Collider Tests for Neutrino Mass Generation in a Supersymmetric World with R-Parity Violation

Brazilian Journal of Physics, vol. 34, no. 1A, March, 2004 175

M. B. Magro Instituto de F´ısica, Universidade de Sao˜ Paulo, CP 66318, 05389-070, Sao˜ Paulo-SP, Brazil.

Received on 18 February, 2003.

We summarize the low energy features of a supersymmetric class of models with bilinear R-parity violation. We analyze two cases where the supersymmetry breaking is mediated either by supergravity or by anomaly induced contributions to the soft parameters and compare both scenarios in the context of recent neutrino conversion data and collider physics. We show that both classes of models have a large potential to discoveries in collider experiments as well as in neutrino experiments.

1 Introduction νµ to ντ flavor oscillations with maximal mixing [8], while the solar data can be accounted for in terms of either small Supersymmetry (SUSY) is a promising candidate for (SMA) and large (LMA) mixing MSW solutions [9], as well physics beyond the Standard Model (SM). The search for as through vacuum or just-so solutions [10]. A large mixing supersymmetric partners of the SM particles constitutes an among ντ and νe is excluded both by the atmospheric data important goal of current high energy colliders like the Teva- and by reactor data on neutrino oscillations [11]. tron, and future colliders like the LHC or a linear e+e− col- It has been recently shown [6] that one can explain lider. However, no positive signal has been observed so far. the neutrino data through SUGRA models with bilinear R- Therefore, if supersymmetry is a symmetry of nature, it is parity violation (BRpV). The attainable range of the squared 2 an experimental fact that it must be broken. The three best difference of the neutrino masses, ∆mij , i, j standing for known classes of models for supersymmetry breaking are the neutrino flavors, favors the interpretation of the atmo- gravity-mediated (SUGRA) [1], where SUSY is assumed to spheric neutrino data. It was possible to fix the atmospheric be broken in a hidden sector by fields which interact with the angle and at the same time obey the CHOOZ constraint. For visible particles only via gravitational interactions; gauge- the solar angle, however, the results depend on whether one mediated [2], where SUSY is broken in a hidden sector and wants to work in a SUGRA motivated scenario or not. For transmitted to the visible sector via SM gauge interactions of the SUGRA scenario it was shown that this R-parity vio- messenger particles; and anomaly-mediated supersymmetry lating model allows only the small mixing and MSW so- breaking (AMSB) [3], which is based on the observation lution (SMA), while for the minimal supersymmetric case that the super-Weyl anomaly gives rise to loop contribution (MSSM) also LMA and vacuum oscillation solutions are to sparticle masses. In this work we will concentrate our possible. Under the assumption of SUGRA conditions the searches in SUGRA and AMSB prescriptions. atmospheric scale is calculable by the renormalization group So far most of the effort in searching for supersymmetric evolution due to the non-zero bottom quark Yukawa cou- signatures has been confined to the framework of R-parity pling. In this case one predicts the small mixing angle (RP ) conserving realizations; however recent data on solar (SMA) MSW solution to be the only viable solution to the and atmospheric neutrinos give a robust evidence for neu- solar neutrino problem. In contrast, for the general MSSM trino conversions [4], probably the most profound discovery model, where the above assumptions are relaxed, on can in particle physics in the recent years. It has been suggested implement a bi-maximal [12] neutrino mixing scheme, in long ago that neutrino masses and supersymmetry may be which the solar neutrino problem is accounted for through deeply tied together [5, 6]. Indeed, SUSY models exhibit- large mixing angle solutions, either MSW or just-so. ing R-parity violation can lead to neutrino masses and mix- It is interesting to notice that neutrino mass models ings [6] in agreement with the current solar and atmospheric based on R-parity violation can be tested at colliders [13, neutrino data. 14]. In this work, we summarize two different approaches to The high statistics data by the SuperKamiokande collab- R-parity violating models that can be tested either at collid- oration [4] has confirmed the deficit of atmospheric muon ers or neutrino data. The first is based on AMSB supersym- neutrinos, especially at small zenith angles, providing a metry braking and the second on SUGRA. In the latter we strong hint for neutrino conversion. Although massless neu- show that is possible to search for R-parity violation SUSY trino conversions [7] can be sizeable in matter, it is fair to say via the production of multileptons (≥ 3`) at the Fermilab that simplest interpretation of the present data is in terms of Tevatron within the framework of the simplest supergravity massive neutrino oscillations. The atmospheric data indicate (SUGRA) model without R-parity [15]. In the first we sum- 176 M. B. Magro marize the main features of a new realization of R-parity model in under preparation. Therefore, in our model, the violating SUSY models with anomaly-mediated supersym- electroweak symmetry is broken by the vacuum expectation metry braking. values of the two Higgs doublets Hd and Hu, and the neutral We consider a supersymmetrical model that includes the component of the third left slepton doublet Le3. We denote following bilinear terms in the superpotential [15] these fields as µ ¶ b √1 0 0 W = W − ε ² Lˆ Hˆ , (1) [χd + vd + iϕd] BRpV MSSM ab i i i H = 2 , d − where the last term violates R-parity. In order to reproduce Hd µ + ¶ the values of neutrino masses indicated by current data [16] Hu Hu = , we choose the parameter space where |²i| ¿ |µ| [6]. The √1 [χ0 + v + iϕ0 ] 2 u u u relevant bilinear terms in the soft supersymmetry breaking µ ¶ √1 [˜νR + v + iν˜i0] sector are 2 τ 3 τ Le3 = . (3) τ˜− V = m2 Ha∗Ha + m2 Ha∗Ha + M 2 Lã∗Lã soft Hu u u Hd d d Li i i The above vev’s vi can be obtained through the min- ³ ´ imization conditions, or tadpole equations, which in the a b ã b −εab BµHd Hu + Bi²iLi Hu , (2) AMSB–BRpV model are

