Wino-Higgsino dark matter in the MSSM from the $g-2$ anomaly

In this letter, we show that the wino-Higgsino dark matter (DM) is detectable in near future DM direct detection experiments for almost all consistent parameter space in the spontaneously broken supergravity (SUGRA) if the muon g-2 anomaly is explained by the wino-Higgsino loop diagrams. We also point out that the present and future LHC experiments can exclude or confirm this SUGRA explanation of the observed muon g-2 anomaly.

It is well known [6][7][8]  to the muon g − 2. #1 In the former case, the bino can be the dominant dark matter (DM), whose detection probability in the direct detection experiments is very low and we can not expect the direct detection of the bino DM in near future [10]. #2 In the latter case the, the DM is mixture of wino and Higgsino, i.e., "wino-Higgsino DM," but its abundance is much smaller than the observed DM density [12].
In this short letter, we consider the latter case, where the wino and Higgsino  imposing the EWSB conditions. #3 Note that the FCNC problem is avoided because all the squarks and sleptons have the common soft mass, m 0 , at the UV scale. #4 We take sign(µ) = +1 to obtain ∆a SUSY µ > 0. Furthermore, since the effects of m 0 can almost be absorbed into the bino mass M 1 , we can take m 0 = 0 without a significant change in our conclusion. We also checked that the A d dependence of the DM detection is very weak, for which we assume A d = 0 at the GUT scale. Accordingly, we have seven parameters defined at the GUT scale, M 1 , M 2 , M 3 , A u , m 2 Hu , m 2 H d and B µ /µ. #5 They are equivalent to the following parameter, which we choose as the model parameters in this work: where To ensure the universal mass, m 0 , it is assumed that the couplings between the matter fields and a SUSY breaking fields are identical, leading to A d = A e . The condition, A d = A e , is not important, though.
#4 As well-known examples to avoid the FCNC problem, a minimal Kahler potential or a sequestered Kahler potential [17,18] (for the matter fields) leads to the common soft mass, m 0 or zero. #5 With the choice of the model parameters, this SUGRA model is almost equivalent to a gaugino mediation model in Ref. [12], where the SUSY CP and flavor problems are solved, and the origin of the non-universal gaugino masses is naturally explained. and the green-shaded region is excluded by the XENON1T experiment [35]. Most of the remaining region will be probed by future direct-detection experiments, such as DarkSide-20k [36], LZ [37], PandaX-4T [38], and XENONnT [39]. The LHC phenomenology of our scenario is rather complicated because of compressed spectra and the mixed nature of neutralinos. Therefore, we do not perform full analyses in this work, but instead introduce a few benchmark points (BPs) for future analyses and provide general brief discussion on the LHC phenomenology.
The BPs are shown in Table 1; note that BP-WH4 is excluded by XENON1T as discussed above, but introduced for completeness. Colored SUSY particles are not displayed because they are heavy due to large M 3 and beyond the present LHC limits. We thus focus on non-colored SUSY particle production at LHC, which are of our interest because our scenario is motivated by the muon g − 2 anomaly and wino-Higgsino partial dark matter.
Chargino searches based on disappearing-track signature are promising for the wino DM. Indeed,χ ± 1 is almost wino-like in the upper-left corner of Fig. 2 and its lifetime, τ (χ ± 1 ), is longer than 10 −11 s; a portion of that region is thus expected to be excluded by the results in Refs. [40,41]. However, those limits do not cover the region with M 2 µ because, due to the Higgsino component ofχ ± 1 , the lifetime is shorter and the production cross section is smaller compared to wino-like chargino.
Although sleptons are as light as ∼ 400 GeV, the slepton channel pp →ll * → 2l + ¡ p T [42,43] does not provide significant limit, either. This is mainly because, unlike bino-LSP models studied in Refs. [14,44], the sleptons are allowed to decay intoχ ± 1 without emitting any hard charged leptons, as depicted in Table 1. The region with M 2 µ are therefore to be searched for by the production of heavier electroweakinos,χ ± 2 andχ 0 2,3 . In fact, as examined in Refs. [14], SUSY models with sizable ∆a SUSY µ from wino-Higgsino loop (Fig. 1) are typically searched for by electroweakino pair-production, which yields signatures with two SM bosons (W ± , h, Z) with large missing transverse momentum. Unlike bino-LSP models studied in Refs. [13,14,44], the expected signature is diverse and involved because various production channels are expected and the electroweakinos are allowed to decay into all the SM bosons. Dedicated LHC analyses are called for and, thanks to

Appendix: SLHA Input
Our benchmark parameter space corresponds to the following SLHA input for spectrum generators such as SuSpect [19]