Testing the higgsino-singlino sector of the NMSSM with trileptons at the LHC

We propose a simplified light higgsino-singlino scenario in the NMSSM, in which the masses of the chargino and the lightest neutralino determine the masses and couplings of all 3 lightest neutralinos. This scenario is complementary to the simplified wino-like chargino/neutralino scenario used conventionally for the interpretation of results from trilepton searches, and motivated by lower bounds on the gluino mass in the case of GUT relations between the wino and gluino masses. We present all masses and mixing angles necessary for the determination of production cross sections of the chargino and the 3 neutralinos in the form of Tables in the M_{neutralino_1} - M_{chargino_1} plane, assuming Higgs mass motivated values for tan(beta)=2 and lambda=0.6. We show that this scenario leads to considerable signal rates, and present constraints in this plane from recent searches for trileptons at the LHC.


Introduction
One of the main tasks of the LHC is the search for supersymmetric (SUSY) particles. These searches have been without success so far, and have lead to lower bounds in the TeV range on the masses of gluinos and squarks of the first two generations.
Interpretations of the present constraints from the trilepton channel in realistic versions of the MSSM have been performed in [18][19][20][21] (see [22][23][24] for the rôle of trilepton final states in some beyond-the-MSSM models). A particularly challenging MSSM scenario would be the case of light and nearly degenerate higgsinos [25,26]. Light higgsinos correspond to a relatively small ( 300 GeV) SUSY Higgs mass parameter µ, which is favored by fine-tuning arguments: µ 2 appears always as a positive mass 2 parameter in the Higgs potential, and must be compensated by negative soft SUSY breaking Higgs mass terms for electroweak symmetry breaking to be possible. This makes large values of µ unnatural, since then the required cancellation must be relatively very precise. On the other hand, a dominantly higgsino-like (neutralino) LSP is a difficult candidate for dark matter: its annihilation cross section in the early universe is typically too large so that, assuming a standard cosmological evolution, its relic density today is too small to comply with the WMAP and Planck result Ωh 2 ∼ 0.1187. Moreover, its direct detection (nucleon) cross section is also too large [21,27] in view of the latest XENON100 results [28] unless the higgsino component is close to 100%.
In the Next-to-Minimal Supersymmetric Standard Model (NMSSM) [29], a SUSY Higgs mass parameter µ eff is generated dynamically through the vacuum expactetion value (vev) of a gauge singlet superfield S, µ eff = λ S , where λ denotes the coupling of S to the MSSM-like Higgs superfields. Again, small values of µ eff are favored by low fine-tuning [30,31]. However, the problems associated with a higgsino-like LSP in the MSSM do not persist in the NMSSM due to the presence of the additional neutralino (singlino) from the superfield S, which can well be lighter than the higgsinos. This allows for a dominantly singlino-like LSP, whose annihilation cross section via Higgs bosons in the s-channel (and/or coannihilation or some higgsino component) can lead to the desired relic density (see [29] and refs. therein), and a sufficiently small direct detection cross section [32][33][34][35] compatible with present XENON100 bounds.
Hence a scenario with light higgsinos and a light singlino, but heavy electroweak gauginos, is viable in the NMSSM. Assuming GUT relations among the electroweak gauginos and the gluino, heavy electroweak gauginos would be an obvious consequence of lower bounds well above 1 TeV on the gluino mass. Since higgsino-singlino mixing would lift the degeneracy among the neutral and charged higgsinos and in the presence of a light singlino-like LSP, searches for charginos and neutralinos in the trilepton channel would be more promising than in the light higgsino scenario within the MSSM [25].
We emphasize that such a scenario would be complementary to the simplified models used by ATLAS and CMS for the interpretation of the trilepton results up to now: In these models, the lightest chargino and the second lightest neutralino are assumed to be wino-like and degenerate, the lightest neutralino is assumed to be bino-like, and the higgsinos are assumed to be heavy and decoupled. The obvious reason for this choice is that now signal rates depend on only two mass parameters (assuming 100% branching ratios into W/Z + χ 0 1 ). In the light higgsino-singlino scenario of the NMSSM (containing one chargino χ ± 1 and 3 neutralinos χ 0 i , i = 1, 2, 3) the masses and neutralino mixing angles depend on the higgsino mass parameter µ eff , the singlino mass, the ratio tan β of Higgs vevs and the coupling λ (see the next Section). The value of ∼ 125 GeV for the SM-like Higgs mass can be obtained naturally in the NMSSM provided λ is large (≈ 0.6) and tan β is relatively small (≈ 2) [23,. Fixing tan β = 2 and λ = 0.6, also the light higgsino-singlino scenario of the NMSSM depends on two mass parameters only. These can be chosen as the physical chargino mass M χ ± 1 (∼ µ eff ) and the LSP mass M χ 0 1 , which have a more direct physical meaning than the higgsino and singlino mass parameters in the Lagrangian.