0 2 2 where the terms proportional to Bi are the ones that vio- t = (m + µ )v − Bµv − µ² v + d Hd d u 3 3 late R-parity. The explicit R-parity violating terms induce 1 2 02 2 2 2 vacuum expectation values (vev) v , i = 1, 2, 3 for the sneu- (g + g )vd(v − v + v ) , i 8 d u 3 trinos, in addition to the two Higgs vev’s vu and vd. 0 2 2 2 t = (m + µ + ² )vu − Bµvd + B3²3v3 − This paper is organized as follows. We summarize in u Hu 3 1 Section 2 the main features of a bilinear R-parity violat- (g2 + g02)v (v2 − v2 + v2) , ing SUSY model with anomaly-mediated SUSY breaking. 8 u d u 3 This section also contains an overview of the supersymmet- 0 2 2 t3 = (mL3 + ²3)v3 − µ²3vd + B3²3vu + ric spectrum in this model as well as the properties of the 1 2 02 2 2 2 CP-odd, CP-even and charged scalar particles, concentrating (g + g )v3(v − v + v ) , (4) 8 d u 3 on the mixing angles that arise from the introduction of the R-parity violating terms. Section 3 contains a phenomeno- 0 0 at tree level. At the minimum we must impose td = tu = 0 logical study of the production of multileptons at the Fer- t3 = 0. In practice, the input parameters are the soft masses milab Tevatron within the framework of a simplest SUGRA mHd , mHu , and mL3 , the vev’s vu, vd, and v3 (obtained model without R-parity. We look at the capabilities of the from mZ , tan β, and mντ ), and ²3. We then use the tadpole RUN II at the Tevatron probe bilinear R-parity violation. Fi- equations to determine B, B3, and |µ|. nally, in Section 4 we draw our final remarks on the models One–loop corrections to the tadpole equations change showed here. the value of |µ| by O(20%), therefore, we also included the one–loop corrections due to third generation of quarks and squarks [15]: 0 ˜ 2 The AMSB-BRpV Model ti = ti + Ti(Q) , (5) 0 In AMSB models, the soft terms are fixed in a non– where ti, with i = d, u, are the renormalized tadpoles, ti are ˜ universal way at the unification scale which we assumed given in (4), and Ti(Q) are the renormalized one–loop con- 16 to be MGUT = 2.4 × 10 GeV. We considered the run- tributions at the scale Q. Here we neglected the one–loop ning of the masses and couplings to the electroweak scale, corrections for t3 since we are only interested in the value assumed to be the top mass, using the one–loop renormal- of µ. ization group equations (RGE) [17]. In the evaluation of Using the procedure underlined above, the whole mass the gaugino masses, we included the next–to–leading or- spectrum can be calculated as a function of the input param- der (NLO) corrections coming from αs, the two–loop top eters m0, m3/2, tan β, sign(µ), ²3, and mντ . In Fig. 1, we Yukawa contributions to the beta–functions, and threshold show a scatter plot of the mass spectrum as a function of the corrections enhanced by large logarithms; for details see scalar mass m0 for m3/2 = 32 TeV, tan β = 5, and µ < 0, −5 [18]. The NLO corrections are especially important for the varying ²3 and mντ according to 10 < ²3 < 1 GeV and −6 gaugino mass M2, leading to a change in the wino mass by 10 < mντ < 1 eV. The widths of the scatter plots show more than 20%. that the spectrum exhibits a very small dependence on ²3

