Hindawi Advances in High Energy Physics Volume 2018, Article ID 6828560, 15 pages https://doi.org/10.1155/2018/6828560

Review Article The Discreet Charm of Higgsino Dark Matter: A Pocket Review

Kamila Kowalska and Enrico Maria Sessolo

National Centre for Nuclear Research, Hoza˙ 69, 00-681 Warsaw, Poland

Correspondence should be addressed to Enrico Maria Sessolo; [email protected]

Received 9 February 2018; Accepted 12 June 2018; Published 11 July 2018

Academic Editor: Yann Mambrini

Copyright © 2018 Kamila Kowalska and Enrico Maria Sessolo. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Te publication of this article was funded by SCOAP3.

We give a brief review of the current constraints and prospects for detection of higgsino dark matter in low-scale supersymmetry. In the frst part we argue, afer performing a survey of all potential dark matter particles in the MSSM, that the (nearly) pure higgsino is the only candidate emerging virtually unscathed from the wealth of observational data of recent years. In doing so by virtue of its gauge quantum numbers and electroweak symmetry breaking only, it maintains at the same time a relatively high degree of model-independence. In the second part we properly review the prospects for detection of a higgsino-like neutralino in direct underground dark matter searches, collider searches, and indirect astrophysical signals. We provide estimates for the typical scale of the superpartners and fne tuning in the context of traditional scenarios where the breaking of supersymmetry is mediated at about the scale of Grand Unifcation and where strong expectations for a timely detection of higgsinos in underground detectors are closely related to the measured 125 GeV mass of the Higgs boson at the LHC.

1. Introduction more information, one has almost always to resort to some theoretical assumptions in order to narrow the search for DM From the particle physics point of view, the simplest, most down. popular, and arguably most robust mechanism leading to Since the 1990s, expectations about the scale of the new the correct amount of cold dark matter (DM) in the early physics beyond the SM (BSM) have been driven by the Universe is thermal freeze-out (see, e.g., [1–4]). Briefy stated, theorists’ discomfort with the hierarchy problem. Tis is the one assumes that the DM consists of one or more matter well-known fact that, in a low-energy efective theory that species that were originally in thermal equilibrium with includes one or more light fundamental scalars (as likely is the Standard Model (SM) afer the Big Bang and that, as the SM with a Higgs boson), one expects enormous quantum the Universe expanded and cooled down, “froze” out of corrections to the scalar’s mass from the physics in the UV equilibrium when their number density became too low for (the Planck scale, in the absence of anything else). Given annihilation and creation processes to take place. the broad separation between the characteristic energies in As is well known, in the context of the freeze-out play, this means that in order to get electroweak symmetry mechanismthemeasurementoftherelicabundanceprovided breaking (EWSB) one should fne tune the fundamental Ω ℎ2 = 0.1188 ± 0.0010 by WMAP and Planck, PL [5, 6], (unknown) Lagrangian parameters at the level, again in the implies a rather specifc value for the thermally averaged absence of anything lighter than the Planck scale, of one part 28 annihilation cross section of the DM into SM particles: ⟨�V⟩≈ in ∼10 , unless, of course, additional degrees of freedom −26 3 3×10 cm /s ≈1pb. Nevertheless, the thermal mechanism were present, preferably close to the Higgs mass itself (say fails to provide any additional information on the nature of ∼ 100 − 1000 GeV). the DM itself since a cross section of that size can result from Remarkably, simply on dimensional grounds, if one of a discouraging wide range of DM mass values, spin quantum these expected TeV-scale BSM particles were to be the DM, its numbers, and DM-SM coupling strengths. Tus, in lack of coupling to the SM extracted from the freeze-out mechanism 2 Advances in High Energy Physics would be of the size of the electroweak coupling constant, Te structure of the review is as follows. In Section 2 we � ≈ (16��2 ⋅1 )1/4 ≈ 0.1 − 1 recalltheparticlesoftheMSSMthatcanprovideagoodDM DM pb . Tis fascinating coincidence, which, in light of its singling out specifcally candidate, classifying them according to their transformation weakly interacting massive particles, or WIMPs, is known properties under the SM gauge symmetry group. In Section 3 as the “WIMP miracle,” maintains its attractiveness to these we single out the higgsino as the most promising candidate days, even if the LHC has failed to discover new particles of the list and review its detection prospects in diferent below the scale of approximately 2 TeV [7, 8]. and complementary experimental venues. We dedicate an Arguably the most complete and well motivated of the additional subsection to the calculation of typical fne tuning known BSM theories still remains low-scale supersymmetry and expectations for the scale of the superpartners in models (SUSY) (see, e.g., [9], for a popular review). From the theo- constrainedattheGUTscale.Wesummarizethemain retical point of view, not only does SUSY provide possibly the treated points and conclude in Section 4. most elegant solution to the hierarchy problem (if one allows for the possibility that, given the current LHC bounds, the theorymighthavetobeamendedtoregainfullnaturalness), 2. Dark Matter in the MSSM but it also leads to a more precise UV unifcation of the One of the features making the MSSM very attractive from gauge couplings than in the SM alone; it provides a solid a phenomenological point of view is that its gauge symmetry rationale for the measured value of the Higgs boson and structure originates directly from the supersymmetrization of top quark masses and, by extension, for radiative EWSB. the SM itself. As such, the fundamental gauge symmetry is From the phenomenological point of view, the Minimal SU(3) × SU(2) × U(1), and the dimensionless couplings are of Supersymmetric Standard Model (MSSM) contains all the the strong, electroweak, or SM Yukawa type. necessary ingredients for successful baryogenesis and pro- One of the consequences is that a potentially viable DM vides a framework for cosmic infation. It thus makes sense particle is also expected to interact with SM-like strength. that, of all possible candidates for WIMPs, through the Since cosmological observations have long excluded the pos- yearsalotofattentionwasdedicatedtotheparticlesofthe sibility of DM particles being charged under color [16] and, on MSSM. the other hand, the DM is by defnition “dark,” or practically In this review we give a compact summary of the subject electrically neutral [3, 17], one is led to conclude that all of DM in the traditional MSSM. Afer briefy surveying viable DM candidates in the MSSM must be classifable on the particles with the potential of providing a good DM the basis only of the SU(2) representation they belong to. candidate, we argue that the nearly pure higgsino neutralino Moreover,theavailablerepresentationsarelimitedtothose survives to these days as perhaps the only one that is not that can be found in the SM: SU(2) singlets, doublets, and the in substantial tension with any phenomenological constraint. adjoint. Interestingly, it does so in a relatively model-independent Before we proceed to briefy review these three groups way, without the need of resorting to narrow or secluded individually, we remind the reader that in order to make regions of the parameter space. We will thus review the the lightest SUSY particle (LSP) stable on cosmological time higgsino’s prospects for detection in direct underground scales, one introduces in the MSSM an additional discrete DM searches, indirect searches for DM in gamma-ray, and symmetry, R-parity [18–22], under which only the super- neutrino telescopes and at the LHC. Incidentally we will show partners of the SM fermions, gauge bosons, and any Higgs that, in those models where SUSY breaking is transmitted to scalar feld are odd. Te origin of R-parity is still an active thevisiblesectoratthescaleofGrandUnifcation(GUT),the subject of research, and addressing the issue goes beyond the detection prospects of higgsino DM become tightly bound scope of the present review. We just point out that R-parity to the typical mass of the sfermions in the spectrum and, violation is strongly constrained phenomenologically, by the as a direct consequence, to the size of the Higgs boson proton decay rate and electroweak precision measurements mass. [23]. In recent months several comprehensive reviews on the Te only particles of the MSSM that are electrically and status of WIMP dark matter have appeared in the literature color-neutral are the neutrinos, their scalar superpartners, [10–13], one of which, coauthored by one of us, dedicated called sneutrinos,and,fnally,theneutralinos.Neutralinos, a full chapter to the MSSM neutralino with particular �
=1,..,4, are Majorana fermion mass eigenstates emerging, attention to the detection prospects of a ∼1TeV higgsino. afer EWSB, from the diagonalization of the mass matrix of While that work is broader in scope, casting light on the four electrically and color-neutral SUSY states (see [24–27] experimental opportunities provided by neutralinos in the forearlystudiesand[3]foracomprehensive,classicreview). context of the wider picture of thermal DM models, DM Two of these particles are gauginos, fermionic superpartners constraints, and existing experimental anomalies, we con- of the SM gauge bosons. Te bino, �̃,inparticular,isthe centrate here instead on the specifc physical characteris- partner of the U(1) gauge boson, while the neutral wino, �̃, tics of higgsinos, underlining what we believe makes them is the partner of the SU(2) gauge boson �3.Teothertwo ̃ ̃ currently stand out as the most interesting elements in the states are neutral higgsinos, �
and �
, which belong to a DM panorama of the MSSM. In this we are not dissimilar, vector-like pair of Higgs doublet superfelds. If the lightest perhaps,torecentlyappearingstudiesinthesametone[14, neutralino, hereafer, indicated simply with �,istheLSPit 15]. can be the DM particle. Advances in High Energy Physics 3

