arXiv:hep-ph/0507055v2 7 Sep 2005 eptnilo h ig etrte a h form the has then sector Higgs the of perpotential tlatbcueteuulLPlmt ontapyt h ige n sin and singlet the to apply not do differe limits significantly LEP be usual can the sin NMSSM the because , least the extra at of an phenomenology as ( the well neutral extra as states, two pseudoscalar– contains one NMSSM and the scalar fields, MSSM the to addition h ett-iia uesmercSadr oe NSM pr the (NMSSM) Model to Standard Supersymmetric Next-to-Minimal The Introduction 1 ags ffcs u locnie easo eetos mosa smuons contra selectrons, of and decays NMSSM consider sbottoms the also (stops, but generation of third effects, framework the largest the on the concentrate in We we letter sleptons case. this attentio and In little MSSM. studied squarks very the been received of to far has compared so as has differences dark hand, observe (singlino) other of the density on relic sector, The [16–23]. in i ftergtsize, right the of lcrwa cl rgntsetrl rmteSS raigscale. breaking SUSY the from entirely originates scale electroweak h MS ig hnmnlg a enivsiae xesvl in extensively investigated a been without has phenomenology Higgs NMSSM The aumepcainvle hscetsa effective an creates this value, expectation vacuum = nteMS,sursadsetn a ea via decay can sleptons and squarks MSSM, the In h MS a eetybcm eypplr oto h Feynman the of Most popular. very become recently has NMSSM The h diino h ige edlast agrpril pcrmtha spectrum larger a to leads field singlet the of addition The ,R L, osdrdcy ffis n eodgnrto frin int generation second and first branchi i of the phenomenology decays that consider the out influencing turns markedly It large, be singlinos. into Higgs decays singlet sb pseudoscalar stau stop, or and scalar heavier a the plus of eigenstate concenmass decays We discussing MSSM. the generation, to third compared as ratios branching sfermion µ eivsiaehwteadto ftesnltHgsfil nt in field Higgs singlet the of addition the how investigate We ncs fn iig and mixing) no of case in rbe fteMS yteadto faguesnltsuperfield singlet gauge a of addition the by MSSM the of problem S ˆ 3 frindcy nosnlt n singlinos and singlets into decays Sfermion emi icse n[5) ealdsuiso h etaiosco ar sector neutralino the of studies Detailed [15]). in discussed is term )CR,Dp fPyis hoyDvso,Gnv,Switzerl Geneva, Division, Theory , of Dep. CERN, 1) )Isiuod F de Instituto 2) )Isiu ¨rTertsh hsk nv Z¨urich, Switz Univ. Physik, f¨ur Theoretische Institut 3) i.e. fteodro h lcrwa cl.I hswy nteNSMthe NMSSM the in way, this In scale. electroweak the of order the of ´ sc opsua,Uiesttd Val`encia, Spain de Universitat Corpuscular, isica .Kraml S. nteNMSSM the in k 1 = ..., , Abstract 1 .Porod W. , .Surscnas ea noguns ˜ , into decay also can Squarks 4. 1 µ λ S ˆ f term, ˜ ( i H ˆ → d 2 eas nls tp sbottom stop, analyse also We . · f , 3 to rsa notelighter the into stau or ottom µ H singlinos. o χ ˆ ˜ h MS.Mroe,we Moreover, NMSSM. the n grto fteedcy can decays these of ratios ng k 0 u ≡ d1t2dgnrto squarks. generation 1st/2nd the nd expect we where staus) and , ,atog ee o,oemay one too, here, although n, + ) f λ rt npriua nthe on particular in trate ˜ i eNSMcagsthe changes NMSSM he eoeivsiaetedecays the investigate refore h ln.Oigt hs extra these to Owing glino. → S 1 3 vdsa lgn solution elegant an ovides κ i CERN-PH-TH/2005-117 ige)Hgsfils–one fields Higgs singlet) hc sautomatically is which , tfo h SM not MSSM; the from nt S f ˆ tte oteMSSM the to them st 31]( oe variant model (a [3–14] erland 3 ′ χ ˜ When . n[4.Tesfermion The [24]. in ln states. glino ue r ie n[2]. in given are rules j ± nteMS:in MSSM: the in n with and S ˆ UT 11/05 ZU-TH ,j i, S 1.Tesu- The [1]. ˆ IFIC/05-30 available e cursa acquires 1 = q i → , (or 2 q g ˜ , if the is light enough. In addition, sfermions of the third generation (f˜ = t,˜ ˜b, τ˜) can ˜ ˜′ ± ± ˜ ˜ 0 0 0 0 have the bosonic decay modes fi fj + W , H and f2 f1 + Z , h , H , A [25]. In the → → ˜ 0 NMSSM, we have additional decay modes into singlinos and singlet Higgs states: fi fχ˜n ˜ ˜ 0 0 0 0 0 → with n = 1, ..., 5 and f2 f1 + A1, A2, H1 , H2 , H3 . Pure singlets and singlinos couple in general very weakly to the→ rest of the spectrum. There are hence two potentially interesting cases: a) large mixing of singlet and doublet Higgs states and/or large mixing of singlinos with 0 0 - and b) (very) light singlet/singlino states. In case b) A1 and H1 are almost pure singlets with masses well below the LEP bound of mh 114 GeV, and the singlino is the ≥ LSP. We investigate these cases in this letter and show that they can markedly influence the sfermion phenomenology. The paper is organized as follows. In Section 2 we explain our notation, the potential and the relevant Feynman rules. In Section 3 we perform a numerical analysis, and in Section 4 we present our conclusions.

