. The Higgs is identified by looking for two b-jets with an invariant mass in the window [100, 140] GeV, while the W-boson is identified through leptonic decays by requiring one signal lepton. Cuts also require $E_T^{\text{miss}} > 240$ GeV, and minimum values of the transverse mass (defined from the lepton transverse momentum and missing transverse momentum). The signal regions are divided into “Low Mass” (LM), “Medium Mass” (MM) and “High Mass” (HM), with four regions for each defined according to the values of the transverse mass and binned according to the con- transverse mass of the two b-jets

$$m_{\text{CT}} \equiv \sqrt{2p_T^{b_1} p_T^{b_2} (1 + \cos \Delta\phi_{bb})},$$

where there are three bins for exclusion limits ($m_{CT} \in [180, 230]$, $m_{CT} \in [230, 280]$, $m_{CT} > 230$) and a “discovery” (disc.) region defined for each $m_T$ region (effectively the sum of the three $m_{CT}$ bins), making twelve signal regions in all.

This search should be particularly effective when other supersymmetric particles (such as sleptons and additional Higgs fields) are heavy. Given constraints on heavy Higgs sectors and colourful particles, it is rather model independent and difficult to evade in a minimal model. The ATLAS collaboration made available substantial additional data via HEPData at [136], in particular including detailed cutflows and tables for the exclusion curves, which are essential for validating our recast code.

The implementation in MadAnalysis 5 follows the cuts of [107] and implements the lepton isolation and a jet/lepton removal procedure as described in that paper directly in the analysis. Jet reconstruction is performed using fastjet [138] in Delphes 3 [122], where b-tagging and lepton/jet reconstruction efficiencies are taken from a standard ATLAS Delphes 3 card used in other recasting analyses [139–142]. The analysis was validated by comparing signals generated for the same MSSM simplified scenario as in [107]: this consists of a degenerate wino-like chargino and heavy neutralino, together with a light bino-like neutralino. The analysis requires two or three signal jets, two of which must be b-jets (to target the Higgs decay); the signal is simulated by a hard process of

$$p, p \rightarrow \tilde{\chi}_1^+, \tilde{\chi}_2^0 + n \text{ jets}, \quad n \le 2.$$

In the validation, up to 2 hard jets are simulated at leading order in MadGraph5_aMC@NLO, the parton shower is performed in Pythia 8.2, and the jet merging is performed by the MLM algorithm using MadGraph5_aMC@NLO defaults. In addition, to select only leptonic decays of the W-boson, and b-quark decays of the Higgs, the branching ratios are modified in the SLHA file (with care that Pythia does not override them with the SM values) and the signal cross-sections weighted accordingly: this improves the efficiency of the simulation by a factor
981 of roughly 8, since the leptonic branching ratio of the W is 0.2157 and the Higgs decays into b-quarks 58.3% of the time.

982 A detailed validation note will be presented elsewhere, including detailed cutflow analysis and a reproduction of the exclusion region with that found in [107]. Here we reproduce the expected (according to the calculated cross-section and experimental integrated luminosity) final number of events passing the cuts for the “exclusive” signal regions, for the three benchmark points where cutflows are available in table 5, where an excellent agreement can be seen. For each point, 30k events were simulated, leading to small but non-negligible Monte-Carlo uncertainties listed in the table.

990 Application to the MDGSSM

To apply this analysis to our model, firstly we treat both the lightest two neutralino states as LSP states; we must also simulate the production of all heavy neutralinos ($\tilde{\chi}_i^0$, $i > 2$) and charginos in pairs. It is no longer reasonable to select only leptonic decays of the W, because we can have several processes contributing to the signal. Indeed, in our case, we can have both

$$ \tilde{\chi}_2^+ \rightarrow \tilde{\chi}_{1,2}^0 + W, \tilde{\chi}_3^0 \rightarrow \tilde{\chi}_{1,2}^0 + H^0 $$

