Probing GeV-scale MSSM neutralino dark matter in collider and direct detection experiments

Given the recent constraints from the dark matter (DM) direct detections, we examine a light GeV-scale (2-30 GeV) neutralino DM in the alignment limit of the Minimal Supersymmetric Standard Model (MSSM). In this limit without decoupling, the heavy CP-even scalar $H$ plays the role of the Standard Model (SM) Higgs boson while the other scalar $h$ can be rather light so that the DM can annihilate through the $h$ resonance or into a pair of $h$ to achieve the observed relic density. With the current collider and cosmological constraints, we find that such a light neutralino DM above 6 GeV can be excluded by the XENON-1T (2017) limits while the survivied parameter space below 6 GeV can be fully covered by the future germanium-based light dark matter detections (such as CDEX), by the Higgs coupling precison measurements or by the production process $e^+e^- \to hA$ at an electron-positron collider (Higgs factory).


I. INTRODUCTION
The existence of cold dark matter (CDM) has been confirmed by many astrophysical experiments. The CDM provides a natural way to account for many properties of galaxies and its predictions are in good agreement with data on large scales. The nature of CDM, however, has remained elusive and been extensively studied in particle physics. Among various hypothesis for CDM, the most compelling one is the Weakly Interacting Massive Particle (WIMP) in the mass range 10-1000 GeV.
So far, the WIMP dark matter has undergone stringent experimental scrutiny. The direct DM detections attempt to measure the nuclear recoil imparted by the scattering of DM.
The recent strong limits on nucleon-WIMP scattering have already excluded (at 90% CL) a spin-dependent cross section above 4.1 × 10 −41 for a WIMP mass of 40 GeV [1] and a spinindependent cross section above 7.7 × 10 −47 for a WIMP mass of 35 GeV [2], approaching the neutrino floor. Besides, the null results from indirect DM detections via gamma rays, positrons and neutrinos as well as collider searches for mono-X signatures also put stringent constraints on various WIMP candidates [3].
The MSSM is one of the most popular extensions of the SM, in which the lightest neutralino can be a natural WIMP dark matter if R-parity is conserved. With the LHC data, the precision electroweak data and flavour measurements as well as the dark matter detection limits, the typical WIMP mass range has been largely excluded, albeit some blind spots in direct detections are still remained due to some accidental cancellation in the couplings of Higgs/Z boson with the neutralino DM. A lower mass limit of the bino-like DM in the 19-parameter MSSM is found to be about 30 GeV when the lighter CP-even Higgs boson (h) is SM-like [4][5][6]. On the other hand, due to accidental cancellation effects in the alignment limit without decoupling [7][8][9][10][11], the heavier CP-even scalar (H) can serve as the observed 125 GeV Higgs boson while the other scalar h can be very light. This provides a possibility that the bino-like DM below 30 GeV can saturate the DM relic density with the help of a light h [12,13]. Since current direct detection experiments have generally poor sensitivities to a light GeV-scale DM, this scenario may be still viable and worth a thorough study.
In this work, we examine such a light bino-like DM in the MSSM with H playing the role of the SM-like Higgs boson. In particular, we focus on the GeV-scale DM in a mass range of 2-20 GeV, in which DAMA [14], COGENT [15] and CRESST [16] experiments have reported some plausible signals of WIMP interaction. We will first utilize the current LHC Run-2 data and DM direct detection results to examine whether such a GeV-scale neutralino DM is still allowed in the MSSM. Then we will explore the prospect of probing such a light DM by the projected germanium-based light dark matter detectors, by the Higgs coupling precision measurements and by the production process e + e − → A(→ bb)h(→ bb) at future e + e − colliders.
The structure of this paper is organized as follows. In Section II, we will briefly describe the alignment limit of the Higgs sector in the MSSM and its implications on the phenomenology of the light neutralino DM. In Section III, we confront our light DM scenario with the current LHC and DM experimental data, and investigate its related phenomenologies in future collider and direct detection experiments. Finally, we draw our conclusions in Section IV.