One of the virtues of AMSB models is that the SU(2) ⊗ and mντ . Throughout this section we use this range for ²3

U(1) symmetry is broken radiatively by the running of the and mντ in all ﬁgures. RGE from the GUT scale to the weak one. This feature is We can see from this ﬁgure that, for m0 & 170 GeV, the 0 preserved by our model since the one–loop RGE are not af- LSP is the lightest neutralino χ˜1 with the lightest chargino + fected by the bilinear RP violating interactions [17]. In this χ˜1 almost degenerated with it, as in RP –conserving AMSB. − work, we made the simplest assumption that R-parity is vi- Nevertheless, the LSP is the lightest stau τ˜1 for m0 . 170 olated only in the third generation. A full three generation GeV. This last region of parameter space is forbidden in Brazilian Journal of Physics, vol. 34, no. 1A, March, 2004 177

RP –conserving AMSB, but perfectly possible in AMSB– violating interactions. Writing the mass terms in the form BRpV since the stau is unstable, decaying into RP –violating   ϕ0 modes with sizeable branching ratios. 1 d 0 0 i0 2  0  Vquadratic = [ϕd, ϕu, ν˜τ ]MP 0 ϕu , (6) 2 i0 ν˜τ In our model, the CP–odd Higgs sector mixes with the imaginary part of the tau–sneutrino due to the bilinear RP we have

2 M 0 = (7)  P  2(0) 2 v3 2(0) m s + µ²3 m sβcβ −µ²3 A β vd A  2 2 2(0) 2(0) c v2 c c c   m s c m c2 − µ² v3 β + 3 β m2 −µ² β + v3 β 2  , A β β A β 3 2 2 2 ν˜τ 3 mν˜τ  vd sβ vd sβ sβ vd sβ  cβ v3 cβ 2 2 −µ²3 −µ²3 + m m sβ vd sβ ν˜τ ν˜τ

the RP conserving limit (²3 = v3 = 0). In order to write this mass matrix we have eliminated m2 , m2 , and B using 1000 Hu Hd 3 the tadpole equations (4). The mass matrix has an explic- ~ itly vanishing eigenvalue, which corresponds to the neutral t2 800 g~ Goldstone boson.