991 and

$$ \tilde{\chi}_3^0 \rightarrow \tilde{\chi}_1^- + W, \tilde{\chi}_2^+ \rightarrow \tilde{\chi}_1^+ + H^0, $$

for example. Therefore we do not modify the decays of the electroweakinos in the SLHA files, and simulate

$$ p, p \rightarrow \tilde{\chi}_{i \ge 1}^{\pm}, \tilde{\chi}_{j \ge 3}^{0} + njets, \quad n \le 2 $$

992 as the hard process in MadGraph5_aMC@NLO, before showering with Pythia 8.2 and passing to the analysis as before.

993 We have not produced an exclusion contour plot for this analysis comparable to the MSSM case in [107], because a heavy wino with a light bino always leads to an excess of dark matter unless the bino is near a resonance. We should generally expect the reach of the exclusion to be better than for the MSSM, due to the increase in cross section from pseudo-Dirac states; since we can only compare our results directly for points on the Higgs-funnel, for $m_{\tilde{\chi}_1} \approx m_h/2$, we find a limit on the heavy wino mass of about 800 GeV in our model, compared to 740 GeV in the MSSM.

1000

1001 References

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1003 [2] J. Ellis, J. S. Hagelin, D. V. Nanopoulos, K. Olive and M. Srednicki, *Supersymmetric relics from the big bang*, Nucl. Phys. B **238**, 453 (1984), doi:10.1016/0550-3213(84)90461-9.

1004 [3] G. Jungman, M. Kamionkowski and K. Griest, *Supersymmetric dark matter*, Phys. Rep. **267**, 195 (1996), doi:10.1016/0370-1573(95)00058-5, arXiv:hep-ph/9506380.

1005 [4] N. Arkani-Hamed, A. Delgado and G. F. Giudice, *The well-tempered neutralino*, Nucl. Phys. B **741**, 108 (2006), doi:10.1016/j.nuclphysb.2006.02.010, arXiv:hep-ph/0601041.

1010
981 of roughly 8, since the leptonic branching ratio of the W is 0.2157 and the Higgs decays into b-quarks 58.3% of the time.

982 A detailed validation note will be presented elsewhere, including detailed cutflow analysis and a reproduction of the exclusion region with that found in [107]. Here we reproduce the expected (according to the calculated cross-section and experimental integrated luminosity) final number of events passing the cuts for the “exclusive” signal regions, for the three benchmark points where cutflows are available in table 5, where an excellent agreement can be seen. For each point, 30k events were simulated, leading to small but non-negligible Monte-Carlo uncertainties listed in the table.

990 Application to the MDGSSM

To apply this analysis to our model, firstly we treat both the lightest two neutralino states as LSP states; we must also simulate the production of all heavy neutralinos ($\tilde{\chi}_i^0$, $i > 2$) and charginos in pairs. It is no longer reasonable to select only leptonic decays of the W, because we can have several processes contributing to the signal. Indeed, in our case, we can have both

$$991 \quad \tilde{\chi}_2^+ \rightarrow \tilde{\chi}_{1,2}^0 + W, \tilde{\chi}_3^0 \rightarrow \tilde{\chi}_{1,2}^0 + H^0 \quad \text{and}$$

$$\tilde{\chi}_3^0 \rightarrow \tilde{\chi}_1^- + W, \tilde{\chi}_2^+ \rightarrow \tilde{\chi}_1^+ + H^0,$$

for example. Therefore we do not modify the decays of the electroweakinos in the SLHA files, and simulate

$$992 \quad p, p \rightarrow \tilde{\chi}_{i \ge 1}^{\pm}, \tilde{\chi}_{j \ge 3}^{0} + njets, \quad n \le 2 \quad \text{as the hard process in MadGraph5_aMC@NLO, before showering with Pythia 8.2 and passing}$$

993 to the analysis as before.

