Probing Higgs-Portal Dark with Weakly Interacting Mediators

S. WESTHOFF Institut f¨urTheoretische Physik, Universit¨atHeidelberg, 69120 Heidelberg, Germany

The hypothesis of dark matter interacting with the uniquely via the Higgs portal is severely challenged by experiments. However, if dark matter is a , the Higgs- portal interaction implies the presence of mediators, which can change the phenomenology significantly. This article discusses the impact of weakly-interacting mediators on the dark- matter relic abundance, direct detection, and collider searches. At the LHC, a typical signa- ture of Higgs-portal fermion dark matter features soft and missing energy, similarly to production in models with . We suggest to re-interpret existing gaugino searches in the context of Higgs-portal models and to extend future searches to the broader class of dark sectors with weakly-interacting .

1 Higgs-portal fermion dark matter

The possibility that dark matter (DM) might interact with the standard model (SM) through the Higgs portal is compelling due to its simplicity. In the case of scalar dark matter, the Higgs-portal interaction can be elementary, compatible with a dark sector that consists of the dark matter candidate only. If dark matter is a fermion χ with mass mχ around the scale of electroweak symmetry breaking (EWSB), the Higgs portal is an effective interaction of mass dimension five, κ1 † iκ5 † eff = (¯χχ)(H H) + (¯χγ5χ)(H H). (1) L Λ Λ This interaction is non-renormalizable and calls for a dark sector with one or several mediator states at a scale Λ. If this new scale is situated well above the scale of EWSB, Λ v with  v = 246 GeV, the Higgs portal is the only link between the dark sector and the SM at energies E Λ, with a naturally weak coupling κ E/Λ 1. The phenomenology of this scenario has   been investigated at colliders, direct and indirect detection experiments, and has been confronted with the observed DM relic abundance. The prevention of over-abundance sets a lower bound on the Higgs-portal interaction. The scalar coupling κ1 induces -independent DM- scattering, which is strongly bounded from above by the lack of a signal at direct detection experiments. At the LHC, for mχ < mh/2, the bound on the invisible Higgs decay h χχ → from Higgs data sets a tight upper limit on κ/Λ. For mχ > mh/2, however, collider signatures are suppressed by an off-shell Higgs . To date, this suppression prevents sensitivity to the Higgs portal above the threshold and makes future collider searches very challenging. 1 A recent combined analysis of these constraints shows that viable scenarios of Higgs-portal fermion dark matter are confined to the Higgs resonance region mχ mh/2, where the observed relic ≈ abundance can be obtained for a small coupling κ. 2 If the mediator scale Λ is around the weak scale, Λ v, the Higgs portal is “open”, i.e., ≈ the elementary couplings of the mediators become visible in DM interactions with the standard model. In particular, collider searches for Higgs-portal dark matter above the Higgs threshold a) b) c)

Figure 1 – Possible realizations of the Higgs portal with fermion dark matter. a) singlet-doublet; b) doublet-triplet; c) singlet-singlet. become possible. The phenomenology of such a scenario depends on the of the mediators. We have investigated three realizations of the fermion Higgs portal, 3 which are displayed in Fig.1: a) a dark sector with a weak singlet fermion and a doublet fermion; b) a doublet fermion and a triplet fermion (see also Ref. 4); c) a singlet fermion and a singlet scalar. A model with a dark triplet fermion and a quadruplet fermion has been discussed in Ref. 5. All dark fermions have vector-like gauge interactions. In the decoupling limit mψ , mψ , mS , we recover D T → ∞ the effective Higgs-portal interactions from Eq. (1). Our goal is to study the impact of mediators on the phenomenology of the respective model, in order to determine characterstic collider signatures. A scalar mediator as in model c) mainly affects Higgs-physics observables through mixing with the . A fermion mediator generally introduces new interactions with the Higgs and weak gauge . Here we will focus on the simplest model with fermion mediators, model a), dubbed the singlet-doublet model. The main features of this model can be extrapolated to models with fermions in larger weak multiplets. In Sec.2, we introduce the singlet-doublet model for the two cases of a Dirac or a Majorana singlet. In Sec.3, we discuss DM-nucleon scattering and the relic abundance in the singlet-doublet model and point out the differences with the effective Higgs-portal scenario. In Sec.4 we describe the strategy for Higgs-portal DM searches at the LHC and give an outlook on the discovery potential of future colliders.