Atthetreelevel,theneutralinomassmatrixtakesthe the thermal cross section for binos, given approximately by following well-known form: the following [35]:

4 4 2 4 4 � � � (�  +� )  



�
� V
� V
⟨�V⟩  ≈ ∑ ( ), [ � 0− ]
2� 4 � (2) [ 1 √2 √2 ]
 (�2 +�2 )
[ �V �V ]

[ 0�
−
] [ 2 ] [ √2 √2 ] � [ ] in terms of the neutralino (bino) mass,
,sfermions’mass [  ] � ,hypercharge�, and freeze-out temperature �
,which M� = [ � V
�V
] , (1)

[− 0−�] � [ √2 √2 ] parameterizes the dependence on velocity of the -wave cross [ ] � ≈ (0.04−0.05)� [ ] section, and is set here approximately at

. [ �V �V ] [
−
−� 0 ] Te bulk has been long known to be strongly constrained √2 √2 by direct SUSY searches at colliders. To give a semiquanti- [ ] tative estimate of these constraints, let us assume that only selectrons and smuons belong to the light SUSY spectrum, a reasonable ansatz in light of the strong LHC bounds on � � where and are SU(2) and U(1) gauge couplings, respec- particles with color [36–38]. Assuming all four lef- and right- V V tively,
and
are the vacuum expectation values (vev) of � = handed slepton states have the same mass, and inserting
� the neutral components of the scalar Higgs doublets, �1 and −1/2, � =−1in (2) one fnds that the cross section is �
� 2 arethesofSUSY-breakingbaremassesofthebinoand ∼1 � < � typicallymuchsmallerthan pb, except in the range
wino, respectively, and is the vector-like mass parameter of � ≲ 100 the Higgs doublet superfelds.
 GeV.Achargedsleptonmassofthissizehasbeen In the remainder of this section we give an overview of long excluded by direct searches at LEP [39]. the mentioned DM candidates of the MSSM, highlighting the If, instead of selectrons and smuons, the light sfermions strongest phenomenological constraints that can be applied happen to be status, the parameter space opens up a little, � ≲ 150 � ≈50 in each case. We will not, however, discuss the neutrinos.
1 GeV for
GeV, due to the nonnegligible It has been long known [28, 29] that the SM neutrinos do mixing between lef and right chiral slepton states, which � not provide, on their own, a viable candidate for cold DM. introduces an -wave component to the annihilation cross Teir mass is O(sfermion mass. conservation constraint. Te resulting vertex takes the form Andinmodelsthatareinsteaddefnedintermsofalimited L ⊃−��̃ �� �−��̃ �� � bino-sfermion-fermion,





