Dark matter candidates in the NMSSM with RH neutrino superfields
Daniel E. Lopez-Fogliani, Andres D. Perez, Roberto Ruiz de Austri
DDark matter candidates in the NMSSM withRH neutrino superfields
Daniel E. López-Fogliani ∗a,b , Andres D. Perez †c , andRoberto Ruiz de Austri ‡d a Instituto de Física de Buenos Aires UBA & CONICET, Departamento de Física, Facultad deCiencia Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina b Pontificia Universidad Católica Argentina, Av. Alicia Moreau de Justo 1500,1107 Buenos Aires, Argentina c IFLP, CONICET - Dpto. de Física, Universidad Nacional de La Plata,C.C. 67, 1900 La Plata, Argentina d Instituto de Física Corpuscular CSIC-UV, c/Catedrático José Beltrán 2, 46980 Paterna(Valencia), Spain
Abstract
R-parity conserving supersymmetric models with right-handed (RH) neutrinos arevery appealing since they could naturally explain neutrino physics and also providea good dark matter (DM) candidate such as the lightest supersymmetric particle(LSP). In this work we consider the next-to-minimal supersymmetric standard model(NMSSM) plus RH neutrino superfields, with effective Majorana masses dynamicallygenerated at the electroweak scale (EW). We perform a scan of the relevant parameterspace and study both possible DM candidates: RH sneutrino and neutralino. Espe-cially for the case of RH sneutrino DM we analyse the intimate relation between bothcandidates to obtain the correct amount of relic density. Besides the well-known reso-nances, annihilations through scalar quartic couplings and coannihilation mechanismswith all kind of neutralinos, are crucial. Finally, we present the impact of current andfuture direct and indirect detection experiments on both DM candidates.Keywords: New Physics, Supersymmetry, Dark Matter, Sneutrino. ∗ [email protected] † [email protected] ‡ rruiz@ific.uv.es a r X i v : . [ h e p - ph ] F e b ontents Although the standard model (SM) is extraordinarily successful, there are still open ques-tions in particle physics. Cosmological observations reveal the presence of dark matter(DM) in the Universe and determine its abundance [1–3], however the SM provides no vi-able candidate. Besides, the observation of neutrino oscillations phenomenon reveals thatneutrinos must have extremely small, but non-vanishing masses [4–8], which are not allowedin the SM.Introducing right-handed (RH) neutrinos is perhaps the simplest extension of the SMfor describing neutrino masses and the observed neutrino oscillations . Although currentresults do not allow to establish the nature of the particle, the couplings of the RH neutrinosand the left-handed (LH) counterparts provide a source of Dirac- or Majorana-type massterm, depending on the model. Small neutrino masses can be realized with very smallYukawa couplings, O (10 − ) , in a Dirac-type way after electroweak symmetry breaking(EWSB) [10–13]. On the other hand, if we allow Majorana masses for the RH neutrinos,from the order of the electroweak (EW) scale to the order of the Grand Unified Theory(GUT) scale, the smallness of the neutrino mass pattern can be achieve by a seesaw mech-anism with neutrino Yukawa coupling from the order of the electron Yukawa coupling toorder one [14–18].In supersymmetric models (SUSY) the hierarchy problem is avoided, and the introduc-tion of RH neutrino superfields can reproduce the neutrino physics. In addition, in modelswith R -parity conservation, the ones that are of interest for this work, besides the usual For a review about the origins of neutrino masses see Ref. [9] and references therein. and extend it with three generations of RH neutrino superfields [43]. In this context wasfirst showed in [44] that thermal RH sneutrinos are good dark matter candidates. Thephenomenology of this model has been widely analysed including: the viability of the RHsneutrino as thermal DM with direct and indirect detection signatures [44–53], the neu-trino sector and DM candidates with spontaneous R-parity or CP violation [43,54–56], andcollider and Higgs physics [57–60]The NMSSM includes in its formulation a singlet superfield to solve dynamically the µ -problem of the MSSM. Moreover, including RH sneutrino superfields, extra terms in thesuperpotential between the RH neutrinos and the singlet superfield are allowed. This hasa threefold effect in the neutrino and sneutrino sectors. First, the mass of the active neu-trinos is generated by a seesaw mechanism, hence the neutrino Yukawa couplings can be ofthe same order as the electron Yukawa couplings. Second, the mass matrix of the sneutrinosector presents distinct features generated when the scalar singlet acquires vacuum expec-tation value (VEV) after EWSB, allowing a particular range for the mixing angle betweenLH and RH sneutrinos. Third, new decay and annihilation channels through the directcoupling to the singlet appear, contributing to the thermal production of sneutrino relicdensity.In this paper, we present a low energy phenomenological SUSY realization with twoDM candidates, the RH sneutrino and the usual neutralino. To explore the model, weperform a scan of the parameter space imposing constraints given by the measured amountof DM in the Universe, direct detection and indirect detection experiments of DM, SUSYand Higgs searches at colliders as well as neutrino physics. We identify the regions whereeither neutralinos or sneutrinos are the LSP and study the mechanisms to obtain the properamount of relic density through thermal processes. As we will see, the sneutrino mainlyuses three mechanisms: resonances with CP-even Higgs, annihilations through scalar quar-tic couplings with two CP-odd Higgs in the final state, and coannihilations with neutralinos.Thus, the relation between both DM candidates is explored in detail. Interestingly, coan-nihilations can be achieved with all kind of neutralinos, not only Higgsinos. Even more,the lightest slepton or colored particle, stau and stop respectively, can also take the role ofthe coannihilating partner. For an NMSSM review see for example Ref. [41, 42].
3e organize the paper as follows. In Section 2, we present the characteristics of theNMSSM plus RH neutrino superfields, and different mechanism to obtain the correct RHsneutrino relic density. Then, in Section 3 we explain the setup of the scan and the ex-perimental constraints that have been considered. In Section 4, we show the scan results,explore the main mechanisms to obtain the correct relic density, and discuss the character-istics of both DM candidates, with especial emphasis on the RH sneutrino. We also presentseveral benchmark points for interesting cases. Finally, we show the impact of current di-rect and indirect detection constraints, and the important regions of the model that wouldbe probed by next generation experiments. The conclusions are left for Section 5.
The next-to-minimal supersymmetric standard model (NMSSM) solves the µ -problem ofthe minimal supersymmetric standard model (MSSM), but cannot explain the neutrinomass pattern. This can be solved including in its formulation RH neutrino superfields,generating dynamically Majorana masses at the EW scale. The superpotential consideredis, W = (cid:15) αβ (cid:16) Y ije ˆ H αd ˆ L βi ˆ e j + Y ijd ˆ H αd ˆ Q βi ˆ d j + Y iju ˆ Q αi ˆ H βu ˆ u j + Y ijN ˆ L αi ˆ H βu ˆ N j + λ ˆ S ˆ H αu ˆ H βd (cid:17) + λ ijN ˆ N i ˆ N j ˆ S + κ S , (1)where ˆ S (L=0) is a singlet superfield, ˆ N (L=1) the neutrino superfield, (cid:15) αβ ( α, β = 1 , ) isa totally antisymmetric tensor with (cid:15) = 1 . As for the case of the NMSSM a Z symmetryis invoked to forbid the appearance of any dimensional parameter. The usual soft SUSYbreaking terms in our case are V soft = (cid:20) (cid:15) αβ (cid:18) A ije Y ije H αd ˜ L βi ˜ e j + A ijd Y ijd H αd ˜ Q βi ˜ d j + A iju Y iju ˜ Q αi H βu ˜ u j + A ijN Y ijN ˜ L αi H βu ˜ N j + A λ λ S H αu H βd (cid:19) + A ijλ N λ ijN ˜ N i ˜ N j S + A κ κ S (cid:21) + h.c. + m φ ij φ † i φ j + m θ ij θ i θ ∗ j + m H d H † d H d + m H u H † u H u + m S S S ∗ + 12 M ˜ B ˜ B + 12 M ˜ W i ˜ W i + 12 M ˜ g a ˜ g a , (2)where φ = ˜ L, ˜ Q ; θ = ˜ e, ˜ N , ˜ u, ˜ d are the scalar components of the corresponding superfields,and the gauginos ˜ B, ˜ W , ˜ g , are the fermionic superpartners of the B , W bosons, and gluons.In this work we take all sfermion soft masses diagonal, m ij = m ii = m i and vanishingotherwise, were summation of repeated index convention was not used. Regarding theYukawa and trilinear couplings, we assume that only the third generation of sfermionsare non-zero, T ij = A ij Y ij , without the summation convention, except in the neutrinocase where Y ijN and A ijN are taken diagonal. Furthermore, we also consider diagonal theparameter λ ijN = λ iiN = λ iN , and its corresponding trilinear coupling, A ijλ N λ ijN = A iλ N λ iN = T iλ N .After electroweak symmetry breaking (EWSB) induced by the soft SUSY-breaking4erms of O ( TeV ) , and with the choice of CP conservation, the neutral Higgses ( H u,d ) andthe scalar singlet develop the following vacuum expectation values (VEVs) (cid:104) H d (cid:105) = v d √ , (cid:104) H u (cid:105) = v u √ , (cid:104) s (cid:105) = v s √ , (3)where v = v