994 We have not produced an exclusion contour plot for this analysis comparable to the MSSM case in [107], because a heavy wino with a light bino always leads to an excess of dark matter unless the bino is near a resonance. We should generally expect the reach of the exclusion to be better than for the MSSM, due to the increase in cross section from pseudo-Dirac states; since we can only compare our results directly for points on the Higgs-funnel, for $m_{\tilde{\chi}_1} \approx m_h/2$, we find a limit on the heavy wino mass of about 800 GeV in our model, compared to 740 GeV in the MSSM.

1000

1001 References

1002 [1] H. Goldberg, *Constraint on the photino mass from cosmology*, Phys. Rev. Lett. **50**, 1419 (1983), doi:10.1103/PhysRevLett.50.1419, [Erratum: Phys. Rev. Lett. **103**, 099905 (2009), doi:10.1103/PhysRevLett.103.099905].

1003 [2] J. Ellis, J. S. Hagelin, D. V. Nanopoulos, K. Olive and M. Srednicki, *Supersymmetric relics from the big bang*, Nucl. Phys. B **238**, 453 (1984), doi:10.1016/0550-3213(84)90461-9.

1004 [3] G. Jungman, M. Kamionkowski and K. Griest, *Supersymmetric dark matter*, Phys. Rep. **267**, 195 (1996), doi:10.1016/0370-1573(95)00058-5, arXiv:hep-ph/9506380.

1005 [4] N. Arkani-Hamed, A. Delgado and G. F. Giudice, *The well-tempered neutralino*, Nucl. Phys. B **741**, 108 (2006), doi:10.1016/j.nuclphysb.2006.02.010, arXiv:hep-ph/0601041.

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[5] C. Cheung, L. J. Hall, D. Pinner and J. T. Ruderman, Prospects and blind spots for neutralino dark matter, J. High Energ. Phys. 05, 100 (2013), doi:10.1007/JHEP05(2013)100, arXiv:1211.4873.

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[7] A. Birkedal-Hansen and B. D. Nelson, Relic neutralino densities and detection rates with nonuniversal gaugino masses, Phys. Rev. D 67, 095006 (2003), doi:10.1103/PhysRevD.67.095006, arXiv:hep-ph/0211071.

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[8] H. Baer, A. Mustafayev, E.-K. Park and S. Profumo, Mixed Wino Dark Matter: consequences for direct, indirect and collider detection, J. High Energ. Phys. 07, 046 (2005), doi:10.1088/1126-6708/2005/07/046, arXiv:hep-ph/0505227.

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[9] H. Baer, T. Krupovnickas, A. Mustafayev, E.-K. Park, S. Profumo and X. Tata, Exploring the BWCA (Bino-Wino co-annihilation) scenario for neutralino dark matter, J. High Energ. Phys. 12, 011 (2005), doi:10.1088/1126-6708/2005/12/011, arXiv:hep-ph/0511034.

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[10] N. Nagata, H. Otono and S. Shirai, Probing Bino-Wino coannihilation at the LHC, J. High Energ. Phys. 10, 086 (2015), doi:10.1007/JHEP10(2015)086, arXiv:1506.08206.

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[11] J. Bramante, N. Desai, P. Fox, A. Martin, B. Ostdiek and T. Plehn, Towards the final word on neutralino dark matter, Phys. Rev. D 93, 063525 (2016), doi:10.1103/PhysRevD.93.063525, arXiv:1510.03460.

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[12] G. Hua Duan, K.-i. Hikasa, J. Ren, L. Wu and J. M. Yang, Probing bino-wino coannihilation dark matter below the neutrino floor at the LHC, Phys. Rev. D 98, 015010 (2018), doi:10.1103/PhysRevD.98.015010, arXiv:1804.05238.

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[16] P. J. Fox, A. E. Nelson and N. Weiner, Dirac gaugino masses and supersoft supersymmetry breaking, J. High Energ. Phys. 08, 035 (2002), doi:10.1088/1126-6708/2002/08/035, arXiv:hep-ph/0206096.

