Distinguishing Majorana and Dirac Gluinos and Neutralinos

While gluinos and neutralinos are Majorana fermions in the MSSM, they can be Dirac fermion fields in extended supersymmetry models. The difference between the two cases manifests itself in production and decay processes at colliders. In this contribution, results are presented for how the Majorana or Dirac nature of gluinos and neutralinos can be extracted from di-lepton signals at the LHC. PACS: 12.60.Jv, 14.80.Ly, 13.85.-t MAJORANA AND DIRAC FERMIONS IN SUPERSYMMETRY In the Minimal Supersymmetric Standard Model (MSSM), the fermionic partners of the neutral, self-conjugate gauge bosons are self-conjugate Majorana fields with two degrees of freedom each. For example, the relation between the gluon and gluino fields and their charge conjugate fields is given by gc = −gT , g̃c = − g̃T , where color indices have been suppressed. Massive Majorana particles are known to mediate fermion-number violating production and decay processes, such as qLqL → q̃Lq̃L, qRqR → q̃Rq̃R, q̃L → ql± l̃∓. (1) These processes thus are central for experimentally testing the Majorana nature of gluinos. To study the characteristic differences between Majorana and Dirac fields, we will focus on a well-defined framework where the gauge fields are embedded in N = 2 superfields [1]. Each N = 2 gauge hypermultiplet contains one vector field, two twocomponent fermion fields, and one complex scalar fields, see Tab. 1. Depending on the structure of supersymmetry (SUSY) breaking, the two fermion components can form two distinct Majorana fields or one Dirac field. The scalar component could lead to interesting phenomenology on its own [2], but will not be discussed here. The two MSSM Higgs doublets can be joined into an N = 2 chiral/anti-chiral hypermultiplet, but the quark and lepton fields will be restricted to N = 1 representations as in the MSSM for the purpose of this work. The results presented here are based on Ref. [3]. Some earlier work on the observability of the Majorana nature may be found in Ref. [4], and consequences for the density of cold dark matter have been elaborated in Ref. [5]. TABLE 1. The N=2 gauge hyper-multiplets. Group Spin 1 Spin 1/2 Spin 0 SU(3) g g̃; g̃′ σg SU(2) W±,W 0 W̃±,W̃ 0;W̃ ′±,W̃ ′0 σ± W ,σ0 W U(1) B B̃; B̃′ σB THE SUSY-QCD SECTOR In our setup, the two gluino components g̃ and g̃′ in the gluon vector hypermultiplet each have the usual kinetic terms, but only the standard gluino interacts with matter: Lgluino interactions = gsTr ( g̃γμ [gμ , g̃]+ g̃′γμ [gμ , g̃′] ) −gs [qLg̃ q̃L −qRg̃ q̃R +h.c.] . (2) The soft supersymmetry breaking mass terms are given by Lsoft gluino masses = − 1 2 [ M′ 3 Tr(g̃′g̃ )+M3 Tr(g̃g̃)+M D 3 Tr(g̃′g̃+ g̃g̃ ′) ] , (3) so they form a 2×2 matrix in the g̃, g̃′-space. In the limit M′ 3 → ∞ the g̃′ decouples and the MSSM gluino sector is recovered. On the other hand, if M3 = M′ 3 = 0 and M D 3 6= 0, the mass matrix has two degenerate eigenvalues. In this case, the two Majorana states are paired into one Dirac field g̃D = 2(1+ γ5)g̃+ 1 2(1− γ5)g̃′ with Dirac mass MD 3 . A smooth path can be defined that interpolates between the Majorana and Dirac limits: M′ 3 = mg̃1 y 1+ y , MD 3 = mg̃1 , M3 = mg̃1M ′ 3/(M ′ 3−mg̃1) . (4) As y is varied between −1 and 0, one of the mass eigenvalues is kept fixed at mg̃1 , while the second eigenvalue changes from ∞ to mg̃1 . Therefore y = −1,0 correspond to the Majorana and Dirac limits, respectively, while for any value in-between we obtain two Majorana gluino mass eigenstates g̃1,2 that are related to g̃ and g̃′ by a non-trivial mixing matrix. A few examples for the y-dependence of partonic cross sections for gluino and squark production are shown in Fig. 1. Since, therefore, the ratio of gluino and squark production rates is different in the Majorana and Dirac limits, this leads to observable effects for di-lepton SUSY signatures at the LHC. In particular, assuming a standard scenario (such as the SPS1a′ scenario [6]) with a bino LSP, mg̃ > mq̃, and the dominant decay chains q̃L → q χ̃± 1 → ql νl χ̃ 1 , q̃R → q χ̃ 1 , (5) the charge of the lepton is related to the charge of the L-squark. This results in a net difference in the ratio of l+l+ and l−l− rates between the Majorana and Dirac case, see Tab. 2. After applying the cuts of Ref. [7] to reduce the Standard Model (SM) background and by combining information of the total di-lepton rates and the jet p⊥ distributions, the two cases can be distinguished with a statistical significance of 11 standard deviations, for an integrated luminosity of 300 fb−1. As we have checked in -1 -0.8 -0.6 -0.4 -0.2 0 0 50 100 150 200 250 300 350 y σ [f b ] σ[qq → q̃Lq̃′ R] σ[qq → q̃Lq̃′ L] = σ[qq → q̃Rq̃′ R] -1 -0.8 -0.6 -0.4 -0.2 0 0 250 500 75