d + v u = 4 m Z / ( g + g (cid:48) ) (cid:39) (246 GeV ) , with m Z the Z boson mass, and g and g (cid:48) the U (1) Y and SU (2) L couplings, correspondingly. Then, the scalar components of thesuperfields ˆ H u , ˆ H d , and ˆ S can be written as H u = (cid:32) H + uv u √ + H R u + i H I u √ (cid:33) , H d = (cid:32) v d √ + H R d + i H I d √ H − d (cid:33) , S = v s √ S R + i S I √ , (4)where the superscripts R and I indicate CP-even and CP-odd component fields, respectively.In the basis ( H R d , H R u , S R ), we denote the CP-even scalar mass matrix as M S . Likewise,dropping off the Goldstone mode, in the basis ( A , S I ), with A = H I u cos β + H I d sin β and tan β = v u v d , the CP-odd scalar mass matrix is denoted M P . The mass eigenstates of theCP-even Higgs h i with i = 1 , , , and the CP-odd Higgs A i with i = 1 , can be obtainedby h h h = S ij H R d H R u S R , (cid:32) A A (cid:33) = P ij (cid:32) AS I (cid:33) , (5)where the matrices S ij and P ij diagonalize the mass matrices M S and M P , respectively.The states are labeled according to the mass hierarchy m h < m h < m h , and m A < m A .We can estimate m A i ∝ A κ κ v s , for the singlet dominated boson, which will be importantlater to allow RH sneutrino annihilations to light CP-odd scalars.To generate an effective µ -term, µ eff = λ v s √ , v s = O ( GeV-TeV ) is needed. Then, thesuperpotential term λ iN ˆ N i ˆ N i S generates dynamically a RH neutrino Majorana mass term M iN = λ iN v s √ ∼ O ( GeV-TeV ) , assuming that the parameters λ and λ iN are O (0 . − .The LH neutrino masses, m ν L , are generated by a seesaw mechanism. The generalneutrino mass matrix is given by M ν = (cid:32) m D m TD M N (cid:33) , (6)therefore, m ν L (cid:39) − m D M − N m TD , (7)with the dirac mass m D (cid:39) Y N v u √ . Thus m ν L (cid:39) Y N v u λ N v s ∼ Y N × EW scale, which implies Y N ∼ − to get neutrino masses within the right order of magnitude.The neutralino and chargino sectors are the same as in the NMSSM. The neutral color-less gauginos mix with the neutral higgsinos-singlinos and generate a symmetric 5 × M χ . In the basis ( − i ˜ B , − i ˜ W , ˜ H d , ˜ H u , S ) we get M χ = M − g v d g v u M g (cid:48) v d − g (cid:48) v u − g v d g (cid:48) v d − λ v s √ − λ v u √ g v u − g (cid:48) v u − λ v s √ − λ v d √ − λ v u √ − λ v d √ κ v s √ . (8)To obtain the mass eigenstates, the neutralino mass matrix can be diagonalized N ∗ M χ N − = diag ( m χ , m χ , m χ , m χ , m χ ) , (9)where m χ < m χ < m χ < m χ < m χ . Then, the neutralino eigenstates can be written as χ i = N i ˜ B + N i ˜ W + N i ˜ H u + N i ˜ H d + N i ˜ S , with the matrix N defining the compositionof the neutralinos.In the chargino sector, the charged Higgsinos and the charged gaugino mix forming twocouples of physical chargino χ ± and χ ± . In the basis ( ˜ W ± , ˜ H ± d,u ) the chargino mass matrixis given by M χ ± = (cid:32) M √ β m W √ β m W µ (cid:33) . (10)Using two unitary matrices the chargino mass matrix can be diagonalized to obtain themass eigenstates U ∗ M χ ± V − = diag ( m χ ± , m χ ± ) , (11)where m χ ± < m χ ± . The sneutrinos form a × mass matrix divided into × submatrices M ν = (cid:32) m RR × × m II (cid:33) , (12)where again the subscripts R and I denote CP-even and CP-odd states, respectively. Theoff-diagonal submatrices are zero due to our choice of CP conservation. The submatricesare m RR = (cid:32) m L i A + i ( A + i ) T m R i + B i (cid:33) , m II = (cid:32) m L i A − i ( A − i ) T m R i − B i (cid:33) , (13)with A + i = Y iN (cid:0) A iN v u + 2 λ iN v u v s − λ v d v s (cid:1) , (14)6 − i = Y iN (cid:0) A iN v u − λ iN v u v s − λ v d v s (cid:1) , (15) B i = 2 λ iN (cid:0) A iλ N v s + κ v s − λ v u v d (cid:1) , (16) m L i = m L i + ( Y iN ) v u + 12 m Z cos 2 β, (17) m R i = m N i + ( Y iN ) v u + 4 ( λ iN ) v s , (18)as before, the index i, j = 1 , , are the family indices. The mixing between LH andRH sneutrinos is suppressed by the small neutrino Yukawa value in Eq. (14) and (15).Considering only one family of neutrinos the mixing angle between LH and RH sneutrinos, θ ˜ ν , can be approximated by tan 2 θ ˜ ν (cid:39) A ± m L − ( m R ± B ) (19) (cid:39) Y N ( A N v u ± λ N v u v s − λ v d v s ) m L + m Z cos 2 β − m N − λ N v s ∓ λ N ( A λ N v s + κ v s − λ v u v d ) , (20)where the upper (lower) sign corresponds to the CP-even (CP-odd) state. For typicalparameter values, A N ∼ A λ N ∼ O ( GeV ) , tan β ∼ O (10) , λ ∼ κ ∼ λ N , we get tan 2 θ ˜ ν ∼ Y N λ N v s v u m L + m Z cos 2 β − m N − λ N v s ∼ − × Y N ∼ O (10 − ) , (21)where we have used that m ˜ L ∼ O (10 ) GeV to evade the stringent collider constraintson SUSY particles, and that λ N v s ∼ O ( EW ) with Y N ∼ − to reproduce the neutrinomasses.Due to the small mixing, the RH sneutrino masses can be taken as m ν Ri (cid:39) m R i ± B i , (22)here also the upper (lower) sign corresponds to the CP-even (CP-odd) state. We can seethat the mass splitting is proportional to λ iN in Eq. (16). If λ N → then m ν Ri (cid:39) m N i . Fortypical parameter values in the NMSSM plus RH neutrinos m ν Ri ≈ m N i + (2 λ iN v s ) ± (cid:0) T iλ N v s + 2 λ iN κ v s (cid:1) . (23)The new parameters with respect to the NMSSM m N , λ N and T λ N can be chosen to set thephysical RH sneutrino mass, without affecting the rest of the mass spectrum. Moreover,the last two parameters also determine the RH sneutrino coupling to the singlet Higgsboson. The existence of direct couplings of the RH sneutrino to Higgs bosons and neutralinos is acrucial feature of this model. The term λ N SN N in the superpotential, and the correspond-ing soft-breaking term A λ N λ N SN N , generate the interactions through a mixing betweenthe singlet and singlino components of S with the CP-even Higgs bosons and neutralinos,7espectively. Large values of λ N imply a more effective sneutrino annihilation, hence asmaller relic abundance. Moreover, the coupling also affects the value of the RH neutrinoand sneutrino masses (see Eq. (23)), but not to the rest of the mass spectrum.We denote ˜ ν R a RH sneutrino, V a vector boson, Z or W ; h i ( A i ) a neutral CP-even(CP-odd) scalar of the Higgs sector (recall that Higgs bosons are mixed with the scalarsinglet); f a SM fermion; ν R a RH neutrino; χ i a neutralino; χ ± j a chargino; ˜ l a slepton; ˜ q asquark; and ˜ g a gluino. The relevant annihilation channels involved to achieve the correctamount of RH sneutrino relic density are:• ˜ ν R ˜ ν R → V V ∗ , V h i , h i h ∗ i , A i A ∗ i , f ¯ f , ν R ¯ ν R via s-channel exchange of a CP-even Higgsboson.• ˜ ν R ˜ ν R → h i h ∗ i , A i A ∗ i via direct quartic coupling involving λ , κ and λ N .• ˜ ν R ˜ ν R → h i h ∗ i via t- and u-channel, exchanging a sneutrino.• ˜ ν R ˜ ν R → ν R ¯ ν R , via t- and u-channel exchanging a neutralino (via λ N ˆ N ˆ N ˆ S ).• In the sneutrino sector, if CP-even and CP-odd states are nearly degenerate in mass,annihilation channels between them have to be taken into account, mainly via s-channel exchange of a CP-odd Higgs boson.• Coannihilation with neutralinos: ˜ ν R χ i → lighter states, and χ i χ ± j → lighter states.• Coannihilation with sleptons, squarks, or gluinos: ˜ ν R ˜ l i → lighter states, ˜ ν R ˜ q i → lighter states, or ˜ ν R ˜ g → lighter states.The viability of the annihilation mechanisms involving s-channel Higgs exchange aswell as annihilation channels with scalar and pseudo-scalar Higgs bosons in the final state,depend on the mass hierarchy of the overall scalar sectors of the model. This relatesthe Higgs and sneutrino sectors. In the NMSSM both CP-even and CP-odd Higgs statescan be very light with significant singlet component, making these annihilation channelskinematically allowed for very light sneutrino masses. Thus, an allowed DM relic densitycan be obtained for low mass DM candidates that would otherwise be excluded. As usual,the annihilation processes that involve s-channel Higgs exchange are enhanced near theresonant mass condition, m ˜ ν R (cid:39) m h i / . We will see that resonances and direct annihilationsthrough quartic coupling to a pair of pseudo-scalar Higgs are especially relevant for lowmass sneutrinos.On the other hand, away from resonances the direct annihilation of RH sneutrinosis not efficient enough leading to an overproduction of DM. However if the mass splittingbetween the RH sneutrinos and other SUSY particles is small coannihilations can be efficientto keep the thermal equilibrium for longer and therefore their relic abundance can fulfillobservations [61].As RH sneutrino couplings with neutralinos is mainly through a Higgs boson exchange(for example using the terms λ N N N S and λSHH ), coannihilations with neutralinos mostlyHiggsino are more efficient. In this case, the allowed sneutrino mass range will inheritthe constraints on the neutralino (and chargino) sectors regarding its masses, i.e. weget m ˜ ν N > ∼ GeV due to collider searches on SUSY particles. As we will see in detail8ater, this is one of the main mechanisms to obtain a correct relic density. However,coannihilations with all kind of neutralinos are possible, allowing to find viable RH sneutrinoDM for a wide range of parameters.