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[17] A. E. Nelson, N. Rius, V. Sanz and M. Unsal, The minimal supersymmetric model without a $\mu$ term, J. High Energ. Phys. 08, 039 (2002), doi:10.1088/1126-6708/2002/08/039, arXiv:hep-ph/0206102.

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[18] I. Antoniadis, K. Benakli, A. Delgado and M. Quiros, A new gauge mediation theory (2006), arXiv:hep-ph/0610265.

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[19] G. D. Kribs, E. Poppitz and N. Weiner, Flavor in supersymmetry with an extended $R$ symmetry, Phys. Rev. D 78, 055010 (2008), doi:10.1103/PhysRevD.78.055010, arXiv:0712.2039.
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[5] C. Cheung, L. J. Hall, D. Pinner and J. T. Ruderman, Prospects and blind spots for neutralino dark matter, J. High Energ. Phys. 05, 100 (2013), doi:10.1007/JHEP05(2013)100, arXiv:1211.4873.

1014
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[6] A. Birkedal-Hansen and B. D. Nelson, Role of W-ino content in neutralino dark matter, Phys. Rev. D 64, 015008 (2001), doi:10.1103/PhysRevD.64.015008, arXiv:hep-ph/0102075.

1017
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[7] A. Birkedal-Hansen and B. D. Nelson, Relic neutralino densities and detection rates with nonuniversal gaugino masses, Phys. Rev. D 67, 095006 (2003), doi:10.1103/PhysRevD.67.095006, arXiv:hep-ph/0211071.

1020
1021
1022

[8] H. Baer, A. Mustafayev, E.-K. Park and S. Profumo, Mixed Wino Dark Matter: consequences for direct, indirect and collider detection, J. High Energ. Phys. 07, 046 (2005), doi:10.1088/1126-6708/2005/07/046, arXiv:hep-ph/0505227.

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[9] H. Baer, T. Krupovnickas, A. Mustafayev, E.-K. Park, S. Profumo and X. Tata, Exploring the BWCA (Bino-Wino co-annihilation) scenario for neutralino dark matter, J. High Energ. Phys. 12, 011 (2005), doi:10.1088/1126-6708/2005/12/011, arXiv:hep-ph/0511034.

1026
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[10] N. Nagata, H. Otono and S. Shirai, Probing Bino-Wino coannihilation at the LHC, J. High Energ. Phys. 10, 086 (2015), doi:10.1007/JHEP10(2015)086, arXiv:1506.08206.

1028
1029
1030

[11] J. Bramante, N. Desai, P. Fox, A. Martin, B. Ostdiek and T. Plehn, Towards the final word on neutralino dark matter, Phys. Rev. D 93, 063525 (2016), doi:10.1103/PhysRevD.93.063525, arXiv:1510.03460.

1031
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[12] G. Hua Duan, K.-i. Hikasa, J. Ren, L. Wu and J. M. Yang, Probing bino-wino coannihilation dark matter below the neutrino floor at the LHC, Phys. Rev. D 98, 015010 (2018), doi:10.1103/PhysRevD.98.015010, arXiv:1804.05238.

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[13] P. Fayet, Massive gluinos, Phys. Lett. B 78, 417 (1978), doi:10.1016/0370-2693(78)90474-4.

1036
1037

[14] J. Polchinski and L. Susskind, Breaking of supersymmetry at intermediate energy, Phys. Rev. D 26, 3661 (1982), doi:10.1103/PhysRevD.26.3661.

1038
1039

[15] L. J. Hall and L. Randall, U(1)$_R$ symmetric supersymmetry, Nucl. Phys. B 352, 289 (1991), doi:10.1016/0550-3213(91)90444-3.

1040
1041
1042

[16] P. J. Fox, A. E. Nelson and N. Weiner, Dirac gaugino masses and supersoft supersymmetry breaking, J. High Energ. Phys. 08, 035 (2002), doi:10.1088/1126-6708/2002/08/035, arXiv:hep-ph/0206096.