II. MSSM HIGGS ALIGNMENT LIMIT AND IMPLICATIONS ON DM
The MSSM has a minimal Higgs sector consisting of two Higgs doublets with opposite hypercharges [17]: The tree-level Higgs potential is given by where µ is the higgsino mass parameter, B is the soft SUSY-breaking bilinear Higgs term, In order to show the alignment limit, we use the Higgs basis (H 1 , H 2 ) defined as [18] where ǫ 12 = −ǫ 21 = 1 and ǫ 11 = ǫ 22 = 0, and there is an implicit sum over the repeated It can be seen that H 0 1 = v/ √ 2 and H 0 2 = 0. The CP-even mass eigenstates are related with the neutral Higgs mass eigenstates where c β−α ≡ cos(β − α) and s β−α ≡ sin(β − α) are defined in terms of the mixing angle α that diagonalizes the CP-even Higgs squared-mass matrix when expressed in the original basis of scalar fields, In terms of the Higgs basis fields, we can rewrite the Higgs potential as At tree-level, the above quartic couplings Z 1 , Z 5 and Z 6 are given by (7) where c 2β ≡ cos 2β and s 2β ≡ sin 2β. Then, we can compute the squared-mass matrix of the neutral CP-even Higgs bosons, with respect to the neutral Higgs states, If √ 2 ReH 0 1 − v were a Higgs mass eigenstate, it would have the same couplings as the SM Higgs boson at tree level. In other words, to obtain a SM-like Higgs boson, one of the neutral Higgs mass eigenstates has to be close to (5) and (8), we can find that [20]. The latter case necessarily corresponds to this alignment limit.
It should be noted that the exact alignment without decoupling, Z 6 = 0, trivially occurs when β = 0 or π/2 (corresponding to the vanishing of either v 1 or v 2 ). However, this will lead to a massless b quark or t quark, respectively, at tree-level. Therefore, the MSSM Higgs alignment Z 6 = 0 can only happen through an accidental cancellation of the tree-level terms with contributions arising at the one-loop level (or higher). In the limit M Z,A ≪ M S , the leading one-loop correction to Z 6 is given by where In Ref. [9], authors numerically solved Eq. (9) and found that a large value of µ is required to achieve the alignment limit without decoupling when tan β is small. Note that the radiative corrections can also affect the SM-like Higgs couplings, in particular the Yukawa couplings of the third generation fermions [7,8,21,22]. The precision measurements of them will further test the MSSM alignment limit.
Since the Higgs alignment is independent of M 2 A , Z 1 and Z 5 , the lighter CP-even Higgs boson h can be light if the heavy Higgs boson H is interpreted as the SM-like Higgs boson.
The appearance of light Higgs boson h will enrich MSSM dark matter phenomenology. As known, a light bino-like neutralino dark matter might overclose universe. Several possible ways for it being a viable thermal relic consistent with the observed abundance have been found, such as a mixture of higgsino and bino in natural SUSY [5,23]. While in the alignment limits, the light Higgs boson h can play the role of mediator. The light bino-like DM can annihilate through it into the SM particles. Besides, they can also directly decay into a pair of h. This pushes the boundaries of how light the cold thermal neutralino relic can be in the MSSM. In the following, we will examine this possibility and focus on the GeV scale neutralino DM.