For RH sneutrino, the scattering with a nucleon N , either N = p, n , at tree level onlyoccurs via t -channel exchange of a neutral CP-even Higgs boson. In the non-relativisticregime, the effective operator L eff (cid:101) ν R − N = g N (cid:101) ν R (cid:101) ν R ¯ ψ N ψ N can be defined, thus the totalspin-independent sneutrino-nucleon scattering cross section is given by [45, 62] σ SI (cid:101) ν R − N = µ red πm (cid:101) ν R g N , (24)where µ red = m N m (cid:101) ν R / ( m N + m (cid:101) ν R ) is the reduced mass of the nucleon with mass m N . Theeffective coefficient results [45, 62] g N = m N (cid:88) i =1 C (cid:101) ν R (cid:101) ν R h i C NNh i m h i = m N (cid:88) i =1 C (cid:101) ν R (cid:101) ν R h i m h i (cid:88) q j = u,c,t f ( N ) q j Y q j m q j S iH u + (cid:88) q j = d,s,b f ( N ) q j Y q j m q j S iH d = m N (cid:88) i =1 C (cid:101) ν R (cid:101) ν R h i m h i (cid:32) √ F ( N ) u v u S iH u + √ F ( N ) d v d S iH d (cid:33) , (25)where S iH u and S iH d are the elements of the matrices defined in Eq. (5) that diagonalize theCP-even Higgs mass matrix. C NNh i involves the Yukawa couplings of the Higgs bosons withthe constituents of the nucleon N represented by its form factors F ( N ) u and F ( N ) d subject toconsiderable uncertainties, with f ( N ) q = m − N (cid:104) N | m q q ¯ q | N (cid:105) . Finally, C (cid:101) ν R (cid:101) ν R h i determinesthe sneutrino-sneutrino-Higgs coupling strength involving the terms λ N (cid:101) N (cid:101) N S , λSH u H d , κS , and A λ N λ N (cid:101) N (cid:101) N S . It is defined as [45] C (cid:101) ν R (cid:101) ν R h i = λλ N √ v u S iH d + v d S iH u ) + (cid:20) (4 λ N + 2 κλ N ) µ eff λ + A λ N λ N √ (cid:21) S iS , (26)the first two terms represent the coupling with the Higgs doublets and the last terms withthe singlet.To estimate the order of magnitude of the spin-independent sneutrino-proton crosssection let us consider that the only relevant scattering proceeds by exchanging the lightestHiggs boson h that is SM-like, then σ SI (cid:101) ν R − p = ( F ( p ) u ) π m p m (cid:101) ν R m h (cid:18) λ λ N tan β (cid:19) , (27) The sneutrino is a scalar field, then there is no axial-vector coupling in the effective Lagrangian, i.e.sneutrino DM results in vanishing spin-dependent cross section. µ red (cid:39) m p for m p (cid:28) m (cid:101) ν R , with m p the proton mass. If wetake F ( p ) u (cid:39) . as default value used by MicrOmegas [63–65] we get σ SI (cid:101) ν R − p = 1 . × − cm (cid:18) GeV m (cid:101) ν R (cid:19) (cid:18) λ . (cid:19) (cid:18) λ N . (cid:19) (cid:18) β (cid:19) . (28)Eq. (27) can be used as a first order approximation as most solutions found present aSM-like Higgs as the lightest CP-even state, and a Higgs boson with H d dominant com-ponent whose contribution to the cross section is suppressed by its large mass. Regardingthe scattering with a nucleon via a t -channel exchange of a singlet dominated scalar, itscontribution is suppressed by the mixing with the doublets, as can be seen from Eq. (25).From the above discussion, the sneutrino direct detection depends on both the Higgssector, mainly through λ and tan β , and the sneutrino parameters λ N and m (cid:101) ν R , involvedin Eq. (23). To obtain representative solutions for different DM candidates, and explore the relevantparameter space of the model, we carried out a series of scans. To find regions compatiblewith a given experimental data, we used a likelihood data-driven method employing the
Multinest [66] algorithm as optimizer .We used the Mathematica package
SARAH [67–69] to build the model, and the code
SPheno [70, 71] to generate the particle spectrum, branching ratios and decay rates. Eachpoint is required not to have tachyonic eigenstates and we only select models that have thelightest neutralino or the lightest RH sneutrino as LSP. Then, we compute the likelihoodassociated to each experimental data set.
MicrOmegas [63–65] is used to compute the DM relic density, the present annihilationcross section ( (cid:104) σ DM v (cid:105) ), and the spin-dependent and spin-independent WIMP-nucleon scat-tering cross sections ( σ SD DM − p and σ SI DM − p ), assuming that the mentioned candidates are thesole DM candidate in the Universe. However, we do not assume that the thermal relicdensity saturates the Planck value in order to allow for the possibility of multicomponentDM. For example, axions might make up a substantial amount of DM, or even gravitinoscoexisting with RH sneutrinos are possible for some parameter regions.For the DM annihilation spectrum we consider constraints on DM indirect detectionsearches obtained from the observation of dwarf galaxies, using Fermi –LAT collaborationdata [72], and the observation of the Galactic center, taken from H.E.S.S. collaborationanalysis [73]. Both data sets were implemented as hard cuts on each of the reportedchannels. Other limits, for example on line signals, are weaker for the neutralino and RHsneutrino signatures.The constraints on the WIMP-nucleon scattering cross sections from DM direct detec-tion experiments (XENON1T [74,75] and PICO-60 [76,77]) are computed using
DDCalc [78]. The main focus of this work is to present characteristic features of the model regarding the DMcandidates. We do not aim to perform an statistical interpretation as done in Ref. [53]. onstraint DM relic density ( Ω Planck cdm h ) . ± . [1]SI cross section ( σ SD DM − p ) XENON1T [74, 75]SD cross section ( σ SI DM − p ) PICO60 [76, 77]Annihilation cross section ( (cid:104) σ DM v (cid:105) ) Fermi –LAT [72] and H.E.S.S. [73]Higgs constraints LEP, Tevatron, and LHC (
HiggsBounds [79–81])Higgs signal LHC and Tevatron (
HiggsSignals [82–84]) BR ( b → sγ ) (3 . ± . × − [85] BR ( B s → µ + µ − ) (2 . +0 . − . ) × − [86] BR ( µ → eγ ) < . × − [87] BR ( µ → eee ) < . × − [88]Light stops and sbottoms LHC [89, 90]R-hadrons (long-lived colored particles) LHC [91]2 and 3 Leptons + missing E T LHC [92–94]Chargino masses m ˜ χ ± > . GeV [95]
Table 1: Constraints that have been applied to our model set (see text for details).We required that the p-value reported by
DDCalc be larger than 5% during the scan. Laterwe apply XENON1T and PICO-60 central values as hard-cuts in our analysis. DM directdetection limits are rescaled by r DM = Ω DM h Ω Planck cdm h , and the indirect detection constraints by r DM , if the thermal relic density is less than the observed value. HiggsBounds [79–81] is used to determine whether the SUSY models satisfy LEP, Teva-tron and LHC Higgs constraints. Negative searches of Higgs-like signals were transformedinto exclusions limits, and given a parameter point with its theoretical prediction in theHiggs sector,
HiggsBounds indicates if the parameter set is allowed or not at 95% confidencelevel with an step likelihood function (i.e. allowed: 1, excluded: 0). In order to assess if thepredicted Higgs sector reproduces the signal observed by ATLAS and CMS complementedwith Tevatron data,
HiggsSignals [82–84] is used to quantitatively determine with a χ measure the compatibility of the NMSSM prediction with the measured signal strengthand mass. We required that the p-value reported by HiggsSignals be larger than 5%.
In addition to the experimental constraints mentioned in the sampling setup, we consideredseveral flavor and SUSY searches that we discuss below. A summary of all the constraintsadopted for our model can be seen in Table 1.