Mass (GeV) This matrix can be diagonalized with a rotation ~ Χ~ + t1 2 ~ ~ Χ 0 (Χ 0) 3 4     600 0 0 A ϕd 0 0 +     0 0 G 0 ϕ H A (H ) = RP u , (9) odd i0 400 ν˜τ ν˜τ

Χ~ 0 2 where G0 is the massless neutral Goldstone boson. Between 200 i0 µ~ ν~ 1(2) τ h0 the other two eigenstates, the one with largest ν˜τ compo- odd τ~ Χ~ + Χ~ 0 2 1 ( 1 ) ν˜ τ~ nent is called CP–odd tau–sneutrino τ and the remaining 1 0 0 state is called CP–odd Higgs A . 200 400 600 800 1000 As an intermediate step, it is convenient to make explicit the vanishing mass of the Goldstone boson with the rotation m0 (GeV)   sβ cβ 0 Figure 1. Supersymmetric mass spectrum in AMSB–BRpV for b v3 RP 0 =  −cβr sβr − cβr , (10) m3/2 = 32 TeV, tan β = 5, and µ < 0. The values of ²3 and vd v3 2 v3 −5 − c r sβcβr r mντ were randomly varied according to 10 < ²3 < 1 GeV and vd β vd −6 10 < mντ < 1 eV. where 1 q r = 2 , (11) v3 2 2 2(0) 2 1 2 2 2 2 02 1 + v2 cβ with m = m + ² + g v and g ≡ g + g . Here, d ν˜τ ν˜τ 3 8 Z 3 Z 2 T b 0 b 2(0) Bµ 2(0) 1 obtaining a rotated mass matrix RP MP 0 RP 0 which has a 2 2 2 2 0 mA = and mν˜ = ML + gZ (vd − vu) (8) G s c τ 3 8 column and a row of zeros, corresponding to . This pro- β β cedure simpliﬁes the analysis since the remaining 2×2 mass 0 odd are respectively the CP–odd Higgs and sneutrino masses in matrix for (A , ν˜τ ) is c  ³ ´  2(0) v2 c4 s2 −c2 c2 m + 3 β m2 + µ² v3 β β v3 β 2 1 A 2 2 ν˜τ 3 2 mν˜τ − µ²3 r 2 vd sβ vd sβ vd sβ sβ Mc 0 =  ³ ´  P c2 . (12) v3 β 2 1 2 1 m − µ²3 r m 2 vd sβ ν˜τ sβ ν˜τ r 178 M. B. Magro

the ratio between the CP–odd Higgs mass mA and the CP– odd tau–sneutrino mass m odd as a function of tan β. ν˜τ 0.8 The CP-even Higgs/sneutrino sector and the Charged