2 The singlet-doublet model

The dark sector of this model consists of two fermion fields, χD and χS, transforming under the SM electroweak group SU(2)L U(1)Y as χD (2, 1/2) and χS (1, 0). The field χD = + 0 × ∼ ∼ (χD, χD) is a doublet of Dirac fermions with vector-like gauge interactions, while the singlet χS can be either a Dirac or a Majorana fermion. To ensure that the lightest state in the dark sector is stable, we impose a Z2 symmetry χD,S χD,S, under which the SM fermions are even. For → − definitions and details, we refer the reader to Ref. 3.

Dirac singlet fermion. If χS is a , the spectrum consists of two neu- 0 + tral Dirac fermions, χS and χD, and a charged Dirac fermion χD. The relevant terms in the Lagrangian are

m mDχ¯DχD mSχ¯SχS yχ¯DχSH + h.c. . (2) L ⊃ − − − 0 After EWSB, the dark Yukawa coupling y introduces mixing betweenχS and χD. We define the mixing angle θa generally as

2 1 mD mS 2 2 2 sin θa = 1 + − , with (∆ma) = (mS mD) + a(yv) . (3) 2 ∆m −  a  0 0 Here a = 2, and the heavy and light mass eigenstates, χh and χl , are given by

0 0 0 0 χ = cos θ2 χS + sin θ2 χ , χ = sin θ2 χS + cos θ2 χ . (4) h D l − D The corresponding mass eigenvalues are

0 1 + m = mD + mS ∆m2 , m = mD. (5) h,l 2 ±  In the basis of mass eigenstates, the interactions of the neutral fermions with the Z and Higgs bosons read

g 2 0 µ 0 2 0 µ 0 1 0 µ 0 0 µ 0 cos θ2 χ¯l γ χl + sin θ2 χ¯hγ χh + sin(2θ2) χ¯hγ χl +χ ¯l γ χh Zµ (6) L ⊃ − 2cW 2 y h 0 0 0 0 0 0 0 0 i b sin(2θ2) χ¯hχh χ¯l χl + cos(2θ2) χ¯hχl +χ ¯l χh h. − √2 − h  i 0 Notice that the fermion mixing affects the interactions of the DM candidate χl with the Higgs boson and induces new interactions with the Z boson. The model is characterized by three parameters, which we choose to be m0, m0 m0, and y. l h − l

Majorana singlet fermion. If χS is a Majorana fermion, the dark sector consists of three c Weyl fermions transforming under SU(2)L U(1)Y as χS (1, 0), χD (2, 1/2), and χ × ∼ ∼ D ∼ (2, 1/2). In two-component notation, the relevant terms in the Lagrangian read − c 1 † c m mDχ χD mSχSχS y(H χDχS χSχ H) + h.c.. (7) L ⊃ D − 2 − − D 1 After EWSB, the mass term for the neutral states is given by m = 2 ( 0)ijχiχj + h.c.. In c0 0 L − M the basis χi = χS, χ , χ , the mass matrix reads { D D} yv yv mS √ √ − 2 2 √yv 0 m 0 =  2 D , (8) M −yv − √ mD 0  2 −    which is diagonalized by the following transformation

1 1 0 cos θ4 √ sin θ4 √ sin θ4 χh − 2 2 χS 0 0 √i √i c0 χm =  2 2  χD . (9)  0  1 1  0  χl sin θ4 √ cos θ4 √ cos θ4 χD  2 − 2        The mixing angle θ4 is given by Eq. (3) with a = 4. The mass spectrum then reads