, number of free parameters in the UV, like the CMSSM [46], √  where tree-level couplings, �
,
= 2��
,
, are expressed in which slepton or stop coannihilation with the bino can in terms of the hypercharge assignment �
,
of the fermion occur naturally for particular choices of the initial conditions, Weyl spinors. the preferred regions of the parameter space are incurring Te pair-annihilation of bino-like neutralinos in the early increasingly strong limits from direct LHC searches [13, 47– Universe proceeds at the leading order through the �-channel 50]. Besides, with gaugino universality at the GUT scale, it diagram shown in Figure 1(a). Te region of the MSSM isastruggletofullyaccommodatethemeasuredvalueofthe 2 parameter space where Ωℎ ≈ 0.12 is obtained in this way Higgs mass at the LHC [47, 51] (this problem is resolved if is historically known as the bulk [33, 34]. One can calculate thegluinomassisafreeparameter,e.g.,[52]).Tus,evenif 4 Advances in High Energy Physics

2 coannihilation of the bino with other sparticles can still lead size of �
/�1,2 [9], and the splitting between the higgsino- to viable regions of the parameter space in the most generic like chargino and the lightest neutralino is approximately parametrizations of the MSSM [53], it is also perhaps not half of that. Moreover, radiative corrections also induce a exceedingly attractive from a natural point of view. nonnegligible and irreducible mass splitting (∼100s MeV) between the charged and neutral states (see, e.g., [62, 63]). R Sneutrino.TesecondSU(2)singletDMcandidateofthe To correctly compute the thermally averaged efective MSSM is the scalar “right-handed” sneutrino. Te right- cross section that yields the DM relic abundance, one must handed sneutrino does not properly belong to the MSSM, take into account all possible annihilations and coannihi- which in its original formulation features massless neutrinos, lations of higgsino states. For �
above the � threshold but naturally emerges in SM extensions with right-handed the dominant fnal state is into � and � bosons (Figures neutrinos, which can give rise to the neutrino mass via small 1(b) and 1(c) give examples of possible diagrams for this Yukawa couplings (if the right-handed neutrino is Dirac), processes), to which higgsino-like neutralinos and charginos or through the see-saw mechanism (if the right-handed couple through the electroweak charged and neutral currents neutrino is Majorana, see, e.g., [54] and references therein). [3]: Te phenomenology of right-handed sneutrinos as DM, however interesting, is very model-dependent. In traditional � +
− �
L ⊃(− �
�� � − �
�1� �2 + h.c.) see-saw models with large-scale Majorana mass the right- 2 4 cos �
handed sneutrino is too heavy to be the DM. On the other (3) � +
2 − hand, for a sneutrino of the “Dirac” type, or, in alternative, − � � � (1 − 2 � )� . 2 �
sin
Majoranabutsuchthatthebaremassisoftheorderof cos
the superpartners’ mass [55, 56], the only really model- Te efective cross section can be obtained at the leading independent vertex with the SM involves a very small Yukawa ̃± ̃0 order in the limit of all four states being degenerate (see, e.g., coupling L ⊃−�] �
� ̃]
−�] ]
� ̃]
.Tus,theinduced �
�
[35]): �-channel processes similar to Figure 1(a), with sneutrinos (charginos) in place of neutralinos (sfermions), and a tiny 21�4 +3�2�2 +11�2 ⟨�V⟩(ef) ≈ . coupling constant are not strong enough to get the correct
 2 (4) 2 512��
Ωℎ . On the other hand, the correct relic density can certainly For heavy, very pure higgsinos, one should include in be obtained thanks to the mixing with the lef-handed ( ) the calculation of ⟨�V⟩ ef corrections due to the Som- sneutrino, and SUSY breaking can generate �-terms of the
 order of the SUSY scale, which provide large couplings to merfeld enhancement, a well-known nonperturbative efect the SM Higgs boson. Te phenomenology of these cases can originating from the fact that if a DM particle is much beveryrichandexceedsthescopeofthisreview.Wedirect heavier than the electroweak gauge bosons and relatively thereadertothevastliteratureonsneutrinoDMforfurther slow, the weak force becomes efectively long-range and the details (see, e.g., [57–60], for early studies and bounds, and impact of the nonrelativistic potential on the interaction cross [61] for a recent LHC analysis). section becomes signifcant [64, 65]. However, in the case of the higgsino the splitting between its charged and neutral components is almost always large enough to efectively 2.2. SU(2) Doublets. We have seen that singlet DM candidates wash out substantial nonperturbative efects originating from in the MSSM are accompanied by some uncomfortable the resummation of ladder diagrams [66–68], so that in a features: they are either strongly constrained by collider frst approximation (4) provides a fairly accurate estimate of ⟨�V⟩(ef) bounds, are only viable in fne-tuned regions of the parameter
 . space, or present a phenomenology that is highly model- One can see that the cross section is typically much larger dependent. We therefore move on to reviewing the next set than ∼1pb, unless �
≈1TeV (the precise numerical value of candidates, the SU(2) doublets. is more about 1.1 TeV, as we shall see). Tus, ∼1TeVhiggsino is on its own a good candidate for the DM in the Universe (Nearly) Pure Higgsino. Te most popular SU(2) doublet DM [69], while a higgsino much lighter than 1 TeV requires one candidate, and the one that appears to us most attractive from to assume the existence of an additional DM component (e.g., 2 a phenomenological point of view, is the higgsino, which is axion [70, 71]), needed to get Ωℎ ≈ 0.12. the main subject of this review. As was the case for the bino, As we shall see in the next sections, ∼1TeV higgsino thereisnopurehiggsinostateaferEWSB,butoneobtainsan isgenerallyassociatedwithalargeSUSY-breakingscaleand almost pure higgsino-like neutralino by diagonalizing M� in forthisreasonitisnotcurrentlyveryconstrainedfroma (1) in the limit |�| ≪ �1,�2. phenomenological point of view. However, its characteristic As supersymmetry assigns a Weyl spinor to each complex properties can give us hope for a timely detection in direct state in the scalar Higgs doublets one counts four physical and indirect DM searches and even, if �
≪1TeV, in higgsino states, which, afer EWSB, give rise to two Majorana ± collider searches. neutralinos, �1 (or �)and�2, and a Dirac chargino, � .When |�| ≪ �1 ≈�2, the tree-level mass splitting between L Sneutrino.Weconcludethissubsectionbyreviewingthe the two higgsino-like neutralinos is of approximately the properties of the only other SU(2) doublet DM candidate in Advances in High Energy Physics 5

 f  W+  Z

 ± f 2

−  f  W + W+

(a) (b) (c)