Assuming heavy sleptons, the chargino χ ± 1 decays with a branching ratio (BR) of 100% into W ( * ) + χ 0 1 . The neutralinos χ 0 2,3 will typically decay with a BR of 100% into Z ( * ) + χ 0 1 . In some cases, decays χ 0 2,3 → χ 0 1 + a CP-odd or CP-even Higgs boson are possible. These depend on the masses and couplings of the Higgs bosons. Subsequently we define a simplified light higgsino-singlino scenario within which such neutralino-to-Higgs decays are absent. Then, given the above values of tan β and λ, M χ ± 1 and M χ 0 1 determine completely the signal rates for chargino + neutralino production into trilepton final states.
It would be very helpful if the ATLAS and CMS collaborations would interpret their results from trilepton searches within such a light higgsino-singlino scenario, as it would allow to test a well motivated region in the parameter space of the NMSSM. It also allows to generalize in a well defined manner the (somewhat unrealistic) assumption M χ ± 1 = M χ 0 2 within the present simplified models, and to study the impact of the lift of this degeneracy.
In the present paper we present the necessary parameters for the determination of the pp → χ ± 1 + χ 0 2,3 production rates in the light higgsino-singlino scenario in the form of Tables in the M χ ± 1 − M χ 0 1 plane: The masses M χ 0 2 and M χ 0 3 of the two additional neutralinos, and the mixing angles of χ 0 2 and χ 0 3 (relevant for the W − χ ± 1 − χ 0 2,3 couplings). As a (preliminary) application we simulated the trilepton event rates in the various signal channels defined in [16], and deduced bounds in the M χ ± 1 − M χ 0 1 plane from the upper limits on the corresponding channel-specific signal cross sections based on 21 fb −1 integrated luminosity at √ s = 8 TeV given there. The Tables should allow the ATLAS and CMS collaborations to perform more precise simulations (in particular of the detector responses) and comparisons with data themselves, notably with future data at larger √ s and/or different signal channels.
In the next Section we define the simplified light higgsino-singlino scenario in the NMSSM, and comment on the Tables given in the Appendix. In Section 3 we describe the simulations of the trilepton final states and show the resulting bounds in the M χ ± 1 − M χ 0 1 plane. Section 4 is devoted to conclusions and an outlook.

The Light Higgsino-Singlino Scenario in the NMSSM
The NMSSM differs from the MSSM due to the presence of the gauge singlet superfieldŜ. In the simplest realisation of the NMSSM, the SUSY µĤ uĤd Higgs mass term in the MSSM superpotential W MSSM is replaced by the coupling λ ofŜ toĤ u andĤ d , and a self-coupling κŜ 3 . Here,Ĥ u couples to up-type quark superfields, andĤ d to down-type quark and lepton superfields. In this version the superpotential W NMSSM is scale invariant, and given by: where the dots denote the Yukawa couplings ofĤ u andĤ d to the quarks and leptons as in the MSSM. Once the scalar component ofŜ develops a vev s, the first term in W NMSSM generates an effective µ-term with µ eff = λ s .
Amongst others, µ eff generates a Dirac mass term µ eff ψ u ψ d + h.c. for the SU(2)-doublet higgsinos ψ u and ψ d . The vevs v u and v d ofĤ u andĤ d generate mixing terms between the singlino ψ S and ψ d , ψ u , respectively. The second term in the superpotential W NMSSM (1) generates a Majorana mass term M S for ψ S with The soft SUSY breaking terms include, amongst others, mass terms for the gauginosB (bino), W a (winos) and G a (gluinos): Altogether the symmetric 5 × 5 mass matrix M 0 in the neutralino sector in the basis leading to mass terms in the Lagrangian of the form In the limit of heavy decoupled winos and bino considered here, M 1,2 ≫ (µ eff , 2|κs|) (we assume µ eff > 0), the light higgsino-singlino sector is described by the lower 3 × 3 sub-matrix M As stated in the introduction, we define subsequently the simplified light higgsino-singlino scenario by λ = 0.6, tan β = 2. M (3) 0 is diagonalized by an orthogonal real matrix N ij , i = 1, 2, 3, j = 3, 4, 5 such that the physical masses M χ 0 i ordered in |M χ 0 i | are real, but not necessarily positive. Denoting the 3 eigenstates by χ 0 i , we have The calculations of the masses and mixing angles as function of the parameters λ, κ (which determines M S ), µ eff and tan β are performed with the help of the public code NMSSM-Tools [59,60]. Due to the radiative corrections to the pole masses, M χ ± 1 differs slightly from µ eff . For the soft SUSY breaking squark and slepton masses we choose 2 TeV, and M 1 = 1 TeV, M 2 = 2 TeV, M 3 = 6 TeV. (These SUSY breaking parameters determine implicitely the SUSY breaking scale which has a mild impact on the radiative corrections.) The soft SUSY breaking parameters A λ and A κ [29] have no impact on the neutralino/chargino sector. They can be chosen such that the SM-like Higgs mass is near 125 GeV; in any case they must be chosen such that all physical Higgs masses 2 are positive.