2 Notation and couplings

2.1 Potential We follow the notation of NMHDECAY [26]. The superpotential is then given as 1,2

c c c 1 3 = ht Qˆ HˆuTˆ + hb Hˆd QˆBˆ + hτ Hˆd Lˆ τˆ λSˆ Hˆd Hˆu + κSˆ (1) W · R · R · R − · 3 with the SU(2) doublet superfields ˆ ˆ + ˆ 0 TL νˆL Hu Hd Qˆ = , Lˆ = , Hˆu = , Hˆd = (2) 0 − BˆL τˆL Hˆ Hˆ      u   d  and the product of two SU(2) doublets Xˆ Xˆ = Xˆ 1Xˆ 2 Xˆ 2Xˆ 1 . (3) 1 · 2 1 2 − 1 2 From Eq. (1) we derive the F -terms

c 0 c − c 0 + FTL = htT H hbB H , FT = ht(TLH BLH ) , (4) R u − R d u − u c + c 0 c − 0 FBL = htTRHu + hbBRHd , FB = hb(TLHd BLHd ) , (5) − ec e − e −e 0 c − 0 FτL = hτ τ H , Fτ = hτ (νLH τLH ) , (6) R d − d − d e c 0e e c e − F 0 = htTLT λSH , F + = htBLT + λSH , (7) Hu R − d Hu − R d e c c 0 e c e c + FH0 = hbBLB + hτ τ τ λSH , F − = hbTLB hτ ν τ + λSH , (8) d e e R L R − u Hd − e eR − L R u yielding the Yukawa part of the scalar potential = F F ∗. Note that the F -terms in e e e e F i ei ei e e Eqs. (7) and (8) imply direct interactions betweenV the S field and the sfermions: P ∗ c ∗ −∗ c ∗ 0∗ ∗ c ∗ 0∗ c ∗ +∗ F htλ BLT S H + TLT S H hbλ BLB S H + TLB S H V ⊇ − R d R d − R u R u ∗ h λ∗τ˜ τ˜c S∗H0 +˜ν τ˜c S∗H+∗ + h.c..   (9) τ eL Re u LeRe u e e e e 1 − Note the different signs of the hb and hτ terms as compared to Eq. (A.1) of Ref. [26]. 2  The superpotential Eq. (1) posesses a discrete Z3 symmetry which is spontaneously broken at the electroweak phase transition. This results in cosmologically dangerous domain walls [27]. We implicitly assume a solution [28] to this domain wall problem which does not impact collider phenomenology.