Figure 1: (a) Te dominant early-Universe annihilation channel for a nearly pure bino-like neutralino. (b), (c) Examples of annihilation and coannihilation tree-level channels into gauge bosons for a predominantly higgsino-like neutralino.

the MSSM: the “lef-handed” sneutrino, scalar superpartner If the wino LSP is heavier than the electroweak gauge of the SM lef-handed neutrino. bosons, its dominant fnal state channel for annihilation Te lef-handed sneutrino is a complex scalar feld with (and coannihilation with charginos) in the early Universe is SU(2) × U(1) quantum numbers equal to the higgsino’s. Like into � (but not �) boson fnal states, to which it couples ±
∓ the higgsino, it has charged and neutral current couplings to as L ∼−��
�� � . Te thermal annihilation cross √ + ∗
− − +
the � and � bosons, L ∼−��/ 2(�
̃]
� �̃
+�
�̃
� ̃]
)− section is dominated by coannihilations of the three wino ∗
��/(2 cos �
)�
̃]
� ̃]
.Temasssplittingofthecharged states, similarly to what happens for the doublet higgsinos. and neutral components of the SU(2) doublet is, however, Annihilation into fermion–antifermion fnal states through much larger for sneutrinos/sleptons than for higgsinos, being a �-channel sfermion exchange, reminiscent of the bino bulk generated through hypercharge D-term contributions [9]: mechanism, has been instead long excluded by LEP limits on �2 −�2 ≈−�2 2� �≡V /V thechargedsleptonmasses.
� ]�
cos ,wheretan

.Tus, one should resist the temptation of interpreting (4) as an Unlike higgsinos, in the wino case mass splitting between accurate estimate of the efective cross section for sneutrinos the charged and neutral fermion component of the SU(2) too, since the coannihilation of charged and neutral states multiplet is generated exclusively by radiative corrections, Δ� =(�2/4�)� 2(� /2) ≈ 166 becomes somewhat less efcient. It turns out [60] that the

sin
MeV [95]. Note (ef) mass required to produce ⟨�V⟩ ≈1pb is about �] ≈ 600− that the mass splitting is typically much smaller than for ]� � 700 GeV. Sneutrinos lighter than that imply the existence of higgsinos, so that one cannot neglect the efects of the Som- an additional component of DM. merfeld resummation on the calculation of the thermal cross A very important constraint on lef-handed sneutrinos section. When one includes the Sommerfeld enhancement numerically, the correct relic density is obtained for �
≈ asDMarisesbecausethey,unliketheMajoranahiggsino- 2.7−2.8 like neutralinos, are not their own antiparticle, so that their TeV[66–68]. For a lighter mass, winos do not saturate elastic scattering with nuclei in direct detection experiments the relic abundance. proceeds also through �-channel exchange of a � boson. By Te Sommerfeld enhancement induces more dramatic virtue of the sneutrino’s neutral current coupling, the spin- modifcations of the efective DM annihilation cross section independent cross section is approximately given by a Fermi- when the average kinetic energy of the WIMP corresponds to 10−3� �SI ≈�2 �2 /8� ≈ 10−3 = speeds of the order of , as in the present-day Universe. like contact interaction,
red
pb −39 2 Tisfacthasledtothederivationofpowerfulindirect 10 � ≈�
�] ≫ cm , where reduced mass red for � astrophysical constraints on the annihilation cross section of �
. Cross sections of this size have been long excluded in wino-like neutralinos [91, 96–99]. By taking into account the underground detector searches [72, 73]. efects of Sommerfeld-enhanced contributions to the anni- hilation of winos into monochromatic gamma rays, as well + − as bounds on the present-day cross section to � � from 2.3. SU(2) Adjoint Triplet difuse gamma radiation from the Galactic Center and Dwarf (Nearly) Pure Wino.TeonlySU(2)tripletDMcandidate Spheroidal satellite galaxies (dSphs), measured in terrestrial in the MSSM is the wino-like neutralino, dominated by the and space telescopes HESS [89, 100] and Fermi-LAT/MAGIC fermionic superpartner of the �3 weakgaugeboson.Te [88], and from cosmic-ray (CR) antiproton data at AMS-02 wino belongs to the adjoint representation of the gauge group [90, 91], one can derive strong independent constraints (albeit (hypercharge �=0) and the wino-like neutralino emerges, afected by signifcant systematic uncertainties) which steeply afer EWSB, from the diagonalization of (1) in the limit raise the stakes on the wino as a viable DM particle, especially |�2|≪�1,�.OnefndsaMajorananeutralino,�,anda in scenarios where it saturates the relic abundance. ± Dirac chargino, � , mass-degenerate at the tree level. In the context of UV complete models of SUSY-breaking, spectra 2.4. Mixed Cases. Te four neutralinos of the MSSM are all with a light wino can arise, for example, in scenarios where Majorana fermions that, afer EWSB, remain neutral under �(1) SUSY breaking is transmitted via anomaly mediation [93, 94]. em and color. In the absence of a well-separated hierarchy 6 Advances in High Energy Physics