odd Higgs/charged slepton sector have similar behavior and their θ 0.7 (a) 0.6 R-parity violating mixing angles can be as large as in the sin 0.5 CP-odd Higgs/sneutrino sector. For a more detailed analy- 0.4 sis, see [17]. 0.3 BRpV also provides a solution to the atmospheric and 0.2 solar neutrino problems due to their mixing with neutrali- 0.1 nos, which generates neutrino masses and mixing angles. It 0 was shown in [6] that the atmospheric mass scale is ade- -0.1 4 6 8 10 12 14 16 18 20 quately described by the tree level neutrino mass tanβ τ ~ ν 12 2 02 (b) tree M1g + M2g ~ 2 mν = |Λ| , (15) 0 3 4∆ A 10 0 m /m 8 ∆ 6 where 0 is the determinant of the neutralino sub–matrix and Λ~ = (Λ1, Λ2, Λ3), with 4 2 Λi = µvi + ²ivd , (16) 0 4 6 8 10 12 14 16 18 20 where the index i refers to the lepton family. The spec- β tan trum generated is hierarchical, and obtained typically with Λ1 ¿ Λ2 ≈ Λ3. As it was mentioned before, for many purposes it is enough to work with RP violation only in the third gen- Figure 2. (a) CP–odd Higgs–sneutrino mixing and (b) ratio be- eration. In this case, the atmospheric mass scale is well ~ 2 2 tween the CP–odd Higgs mass and the sneutrino mass as a function described by Eq. (15) with the replacement |Λ| → Λ3. tan β m = 32 µ < 0 100 < m < 300 of for 3/2 TeV, and 0 GeV. In Fig. , we plot the neutrino mass as a function of Λ3 in AMSB–BRpV with the input parameters m3/2 = 32 TeV, We quantify the mixing between the tau–sneutrino and µ < 0, 5 < tan β < 20, 100 < m0 < 1000 GeV and −5 the neutral Higgs bosons through 10 < ²3 < 1 GeV. The quadratic dependence of the neutrino mass on Λ3 is apparent in this ﬁgure and neutrino 2 odd 0 2 odd 0 2 2 sin θodd = |hν˜τ |ϕui| + |hν˜τ |ϕdi| . (13) masses smaller than 1 eV occur for |Λ3| . 0.6 GeV . More- over, the stars correspond to the allowed neutrino masses If we consider the RP violating interactions as a perturba- when the tau–sneutrino is the LSP. In general the points with tion, we can show that a small (large) m0 are located in the inner (outer) regions of this scattered plot. ³ ´2 v3 2 2(0) c m − µ²3 2 2 vd β ν˜τ v3 2 From Fig. 3, we can see that the attainable neutrino sin θodd ' ³ ´2 + 2 cβ , (14) 2(0) 2(0) v masses are consistent with the global three–neutrino oscil- s2 m − m d β A ν˜τ lation data analysis in [19] that favors the ντ → νµ oscillation hypothesis. At tree level, only one neutrino acquires indicating that this mixing can be large when the CP–odd a mass [20], which is proportional to the sneutrino vev in 0 Higgs boson A and the sneutrino ν˜τ are approximately de- a basis where the bilinear R-parity violating terms are re- generate. moved from the superpotential. At one-loop, three neutrinos Figure 2a displays the full sneutrino–Higgs mixing (13), get a non-zero mass, producing a hierarchical neutrino mass with no approximations, as a function of tan β for m3/2 = spectrum [15]. Although only mass squared differences are 32 TeV, µ < 0 and 100 < m0 < 300 GeV. In a large constrained by the neutrino data, our model naturally gives a fraction of the parameter space this mixing is small, since hierarchical neutrino mass spectrum, therefore, we extract a it is proportional to the BRpV parameters squared divided na¨ıve constraint on the actual mass coming from the analysis

by MSSM mass parameters squared. However, it is possi- of the full atmospheric neutrino data, 0.04 . mντ . 0.09 ble to ﬁnd a region where the mixing is sizable, e.g., for our eV [19]. In addition, we notice that it is not possible to ﬁnd choice of parameters this happens at tan β ≈ 15. As ex- an upper bound on the neutrino mass if angular dependence pected, the region of large mixing is associated to near de- on the neutrino data is not included and only the total event generate states, as we can see from Fig. 2b where we present rates are considered. Brazilian Journal of Physics, vol. 34, no. 1A, March, 2004 179

β tan = 3 M0 = 50 GeV 2 ) 10

1.2 % τud BR ( τ

ν 1 m (eV)

0.8 10 ν + - 3l l 0.6 ν - 3bb 0.4

1 0.2

-0.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10 -6 -5 -4 -3 -2 -1 10 10 10 10 10 10 Λ (GeV2) mν (eV) 3 β tan = 35 M0 = 150 GeV 2 ) 10

Figure 3. Tau neutrino mass as a function of Λ3 for 5 < tan β < % 20, 100 < m0 < 1000 GeV, m3/2 = 32 TeV and µ < 0. The stars correspond to the points where the tau-sneutrino is the LSP. BR (