Subsequently we consider M χ ± 1 in the range M χ ± 1 = 100 . . . 400 GeV in steps of 20 GeV. The corresponding values of µ eff are tabulated in Table 1 in the Appendix.
For M χ 0 1 we consider the range M χ 0 1 = 0 . . . 100 GeV in steps of 10 GeV. For fixed λ, tan β and for each given µ eff , the desired values for M χ 0 1 can be obtained by suitable values of κ. Actually, low values of M χ 0 1 require negative values for κ (we recall that we assume µ eff > 0). Along a strip around κ ∼ 0, negative and positive values of κ (of different absolute values) can lead to the same values of M χ 0 1 . We chose the convention κ > 0 whenever possible, which lifts this ambiguity. The corresponding values for κ are tabulated in Table 2 in the Appendix. Note that M χ 0 1 = M χ ± 1 (= 100 GeV) is not possible for M S ≤ µ eff as considered here, since even for M S = µ eff mixing in the neutralino sector will always imply M χ 0 1 < M χ ± 1 (by at least 3 GeV). Now the masses and mixing angles of χ 0 2 and χ 0 3 are uniquely determined. In the Tables 3 and 4 in the Appendix we list M χ 0 2 and M χ 0 3 in the considered range of M χ ± 1 and M χ 0 GeV in the lower left-hand corner, the mixing angles differ considerably from the other part of the plane.) The mixing angles N i,j with i = 2, 3, j = 3, 4 appear in the Feynman rule for the vertex in W + → χ + 1 + χ 0 2,3 corresponding to an incoming W + µ , an outgoing higgsino-like chargino χ + 1 and outgoing neutralinos χ 0 2,3 ; the projectors P L , P R act on the neutralino 4-spinors: Note that the last factor 1/ √ 2 is absent in the coupling of W to wino-like charginos and neutralinos (not shown here); as a consequence the production rates of higgsino-like charginos and neutralinos considered here are smaller than those of wino-like charginos and neutralinos assumed in the simplified models used by ATLAS and CMS. The mixing angles N 2,3 , N 2,4 , N 3,3 and N 3,4 are tabulated in the Tables 5, 6, 7 and 8, respectively, in the Appendix. Since the signs of physical spinors can be flipped without affecting the cross sections, we used this freedom to simplify the tables in the lower left-hand corner where frequent sign changes appear as consequence of the numerical diagonalisation routine.
Given the decoupled winos and bino, the (absolute values of) the singlino components of Assuming BRs of 100% for the decays χ 0 2 → Z ( * ) +χ 0 1 , χ 0 3 → Z ( * ) +χ 0 1 and χ ± 1 → W ( * ) +χ 0 1 , the masses and the W −χ ± 1 −χ 0 2,3 vertices suffice to determine the production cross sections and signal rates into trilepton channels in this light higgsino-singlino scenario. Hence this scenario is now well defined (on the points given in the Tables), and can be used to interpret results from searches for trileptons and missing energy. If desired, the parameters of additional points in the M χ 0 1 − M χ ± 1 plane can be provided.

Present LHC Constraints on the Light Higgsino-Singlino Scenario
Recent results from searches for trileptons and missing energy at the LHC at √ s = 8 TeV and ∼ 20 fb −1 of integrated luminosity have been published in [16,17]. Subsequently we use the upper bounds (at the 95% confidence level) on event rates in the specific search channels given by ATLAS in the Table 1 in [16]. For the simulation we proceed as follows: The cross sections for pp → χ ± 1 + χ 0 2 and pp → χ ± 1 + χ 0 3 production are obtained from Prospino at next-to-leading order (NLO) [61][62][63]. The matrix elements are generated by MadGraph/MadEvent 5 [64], which includes Pythia 6.4 [65]. The output is given to the fast detector simulation DELPHES [66,67]. We have verified that the cut flows given in Table 5 in  We note that the bounds in the M χ 0 1 −M χ ± 1 plane are significantly weaker than the bounds in Fig. 8(b) in [16]. The reason herefore is the significantly lower production cross section for higgsino-like charginos and neutralinos compared to wino-like charginos and neutralinos assumed in the simplified model in [16]. The fact that here we include in addition the production of χ 0 3 does not compensate for the smaller couplings to W * (also due to mixings with the singlino), moreover M χ 0 3 is substantially larger than M χ 0 2 . Searches for e + e − → Z ( * ) → χ 0 2 χ 0 1 had already been preformed at LEP, notably by the DELPHI [68] and OPAL [69] collaborations. Since the Z−χ 0 2 −χ 0 1 vertex is equally well defined in the present scenario, corresponding constraints (as implemented in NMSSMTools [59,60]) can be applied and lead to the excluded blue hashed region in Fig. 1. Actually, inside the blue hashed region (for M χ 0 1 < M Z /2 and low M χ ± 1 where the higgsino components of χ 0 1 are not negligibly small), some points are also excluded by a too large contribution to the invisible Z width from Z → χ 0 1 χ 0 1 . Hence, even in this somewhat delicate light higgsino-singlino scenario, already the present LHC constraints are significantly stronger than the bounds from LEP.