  10−8

−9 10 XENON 1T 90% C.L. h (m =1.0 TeV) (pb) ３） p  10−10 gg

Figure 2: Te main interaction between the neutralino and heavy 10−11 nuclei in underground detectors in the limit of squarks and heavy 0.90 0.92 0.94 0.96 0.98 1.00 � = 125 Higgsbosonsbeingmuchheavierthan ℎ GeV and in general fＢＣＡＡＭＣＨＩ outside of LHC reach. Figure 3: Te neutralino-proton spin-independent cross section, SI �
, for a typical case of predominantly higgsino-like neutralino DM � = 1.0 � ≡� with
TeV as a function of higgsino purity higgsino ( ℎ). among �1, �2,and�, the lightest mass eigenstate will be an admixture of the SU(2) gauge multiplets discussed in Sections 2.1–2.3 but, unlike those cases, it will present properties that running tachyonic at the low scale.), the coupling to the difer signifcantly from a pure gauge eigenstate. nucleon can thus be expressed entirely in terms of the When |�1|≈|�|the neutralino is in a highly higgsino fraction (or purity), �ℎ, which depends on the mixed bino/higgsino state. Mixed neutralinos of this kind elements of the unitary matrix, �, diagonalizing (1). (sometimes also called “well-tempered” [35]), originally [� ,� ,� ,� ]=� �† If diag
1
2
3
4 M� , one can defne observed in mSUGRA parameter space [101–103] but that can 2 2 arise under diferent boundary conditions (e.g., [104, 105]), �ℎ ≡|�13| +|�14| and express the coupling of interest as enjoyed some popularity, especially before the advent of the L ∼(�√�ℎ(1 − �ℎ)/4)��ℎ. Note, incidentally, that deriving 2 LHC, because they can easily lead to Ωℎ ≈ 0.12 for values an explicit form for the elements of matrix � in terms of of the � parameter as low as few hundreds GeV, which bare masses �1, �2,and� is not a trivial task even at the are favored to solve the hierarchy problem. However, the tree level, and useful formulas in this regard can be found in rapid progress made in the bounds on the spin-independent several papers, for example, [107–110]. By simple inspection cross section of the neutralino scattering of nuclei in direct of (1), however, one can infer a rough approximation for the WIMP detection searches, combined with a failure to directly higgsino fraction in the limit of nearly pure higgsinos, |�| ≪ observe scalar fermions and heavy Higgs bosons at the LHC, �2 ≈�1: have rendered scenarios where the lightest neutralino is a rich �2 admixture of gaugino and higgsino much less appealing if not 1−� ≈
. ℎ � � 2 (5) excluded altogether (see, e.g. [106], for a very recent update of (�1,2 − ���) the constraints on bino-higgsino, and [99] for wino-higgsino scenarios). Equation (5) becomes quite accurate for �ℎ ≳ 0.999. To briefy set the issue on quantitative grounds, let us Te spin-independent cross section of the neutralino �SI =(4�2 /�)|A |2 estimate the strength of the coupling with which neutralino with protons (nucleons),
red
,canbe admixtures of higgsino and gaugino contribute to the spin- parameterized for moderate-to-large tan � simply as follows independent cross section. We recall that, in the limit of the [3]: squarks and heavy Higgs bosons being much heavier than �ℎ = 125 GeV, which has become a reasonable assumption �√� (1 − � ) � �
ℎ ℎ afer the frst two runs of the LHC, the main interaction A (� )≈�

, (6)
ℎ ef 9 V �2 between the neutralino and heavy nuclei in underground ℎ � detectors proceeds as in Figure 2, via -channel exchange of � the 125 GeV Higgs boson and an efective coupling to gluons in terms of the gluon fractional content of the proton,

(we use the default value for micrOMEGAs v4.3.1 [111], �

= through the heavy quark loops. 0.92 � ≈ 0.9 − 1 ), and a phenomenological fudge factor, ef , As the neutralino LSP-Higgs-neutralino LSP tree-level A vertex directly stems from applying the gauge covariant which takes into account the dependence of
on twist-two derivative on the Higgs doublets, it is nonzero only for a operators [112] and higher-order loop corrections [113]. �SI gaugino/higgsino admixture. For tan � sufciently large to We show in Figure 3 a plot of
as a function of purity ensure a predominantly SM-like Higgs boson (tan �>3−4 �ℎ for a �
=1TeV neutralino (to a frst approximation is a condition ofen fulflled, for instance, in scenarios where theDMmassafectsthecrosssectiononlythroughthe � ≈� EWSB is obtained radiatively via the renormalization group reduced mass leading to red
). One can see that, for evolution of sof SUSY-breaking parameters constrained at admixtures dominated by the higgsino fraction, the most SI some high scale, as it prevents certain sof masses from recent XENON-1T 90% CL upper bound [75] on �
enforces Advances in High Energy Physics 7