2 We also need the soft SUSY-breaking potential for the derivation of the couplings, c.f. Eq. (A.4) of [26],

c c c 1 3 soft = htAtQ HuT + hbAbHd QB + hτ Aτ Hd Lτ λAλSHd Hu + κAκS . (10) V · R · R · R − · 3 2.2 Sfermion–Higgse e interactione e ee

0 In the following, we denote the neutral scalar and pseudoscalar Higgs by Hi (i =1, 2, 3) 0 0 0 ˜ ˜∗ and Al (l = 1, 2), respectively. The interaction of Hi and Al with a pair of sfermions fjfk (j, k =1, 2) can be written as:

S 0 ∗ P 0 ∗ ˜˜ = g H f˜ f˜ + g A f˜ f˜ . (11) Lffφ ijk i j k ljk l j k Apart from D-term contributions, the Higgs–sfermion couplings are proportional to the Yukawa S,P couplings hf . We therefore write gijk explicitly for the third generation. For stops, we have

S t˜ 1 ∗ t˜∗ t˜ t˜∗ t˜ (g ) = ht (µ R R + µeff R R ) vdDjk Si ijk √ eff j1 k2 j2 k1 − 2  2  1 t˜∗ t˜ ∗ t˜∗ t˜ 2 ht (AtR R + A R R ) vuDjk + √2vuh δjk Si − √ j1 k2 t j2 k1 − t 1  2  1 ∗ t˜∗ t˜ t˜∗ t˜ + vdht (λ Rj Rk + λRj Rk ) Si3 , (12) √2 1 2 2 1

P t˜ i ∗ ∗ t˜∗ t˜ (g ) = ht (µ Pl2 + AtPl1 + vdλ Pl3)R R ljk − √2 eff j1 k2 i ∗ t˜∗ t˜ + ht (µeff Pl2 + At Pl1 + vdλPl3)Rj Rk , (13) √2 2 1 where µeff is the effective µ term:

µeff λs (14) ≡ with s = S the vev of the singlet S. (In the presence of an additional generic µ term µHˆdHˆu, h i µeff µeff = λs + µ.) For sbottoms, we get →

S ˜b 1 ˜b ∗ ˜b ∗ ˜b ∗ ˜b 2 (g ) = hb (AbR R + A R R )+ vdDjk + √2vdh δjk Si ijk − √ j1 k2 b j2 k1 b 2  2  1 ˜ ˜ ˜ ˜ + h (µ∗ Rb ∗Rb + µ Rb ∗Rb )+ v D S √ b eff j1 k2 eff j2 k1 u jk i1  2  ∗ 1 ∗ ˜b ˜b ˜b ∗ ˜b + vuhb (λ Rj Rk + λRj Rk ) Si3 , (15) √2 1 2 2 1

P ˜b i ∗ ∗ ˜b ∗ ˜b (gljk) = hb (AbPl2 + µeff Pl1 + vuλ Pl3)Rj Rk − √2 1 2 i ∗ ˜b ∗ ˜b + hb (Ab Pl2 + µeff Pl1 + vuλPl3)Rj Rk , (16) √2 2 1

˜b τ˜ and analogously for staus with the obvious replacements hb hτ , Ab Aτ and R R . → → → 3 T3L Qf YL YR t˜ 1/2 2/3 1/3 4/3 ˜b 1/2 1/3 1/3 2/3 − − − τ˜ 1/2 1 1 2 − − − − Table 1: Isospin, and hypercharges of stops, sbottoms and staus.

f˜ In Eqs. (16)–(19), Sij and Pij are the Higgs mixing matrices as in [26], and R are the sfermion mixing matrices diagonalizing the sfermion mass matrices in the notation of [29, 30]:

2 ∗ ˜ ˜ m a mf f1 f˜ fL 2 2 f˜ f˜L f f˜ † = R , diag(mf˜ , mf˜ )= R 2 (R ) (17) f˜ f˜ 1 2 af mf m  2  R f˜R ! ∗ ∗ 0 0 where at = At µ cot β and ab,τ = Ab,τ µ tan β. Furthermore, vd = H , vu = H and − eff − eff h d i h ui tan β = vu/vd. The D-terms are given by

f˜ 1 2 ′2 f˜∗ f˜ ′2 f˜∗ f˜ D = (g T3L YLg )R R YRg R R (18) jk √2 − j1 k1 − j2 k2   ′ 2 2 where g and g are the SU(2) and U(1) gauge couplings: g =4√2GF MW with GF the Fermi ′2 2 2 2 2 2 constant and g = g tan θW = 4√2GF (MZ MW ) using the on-shell relation sin θW = 2 2 − (1 M /M ) for the Weinberg angle θW ; T L and Y , are the 3rd component of the isospin − W Z 3 L(R) and the of the left (right) sfermion, respectively. We have Y = 2(Qf T3) where Qf is the electric charge. For completeness, the sfermion quantum numbers are listed− in Table 1. ˜ ˜ Notice that in the CP-conserving case the pseudoscalars only couple to f1f2 combinations P P S S P P and hence gl11 = gl22 = 0 in Eqs. (13) and (16); moreover gi12 = gi21 and gl12 = gl21. Notice also that in the CP-violating case, the scalar and pseudoscalar Higgs states will− mix to mass 0 eigenstates h1...5 similar to the MSSM case. The couplings of the charged Higgs bosons to sfermions are the same as in the MSSM.

2.3 Sfermion–neutralino interaction The sfermion interaction with has the same form as in the MSSM,

f˜ f˜ 0 ˜ 0 = g f¯(a P + b P )˜χ f˜ + h.c.. (19) Lffχ˜ in R in L n i The only difference is the addition of the singlino state S˜:

0 ˜ ˜ ˜ ˜ ˜ χ˜n = Nn1B + Nn2W + Nn3Hd + Nn4Hu + Nn5S (20) with n = 1...5, N the matrix diagonalizing the 5 5 neutralino mass matrix in the basis × (B,˜ W,˜ H˜d, H˜u, S˜):

M 0 mZ sW cβ mZ sW sβ 0 1 − 0 M mZ cW cβ mZ cW sβ 0  2 −  N = mZ sW cβ mZ cW cβ 0 µeff lvsβ , (21) M − − −  mZ sW sβ mZ cW sβ µeff 0 lvcβ   − − −   0 0 lvsβ lvcβ 2κs   − −    4 with sW = sin θW , cW = cos θW , sβ = sin β, cβ = cos β, and

∗ † N N N = diag(m 0 , m 0 , m 0 , m 0 , m 0 ) . (22) M χ˜1 χ˜2 χ˜3 χ˜4 χ˜5 f˜ f˜ We can hence use the couplings ain and bin as given in [29,30] with the neutralino index running from 1 to 5 instead from 1 to 4. It is worth noting that the couplings between sfermions and singlinos only occur via the neutralino mixing. This is in contrast to the Higgs couplings where additional terms originating from Eq. (9) are present in the sfermion–singlet interaction. Note also that [26] and [24] use the basis (B,˜ W,˜ H˜u, H˜d, S˜) for the neutralino system. Therefore, the indices 3 and 4 of the neutralino mixing matrix N need to be interchanged when comparing [24, 26] and this paper.