III. PHENOMENOLOGICAL STUDIES AND RESULTS
We scan the relevant parameters in the following ranges: Here, the lower value of M 1 is inspired by the Lee-Weinberg bound of WIMP dark matter [24]. It should be mentioned that the bino-like DM in 19-parameter pMSSM with h being the SM-like Higgs boson has to be heavier than 30 GeV [4]. However, this conclusion may not be valid in the alignment limit with H being the 125 GeV Higgs boson, which motivates our upper value of M 1 . In order to realize alignment limit at reasonably low tan β values that are experimentally allowed, one needs µ/M S ≥ O(2 ∼ 3) so that we require µ ≥ 2 TeV [9]. Besides, we demand the heavy stops and/or large Higgs-stop trilinear soft-breaking coupling to achieve the correct Higgs mass. It is noted that the vacuum stability may give a very strong bound on the large value of µ/M S , which is considered in our study by using the approximate formulae in Ref. [25]. Given the LEP and LHC bounds on the first two The advanced numerical techniques, such as MultiNest sampling, may improve our scan efficiency.
In Fig. 1 we display samples satisfying constraints (1)-(3) on the plane of mχ0 1 versus m h . We can see that there are two ways to satisfy the requirement of observed DM relic density: one is that DMs annihilate into the SM particle through s-channel mediated by a light h boson (red dots), which requires that m h is about twice of mχ0 1 ; the other is that DMs directly annihilate into a pair of h bosons through the t-channel (blue dots). The  In Fig.2, we show 95% C.L. upper limits from Fermi-LAT and Planck data on the thermally-averaged t-channel cross-section σv χ 0 1χ 0 1 →hh for 4µ and 4τ final states [35]. We can see that our samples are far below those bounds because of suppressions of Higgs branching ratios. It should be mentioned that there is now no corresponding limit for bb final states when mχ0 1 < 15 GeV [35]. Moreover, the s-channel cross section σv χ 0 1χ 0 1 →h→2µ,2τ,2b can also evade the indirect detection bounds [36] due to p-wave suppression.
In Fig.3 we present the Higgs couplings normalized to the SM values. It can be seen that the coupling HV V (V = Z, W ) is very close to the SM prediction while the coupling hV V is highly suppressed. This verifies our scan results that H is the SM-like Higgs boson. For  [37] are also plotted (the region above each line is the corresponding observable region).
the heavy Higgs H, the down-type Yukawa couplings Hbb and Hτ + τ − are enhanced sizably, which can be tested in the future HL-LHC and ILC. On the other hand, the up-type Yukawa coupling Htt has a small deviation from the SM value and is below the ILC sensitivity.
Since the light Higgs boson h always accompanies the light DM as shown in Fig. 1, we calculate the production processes of h at the LHC. In Fig. 4 gg +bb → A are included by using SusHi-1.6.1 [38]. Through Monte Carlo simulations for the signals and backgrounds, we find these two processes unobservable at the LHC because the decay products of h is soft and the mass splitting between the CP-odd Higgs boson A and its final states Zh is small. Besides, the light Higgs boson h can also be singly produced through gluon fusion or bb annihilation, which, however, also suffers from the huge SM backgrounds and is found unobservable at the LHC.
Next, we explore the potential of testing our light DM and light Higgs boson scenario at a 240 GeV electron-positron collider (Higgs factory). In Ref. [39,40], the authors studied mono-Z and mono-photon signatures in effective operator framework at an e + e − collider.
However, such production rates are very small in our case sinceχ 0 1 is very bino-like and its coupling with Z boson is negligible weak. Note that from the Higgs-gauge boson interactions in Eq. (11) we can see that the coupling |C hAZ | is sizeable because of β − α → π in the alignment limit without decoupling: Therefore, we investigate the observability of the process e + e − → A(→ bb)h(→ bb) at a 240 GeV Higgs factory. We generate parton level events using MadGraph5 aMC@NLO [41].
The events are then passed to Pythia [42] for showering and hadronization. The detector simulation is implemented with Delphes [43], where we use the CEPC detector card [44]. The b-tagging efficiency is 80%. The main SM backgrounds includes e + e − → Z(→ bb)H(→ bb), 3j and 4j. The detailed event selections are the followings: • We require exactly three jets with p j T > 25 GeV, |η j | < 3.5 in the final states. Two of three jets are b-jets. The third jet is required to have p T > 45GeV.
• We require the invariant mass m bb to be within 95-130 GeV.
In Table I we present a cut flow of the cross sections for the signal and backgrounds at a 240 GeV e + e − collider with an integrated luminosity L = 100f b −1 . We can see that the background e + e − → 3j is still about one order larger than the signal after the p j T cut. The requirement of m bb around m A can significantly suppress this background. The resulting statistical significance S/ √ S + B of the signal can reach 8.67σ with S/B = 18.23%.

IV. CONCLUSIONS
In this work, we examined a light GeV-scale neutralino dark matter (2-30 GeV) in the MSSM. Such a light WIMP DM can be realized in the Higgs alignment limit without decoupling, which can pairly annihilate into the Standard Model particles through a light CP even Higgs boson or into a pair of light CP even Higgs bosons to provide the correct relic density. With the collider and cosmological constraints, we found that the DM with 6 GeV mχ0 1 30 GeV has been excluded by the XENON-1T (2017) limit. By analyzing the surviving parameter space with 2 GeV mχ0 1 6 GeV, we found that such a light GeVscale neutralino dark matter can be tested by the future germanium-based light dark matter detectors (such as CDEX), by the Higgs coupling precision measurements or by searching for the light Higgs boson h through the process e + e − → hA at a Higgs factory.