0 1 0 m = mD + mS ∆m4 , m = mD = m+. (10) h,l 2 ± m  The couplings of the neutral fermions to Z and h are given by

g 0∗ 0∗ µ 0 i sin θ4 χh cos θ4 χl σ¯ χmZµ + h.c. (11) L ⊃ 2cW − y 0 0 0 0  0 0 b sin(2θ4) χ χ χ χ 2 cos(2θ4)χ χ h + h.c.. − 2 h h − l l − h l h  i Unlike in the Dirac case, the Majorana fermions have no mass-diagonal couplings to the Z boson. The parameter space of this model consists of m0, m0 m0, and y. This scenario corresponds l m − l to the bino- system (with decoupled wino) in the Minimal Supersymmetric Standard Model (MSSM) for tan β = 1 and y = g0/√2. 8

0 + 0 0 χl W χl Z χl Z − 0 0 χ χm,h χm,h 0 − 0 0 χl W χl Z χl Z FIG. 1: Feynman diagrams for the dominant annihilation channels in the Majorana DM models with fermion mediators. Figure 2 – Dominant annihilation channels of Majorana fermion dark matter in the singlet-doublet model.

On the other hand, if mD,mT 200 GeV, the mass ordering is mc

In the limit mT ,mD2, m2T mD2 mZ the radiative splittings are given by mχ|mN fN| q (N) q mN 2 (N) Q mN σN = k 2 , fN = GZ + fT q Gh + fTG Gh , (12) (mχ + mN ) π g2 mqe2 27 mQ m+ = (m q c2 m ),q m+ = m . Q (35) T 8⇡ WX W ZX D 8⇡ Z X Thewith correctionsk = 1(4) to for the Dirac o↵-diagonal (Majorana) elements dark in matter, the mass light matrix have beenq = u, neglected d, s and above, heavy which quarks is justifiedQ = (N) (N) forc,yv b, t, andmT nucleonmD . The form one-loop factors correctionsfT q and f canTG also. Vector be neglected and scalar for the currents calculation induce of the the mixing dominant angles. ⌧ | | + + 0 Sincespin-independent the corrections DMmT interactionsand mD are with positive, the the nucleus. lightest The state corresponding of the spectrum effective is the neutral couplings state forc ,a 0 0 DMDirac candidate. and Majorana As is apparent dark matter in Eq. (33), read the Z boson coupling to a DM pair c c is absent and the Higgs coupling is proportional to sin(2✓2). Direct detection signals are thus suppressed for a small mixing angle ✓2. 2 3 2 q g (Tq 2sW Qq) 2 q g mq y Dirac χS + χD : GZ = −2 2 cos θ2,Gh = 2 sin(2θ2); (13) III.− THERMAL4cW mZ RELIC DENSITY 2mh mW √2 g mq Majorana χ + χ : Gq = 0,Gq = y sin(2θ ). As described above,S weD assumeZ that the fermionic Higgs portal is responsibleh 2 for explaining4 the entire dark 4mh mW matter density through thermal freeze-out in the early universe. q ForIn the Dirac singlet-singlet dark matter, model, the DMZ-mediated preferentially interaction annihilatesG intodominatesh2h2 and theh2h1 crossfinal section.states, if kinematically The non- allowed. The amplitude for h h is proportional to cosZ 2 ↵,where↵ is the h–S mixing angle, so that observation of spin-independent! 2 scattering2 at direct detection experiments sets a strong bound annihilation can be ecient even for very small values of ↵. For m < (mh1 + mh2 )/2, the main annihilation on the dark-fermion mixing+ angle, cos θ2. Majorana dark matter does not couple to the vector channels are into h1h1 and W W , where the latter proceeds via o↵-shell h1,2 exchange in the s-channel. For ¯ q smallcurrent, values so of thatm,the nucleonbb final scattering state can alsois induced become only relevant. by the The scalar rates for coupling these processesGh from grow Higgs with ex- sin ↵. Thechange. requirement Current of a experiments suciently large are sensitive annihilation even cross-section to this smaller then imposes rate, yielding a lower a bound strong on bound sin ↵. on yForsin(2 theθ4 Majorana). In either DM case, models to with be compatible fermion mediators with direct (the Majorana detection singlet-doublet results, the DM model state in Sec. must II B be and the Majorana doublet-triplet model0 in Sec. II C), the main channels for pair annihilation of the neutral DM an almost pure weak singlet, χ χS, with a strongly suppressed dark Yukawa coupling y. candidates involve WW and ZZ finall ∼ states. These processes are mediated by one of the mediator fermion 0 0 states in the t-channel, see Fig. 1, since the Zl l coupling vanishes exactly. For the Majorana singlet-doublet The suppression of electroweak couplings has important consequences on0 the DM relic model, annihilation via the s-channel Higgs-boson resonance is also a viable option for ml mh/2. In this case,abundance. resonant enhancement Dirac DM annihilation from the Higgs-boson proceeds propagator dominantly leads through to a sus-channelciently largeZ-boson annihilation⇡ exchange, cross- section0 0 to produce∗ the¯ correct0 relic density. The dominant annihilation final states are then given by the χl χl Z ff. (For ml & 1 TeV, annihilation into WW , ZZ final states becomes relevant.) → → ¯ + leadingFor Majorana Higgs decay dark modes, matter,i. e. thebb, WW dominant⇤, gg and annihilation⌧ ⌧ . is into pairs of electroweak gauge bosons In contrast, in the Dirac singlet-doublet model, the DM annihilation mainly proceeds through