Conclusions and outlook
The main purpose of the present paper is the presentation of a simplified, but well-motivated light higgsino-singlino scenario in the NMSSM. It is complementary to the simplified wino-like chargino/neutralino scenario used conventionally by ATLAS and CMS for the interpretation of results from trilepton searches, but leads equally to considerable signal rates. (Assuming GUT-like relations among the gaugino mass parameters, the wino mass term is bounded from below by about 1/3 of the lower limit on the gluino mass, disfavouring light winos.) Hence present and future searches for chargino/neutralino production at the LHC merit to be interpreted in this scenario as well.
We have presented all necessary masses and mixing angles for the determination of production cross sections of the chargino and the 3 neutralinos in the form of Tables in the M χ 0 1 − M χ ± 1 plane, assuming Higgs mass motivated values (in the NMSSM) for tan β = 2 and λ = 0.6; however, as long as λ remains sizeable and tan β small, the masses and mixing angles depend little on these specific values. Masses and mixing angles for additional points in this plane can be provided by the author, or be obtained with the help of the public code NMSSMTools [59,60].
The present constraints in the M χ 0 1 − M χ ± 1 plane from the ATLAS search for trileptons [16] (assuming heavy sleptons) have been obtained using the simplified detector simulation DELPHES [66,67]; this simulation should actually be redone by the LHC collaborations themselves. In any case it shows that the signal rates in this scenario are measurably large, and that relevant constraints are obtained in the absence of signals.
In addition to the trilepton final state, the simplified higgsino-singlino scenario can also be tested in searches for four leptons plus E miss T [17,70]. The relevant processes would be pp → Z * → χ 0 i χ 0 j with i, j = 2, 3, χ 0 i,j → χ 0 1 +Z ( * ) and leptonic decays of Z ( * ) (or, alternatively, hadronic decays of one of the Z ( * ) [17,71]). Again, the masses and mixing angles given here allow for the determination of the production cross sections. These are dominated by χ 0 2 + χ 0 3 production with, however, a cross section of only ∼ 20 − 25% of the one for trileptons. At present, the results of these searches are interpreted in SUSY models with gauge mediation where χ 0 1 is replaced by a practically massless gravitino. Hence, re-analysises of these (and future) results are desirable in the context of the present scenario.
In how far does this simplified light higgsino-singlino scenario differ from more general regions in the parameter space of the NMSSM? First, if the wino mass parameter M 2 is not as large as assumed here (2 TeV), the lightest chargino and neutralinos can have sizeable wino components which lead typically to an increase of the production cross sections. Hence the present scenario is conservative in this respect. On the other hand, the neutralinos χ 0 2,3 will not necessarily have branching ratios of 100% into Z ( * ) + χ 0 1 , notably if decays into some of the lighter of the 5 CP-even or CP-odd neutral Higgs states of the NMSSM are frequent. Clearly such decays would reduce the signal rate in the trilepton channel considered hereeven if χ 0 2,3 decay into a light pseudoscalar A 1 with M A 1 < 2M b and A 1 decays dominantly into A 1 → τ + τ − [72,73]. Decays of χ 0 2,3 into heavier Higgs states (decaying into bb), however, start also to be constrained by corresponding searches [74]. Implications of these latter results on more general regions in the parameter space of the NMSSM remain to be worked out.
Below we list in the form of Tables in the M χ 0 1 − M χ ± 1 plane various parameters relevant for the simplified light higgsino-singlino scenario in the NMSSM. First, in Table 1 we show the values of µ eff leading to specific values for M χ ± 1 (which do not depend on M χ 0 1 ). In Table 2 Table 8: N 3,4 as function ofM χ 0 1 and M χ ± 1 .