10 3 Multilepton searches at the Teva- tron

1 We also have searched for R-parity violating signals at the Run II of the Fermilab Tevatron in a scenario where supersymmetry is broken through SUGRA models. The parameter space of our SUGRA model, which exhibits R-parity -1 violation only in the third generation, via the addition of the 10 -6 -5 -4 -3 -2 -1 bilinear terms (1) and (2), is 10 10 10 10 10 10 mν (eV) m , m , tan β , sign(µ) ,A , ² and m , (17) 1 0 1/2 0 3 ντ Figure 4. χ˜0 branching ratios as a function of mντ for A0 = 0, −3 µ > 0, and ²3 = 10 GeV.We fixed m1/2 = 175 GeV in the case where the parameters m1/2 and m0 characterize the com- of tan β = 3 and m1/2 = 125 GeV in the case of tan β = 35. 0 0 mon gaugino mass and scalar soft SUSY breaking masses at The solid lines denote χ˜1 → ν3bb (squares); χ˜1 → τν`` (circles); 0 + − 0 the unification scale, A is the common trilinear term, and and χ˜1 → ν3` ` (stars). The dashed lines denote χ˜1 → invisible 0 0 0 tan β is the ratio between the Higgs field vev’s. We charac- (squares); χ˜1 → τud (circles); and χ˜1 → ν3qq (stars). terize the BRpV sector by the ²3 term in the superpotential and the tau neutrino mass mντ since it is convenient to trade In R-parity conserving scenarios, the trilepton produc- 0 ± ± the bilinear vev v3 by mντ . In our simplified one-generation tion at the Tevatron proceeds via pp → χ˜2χ˜1 with χ˜1 → 0 0 + − 0 0 description considered here we fix, for definiteness, one rep- `νχ˜1, χ˜2 → ` ` χ˜1, and the LSP (χ˜1) leaving the detector resentative value for mντ = 0.1 eV. invisibly, producing then, 3 leptons in the final state. The The presence of BRpV induces a mixing between the main SM backgrounds for the trilepton production are dis- neutrinos and neutralinos, giving rise to the R-parity violat- played in Table 3. In order to suppress these backgrounds, ing decays of the LSP. In our model, the lightest neutralino we have imposed the soft cuts SC2 defined in Ref. [21], 0 + − presents leptonic decays χ˜1 → ν` ` , semi-leptonic ones which were tailored for scenarios containing soft signal lep- 0 0 0 0 χ˜1 → νqq or `qq , and the invisible mode χ˜1 → ννν. The tons coming from τ decays. In our analysis, the signal and importance of the νbb decay mode increases for large ²3, backgrounds were generated using PYTHIA [22], except for 0 ? ? since the effective coupling λ333 is proportional to ²3 after the WZ (γ ) which was computed using the complete ma- a suitable rotation. For a fixed value of ²3, the branching trix elements. The trilepton cross section for the SM back- ratio into νbb decreases with increasing mντ , as can be seen grounds after cuts are shown in Table 3. 1 0 from Fig. 4. In general, the χ˜0 decays mainly into τqq for As a good approximation, we have assumed that BRpV 1 large m0 or small ²3, while its decays are dominated by νbb is only important for the χ˜0 decays and we incorporated at small m0 and large ²3 and/or tan β. these new modes in PYTHIA, leaving the other decays un- 180 M. B. Magro

changed. In fact, the R-parity violating decay modes are reducing the missing ET . Besides that, the leptons from the 1 strongly suppressed when the R conserving ones have a few χ˜0 decay can give rise to additional isolated leptons which GeV of phase space. Assuming that gluinos and squarks are can contribute to the trilepton signal or suppress it due to the too heavy to be produced at the Tevatron, we considered the presence of more than three isolated leptons. ˜˜? ˜ 0 0 following processes: pp → `` , ν˜`, χ˜i χ˜j (i(j) = 1, 2), + − 0 ± χ˜1 χ˜1 , and χ˜i χ˜1 (i = 1, 2). 1 The χ˜0 decays can contain charged leptons, and there- 3 leptons - tanβ = 3 fore, we should also analyze multilepton (≥ 4`) produc- 300 tion. In order to extract this signal, we applied the trilepton case cuts but accepting leptons with |η(`)| < 3. We also (GeV) 250 1/2

required the presence of an additional isolated lepton with m pT > 5 GeV and demanded the missing transverse energy 200 to be larger than 20 GeV. The main SM backgrounds for this process are tt, WZ, and ZZ productions whose cross 150 sections after cuts are shown in Table I. 100 Table I. Background cross sections in fb for the trilepton and multilepton signatures at the Tevatron Run II. 50