Flavor:
We take into account current constraints on some flavor observables calculatedwith
SPheno . b → sγ is a flavour changing neutral current (FCNC) process forbidden attree level in the SM. However, it occurs at leading order through loop diagrams and becomes11otentially sensitive to new physics. Similarly, B s → µ + µ − is also forbidden at tree level inthe SM but occurs radiatively. We use the following experimental determinations [85, 86]: BR ( b → sγ ) = (3 . ± . × − , (29) BR ( B s → µ + µ − ) = (2 . +0 . − . ) × − . (30)For BR ( b → sγ ) we considered the calculated average in Ref. [85] using the experimentalvalues [96–100]. For BR ( B s → µ + µ − ) we considered the ATLAS Collaboration determi-nation [86], which is in agreement with the LHCb measurement based on 8 TeV data [101]and a former statistical combination of CMS and LHCb measurements with 7 and 8 TeVdata [102]. We have also considered the theoretical uncertainties for each observable as 10%of the corresponding best fit value. We do not include constraints as the muon anoma-lous magnetic moment, or B d → µ + µ − [101], since we are not trying to solve any possiblediscrepancy with respect to the SM predictions.The SM allows charged lepton flavour violating (LFV) processes with only extremelysmall branching ratios ( < − ) even taking into account neutrino mass differences andmixing angles. Such decays free from SM background are very sensitive to new physics,in particular to SUSY models. We considered the LFV constraint from BR ( µ → eγ ) < . × − [87] at 90% C.L., and BR ( µ → eee ) < . × − [88] at 90% C.L. Light stops and sbottoms:
Due to our choice of free parameters and fixed values(see the next subsection), the lightest squarks are mainly stops and sbottoms, thereforethe constraints we consider focus on these particles. Some neutralinos, especially Binodominated, can coannihilate with a colored particles to obtain an allowed amount of relicdensity. The two-body decay channel ˜ t → t χ and three-body decay channel ˜ t → b W χ are kinematically forbidden when the lightest stop is nearly degenerate with the neutralino,which is needed to get an efficient coannihilation mechanism. Hence, we also take intoaccount current constraints for a compressed mass spectrum. The dominant light stop decaywould be via flavor-changing neutral current (FCNC) two-body decay channel ˜ t → c χ ,and a contribution given by the four-body decay channel ˜ t → b f ¯ f (cid:48) χ . If the lightestcolored particle is a sbottom, then ˜ b → b χ is relevant. The exclusion limits are given interm of the stop (or sbottom) and neutralino masses [89, 90].RH sneutrinos can also achieve an allowed relic abundance through coannihilations withsquarks. Due to the low interaction rate between the RH sneutrino and the lightest squark,along with the small mass splitting to get efficient coannihilation, stops and sbottoms wouldhave decay lengths larger than 100 kilometers. For these scenarios, constraints on long-livedcolored particles at the LHC, called R-hadrons, have to be applied. Hence, we considerATLAS constraints with √ s = 13 TeV and L = 36 . fb − , imposing m ˜ t > GeV and m ˜ b > GeV [91] for RH sneutrinos LSP with stop or sbottom NLSP, respectively.
Leptons + missing E T final states: LHC searches for electroweak production ofcharginos and sleptons decaying into final states with 2 and 3 leptons plus missing trans-verse energy are relevant, in particular for Bino dominated χ and Wino dominated χ and χ ± [92–94]. Charginos:
We apply a cut for the chargino masses ( m ˜ χ ± > . GeV) following12EP searches [95]. Finally, we would like to mention that coannihilations between thelightest neutralino LSP and the lightest chargino NLSP, may imply disappearing-tracksignatures in pp collisions due to long-lived charginos, if their masses are nearly degenerate.However, extremely pure Higgsinos or Winos and neutrino-chargino mass difference of ≈ MeV [103] are needed. We do not have any point in our scan fulfilling those conditions,hence we do not have exclusions from the latter restrictions.
Following the considerations made in previous sections, in the sfermion sector we fix thedimensional parameters that are not especially relevant to our analysis, m e i = m L i = m d i =2 . × GeV with i = 1 , , , and m N i = m u i = m Q i = 2 . × GeV with i = 1 , .The values taken are sufficiently large to be consistent with LHC sparticles searches.We also set T d = T d = 256 GeV, and T e = T e = − GeV taking into accountthe corresponding Yukawa couplings. The neutrino Yukawa couplings are only relevantto reproduce the neutrino mass pattern, hence they are set Y iN = 10 − when the scan isfocused on finding solutions with neutralino or RH sneutrino LSP. We consider vanishing T iN = A iN Y iN as an approximation due to the small neutrino Yukawa couplings and that wetake A i N ∼ O ( GeV ) . To simplify the analysis, we set λ iN = − . , and T iλ N = 0 for i = 1 , ,to obtain two families of heavy sneutrinos.The gaugino sector is described by its soft-breaking masses M , M , and M ; we fix thegluino mass parameter M = 3 TeV to avoid LHC constraints on gluino strong production.In the Higgs-scalar singlet sector the soft-breaking masses are related with the vacuumexpectation values (VEVs) by the minimization conditions of the Higgs potential afterelectroweak symmetry breaking (EWSB). Then, it is conventional to take as free parameters(inputs) the following: the ratio of the Higgs VEVs tan β ≡ v u /v d , λ , κ , the effectivehiggsino mass parameter µ eff = λ v s / √ , T λ = A λ λ and T κ = A κ κ .We are left with the following set of variables as independent parameters: M , M , tan β, µ eff , λ, κ, λ N , T λ , T κ , T λ N , m N , m u , m Q , T u . (31)We carried out a scan over these parameters within the ranges depicted in Table 2 usinglog priors (in logarithmic scale). The ranges were set taking into account the followingconsiderations:• The range of tan β , T u and the soft squark masses of the 3rd generation, are helpfulto reproduce the correct SM-like Higgs mass.• The upper bounds of λ , κ , λ N and tan β are set to satisfy perturbativity of the theoryup to Planck scale.• LEP searches for chargino and neutralino requires m ˜ χ ± > . GeV, then µ eff > GeV. We also expect µ eff (cid:39) O (100) GeV because it is directly related to m Z , but weallow values of O ( TeV ) to be general.• The range of M , M , µ eff , λ and κ allow us to find neutralinos with differentcompositions. 13 arameter Range M (20, 3000) GeV M (20, 3000) GeV µ eff (100, 5000) GeV tan β (2, 50) λ (0.001, 0.8) κ (0.001, 0.8) λ N (-0.4, -0.001) T λ (0.001, 600) GeV T κ (-30, -0.001) GeV T λ N (-1100, -0.001) GeV m N ( , . × ) GeV m u ( . × , × ) GeV m Q ( . × , × ) GeV T u (700, 10000) GeV Parameter Fixed value M λ iN , i = 1 , -0.5 T iλ N , i = 1 , m N i , i = 1 , . × GeV m u i , i = 1 , . × GeV m Q i , i = 1 , . × GeV m d i , i = 1 , , . × GeV m e i , i = 1 , , . × GeV m L i , i = 1 , , . × GeV T d
256 GeV T e -98 GeV T iN , i = 1 , , Table 2: Sampling ranges and fixed parameters used in our scan.• The signs of λ N , T λ N and κ , are set to obtain a CP-even state as the lightest RHsneutrino (see Eq. 23).• The sign of T κ is set to allow light CP-odd Higgs state with dominant singlet contri-bution.• The range and fixed values of λ iN , T iλ N and m N i , allow us to find one family of lightRH sneutrinos and two heavy ones. In Fig. 1 we show the relic density as a function of the DM candidate mass for the parameterpoints that fulfill the constraints considered in this work. The results correspond to thebroad range of input parameters shown in Table 2, with additional explorations in severalinput parameter subranges. The identity of the LSP, and dominant composition for the14
200 400 600 800 1000 1200 1400 m DM (GeV) D M h Bino 99%Bino 90%Wino 99%Wino 90%Higgsino 99%Higgsino 90%Singlino 99%Singlino 90%Other mixtures ~ ν R Planck 2018
Figure 1: Relic density versus LSP mass for the parameter points that fulfill all the con-straints considered in this work. The color coding represents the LSP identity, and in thecase of neutralino, the dominant composition as labeled. The red solid line corresponds tothe amount of DM measured by the Planck Collaboration.neutralino case, is coded in color as indicated on the figure (we define a pure neutralinoif | N j | > . , with dominant component j defined in Eq. (9)). Due to the fact that theoff-diagonal elements of the neutralino and chargino mass matrices are at most ∼ m W (seeEq. (8) and (10)), and the scan ranges chosen, neutralinos are typically pure electroweakeigenstate.For the neutralino DM case, the mass lower limit is established by a combination of LEPand relic density constraint, while the upper limit due to the input parameter ranges. Oneof the most stringent limits that constraints Bino and Singlino dominated neutralinos is thePlanck upper limit on cold DM abundance, since models with the mentioned candidatestend to produce too high relic density. However, points with this kind of neutralinos and Ω DM h = Ω Planck cdm h can be found in the entire mass range. On the other hand, solutionsthat saturate the relic density with Higgsinos or Winos are restricted to ∼ GeVDM masses.To briefly analyse the channels used by different types of neutralinos, in Fig. 2 weshow the lightest chargino vs the neutralino mass, without including the points with RHsneutrino as DM candidate. We can clearly see that for almost all Higgsino and Winodominated neutralinos, coannihilations with charginos are important to obtain an allowedrelic abundance. Notice that Wino-like neutralinos in green lie below the blue points. Through out the rest of the text we will refer to the lightest neutralino as neutralino for simplicity,unless otherwise specified.