s-channel through t-channel exchange of mediators, as shown0 in Fig.2. Assuming thermal freeze-out, Z-boson exchange. Only for very large DM masses, ml (1 TeV), annihilation into WW and ZZ final statesthe strong through suppressiont-channel fermion due to exchange direct detectionbecomes important. constraints⇠ O leads to an over-abundance of dark 0 ± 0 0 matter,In the singlet-doublet unless co-annihilation models (bothχl χ for, χl theχm Majoranawith mediator and Dirac states cases), enhances the lightest the annihilation neutral fermion rate. is constrainedThe relic abundanceto be mostly as singlet, observed to avoid by the the Planck strong collaboration, direct detection6 bounds for doublet dark matter (see Sec. IV). However, the singlet nature of DM in these models also suppresses the annihilation cross-section, thus typically yielding too large of a relicPlanck density.2 Nevertheless, the correct DM density could still be obtained 0 0 0 ΩDM h = 0.1199 0.0022, (14) if l ± and l m co-annihilation processes contribute at a± sizeable level. As a result, the allowed parameter spacecan is be limited obtained to relatively with co-annihilation small values for from the mass a spectrum splitting m ofD darkmS. fermions One exception with is small the Higgs mass resonance split- region for the Majorana singlet-doublet model, where the correct value for the annihilation cross-section can tings m+ m0, m0 m0 of a few tens of GeV. A narrow spectrum thus results to be a typical be obtained− withoutl co-annihilation.h,m − l feature of Higgs-portal dark matter with mixing dark fermions. An exception is Majorana dark matter near the Higgs resonance, mχ mh/2. In this case, the observed relic abundance can ≈ be obtained without co-annihilation through resonant Higgs decay into b¯b, WW ∗, gg and τ +τ − final states, and larger mass splittings are possible. ai a ute eehne ylwrn h uso h rnvremmnao h charged the of spectra. compressed momenta with transverse products. symmetric the decay on soft cuts to sensitive the signal-to-background state, more lowering The final be by energy. the to enhanced missing boosts leptons large be jet of further hard requirements can additional trigger ratio the an pass Requiring to detector. splittings helping the mass thus escape small that The left. and 4, Fig. in shown m is diagram Feynman corresponding A process dominant mediators the The through jets) interactions. (or weak leptons pro- and through resonantly states energies be DM should LHC into mediators dark at decay the mixing then collisions scale, with weak -proton matter the dark in abun- around Higgs-portal relic duced states of and DM signature detection Assuming collider direct characteristic from fermions. a constraints to the satisfy colliders leads to dance, at necessary leptons spectrum, soft narrow with The searches fermion Dark the between 4 possibility relation the parametric is direct the difference by changes scattering. this excluded which DM-nucleon with for and is mediators, scenario reason density scale the decoupling relic main weak with the The the co-annihilation from viable around DM observations. different a matter of density is are dark relic This scale where and weak (1), scale. detection the Eq. same matter from around the mediators dark matter of heavy Dirac dark are mediators fermion for if Notice, with space option, models parameter rate. annihilation Higgs-portal the LAT. DM that Fermi of suppressed the shows corner the from upper-left to data the recent due by scenarios, of these exclusion to the are sensitive areas however, as red not Upper LUX (14) is efficient. from Eq. not tion bounds is from tight co-annihilation abundance where by area), relic excluded red observed (lower parameters density, The splittings three mass relic small the splitting. observed of mass the one small obtain fixes the to given required focus fine-tuned, is We ingly co-annihilation (right). matter where dark range GeV Majorana 100 mass and DM (left) the matter dark on Dirac for model singlet-doublet Ω abundance. mission, relic the Planck and the constraints detection from indirect obtained and splitting value direct mass by the allowed constant remain to (right) areas Majorana a fixed white and The is to (left) respectively. Dirac density correspond with relic model curves singlet-doublet The the Colored of matter. space parameter dark the fermion on Constraints – 3 Figure y h,m 0 10 10 10 otlpo intrshv ensuidadotmzdfrteLCi h otx fsuper- of context the in LHC the for optimized and studied been have signatures Soft- the on abundance relic and detection direct from constraints the summarize we 3, Fig. In -3 -2 -1 − Fermi LHC14 HL-LHC m 200 m < l 0 edt otlposi h nlsae copne ymsigeeg rmD states DM from energy missing by accompanied state, final the in leptons soft to lead l 0 χ q δ < q ¯ m − =0.1 0 0.05 0.02 400 → → e.For TeV. 1 χ W l 0 m W ∗− ILC l [GeV] ∗− 0.01