3 Numerical results

We have implemented all 2-body sparticle decays of the NMSSM in the SPheno [31] package. The Higgs sector of the NMSSM is calculated with NMHDECAY [26] linked to SPheno. For our discussion of sfermion decays in the NMSSM, we choose the benchmark scenario 3 of [24] which is characterized by

λ =0.4, κ =0.028, tan β =3, µeff = λs = 180 GeV,

Aλ = 580 GeV, Aκ = 60 GeV, M = 660 GeV, (23) − 2 2 with M1 = (g1/g2) M2 0.5M2 by GUT relations as an illustrative example. This leads to a 0 ≃ 0 lightχ ˜1 with a mass of 35 GeV which is to 87% a singlino. Theχ ˜2 weights 169 GeV and is dominantly a . Moreover, we have a light scalar Higgs with a mass of mH1 = 36 GeV and a light pseudoscalar with mA1 = 56 GeV, both being almost pure singlet states and thus 0 0 0 0 0 0 evading the LEP bounds. H2 , H3 , and A2 are SU(2) doublet fields similar to h , H and A in the MSSM. The relic density in this scenario is Ωh2 =0.1155 [24]. In this letter, we are interested in the decays f˜ f˜ H0, f˜ f˜ A0, and f˜ fχ˜0, 2 → 1 1 2 → 1 1 1,2 → 1 with f˜ = t,˜ ˜b, τ˜. In order to see the relevance of these decays, we perform a random scan over the parameters of the third generation, MQ˜3 , MU˜3 , MD˜ 3 , ML˜3 , ME˜3 , At, Ab, Aτ . The sfermion mass parameters are varied between 100–800 GeV, and the trilinear couplings in their whole possible range allowed by the absence by charge or colour breaking minima. We compute the mass spectrum and the branching ratios at each scan point, accepting only points which pass the experimental bounds from LEP (the bounds from the LEP Higgs searches are fully NMHDECAY 0 implemented in [26]). Owing to radiative corrections, the mass of H2 varies between

100 GeV and 117 GeV in the scan. The effect on the other quantities, in particular mH1 , ∼ 2 mA1 and Ωh , is negligible. As a sideremark we note that renormalization-group (RG) arguments can be used to set lower bounds on the SU(2) doublet sfermion masses. Requiring, for example, that m2 remain f˜L > positive all the way up to the GUT scale implies mf˜L 0.9M2 for the first and second generation at the weak scale. The corresponding bounds for the∼ third generation are much lower because the Yukawa couplings contribute to the RG running with opposite sign as the SU(2) gauge coupling. We refrain, however, from imposing any such RG-inspired constraint in our analysis for two reasons: firstly because it is our aim to discuss the weak-scale phenomenology in the most general way using just one illustrative benchmark scenario, and secondly because the

5 actual scale of SUSY breaking is unknown and may well be much lower than MGUT (see e.g. the NMSSM variants of the models presented in [32]). Let us now discuss the sfermion branching ratios. Figure 1 shows scatter plots of the ˜ 0 0 0 branching ratios of b2 andτ ˜2 decays into A1, H1 and H2 as function of the heavy sfermion 0 0 mass, m˜b2 or mτ˜2 . As can be seen, decays into the singlet Higgs bosons H1 or A1 can have < sizable branching ratios provided the sfermions are relatively light, m˜b2,τ˜2 400 GeV. This feature can easily be understood from the partial width of the decay of a heavier∼ sfermion into a lighter one plus a massless singlet. For sbottoms we have, for instance,

2 2 c v m˜ ˜ ˜ 2 2 u b1 Γ(b2 b1S)= hb λ 1 m˜b2 , (24) → 32π m˜ − m˜  b2  "  b2  #