200 400 600 800 1000 1200 1400 m χ (GeV) m χ ± ( G e V ) Bino 99%Bino 90%Wino 99%Wino 90%Higgsino 99%Higgsino 90%Singlino 99%Singlino 90%Other mixtures m χ ±1 = m χ Figure 2: Lightest chargino vs lightest neutralino. Solutions with RH sneutrino LSP arenot included. Almost all Higgsino and Wino (below the blue points) dominated neutralinoscoannihilate with charginos to obtain an allowed relic density. Low mass Bino and Singlinoannihilation mechanisms employ resonances.Singlinos with non negligible Higgsino contribution also employ this mechanism. For lowmasses, resonant conditions through Z and h i are dominant, and depicted as vertical narrowstrips (see also Fig. 1). For higher masses, coannihilation channels with squarks are relevantfor Bino and Singlino neutralinos.Two relevant parameter in the neutralino sector are λ and κ , related to the Higgsinoand Singlino masses, respectively (see Eq. (8)). As expected, χ can be Higgsino dominatedfor λ < κ , and Singlino dominated if λ > κ . Notice that the gauginos are not directlycoupled with the Singlinos, hence Bino and Wino dominated neutralinos can be achievedfor any relation between λ and κ . The mentioned parameters will be relevant later whenwe discuss RH sneutrino DM SI cross section, since λ is involved in Eq. (27). This will beparticularly important for RH sneutrino-Higgsino coannihilations.Next we will focus on the sneutrino sector. Similarly to the case of Bino and Singlinodominated neutralinos, the small coupling of the RH sneutrino with the rest of the particlesresults in a very high RH sneutrino relic abundance. However, as seen in Subsec. 2.2,there are three main mechanisms to efficiently annihilate the RH sneutrinos: the resonantsneutrino mass condition m ˜ ν R (cid:39) m h i / , annihilations via direct quartic couplings, and thecoannihilation condition where the mass splitting between a RH sneutrino and a secondsparticle is small.In Fig. 3 we show only the points with RH sneutrino as DM candidate. The left paneldepicts the main channels used by RH sneutrinos to obtain an allowed relic density. For m ˜ ν R < ∼ GeV, the dominant processes are resonances with the lightest CP-even scalar16
200 400 600 800 1000 1200 1400 m DM (GeV) D M h Neutralino coannihilationResonance with h Resonance with h Annihilation to A Squark coannihilationOther channelsPlanck 2018 m DM (GeV) D M h ~ ν R Planck 2018 l o g [( m χ m ~ ν R ) / m ~ ν R ] Figure 3: Relic density versus LSP mass, only for points with RH sneutrino DM. The colorcoding on the left panel represents the main channels used by RH sneutrinos to obtainan allowed relic density. The color coding on the right panel shows the weighted massdifference between neutralino and RH sneutrino. Points towards the blue tone correspondmainly to coaniquilations with neutrinos. The red solid line corresponds to the amount ofDM measured by the Planck Collaboration.(orange) and annihilations via direct quartic couplings to the lightest pseudo-scalar (green),with almost no coannihilations due to collider constraints on charginos. On the other hand,for m ˜ ν R > ∼ GeV the dominant mechanisms are coannihilations with neutralinos (blue).However, very important contributions come from resonances with the second lightest CP-even scalar (red), and annihilations via direct quartic couplings. The former mechanismis especially important to obtain low relic densities and can be the only channel presentfor low enough abundances. The latter mechanism will be relevant for direct detectionexperiments, being the dominant channel to yield signals in the ballpark of next generationinstruments. Coannihilations with stops are present for m ˜ ν R > ∼ GeV with extremelylow sneutrino-nucleon scattering cross section. We would like to remark that in each massregion, solutions for the mentioned channels with Ω DM h = Ω Planck cdm h can be found.An important requirement for coannihilation solutions is that the coannihilation partnershould have efficient annihilation channels. If we decouple the RH sneutrinos, the relicabundance of the remaining LSP has to be within experimental constraints. Also, the relicdensity that RH sneutrinos can achieve with the mentioned mechanism is bounded frombelow by the relic density that would have obtained its coannihilation partner if it werethe LSP.The color coding of the right panel of Fig. 3 represents the value of log [( m χ − m ˜ ν R ) /m ˜ ν R ] .Coannihilations with neutralinos are important for a mass splitting (cid:46) , i.e. when log [( m χ − m ˜ ν R ) /m ˜ ν R ] (cid:46) − . In Fig. 1, we can see that Higgsinos and Winos LSP arearranged in two easily identifiable curves. In the right panel of Fig. 3, points in darkblue, i.e. RH sneutrinos LSP with the lowest mass splitting, lie in the regions drawn bythe mentioned curves. Furthermore, comparing with the left panel of Fig. 3, we can also17
25 50 75 100 125 150 175 200 m DM (GeV) D M h ~ ν R Planck 2018 | λ N | m DM (GeV) r D M σ S I D M p ( c m ) ~ ν R XENON1TLZDARWINNeutrino Floor | λ N | Figure 4: Relic density (left) and scaled spin-independent direct detection cross section(right) vs RH sneutrino mass for a scan in the ( µ eff , λ N , T λ N , m (cid:101) N ) space (see text fordetails). Three annihilation channels can be identify: resonance with a SM-like Higgs andannihilation through scalar quartic coupling for m DM (cid:46) GeV, and coannihilation withHiggsino dominated neutralinos for m DM (cid:38) GeV.identify these curves as the relic density lower limit of RH sneutrino DM with Higgsino orWino coannihilations.To summarize, the parameter space of RH sneutrino-neutralino coannihilations lieswithin m LSP ˜ ν R < m LSPχ and Ω LSPχ h < Ω LSP ˜ ν R h < Ω Planck cdm h , (32)where the subscript χ ( ˜ ν R ) with the superscript LSP emphasizes whether the RH neutrinois (not) decoupled. Finally, notice that for a fixed DM mass, Winos LSP can achieve lowerrelic densities, therefore the points using coannihilations with neutralinos in the regionbelow the Higgsino curve are dominated by Wino-like neutralinos.We should highlight here that, as expected, it is much easier for
Multinest to find neu-tralinos rather than RH sneutrinos as DM candidate fulfilling all the constraints imposed (ifwe run the scan with the input parameter broad range shown in Table 2 we get about O (20) candidate points with neutralino LSP per point with sneutrino LSP). The solutions involv-ing coannihilation channels with RH sneutrino are usually found after Multinest finds aviable neutralino. Then, to minimize the likelihood, the code scans a similar parameterregion and a viable RH sneutrino could be achieved as a result of this process.The above discussion can be used as a hint to search for RH sneutrino with the correctrelic density. If a parameter point with neutralino DM is viable, varying m ˜ N , λ N , T λ N , and κ according to Eq. (23), we can get different values of m ˜ ν R while leaving approximatelyunchanged the rest of the mass spectrum. Then, a RH sneutrino as DM candidate with mass m ˜ ν R ∼ m χ could be found using a viable neutralino solution as seed and the coannihilationmechanism to obtain a correct thermal relic abundance. Fig. 1 includes some exampleswhere a deeper exploration of the parameter space was performed in this way.18 ixed Parameters M m u × GeV M m Q × GeV tan β T u λ T λ κ T κ -0.0195 GeV Scan Range λ N [-0.126, -0.103] T λ N [-38.8, -32.1] GeV µ eff [158.7, 192.1] GeV m N [3757.6, 4546.7] GeV Table 3: Set of inputs for the scan shown in Fig. 4.To illustrate the rest of the main mechanisms to obtain solutions for different RHsneutrino masses, in Fig. 4 we present the results of a dedicated scan. Three importantchannels can be easily identified: a resonance with a SM-like Higgs, annihilation throughscalar quartic coupling, and coannihilation with Higgsino dominated neutralinos. Thesolutions with RH sneutrino presented in the figure were found considering a scan over onlyfour parameters ( µ eff , λ N , T λ N , m (cid:101) N ), whose range can be seen in Table 3 together withthe fixed value of rest of the parameters. This set of inputs results in a Higgsino dominatedneutralino with m χ ∼ − GeV, and a light pseudo-scalar with m A ∼ − GeV.For m (cid:101) ν R (cid:46) GeV the first two mechanisms to achieve a correct amount of relicdensity can be noticed: a funnel condition for m (cid:101) ν R (cid:39) m h / depicted as a vertical narrowstrip, and annihilation through direct quartic coupling (cid:101) ν R (cid:101) ν R → A A . The latter couplingis determined by C (cid:101) ν R (cid:101) ν R A A = − (cid:18) λ N − λ N κ (cid:19) , (33)where we have assumed that the lightest pseudo-scalar is singlet dominated. A moreefficient annihilation and hence a lower relic density is achieved for increasing values of λ N ,as can be seen from the left panel of Fig. 4. In this case, allowed points with low masssneutrinos can be obtained up to m (cid:101) ν R ∼ GeV when the four point interaction becomeskinematically forbidden.As discussed in Subsection 2.3 (see Eq. (27)), σ SI (cid:101) ν R − p increases for larger values of λ N ,i.e. larger sneutrino-sneutrino-Higgs coupling. This is shown on the right panel of Fig. 4,especially for m (cid:101) ν R (cid:46) GeV, where the solutions for this particular scan present lowdispersion in Ω DM h for each value of m DM . Notice that for points using direct quarticcoupling r DM ∼ Ω DM h ∼ m DM and σ SIDM − p ∼ m − DM , hence the scaled SI cross section isapproximately constant.For m (cid:101) ν R (cid:38) GeV the annihilation mechanism involving pseudo-scalar particles be-comes inefficient due to its dependence with the sneutrino mass, resulting in overproductionof DM. However, for m (cid:101) ν R ∼ − GeV, solutions involving coannihilation with theHiggsino dominated neutralino are obtained. In this case, despite having points with λ N inthe same range as in the previous region, the suppression coming from a higher m (cid:101) ν R results19n a lower σ SI (cid:101) ν R .To exemplify this and other mechanisms found, several benchmark points with RHsneutrino as DM candidate are shown in Appendix A. In Table 4 BP1-4 consider coanni-hilations with Higgsino, Wino, Singlino, and Bino dominated neutralinos, respectively. InTable 5 we show an example for coannihilation with stop in