�ℎ >98%,sothatviableDMcandidatesoughttobeveryclose alternative strategies in other experimental venues. We will to a pure higgsino state. also give some predictions for the scale of the superpartner Since the purity of well-tempered higgsino-dominated particles in traditional models and briefy discuss the issue of neutralinos stays well below 90% in those models attempting fne tuning. to provide a satisfactory solution to the hierarchy problem while saturating the relic abundance [35], we conclude that, 3.1. Prospects for Detection in Direct and Indirect Searches. barring increasingly narrow corners of the parameter space We begin in Figure 4(a), where we plot the rescaled [106], these scenarios have become very hard to rescue or spin-independent neutralino-nucleon cross section ver- justify in light of the most recent direct detection bounds. sus neutralino mass for a nearly pure higgsino under To conclude this subsection, we fnally recall that, in cases |� |<|�|≲1−2 CMSSM/mSUGRA boundary conditions [46] (We remind where 1 TeV, one obtains scenarios where the reader that this means scanning simultaneously over 4 the mixed neutralino is predominantly bino-like, but also free parameters: �0, the universal sof SUSY-breaking scalar acquirescouplingsthatoriginatefromitsadmixturewith mass at the GUT scale; �1/2, the universal GUT-scale gaugino higgsino states, so that additional mechanisms for obtaining � ⟨�V⟩≈1 mass; 0, the universal GUT-scale sof trilinear coupling; and pb with respect to Section 2.1 are possible. tan �, the ratio of the Higgs doublets’ vevs. We scan them in Tese mechanisms, ofen called funnels,involveresonant this study over broad ranges: �0,�1/2 ∈ [0.1 TeV,30TeV], or close-to-resonant �-channel annihilation of two neutralino � ∈[−30 ,30 ] �∈[1,62] � 0 TeV TeV ,tan . Additionally, one LSPs via a nearly on-shell mediator which could be the chooses the sign of �, which we set here to positive, as its boson (if �
≈�
/2) [25], the SM Higgs boson (if �
= 60 − 65 sign does not much afect the region of parameter space with GeV) [114], or one of the heavy Higgs bosons of the nearly pure higgsino DM (see, e.g., [47, 116]). Note that the MSSM [33]. chosen input mass ranges encompass the parameter space Note that the �-funnel parameter space is strongly con- region shown in Figure 4 in its entirety. In it one fnds �1/2 ≲ strained by the LHC. Te coupling of the lightest neutralino to 0.6� 5 ≲� ≲25 2.5 ≲� ≲15 � 0,with TeV 0 TeV, TeV 1/2 TeV the boson is due exclusively to the isospin neutral current, duetotheHiggsmassmeasurement,seediscussionbelow.). cf. Section 2.2, which means that in mixed bino-higgsino Te color code depicts the higgsino DM relic abundance. scenarios it is directly proportional to the higgsino fraction. 2 For the points of the parameter space corresponding to Ωℎ As a consequence, �ℎ cannot take excessively small values or, 2 below the Planck measurement [6], Ω ℎ ≈0.12,wedirectly in other words, � cannot be much larger than �1 ≈�
/2. PL �SI �=Ωℎ2/Ω ℎ2 Te relative proximity of a mostly higgsino-like chargino rescale
by PL , assuming implicitly that the and a mostly bino-like neutralino subjects this region of the fraction of higgsino DM we measure locally today traces parameter space to strong bounds from direct LHC multi- closely its early time large-scale freeze-out value. Solid tilted lepton searches [115]. lines show recent direct upper bounds from the PandaX- Light and heavy Higgs boson funnels are less constrained II [74] (maroon) and XENON1T [75] (blue) underground from direct LHC SUSY searches than the � funnel, since the experiments. Te latter is not much more constraining direct coupling to the lightest neutralino is dependent on than an earlier bound from the now decommissioned LUX √�ℎ and the mediator can be quite heavy. However, there [76]. Dot-dashed lines show the projected reach of several exist complementary observables which can constrain these upcoming and planned experiments. + − Wealso show in Figure 4(a) as a thin black line the current regions, like the branching ratio BR (�
�→ � � ) [116] and direct searches for heavy Higgs bosons in the �� channel lower bound on mass from direct searches for compressed [117]. Moreover, as was the case for the coannihilations of electroweakinos in fnal states with two low-momentum the bino, most phenomenological scenarios require ad hoc leptons at the LHC ([82, 83], following a proposal and case arrangement of the parameters to obtain the right ratio of studies by [120, 121]), which is sensitive to higgsino DM for �
−�
=3−30 neutralino to scalar mass, although this is not necessarily the mass splitting 2 1 GeV.Oneshouldalsobe case for some parameter-space regions of GUT-constrained awareoftheestimatedputativereachoftheILCintesting scenarios like the CMSSM, in which the renormalization higgsinos [122], which we do not show in the plot for lack 240 (480 ) group evolution (RGE) of sof masses from a handful of of space. It extends to approximately GeV GeV , free parameters can lead more naturally to the right mass independently of mass splitting, if the beam energy is set to � = (500 )2 � = 10002 2 coincidence (see, e.g., [118, 119] for early studies). GeV ( GeV ). In Figure 4(b) we show the rescaled spin-dependent SD neutralino-proton elastic scattering cross section, ��
,ver- 3. Phenomenology of Higgsino Dark Matter sus neutralino mass. We show with solid lines existing Te discussion of Section 2 has led us to conclude that the indirect upper bounds from observations of neutrinos from sole DM candidate of the MSSM emerging almost unscathed the Sun in the neutrino telescopes IceCube [84] (green) and �+�− from the wealth of observational data of recent years is the Antares [85] (red), interpreted for a predominantly nearly pure higgsino. We therefore dedicate this section to annihilation fnal state, which give a good approximation the analysis of the prospects for detection of a higgsino-like for the nearly pure higgsino case [53, 123]. Dashed lines of neutralino in direct DM detection searches, collider searches, diferent colors give various projections for the future direct SD and indirect astrophysical signals, and spend a few words on reach in �
of underground detectors. 8 Advances in High Energy Physics

(a) (b)

SI Figure 4: (a) Spin-independent neutralino-nucleon cross section �
rescaled by the relic abundance, as a function of neutralino mass �
, for a nearly pure higgsino with CMSSM/mSUGRA boundary conditions subject to �ℎ ≈ 125 GeV and LHC Higgs bounds. Solid lines show the 90% CL upper bounds from PandaX-II [74] (maroon) and XENON1T [75] (LUX [76]) (blue). Dot-dashed lines show the projected reach for DEAP-3600 [77] (orange), XENON1T/nT [78] (blue), DarkSide G2 [79] (maroon), LZ [80] (black), DARWIN (purple) [81]. Tin solid black line shows the current lower bound on mass from direct searches at the LHC [82, 83]. (b) Rescaled spin-dependent neutralino nucleon SD cross section �
as a function of neutralino mass �
, for the a nearly pure higgsino in the CMSSM/mSUGRA. Solid lines show the 90% CL indirect upper bounds from IceCube [84] (green) and Antares [85] (red). Dashed lines show projections for LZ [86] (violet), XENON1T [78] (purple), Pico-500 [87] (blue), and DARWIN [81] (black).