→ 600 X1T

→ χ LUX m − χ l 0 χ l 0 > m,h 0 ` m − 800 e,temxn ewe akfrin eoe increas- becomes fermions dark between mixing the TeV, 1 ν l 0 ¯ , 8 7 , ` χ , h eann loe aaee pc tewiearea) white (the space parameter allowed remaining The m n te ietdtcineprmns nietdetec- Indirect experiments. detection direct other and h,m 0 FCC-hh m,h 0 1000 − 9 , 10 → m , 11 l 0 δ

χ 0 0 , m mm-ml [GeV] l 0 Ref. 10 20 30 40 y 0 Z ≡ tas xldsteprmtrrneof range parameter the excludes also It . ∗ ( 11 → m 200 h 0 rdcsapoiigsgauefrrun for signature promising a predicts χ − l 0 HL-LHC LHC14 ` m − l 0 ` ) + /m y=0.1 0.01 0.03 400 ,

l 0 ILC n akYkw coupling Yukawa dark and m ( l 0 ` [GeV] = 600 Ω DM ,µ e, 0.12 < X1T )

. LUX 800 χ m Ω = + − DM Planck FCC-hh (15) m 1000 l 0 y , , . 2 2 Detector description and event reconstruction

b `(⌫) ⌫(`) f ˜ f´ + t ˜1 ⌫˜(`˜) 0 p 0 p ˜1 ˜1 0 p ˜1 p 0 ˜1 ˜ 0 `˜(⌫˜) t f´ ˜2 f b `(⌫) `(⌫)