BP5 . Finally,
BP6-8 , shownin Table 6, we present the parameters for a RH sneutrino that annihilates via direct quarticcoupling to a pair of light pseudo-scalars, a resonance with the SM-like Higgs boson, anda resonance with the second lightest Higgs boson, h , correspondingly.Regarding the viability of the DM candidates of the model, we can conclude the follow-ing:• As expected, for neutralinos with masses below ∼ GeV, resonant conditionsthrough Z and h i are dominant, especially for Bino and Singlino-like neutralinos.They are depicted as vertical narrow strips. A significant Higgsino fraction is usuallyneeded, although if the h Higgs boson has dominant singlet component, some pureSinglinos can be found via funnel using the κ ˆ S term (see for example, benchmarkpoint BP3 in Table 4).• For Bino and Singlino neutralinos in the upper middle mass region, annihilationsinvolving A i are also present. In the same region, Bino-like neutralino coannihilationchannels with stops are relevant.• As expected, Wino and Higgsino dominated neutralinos result in a low relic density formasses below ∼ TeV. They are arranged in two easily identifiable curves, and pointswith a mixture of Wino and Higgsino-like neutralinos lie between both sets. Below ∼ GeV these kind of neutralinos cannot be found due to chargino constraints.• RH sneutrinos with very low relic density can be found in the entire mass range,particularly through coannihilations and resonances.• For m (cid:101) ν R < ∼ GeV annihilations via direct quartic couplings to a pair of light CP-odd Higgs, and resonances to CP-even Higgs are the dominant channels to obtainan allowed RH sneutrino DM relic abundance. The former mechanism is possiblebecause we are considering an NMSSM-like model.• For m (cid:101) ν R > ∼ GeV annihilations via direct quartic couplings are still significant, butcoannihilations with Higgsino neutralino are dominant. Nonetheless, coannihilationwith all kind of neutralinos (especially with Wino neutralinos) can be found. An-other important contribution comes from resonances with the second lightest CP-evenscalar, especially for low relic densities where it can be the only channel available.• For high RH sneutrino masses, coannihilation with sbottoms and stops are possible.For m (cid:101) ν R > ∼ GeV coannihilations with the mentioned sparticles are dominant.We would like to mention that coannihilations with staus and gluinos are feasible forRH sneutrino masses > ∼
430 GeV and 2 TeV, respectively [91], but are not presentdue to our choise of parameter values.20
200 400 600 800 1000 1200 1400 m DM (GeV) r D M σ S I D M p ( c m ) Bino 99%Bino 90%Wino 99%Wino 90%Higgsino 99%Higgsino 90%Singlino 99%Singlino 90%Other mixturesXENON1TLZDARWINNeutrino Floor m DM (GeV) r D M σ S DD M p ( c m ) Bino 99%Bino 90%Wino 99%Wino 90%Higgsino 99%Higgsino 90%Singlino 99%Singlino 90%Other mixturesPICO-60PICO-500DARWINNeutrino Floor (PICO) m DM (GeV) r D M σ S I D M p ( c m ) Neutralino coannihilationResonance with h Resonance with h Annihilation to A Other channelsXENON1TLZDARWINNeutrino Floor
Figure 5: The first row presents the scaled spin-independent (top-left) and spin-dependent(top-right) direct detection cross sections for neutralino DM, the color coding represents itscomposition. The bottom row shows the scaled spin-independent direct detection cross sec-tions for RH sneutrino DM; the color coding corresponds to the main channels used by RHsneutrinos to obtain an allowed abundance. The solid red curves show current experimen-tal sensitivities from XENON1T [74, 75] and PICO-60 [76, 77] for SI and SD, respectively.Projected sensitivities for DARWIN [104], LZ [105] and PICO-500 [106] experiments areshown as black dotted and dot-dashed curves. The black dashed curves show the neutrinofloor taken from Ref. [107, 108]; for the SD case, the neutrino background depicted corre-sponds to experiments using C F as detector material, like PICO. The scaling factor r DM accounts for the possibility that the calculated thermal relic density lies below the Planckmeasurement. 21 .2 Direct and Indirect detection constraints In this section, we present the impact of current and near future direct and indirect detec-tion DM experiments on the model. In Fig. 5 we show the predicted scaled spin-independent(SI) and scaled spin-dependent (SD) scattering cross sections of the LSP with a target nu-cleus for the allowed points of our scan. The first row of figures corresponds to neutralinoDM, and the second row to RH sneutrino DM. The scaling factor r DM = Ω DM h Ω Planck cdm h allow usto compare solutions with relic density below the Planck measurement against publishedconstraint. This is particularly relevant for low mass Higgsinos and Winos. We also presentthe current experimental constraints from XENON1T [74, 75] and PICO-60 [76, 77], andthe neutrino background floor [107, 108] for SI and SD cross sections.The projected sensitivities from DARWIN [104], LZ [105] and PICO-500 [106] are alsoshown in Fig. 5. Upcoming experiments will be able to probe an important region ofthe neutralino DM parameter space, for example, almost all the predicted points withHiggsinos could be tested by LZ. On the other hand, DARWIN will be important to probethe available parameter space up to the neutrino floor for SI, covering also the majorityof Winos, Binos and Singlinos predicted. The SD neutrino background depends heavilyon the material of the detector, (see Ref. [108]). A significant region will be tested byPICO-500 and DARWIN. As in the SI case, this is especially true for Higgsinos, as well asfor Bino and Singlino resonances with Z and light h i .On the other hand, next generation experiments will also probe RH sneutrino DM. Inthe bottom panel of Fig. 5 the same color coding as in the left panel of Fig. 3 is used,representing the main channels used by RH sneutrinos to obtain an allowed abundance.As can be seen, almost all points that would be explored by LZ and DARWIN do notcoannihilate with neutralinos. In fact, the dominant mechanism in this region involvesannihilations to a pair of pseudo-scalars through direct quartic coupling. For m ˜ ν R (cid:38) GeV resonances with heavy CP-even Higgs scalar are important.Solutions with RH sneutrino DM using coannihilations with neutralinos prefer low val-ues of | λ N | and λ , therefore tend to produce very small SI cross section values (see the SIcross section approximation shown in Eq. (27)). In our scan, we allow values as low as 0.001for these inputs, resulting in very small σ SI (cid:101) ν R − p . For increasing DM masses, most solutionswith coannihilations tend to cut deeper into the neutrino coherent scattering background,making them very challenging to test with current techniques. Nonetheless, some pointsthat coannihilate with neutralinos lie in the region to be probed by LZ and DARWIN. Ingeneral, these solutions also present contributions from annihilations to a pair of pseudo-scalars or resonances with h i . These mechanisms allow larger values of | λ N | , as can be seenin the left panel of Fig. 6.The other two relevant parameters also involved in the RH sneutrino SI cross sectionestimate are m DM and tan β . On the right panel of Fig. 6 the color coding shows the valueof tan β , and as expected from Eq. (27), we get decreasing values of tan β for increasingvalues of m DM . The impact of both parameters is counteracted to keep r DM × σ SI (cid:101) ν R − p ∼ constant. Finally, we would like to remark that the region with RH sneutrino DM thatcould be explored by next generation experiments prefers low values of tan β , in particularfor m ˜ ν R (cid:38) GeV we get tan β < ∼ . In that regard, for m ˜ ν R (cid:38) GeV, it is dificult toobtain a solution with σ SI (cid:101) ν R − p up to the XENON1T bound, because λ and λ N ( tan β ) needto take values close to their allowed upper (lower) limits (see Table 2 and Eq. (27)).22