2 2 which is suppressed by a factor (vu/m˜b2 ) for heavy sbottoms. The factor c is c = cos 2θ˜b for the scalar and c = 1 for the pseudoscalar singlet. Analogous expressions hold for staus with 0 b τ and for stops with b t and vu vd. Decays into the SU(2) doublet Higgs H2 can also have→ large branching fractions,→ provided→ the splitting of the sfermion mass eigenstates is large 0 0 enough. Here note that for the parameter choice Eq. (23), A1 and H1 decay predominantly into ¯ ¯ 0 bb and may hence only be distinguished by the different bb invariant masses. The H2 on the 0 0 other hand, decays to about 60% into H1 H1 and hence into a 4b final state. Both signatures, 0 0 ¯ the one from decay into a H1 or A1 leading to bb with small invariant mass as well as the 4b’s 0 from the decay into H2 , are distinct from the usual MSSM case. We next turn to sfermion decays into singlinos. Figure 2 shows scatter plots of the branching ratios of t˜ decays into tχ˜0, bχ˜±, and of ˜b decays into bχ˜0 . As expected, t˜ bχ˜± and 1 1 1 1 1,2 1 → 1 ˜b bχ˜0 (˜χ± andχ ˜0 being mostly doublet higgsinos) are in general the dominant modes if 1 → 2 1 2 kinematically allowed. Nevertheless, as can be seen from the upper two plots of Fig. 2, decays into the singlino LSP can have sizable branching fractions, even if other decay modes are open. The size of the branching ratio into the singlino is mainly governed by its admixture from the doublet higgsinos, i.e. by the size of the λ parameter. Similar features appear also in the stau decays as illustrated in Fig. 3. The pattern ofτ ˜1 is quite similar to that of ˜b1, with > 10% branching ratio into the singlino for mτ˜1 < 200–250 GeV, depending on the L/R character∼ of the stau. For theτ ˜2, the branching ratio of∼ the decay into the singlino is even more important. 0 In fact it can be 10–50% over a large part of the parameter space even if the decay intoχ ˜2 is open. ± 0 In this context note also theχ ˜1 andχ ˜2 will cascade further into the singlino LSP, see e.g. [17, 18, 22]. This is quite distinct from the MSSM, where the singlino is absent and all 0 decay chains end in what in our case is theχ ˜2. Obviously, this also affects cascade decays of squarks of the first and second generation (and likewise of gluinos), since in case of a singlino LSP there is one more step in the chain as compared to the MSSM. At the LHC, a singlino LSP can in fact lead to similar signatures as a or LSP. The presence of light scalar or pseudoscalar Higgs bosons in the decay chains may be a way to distinguish the NMSSM from ˜ 0 ˜ other scenarios. If λ is large enough the decays fi fχ˜1 with fi = NLSP may also be used for ˜ → 6 discrimination, since the corresponding fi decays into gravitino or axino would not occur. We will discuss this in more detail in a forthcoming paper. Last but not least we consider the decays of sfermions of the first two generations. Owing to the small Yukawa couplings, decays into Higgs bosons are negligible in this case. Decays into singlinos can, however, be important. As an example, Fig. 4 shows the branching ratios ofe ˜ (being the same as those ofµ ˜ ) for the scenario of Eq. (23). For me 180–370 GeV, L,R L,R ˜ ≃ 6 ) ) 0 1 0 1 A A 1 1 ˜ τ b ˜ → → 2 2 τ b ˜

m˜b2 [GeV] mτ˜2 [GeV] ) BR(˜ ) BR( 0 0 1 1 H H 1 1 ˜ τ b ˜ → → 2 2 b τ ˜

m˜b2 [GeV] mτ˜2 [GeV] ) BR(˜ ) BR( 0 0 2 2 H H 1 1 ˜ τ b ˜ → → 2 2 τ b ˜ BR( BR(˜

m˜b2 [GeV] mτ˜2 [GeV]

˜ 0 0 0 Figure 1: Branching ratios of b2 (left) andτ ˜2 (right) decays into Higgs bosons A1,H1 ,H2 for scenario 3 of [24], c.f. Eq. (23), as function of the mass of the decaying particle.