Te relic density and DM observables are here calcu- 10−9 lated with micrOMEGAs v4.3.1 [111]. Te supersymmetric Higgsino LSP spectrum is calculated with SPheno v4.0.3 [124, 125], and −10 (GUT–scale SUSY breaking) all model points are subject to LHC Higgs constraints from 10 HiggsSignals/HiggsBounds [126–129] and to the Higgs mass measurement [130]. Te Higgs mass is calculated, like (pb) 10−11 ３） the SUSY spectrum, with the latest version of SPheno,which p  yields, in the regime where sof SUSY-breaking masses are −12 well above ∼1TeV, a value in excellent agreement with other 10 2 theory unc. numerical packages, SusyHD [131] and FlexibleSUSY [132]. Te calculated value is subject to an overall estimated theory 10−13 uncertainty of approximately 2 GeV [133], which we take into 118 120 122 124 126 128 130 132 accountinFigure4.NotethatwhentheSUSYspectrumlies mℎ (GeV) in the several TeV regime or above, all electroweak precision �SI and favor observables, including the anomalous magnetic Figure 5: Lower bound on
as a function of Higgs mass for a moment of the muon, are expected to roughly maintain their higgsino LSP of arbitrary mass in generic models where the breaking SM value. of supersymmetry is transmitted at the GUT scale and the physical We have chosen to show in Figure 4 the higgsino spectrum and EWSB are obtained afer RGE to the low scale. parameter space under CMSSM boundary conditions, which provide a reasonable ansatz for models with scalar univer- sality inspired by supergravity, and more generally cast in a between minimum cross section and Higgs mass translates SI lean framework scenarios in which supersymmetry breaking in Figure 4(a) into a lower bound on �
when �
≈1TeV. is transmitted to the visible sector at some high scale (the To qualitatively understand what is happening, let us GUT scale) and EWSB is obtained radiatively around the recall from Section 2.4 that in order to push down �SI for minima of the MSSM scalar potential. In models defned in
a predominantly higgsino-like neutralino one must increase this way one observes, for a higgsino-like neutralino, strong purity �ℎ or,inotherwords,raisethewinoandbinomasses, correlation between the Higgs boson mass and the allowed �SI cf. (5). Very heavy winos/binos at the GUT scale feed through minimum value of
.WeshowthisinFigure5,where the RGE on the low-scale value of the sof SUSY-breaking �SI weplotthelowerboundon
as a function of Higgs up-type Higgs doublet mass, which carry SU(2) isospin and massforahiggsinoLSPofarbitrarymass.Tecorrelation hypercharge and also tend to push down the right-handed Advances in High Energy Physics 9

+ − stopmass.Tishappenseveninscenarioswherethegluino profle assumption. We adopt the bounds in the � � fnal mass is not universal and can be found relatively close to the state interpretation, which give a good approximation for the higgsino, like those analyzed in [134]. ∼1TeV higgsino. + − In order to keep the Higgs doublet sof mass under For the � � fnalstateweshowinsolidgreenthe control, so as to obtain a higgsino-like LSP afer EWSB, determination by [91] of the 95% CL upper bound on �V from and avoid tachyonic physical states, numerical scans are in antiproton CR data at AMS-02 [90], under the NFW profle thissituationdriventolargenegative�0 and/or larger sof assumption. Note that the bound is subject to uncertainties scalar mass. Both solutions have the net efect of pushing related to the choice of difusion model for CR propagation up the Higgs boson mass and give rise to the behavior we intheGalaxy.Someofthesechoicescaninfactweakenit observeinFigure5(Teattractiveness,fromthephenomeno- [91], and push it up to approximately the level of the HESS logical point of view, of a lower bound on the neutralino limit. Finally, dashed blue line shows the projected statistical scattering cross section determined by the Higgs mass mea- reachofCTA500h,undertheEinastoprofleassumption surement was pointed out early on in Bayesian analyses of [53, 144]. Note that including the systematic uncertainty the CMSSM/NUHM [13, 47, 116]. Te exact minimal cross from difuse astrophysical radiation will most likely weaken section depends strongly on the calculation of the Higgs the extent of the projected reach [123, 145]. Also note in mass itself, and on how it translates into mass predictions for Figure 6(a) that some model points are characterized by �V the sparticles. In SPheno v4.0.3, �ℎ ≈ 125 GeV leads to signifcantly above the thermal relic expectation, due to the less optimistic expectations for the mean SUSY scale than in presence of the heavy pseudoscalar Higgs mass at �
≈2�
the versions of SOFTSUSY [135] or FeynHiggs [136] used in [47, 53]. Regions of the parameter space that allow for this [47, 116]. Hence the parameter space in Figure 4(a) extends serendipitous coincidence thus see their indirect detection SI to lower �
values than in those studies.). prospects improve signifcantly. Tere is no apparent lower bound on the scattering cross We show in Figure 6(b), as a magenta solid line, the section if we relax the requirement of radiative EWSB from current 95% CL upper bound on the annihilation cross boundary conditions generated at the GUT scale. Tis is the section (times velocity) to gamma-ray lines from the fnal case,forexample,inmodelswherethetypicalmassofscalar 254h data at HESS [92] under the Einasto profle assumption. ∼1 particles is by several orders of magnitude decoupled from the Te line is compared to the cross section of our TeV electroweak vev (see, e.g., [137–139]), and one does not expect higgsino points, which lie well below the limit. to infer strict relations between the mechanism of SUSY- breaking and EWSB. Te relic density alone determines then 3.2. Te Sof SUSY Scale and Fine Tuning. We conclude with � the mass of the higgsino-like DM, and purity ℎ can be a few words about the expected scale of the supersymmetric extremely close to 1. We generically indicate with a black particles associated with higgsino DM. In truth, little is arrow in Figure 4(a) the parameter space for higgsino DM known in this regard, as the issue is highly model-dependent in those models, which can extend well below the neutrino and there is not one only way of inferring the scale of SUSY background foor [63, 140]. breaking. Tis highly inaccessible part of the higgsino parameter Of course, expressions similar to (5)-(6) can give us a space proves particularly tricky to probe. For underabundant lower bound on the scale of the electroweak gauginos for higgsinos, �≪1TeV, interesting venues for detections can SI every given upcoming new constraint on �
,buttobe � ± −� ≈ be provided, for very small mass splitting,

precise one should then take into account the rich parametric 150 MeV, by future collider searches for disappearing tracks dependence of the full formulas. Equivalently, the Higgs mass [141, 142]. If there is a sizable CP violating phase, future measurement tells us that in all likelihood stops and gluinos electron dipole moment experiments might be sensitive to sit well above the LHC reach, but little more than that is parameter space with purity in excess of 99.99% [63]. And known, as expectations depend strongly on parameters like possibly new venues for detection are given by the cooling tan � and the trilinear coupling �
. curve of white dwarfs [15]. Additional opportunities for Tus, without pretence of presenting any universally the future detection of higgsino-like compressed spectra, valid result, but to just show an example of a model where in particular for long-lived particles with a relatively short the measurement of the Higgs mass actually does provide lifetime, can arise then in electron-proton colliders [143]. predictions for the maximally allowed typical scale of the We fnally show in Figure 6 the status of indirect superpartners, we present in Figure 7(a) the distribution detection bounds and projections in gamma-ray searches 1/2 ofthemeanstopmass,� =(�
�
) , under in space and terrestrial telescopes for ∼1TeV higgsino SUSY 1 2 � ,��SI DM under CMSSM/mSUGRA boundary conditions (we CMSSM/mSUGRA boundary conditions in the (