200 400 600 800 1000 m DM (GeV) r D M σ S I D M p ( c m ) ~ ν R XENON1TLZDARWINNeutrino Floor l o g ( | λ N | ) m DM (GeV) r D M σ S I D M p ( c m ) ~ ν R XENON1TLZDARWINNeutrino Floor t a n β Figure 6: Scaled spin-independent direct detection cross sections for RH sneutrino DM;the color coding corresponds to the value of λ N (left), and the value of tan β (right) foreach point. The rest of the references are the same as in Fig. 5.Although SI experiments provide a more sensitive tool according to the projected ex-periments, a joint SI and SD analysis offers the opportunity to disentangle the LSP identitybetween the two DM candidates of the model. For example, for coannihilation points, aslight variation of the free parameters in the sneutrino sector can give us RH sneutrino DMor neutralino DM with approximately the same mass. This situation could be unraveledas coannihilating RH sneutrinos tend to have a very small SI cross section. On the otherhand, if we consider RH sneutrino DM that annihilates through a quartic coupling, we canget a similar SI signature to the case of neutrino DM, but with vanishing SD signal. Ofcourse, in the case of neutralino DM, a combination of SI and SD experiments can helpdetermine its composition.To analyse the impact of current and future indirect detection experiments, in Fig. 7,we show the normalized thermally averaged annihilation cross section, r DM × (cid:104) σv (cid:105) , as afunction of the DM mass, where r DM is the DM relic density fraction defined previously.Upper bounds on annihilation cross sections are derived for pure channels. In ourscan we obtain a mixture of several annihilation channels, therefore the data sets wereimplemented on each of the reported channels. In case of annihilation final states for whichlimits have not been reported by the collaborations, we employ the most relevant existingbounds. In particular, for the e − e + channel we consider the same limit as for µ − µ + , for u ¯ u , d ¯ d , s ¯ s , c ¯ c , A A , ZZ and hh we use b ¯ b , and for H − H + the bound for W + W − .It is worth noticing that in our analysis we apply indirect detection constraints at facevalue because direct detection limits are usually more restrictive to set the allowed param-eter points. However uncertainties associated with DM density profiles and astrophysicalbackground modeling result in bounds on the annihilation cross section that can vary upto an order of magnitude [110, 111].In Fig. 7, the solid red curve corresponds to the limit of b ¯ b final state set by Fermi –LATfrom the observation of dwarfs galaxies [72], to guide the eye. The dashed red curve obtained23
200 400 600 800 1000 1200 1400 m DM (GeV) r D M σ v ( c m s ) Bino 99%Bino 90%Wino 99%Wino 90%Higgsino 99%Higgsino 90%Singlino 99%Singlino 90%Other mixtures ~ ν R b ¯ b Fermi LAT (dwarfs)H.E.S.S. 2016 (Einasto)CTA (Einasto)
Figure 7: Distribution of the scanned points in the ( m DM , r DM (cid:104) σv (cid:105) ) space, where r DM is the DM relic density fraction. The color coding represents the LSP identity, and thedominant composition in the case of neutralino, as in Fig. 1. The current upper 95% C.L.limits from Fermi –LAT to b ¯ b from the observation of dwarfs [72], and the limits of H.E.S.S.from observations of the Galactic center using Einasto profile [109] are indicated as solidand dashed red curves, respectively. The projected CTA sensitivity [109] is shown as adot-dashed magenta curve.by H.E.S.S. collaboration [73] represents annihilation lower limits from observations of theGalactic center using Einasto profile calculated in Ref. [109]. The dot-dashed magentacurve corresponds to the projected CTA [112] 95% C.L. sensitivity to DM annihilationderived from observations of the Galactic center assuming 500 hour homogeneous exposureand Einasto profile [109]. As can be seen, a small fraction of points will be explored byCTA. In the case of neutralino DM, the region that would be probed is constituted ofmostly Wino dominated points with r DM > . , i.e. with masses > ∼ GeV. ConsideringRH sneutrino DM, CTA will study points with dominant annihilation channel involvingdirect quartic coupling to pseudo-scalars, and masses up to ∼ GeV.Finally in Fig. 8 we present the complementarity of direct and indirect detection ex-periments and the future prospects of detection. The experimental constraints consider m DM ≈ GeV to help the reader. While the next generation of direct detection ex-periments will cut deep into the parameter space, a complementary approach would beimportant to determine the characteristics of dark matter, especially for Winos and RHsneutrinos. 24 r DM σ SIDM p (cm ) r D M σ v ( c m s ) Bino 99%Bino 90%Wino 99%Wino 90%Higgsino 99%Higgsino 90%Singlino 99%Singlino 90%Other mixtures ~ ν R Current limitLZCTANeutrino floor
Figure 8: Direct and indirect detection complementarity. Scanned points in the( r DM σ SIDM − p , r DM (cid:104) σv (cid:105) ) plane with the same color coding as in Fig. 1. XENON1T and Fermi –LAT set the current direct and indirect detection upper limits, respectively. Asrepresentative values for the neutrino floor, current upper limits and projected sensitivitywe consider m DM ≈ GeV.
In this work we have analysed the next-to-minimal supersymmetric standard model in-cluding right-handed neutrinos superfields. This model is the simplest R -parity conservingextension that simultaneously solves the µ -problem of the MSSM and explains neutrinophysics in a natural way. In this framework, besides the usual neutralino, the RH scalarpartner of the neutrino becomes a good DM candidate.As RH sneutrinos do not interact directly with SM particles, we would typically expectDM overproduction and very small SI scattering cross section with nucleons, even belowthe neutrino background. However, one crucial feature of the model is the existence ofRH sneutrino direct couplings to Higgs bosons and to neutralinos. This fact arises due tointeraction terms between RH neutrino and singlet fields ( λ N SN N , and the correspondingsoft-breaking terms), absent in the NMSSM. Then, the extra terms are key factors toobtain the correct amount of relic density, and to allow small but measurable DM-nucleonscattering and DM annihilation cross section.To explore the model, we have carried out a scan of the parameter space employing
Multinest as optimizer. Several constraints have been imposed, including the measuredamount of DM in the Universe, direct and indirect DM detection experiments, Higgs data,flavor physics, and SUSY searches at colliders probing light stops, sbottoms, charginos andleptons plus missing E T in the final state. Additionally, we have analysed the impact and25omplementarity of near future direct and indirect detection endeavours.Although in our scan we have used a likelihood data-driven method, we have not per-formed an statistical interpretation as done in Ref. [53]. Instead, we have identified regionswith viable DM candidates and we have studied their characteristic features for a broaderparameter space, which in turn results in a wider DM mass range allowed. Moreover, wehave not assumed that the thermal relic density saturates the experimental value, allowingmulticomponent DM scenarios in order to be as general as possible.We have studied both neutralino and RH sneutrino as DM candidates, and concludedthat viable solutions can be obtained for a wide range of DM masses, from a few GeV toabove 1 TeV, over a broad parameter space. Since the neutralino behaves similarly to theNMSSM one, we have emphasized our analysis on the RH sneutrino. We have found thatto get an allowed relic abundance, RH sneutrino mainly uses three mechanisms to be inequilibrium with the thermal bath in the early Universe: resonances with CP-even Higgs,annihilations through scalar quartic couplings with two CP-odd Higgs in the final state,and coannihilations with Higgsinos.Resonances with CP-even Higgs bosons are well-known features, and one of the mainchannels used for low mass RH sneutrinos, m ˜ ν R < GeV. However, they are still impor-tant for heavier masses especially when h is singlet dominated.Annihilations through direct quartic couplings to a pair of pseudo-scalars, whose im-portance has been overlooked in previous studies, play a very important role for the entiremass range. Solutions with these mechanisms, can satisfy in a natural way current con-straints and lie in a region that would be tested by next generation direct and indirectdetection experiments, providing a very appealing prospect. For m ˜ ν R < GeV, theseannihilation channels are kinematically allowed as CP-odd Higgs states with significantsinglet component can be very light in NMSSM-like models.Finally, most solutions present coannihilations with Higgsinos. Furthermore, coannihi-lations with all kind of neutralino have been found, even with another sparticles like stops.It is worth mentioning that significant contributions come from coannihilation with Winos,also overlooked in previous works. These mechanisms require some fine tuning betweenthe RH sneutrino and its coannihilation partner, i.e. a mass difference (cid:46) . Then, wehave seen that the former particle inherits restrictions and properties from the latter, inparticular, the RH sneutrino relic abundance lower limit is determined by the relic densityof the corresponding neutralino.Another crucial feature of the model is that the parameters involved in the RH sneu-trino mass, like m ˜ N , λ N , and T λ N , do not affect the rest of the mass spectrum. In this way,we can find easily parameter points with RH sneutrinos DM through coannihilations, usingviable neutralino points as seeds. Nonetheless, the mentioned parameters are involved inthe DM-nucleon scattering rate, which generally results in extremelly low SI cross sectionsbeyond the sensitivity of next generation experiments for heavy RH sneutrinos, unless sig-nificant contributions of other annihilation mechanisms are also present, like the mentionedresonances or quartic coupling channels. 26 cknowledgments The work of DL and AP was supported by the Argentinian CONICET, and also acknowl-edges the support through PIP11220170100154CO. They would like to thank the teamsupporting the Dirac High Performance Cluster at the Physics Department, FCEyN, UBA,for the computing time and their dedication in maintaining the cluster facilities. DL also ac-knowledges the Spanish grant PGC2018-095161-B-I00. R. RdA acknowledges partial fund-ing/support from the Elusives ITN (Marie Sklodowska-Curie grant agreement No 674896),the “SOM Sabor y origen de la Materia" (FPA 2017-85985-P). The authors thank C. Muñozfor useful comments.