FigureFigure 4 – 1: Left: Signal typical models collider signature for top of squark Higgs-portal pair dark production matter with mixing with darksubsequent fermions (here: four-body singlet- decays doublet(left), and model - with Majorana singlet). Right: pair production LHC signature with of supersymmetric decays via gauginos sleptons with and soft sneutrinos leptons. 12 (right). labels are suppressed. II with up to three soft leptons, a hard jet and missing energy. We have re-casted their analysis forlepton our Higgs-portal topology offers models. the The second-highest results are shown branching in Fig.3 fraction for √s = after 14 TeV the andpurely luminosities hadronic mode. ofIn 300 this fb channel−1 (black we dashed consider curves) only and , 3000 fb− which1 (black can dotted be efficiently curves). The reconstructed LHC is expected and to identified with transverse momenta as low as 5 GeV. For the dilepton topology0 we require a second test the co-annihilation scenario of fermion Higgs-portal dark matter for ml . 250 GeV. leptonSearches ( for leptons or ) and missing of opposite energy charge.at the LHC The during single run and I have double not lead electron to constraints final states are onnot Higgs-portal used because scenarios, they have since thereduced predicted sensitivity lepton momenta compared are to too the soft muon to pass channels the trigger due to the andhigher analysispT thresholds cuts. Recently, required a dedicated for . search Infor addition, supersymmetric selected gauginos events with are required soft leptons to have an hasenergetic been performed jet compatible with 8-TeV with data. the ISR12 Compressed signature, atgauginos most one are oneadditional possible jet scenario of moderate among to high models with a fermionic dark sector. They lead to a similarmiss collider phenomenology, as can pT, no hard leptons, and a significant amount of ET . The dominant SM backgrounds to this be seen by comparing the final states of the processes displayed in Fig.4. The opportunity to search are pair production of top quarks, W boson or Z/g⇤ production in association with jets, testand a diboson broader (VV)class of production. models with Their soft-lepton contributions signatures to should the signal not be region missed. (SR) We are therefore estimated by suggest to re-interpret current and future searches for supersymmetry with soft leptons in terms correcting the predictions from simulation using the event yields observed in several control of Higgs-portal fermion dark matter. By optimizing the analysis for the parameter space of regions (CRs) in data. Data are also used to validate this procedure and to derive systematic Higgs-portal models, we might be able to test the co-annihilation scenario with existing data alreadyuncertainties. today. To probe higher DM masses in our models, future colliders will be helpful. Again, we+ 0 The results of the dilepton search are also interpreted in terms of the model of c1 -c2 pair haveproduction re-casted discussed existing projections above. For of supersymmetry small c+ c0 searchesmass splittings, with soft leptons the leptons for the in planned the final state electron- ILC with √s = 1 TeV 13 and1 a possible1 100-TeV proton-proton collider. 14,15 would be soft and therefore within the signal region0 of the dilepton search. e e The ILC is expected to test the DM mass range up to ml . 500 GeV, almost half the collider energy, due to its very clean environment. Ae 100-TeVe collider will ultimately be able to reach TeV-scale2 Detector masses and description thereby test these and models event conclusively. reconstruction AcknowledgmentsThe CMS detector has been described in detail in Ref. [26]. Its central feature is a supercon- ducting solenoid that provides a homogeneous field of 3.8 T in a volume containing a silicon Ipixel thank and the strip organizers tracker, of a the lead 51st tungstate Rencontres crystal de Moriond electromagnetic for inviting calorimeter, me to speak and at athis brass and interesting and inspiring conference. Furthermore, I wish to thank Ayres Freitas and Jure Zupan scintillator calorimeter. Muons are measured in gas-ionization chambers embedded in for collaboration and sharing insight on this topic. I acknowledge funding by the Carl-Zeiss the steel flux-return yoke surrounding the solenoid. 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