) implicitly assume that the chances for detection maximize plane with higgsino DM. One can see that by approximately if higgsinos saturate the relic abundance). In Figure 6(a), the next round of XENON-1T data we will be starting to probe solid black line shows the most recent 90% CL upper bound the 10 TeV range of the superpartners if the DM is entirely on the present-day �V from the statistical combination of composed of higgsinos. Note also that, for higgsino mass Fermi-LAT and MAGIC observations of dSphs [88], and the �
≲ 140 GeV,theLHCisalreadyexcluding,withdirect magenta line draws the recent bound from 10-year observa- sof-lepton bounds on electroweakinos, the parameter space � ≲8−10 tion of the Galactic Center at HESS [89] under the Einasto corresponding to SUSY TeV. 10 Advances in High Energy Physics

CMSSM/mSUGRA CMSSM/mSUGRA ≈  ≈  mh GeV mh GeV −24  −27  10 fhiggsino > % 10 fhiggsino > % ) -1 Ｍ

3 HESS 254h (Einasto) Fermi-LAT + MAGIC (dSphs) ) -1

Ｍ −25 −28

3 10 10 HESS 254h (Einasto)

Ｐ (＝Ｇ AMS-02 CR (NFW)

10−26 10−29 Ｐ ( → ) (＝Ｇ

CTA proj. 500h (Einasto, stat. only)

10−27 10−30 800 900 1000 1100 1200 1300 1400 1500 800 900 1000 1100 1200 1300 1400 1500

m (GeV) m (GeV)

(a) (b)

Figure 6: (a) Indirect detection bounds and projections in gamma-ray searches in space and terrestrial telescopes for ∼1TeV higgsino DM under CMSSM/mSUGRA boundary conditions. Solid black line shows 90% CL upper bounds on the present-day annihilation cross section + − to � � from the statistical combination of Fermi-LAT and MAGIC observations of dSphs [88]; solid magenta line shows the recent bound from 10-year observation of the Galactic Center at HESS [89] under the Einasto profle assumption; solid green line shows the upper bound from antiproton cosmic-ray (CR) data at AMS-02 [90] according to [91] for the NFW profle; and dashed blue line shows the projected reach of CTA 500h under the Einasto profle assumption [53]. (b) In magenta, the current 95% CL upper bound on the annihilation cross section (times velocity) to gamma-ray lines, �

V, from HESS [92] under the Einasto profle assumption, compared to the cross section of our ∼1TeV higgsino points.

(a) (b)

� =(� � )1/2 � ,��SI Figure 7: (a) A plot of SUSY 
1 
2 in the (

) plane with higgsino DM under CMSSM/mSUGRA boundary conditions. (b) SI EWSB fne tuning for points with higgsino DM in the (�
,��
)plane.

SI Finally, like all BSM models developed at least in part to we plot in the (�
,��
)planethesizeoftheusualBarbieri- deal with the hierarchy problem, afer the frst two runs of Giudice measure [146, 147] (following the prescription of the LHC models with higgsino DM have become marred by a [148]) (We remind the reader that the Barbieri-Giudice mea- |� �2 /� � | certain amount of EWSB fne tuning. Te severity of this issue sure is generally defned as max
� log
log
,where depends, of course, on the specifc features of each model: �
are the model’s input parameters at the typical scale of howEWSBisobtainedandtherelationtothemassofthe the messengers for SUSY breaking. In the CMSSM these are Higgs boson. In the context of the CMSSM, the fne tuning the GUT-defned parameters �0, �1/2, �0, �0, �0.). No point associated with higgsino DM is shown in Figure 7(b), where showsEWSBfnetuningoflessthanapartin100,asdirect Advances in High Energy Physics 11 consequence of the Higgs mass measurement, and one can with the 125 GeV Higgs mass when tan � is close to 1), observe the well-known fact that higgsino points favored by the prospects for detection are more tricky to assess, but expectations of naturalness correspond to �
<1TeV and not without hope. We have drawn the reader’s attention 2 lead to Ωℎ ≪ 0.12. For the specifc case of the ∼1TeV to a few references that promoted alternative venues for higgsino, a failure to observe a signal in, say, the next round the explorations of this more feeting scenarios. Promising of XENON-1T data will imply a fne tuning greater than one venues are given by the experimental determination of dipole 3 part in 10 , with rapid increase with each successive milestone moments, disappearing track signatures in colliders, and the exclusion (Tere exist ways of embedding the MSSM in UV measurement of cooling curves in white dwarfs and neutron completions that can lead to lower fne tuning for higgsino stars. DM, see, e.g., [134, 149].). Overall, we hope this might serve as an agile but com- However, we emphasize that a large fne tuning is by prehensive report on the consistency of the higgsino DM no means exclusive to the CMSSM, to higgsino DM, or picture,andonthemultipleopportunitiesthatariseforits even to SUSY in general (see, e.g., [150] for fne tuning in observationinthenotsodistantfuture. a non-SUSY scenario). As a matter of fact, the majority of phenomenological DM models found in the literature do Conflicts of Interest not even attempt to construct a UV completion that could directly relate their free parameters to the physics of the Te authors declare that there are no conficts of interest high scale. It is very possible that once a discovery is fnally regarding the publication of this article. made many of the suspended questions will start to fnd their answers. Higgsinos appear to be just in the perfect position Acknowledgments to usher, in case of their eventual discovery, a new era of understanding. 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