A Benchmark points: RH sneutrino as DM candidate
In this appendix, we show some benchmark points to illustrate different annihilation chan-nels that RH sneutrinos can have to get an allowed relic density.We begin showing coannihilations with neutralinos. This mechanism depends heavilyon the type of coannihilation partner, which has to annihilate efficiently, since RH sneutrinorelic abundance have the would-be relic density of the former as lower limit. Higgsinos orWinos LSP with m χ (cid:46) TeV usually result in low relic abundances, and at the same time,can evade the stringent direct detection constraints. On the other side, Binos can have relicabundance within current constraints through resonances, or coannihilations with heavysquarks. Finally, unless a resonance is present, Singlinos tend to have huge relic abundancesdue to its small coupling with the rest of the particles.For those reasons, and the presence of the terms λ N SN N and λSH u H d in the superpo-tential, coannihilation with Higgsino via s-channel singlet exchange is the main process toget viable RH sneutrino DM. Coannihilations with Winos are also relevant and a significantfraction of solutions use this mechanism. Nevertheless, to consider RH sneutrinos via Binoor Singlino coannihilation processes can be important to achieve the correct relic abun-dance, especially for low DM mass, where Higgsino and Wino neutralinos are constraint bychargino searches.In Table 4 we show sets of inputs for several benchmark points with RH sneutrino DMthrough different coannihilation mechanisms with neutralinos. We would like to commentthat in all the examples shown in this appendix h is a SM-like Higgs. BP1:
Higgsino dominated neutralino coannihilation. With this benchmark point weshow the dominant mechanism to generate RH sneutrino with an allowed amount of relicdensity. RH sneutrino annihilates through neutralino-chargino coannihilation, both witha dominant content of Higgsino. As the Higgsino neutralinos and the Higgsino charginohave approximately the same mass, LEP constraint on chargino searches impose m χ (cid:38) GeV. Therefore, these kind of RH sneutrinos can be found for 100 GeV (cid:46) m ˜ ν R (cid:46) . TeV.
BP2:
Wino dominated neutralino coannihilation. Unlike the previous case, only thelightest neutralino and lightest chargino are involved, both with important Wino content.As before, these RH sneutrinos can be found for 100 GeV (cid:46) m ˜ ν R (cid:46) . TeV.
BP3:
Singlino dominated neutralino coannihilation. Only the lightest neutralino isinvolved. However, as the singlino neutralino uses the same resonant annihilation channelsthat can be used by the RH sneutrino, the coannihilation mechanisms is not the dominant27 arameters BP1 BP2 BP3 BP4 M M µ eff tan β λ κ λ N -0.0327 -0.00869 -0.00560 -0.00181 T λ T κ -3.10 GeV -0.0742 GeV -0.105 GeV -1.42 GeV T λ N -0.258 GeV -0.114 GeV -3.55 GeV -3.26 GeV m N × GeV × GeV × GeV × GeV m u × GeV × GeV × GeV × GeV m Q × GeV × GeV × GeV × GeV T u Spectrum m ˜ ν R m χ N × − × − × − N × − × − N + N × − N × − × − × − m χ m χ ± m h m h S × − m A P Dark Matter ˜ ν R ˜ ν R ˜ ν R ˜ ν R Ω DM h σ SIDM − p × − cm × − cm × − cm × − cm main χ , χ , → SM χ χ → SM ˜ ν R ˜ ν R → A A ( ∼ q ˜ q → SM ( ∼ annihilation χ , χ ± → SM χ χ ± → SM ˜ ν R ˜ ν R → SM ( ∼ q χ → SM ( ∼ channels χ ± χ ± → SM χ ± χ ± → SM χ χ → SM ( ∼ χ χ → SM ( ∼ Table 4: Set of inputs for several benchmark points with RH sneutrino DM through coan-nihilation mechanism with neutrinos. N , S and P are the mass mixing matrixes of theneutralino, the CP-even Higgs and CP-odd Higgs sectors, respectively.28ne. In this example, the RH sneutrino annihilates to a pair of lightest pseudo-scalar parti-cles dominantly (52%), but the contribution from coannihilation channels is not negligible(more than 11%) due to a not negligible Higgsino component.We can probe the same parameters as in BP3 but choosing a higher value of m N =3 . × GeV . This only affects the sneutrino masses, which turns out to be higherand not the LSP, m ˜ ν R = 532 . GeV, but leaves the rest of the mass spectrum unchanged.Then, the DM candidate is a singlino dominated neutralino, with Ω DM h = 0 . , thatannihilates mainly to a pair of lightest pseudo-scalar particles (53%).Notice that in both cases the singlino neutralino fulfills the resonant condition withthe second lightest CP-even Higgs scalar. It has m h (cid:39) . GeV and dominant singletcomposition. Unlike BP1 and BP2, the term κ S S S is also involved in the singlino case.
BP4:
Bino dominated neutralino coannihilation. Binos LSP usually give large relicdensity values. Hence low Binos need to fulfill a resonant condition to achieve an allowedrelic abundance and evade direct detection constraints. For higher mass range, they canalso use a coannihilation channel which demands more particles with same mass. In thisbenchmark point besides a Bino with non negligible Higgsino contribution, a low massstop is present, then m ˜ ν R ∼ m χ ∼ m ˜ t . Therefore, collider signatures on compressedscenarios are important. Since we have the following mass hierarchy m ˜ ν R < m χ < m ˜ t ,with m ˜ t = 390 GeV, then the stop would decay to a quark and the Bino neutralino. Thelatter would subsequently decay into RH sneutrino and SM particles, but due to phase spacesuppression the signal would consist of missing transverse energy, i.e. the constraints turnout to be the same as simply considering neutralino LSP without a lighter RH sneutrino.In Table 5 we show a benchmark point (
BP5 ) resulting in a RH sneutrino DM throughcoannihilation mechanism with a colored sparticle, a stop. Therefore, collider signatures onlong-lived colored particles (R-hadrons) are relevant due to phase space and lack of directsneutrino-stop coupling. Notice that in
BP4 a Bino neutralino is lighter than the stop, soin that case any stop produced in a collider would be able to decay within the detector.In Table 6 we show benchmark points with a RH sneutrino DM using different annihi-lating channels. In
BP6
RH sneutrino annihilates directly to a pair of light pseudo-scalarHiggs with singlet dominant composition, via quartic coupling. This channel is especiallyimportant for direct detection experiments, and for low mass sneutrinos that can not an-nihilate using a resonance nor a coannihilation mechanism with Bino neutralinos.In
BP7 we present a parameter point with a m ˜ ν R ∼ m h / fulfilling the resonantcondition with the SM-like Higgs boson. As we can see, very low relic abundances can beachieved this way.In BP8 we show an example with a RH sneutrino DM that presents the three mainmechanisms discussed in this work: annihilation to a pair of CP-odd Higgs, resonance witha CP-even Higgs (in this case with the second lightest Higgs that has a singlet dominantcomposition) and coannihilation with Higgsino dominated neutralino. Notice that solu-tions with different annihilation channel weights can be obtained modifying the relevantparameters, the RH sneutrino mass (e.g. λ N ), the Higgs sector mass (e.g. λ , κ ), or theHiggsino mass (e.g. µ eff ). 29 arameters BP5 M T λ M T κ -0.618 GeV µ eff T λ N -1.818 GeV tan β m N × GeV λ m u × GeV κ m Q × GeV λ N -0.00124 T u Spectrum m ˜ ν R m h m ˜ t m h m ˜ b S × − m χ m A N + N P m χ ± m A Dark Matter ˜ ν R Ω DM h σ SIDM − p × − cm main ˜ t ˜ t ∗ → SM ( ∼ annihilation ˜ t ˜ b → SM ( ∼ channels Table 5: Same as 4 but benchmark point with RH sneutrino DM through coannihilationmechanism with stops. 30 arameters BP6 BP7 BP8 M M µ eff tan β λ κ λ N -0.114 -0.193 -0.413 T λ T κ -0.0195 GeV -0.916 GeV -0.647 GeV T λ N -35.33 GeV -0.294 GeV -12.47 GeV m N × GeV × GeV × GeV m u × GeV × GeV × GeV m Q × GeV × GeV × GeV T u Spectrum m ˜ ν R m χ m χ m χ ± m h m h S × − m A P m A Dark Matter ˜ ν R ˜ ν R ˜ ν R Ω DM h × − σ SIDM − p × − cm × − cm × − cm main ˜ ν R ˜ ν R → A A ˜ ν R ˜ ν R → b ¯ b ( ∼ ν R ˜ ν R → A A ( ∼ annihilation ˜ ν R ˜ ν R → g g ( ∼ ν R ˜ ν R → SM ( ∼ channels ˜ ν R ˜ ν R → τ ¯ τ ( ∼ χ χ → SM ( ∼ ν R ˜ ν R → c ¯ c ( ∼ Table 6: Same as 4 but benchmark points with RH sneutrino DM through direct annihila-tion to a pair of pseudo-scalars, resonances and coanihhilations.31 eferences [1]
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