0 σ (fb) trilepton multilepton 0 200 400 600 800 1000 WZ (Z → ττ) 0.17 0.01 ∗ ∗ ∗ m (GeV) W Z ,W γ → lll 0.12 - 0 0 W∗Z∗,W∗γ → ll l0 0.15 - tt 1.15 0.16 Figure 5. Reach of Fermilab Tevatron Run II using the trilepton ∗ ∗ signal in the m0 ⊗ m1/2 plane for A0 = 0, tan β = 3, µ > 0, Z Z 0.05 0.10 −3 ²3 = 10 GeV, and mντ = 0.1 eV. The black circles are theoreti- total 1.64 0.27 cally excluded, while the white circles are experimentally excluded by sparticle and Higgs boson searches at LEP2. The black squares denote points accessible to Tevatron experiments at 5σ level with 2 fb−1 of integrated luminosity, while the white squares are accessi- m ⊗ m −1 We investigated the regions of the 0 1/2 plane ble with 25 fb . Points denoted by diamonds are accessible at the where the trilepton and multilepton signals can be estab- −1 −1 3σ level with 25 fb , while the stars correspond to the region not lished at the Tevatron for integrated luminosities of 2 fb accessible to Tevatron. The grey area indicates the region where −1 and 25 fb and ﬁxed values of A0, tan β, sign(µ), ²3, and the neutralino has a large decay length, indicating that the results mντ . We exhibit our results in the m0 ⊗ m1/2 plane, denot- should be carefully revised. ing by black circles the theoretically excluded points, and by white circles the experimentally excluded regions by sparticle and Higgs boson searches at LEP2 [23]. The black We present the Tevatron reach in the multilepton chan- squares represent points accessible to Tevatron experiments nel in Fig. 6 for the same parameters adopted in Fig. 3. at 5σ level with 2 fb−1 of integrated luminosity, while the As we can see, the channel reach is larger than the trilep- white squares are accessible with 25 fb−1. Points denoted ton one, increasing the discovery potential for larger values by diamonds are accessible only at the 3σ level with 25 of m1/2 or small m0. In this region it is clear that the re- fb−1, while the stars correspond to the region not accessi- duction of the trilepton signal is largely due to the presence 1 ble to the Tevatron. In the gray area, the χ˜0 decay length is of additional isolated leptons. We present the combined re- rather long and this can modify our results, indicating that sults for the trilepton and mulilepton searches in Fig. 7. It these points should be subject to a more detailed analysis. is interesting to notice that the presence of R-parity violat- For more information on the decay lenght behavior see the ing interactions leads to a 5σ SUSY discovery even at large full analysis at [24]. In Fig. 5, we present the region of the m0, a region where the usual R-parity conserving SUGRA m0 ⊗ m1/2 plane that can probed at the Tevatron using the model has no discovery potential at all. Moreover, this re- −3 trilepton signal for A0 = 0, tan β = 3, µ > 0, ²3 = 10 sult is only achieved by combining trilepton and multilepton

GeV, and mντ = 0.1 eV. For these values of the parameters, signals. Nevertheless, a part of this result should be taken 1 0 the χ˜0 decays mainly into τqq and inside the detector for with care. For m1/2 . 170 GeV the lightest neutralino is masses larger than 70 GeV. lighter than 70 GeV and has a large decay length for the pa- It is interesting to compare our results presented in Fig. 5 rameters used in this analysis. Therefore, it is not guarateed with the ones in Ref. [21]. The presence of BRpV interac- that it will decay before the calorimeters. In principle, this tions reduces the Tevatron reach in the trilepton channel for could lead to spectacular events, which could increase the small values of m0. Here we have three competing effects: sensitivity to BRpV, however, we consider them outside the on the one side there are new contributions to the process, scope of our analysis. In any case, it is clear that the pres- however, the decay of the neutralino into νbb produces a ence of BRpV enhances the signal for m1/2 & 170 GeV and larger hadronic activity, destroying the lepton isolation, and large m0. Brazilian Journal of Physics, vol. 34, no. 1A, March, 2004 181