1043
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[17] A. E. Nelson, N. Rius, V. Sanz and M. Unsal, The minimal supersymmetric model without a μ term, J. High Energ. Phys. 08, 039 (2002), doi:10.1088/1126-6708/2002/08/039, arXiv:hep-ph/0206102.

1046
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[18] I. Antoniadis, K. Benakli, A. Delgado and M. Quiros, A new gauge mediation theory (2006), arXiv:hep-ph/0610265.

1048
1049
1050

[19] G. D. Kribs, E. Poppitz and N. Weiner, Flavor in supersymmetry with an extended R symmetry, Phys. Rev. D 78, 055010 (2008), doi:10.1103/PhysRevD.78.055010, arXiv:0712.2039.
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[20] S. De Lope Amigo, A. E. Blechman, P. J. Fox and E. Poppitz, *R-symmetric gauge mediation*, J. High Energ. Phys. **01**, 018 (2009), doi:10.1088/1126-6708/2009/01/018, arXiv:0809.1112.

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[21] K. Benakli and M. D. Goodsell, *Dirac gauginos in general gauge mediation*, Nucl. Phys. B **816**, 185 (2009), doi:10.1016/j.nuclphysb.2009.03.002, arXiv:0811.4409.

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[22] K. Benakli and M. D. Goodsell, *Dirac gauginos and kinetic mixing*, Nucl. Phys. B **830**, 315 (2010), doi:10.1016/j.nuclphysb.2010.01.003, arXiv:0909.0017.

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[23] K. Benakli and M. D. Goodsell, *Dirac gauginos, gauge mediation and unification*, Nucl. Phys. B **840**, 1 (2010), doi:10.1016/j.nuclphysb.2010.06.018, arXiv:1003.4957.

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[24] R. Fok and G. D. Kribs, *μ to e in R-symmetric supersymmetry*, Phys. Rev. D **82**, 035010 (2010), doi:10.1103/PhysRevD.82.035010, arXiv:1004.0556.

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[26] G. D. Kribs, T. Okui and T. S. Roy, *Viable gravity-mediated supersymmetry breaking*, Phys. Rev. D **82**, 115010 (2010), doi:10.1103/PhysRevD.82.115010, arXiv:1008.1798.

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[28] R. Davies, J. March-Russell and M. McCullough, *A supersymmetric one Higgs doublet model*, J. High Energ. Phys. **04**, 108 (2011), doi:10.1007/JHEP04(2011)108, arXiv:1103.1647.

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[29] K. Benakli, M. D. Goodsell and A.-K. Maier, *Generating μ and Bμ in models with Dirac gauginos*, Nucl. Phys. B **851**, 445 (2011), doi:10.1016/j.nuclphysb.2011.06.001, arXiv:1104.2695.

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[34] R. Argurio, M. Bertolini, L. Di Pietro, F. Porri and D. Redigolo, *Holographic correlators for general gauge mediation*, J. High Energ. Phys. **08**, 086 (2012), doi:10.1007/JHEP08(2012)086, arXiv:1205.4709.

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[35] R. Argurio, M. Bertolini, L. Di Pietro, F. Porri and D. Redigolo, *Exploring holographic general gauge mediation*, J. High Energ. Phys. **10**, 179 (2012), doi:10.1007/JHEP10(2012)179, arXiv:1208.3615.

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[22] K. Benakli and M. D. Goodsell, *Dirac gauginos and kinetic mixing*, Nucl. Phys. B **830**, 315 (2010), doi:10.1016/j.nuclphysb.2010.01.003, arXiv:0909.0017.

[23] K. Benakli and M. D. Goodsell, *Dirac gauginos, gauge mediation and unification*, Nucl. Phys. B **840**, 1 (2010), doi:10.1016/j.nuclphysb.2010.06.018, arXiv:1003.4957.

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