− 0 the decayse ˜ νeχ˜ ande ˜ eχ˜ clearly dominate, giving a 2-step cascade decay into the L → 1 R → 2 singlino LSP. Nevertheless even in this case the decayse ˜ eχ˜0 have sizable rates, being of L,R → 1 the order of 10% fore ˜R. The reason is that the relative importance of the decays into ± and neutralinos is determined by the components of the these , andχ ˜1 and 0 0 χ˜2,3 are mainly higgsino-like in our scenario. Only when the decay intoχ ˜4, which is mainly a bino, gets kinematically allowed the direct decays into the singlino become negligible. Also for the decays of up and down squarks into singlinos we find branching ratios of (1–10)%. The implications for collider phenomenology will be discussed in detail elsewhere. O

4 Conclusions

We have discussed the decays of sfermions in the NMSSM. We have shown that for stops, sbottoms and staus, in addition to the decay modes already present in the MSSM, decays into light singlet Higgs bosons, f˜ f˜ + A0,H0, as well as decays into a singlino LSP, f˜ fχ˜0 2 → 1 1 1 i → 1 7 ) ) 0 1 0 1 ˜ χ ˜ χ b t → → 1 1 ˜ t b ˜ BR( BR(

mt˜1 [GeV] m˜b1 [GeV] ) ) 0 2 ± 1 ˜ ˜ χ χ b b → → 1 1 ˜ t b ˜ BR( BR(

mt˜1 [GeV] m˜b1 [GeV]

˜ 0 ± ˜ 0 Figure 2: Branching ratios of t1 decays into tχ˜1 and bχ˜1 (left) and of b1 decays into bχ˜1 and 0 bχ˜q (right) for the parameters of Eq. (23).

(i = 1, 2) withχ ˜0 S˜, can be important. This is in particular the case for light sfermions. 1 ≃ The presence of these decay modes modifies the signatures of stop, sbottom and stau events as compared to the MSSM. Also for first and second generation sfermions it turned out that the decays into a singlino LSP can be quite important. Even if other decay modes are open, ˜ 0 0 ˜ fi fχ˜1 withχ ˜1 S can have (10%) branching ratio. Moreover, decays (of any SUSY particle)→ into singlinos≃ or singlet HiggsO bosons may significantly influence cascade decays of squarks and gluinos at the LHC. In particular in case of a singlino LSP, there is one more possible step in the decay chain than in the MSSM. A singlino LSP in the NMSSM can in fact lead to similar signatures at the LHC as a gravitino or axino LSP in the MSSM. The decays discussed in this letter may help discriminating these scenarios.

Acknowledgments

We like to thank J.F. Gunion and C. Hugonie for useful discussions on the NMSSM and on NMHDECAY. We also thank G. B´elanger and A. Pukhov for comparisons with the NMSSM version of micrOMEGAs. The work of S.K. is financed by an APART grant of the Austrian Academy of Sciences. W.P. is supported by a MCyT Ramon y Cajal contract, by the Spanish grant BFM2002-00345, by the European Commission Human Potential Program RTN network HPRN-CT-2000-00148 and partly by the Swiss ’Nationalfonds’.

8 ) ) 0 1 0 1 τ˜ τ˜R ˜ ˜ 2 χ χ τ τ ∼ τ˜1 τ˜L → → ∼ 2 1 τ τ τ˜ τ˜L 2 ∼ τ˜1 τ˜R BR(˜ BR(˜ ∼

mτ˜1 [GeV] mτ˜2 [GeV]

0 0 Figure 3: Branching ratios ofτ ˜1 τχ˜1 (left) andτ ˜2 τχ˜1 (right) decays for the parameters of Eq. (23). → →

1 1 0.5 0.5 ) ) R L 0.2 0.2 e e 0.1 0.1 BR(˜ BR(˜ 0.05 0.05 0.02 0.02 0.01 0.01 100 150 200 250 300 350 400 450 100 150 200 250 300 350 400 450

me˜L [GeV] me˜R [GeV]

Figure 4: Branching ratios ofe ˜L (left) ande ˜R (right) decays for the parameters of Eq. (23). 0 The full, dashed, dotted, dash-dotted, and dash-dash-dotted lines are for the decays into eχ˜1, 0 0 0 − eχ˜2, eχ˜3, eχ˜4, and νχ˜1 , respectively. The branching ratios for smuonsµ ˜L,R are the same as for the selectrons. References

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