4 or + leptons - tanβ = 3 combined results - tanβ = 35 350 350 (GeV) 300 (GeV) 300 1/2 1/2 m 250 m 250

200 200

150 150

100 100

50 50

0 0 0 200 400 600 800 1000 0 200 400 600 800 1000

m0 (GeV) m0 (GeV)

Figure 6. Reach of Fermilab Tevatron Run II in the 4 or more lep- Figure 8. Reach of Fermilab Tevatron Run II combining trilepton and multilepton results for A0 = 0, tan β = 35, µ > 0, ton channel. All parameters and conventions were chosen as in −3 Fig. 5. ²3 = 10 GeV and mντ = 0.1 eV. The conventions are as in Fig. 5.

combined results - tanβ = 3 350 4 Conclusions

(GeV) 300 We have shown in the previous sections that our model ex-

1/2 hibiting Anomaly Mediated Supersymmetry Breaking and m 250 Bilinear RP Violation is phenomenologically viable. In par- ticular, the inclusion of BRpV generates neutrino masses 200 and mixings in a natural way. Moreover, the RP breaking 150 terms give rise to mixings between the Higgs bosons and the sleptons, which can be rather large despite the smallness of 100 the parameters needed to generate realistic neutrino masses. These large mixings occur in regions of the parameter space 50 where two states are nearly degenerate.

0 The RP violating interactions render the LSP unstable 0 200 400 600 800 1000 since it can decay via its mixing with the SM particles (lep- m (GeV) tons or scalars). Therefore, the constraints on the LSP are re- 0 laxed and forbidden regions of parameter space become allowed, where scalar particles like staus or sneutrinos are the Figure 7. Reach of Fermilab Tevatron Run II combining trilep- LSP. Furthermore, the large mixing between Higgs bosons ton and multilepton results. All parameters and conventions were chosen as in Fig. 5. and sleptons has the potential to change the decays of these particles. These facts have a profound impact in the phe- nomenology of the model, changing drastically the signals at colliders [25]. Finally, Fig. 8 displays the Tevatron reach for the com- We also have studied the trilepton and multilepton reach bined channels for the case A0 = 0, tan β = 35, µ > 0, of the Tevatron in the simplest supergravity model where an −3 ²3 = 10 GeV and mντ = 0.1 eV. For this choice of pa- effective bilinear term in the superpotential parametrizes the 0 0 rameters, the main χ˜1 decay mode is τqq , however, there is explicit breaking of R-parity. We have then shown how the a sizeable contribution of the νbb channel at small m0. As presence of BRpV interactions leads to a suppression of the expected, the SUSY reach decreases at small m0 as we in- trilepton signal for small values of m0 and/or large values 1 0 crease tan β, however there is a slight gain at large m0. We of ²3 due to the χ˜0 decay into or τqq or νbb. However, the 1 also can see that the Tevatron reach diminishes when tan β χ˜0 decays lead to a drastically extended reach at large m0, 0 is increased. Again, the gray area in the Fig. 8 shows the compensating the large hadronic decay of χ˜1. Moreover, the region where the LSP decay is rather long. We can see that presence of additional isolated leptons in the signal allows for tan β = 35 this region is smaller and we should take us to look for multilepton events, specially important at large with care the results in the region with m1/2 . 140 GeV m0. This new topology is useful not only for discovery, but and m0 & 190 GeV, where the lightest neutralino is lighter also to verify whether R-parity is conserved or not. For a than ∼ 60 GeV. more detailed discussion on the results, see Ref. [24]. 182 M. B. Magro

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