Precise measuring mass and spin of dark matter particles at ILC via singularities in the single lepton energy spectrum
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recise Measuring Mass and Spin of Dark Matter Particles at ILC via Singularities in the Single Lepton Energy Spectrum1 I. F. Ginzburg Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk, Russia Abstract—We consider models, in which stability of Dark Matter particles D is ensured by the conservation of the new quantum number, called Dparity here. Our models contain also charged Dodd particle D±. We propose method for precision measuring masses and spin of Dparticles via the study of energy distribution of single lepton (e or μ) in the process e+e– → D+D– → DDW+W– with the observable state dijet + μ (or e) + nothing. It is shown that this distribution has kinematically determined singular points (upper edge and kinks or peak). Measuring of their positions allow to determine precisely masses of D and D±. After this, even a rough measuring of corresponding cross section allows to determine the spin of D particles. DOI: 10.1134/S106377961401033X 1
We consider a wide class of models, in which Dark Matter (DM) consists of particles D similar to those in SM, with the following properties (the examples are: MSSM where D is the lightest neutralino with spin 1/2 [1], and inert doublet model IDM [2] where D is the Higgslike neutral). 1. Neutral DM particle D with mass MD and spin sD = 0 or 1/2 has new conserved discrete quantum number. I call it Dparity. All known particles are Deven, while the DM particle is Dodd (for MSSM Dparity means Rparity). The Dparity conservation ensures stability of the lightest Dodd particle D. 2. In addition to D, a charged Dodd particle D± exist, with the same spin sD and with masses M+. (In MSSM D± is the lightest chargino, in the IDM D± is similar to the charged Higgs.) Other Dodd par ticles, if they exist, are very heavy. (The case with another neutral DA, lighter than D± is considered in [3]). 3. These Dparticles interact with the SM particles only via the Higgs boson and the covariant derivative in the kinetic term of the Lagrangian—gauge interac tions with the standard electroweak gauge couplings g, g' and e (for coupling to Z—with possible reducing mixing factor), D+D–γ, D+D–Z, D+DW–. A possible value of mass MD is limited by stability of Dparticles during the age of the Universe [4, 5]. We assume 4 GeV ⱗ MD ⱗ 80 GeV. The nonobser vation of processes e+e– → D+D– at LEP gives M+ > 90 GeV [6]. The neutral D can be produced and detected via production D± and its decay D± → DW±. To discover DM particle, one needs to specify such processes with clear signature. The e+e– Collider ILC/CLIC at s =
2E > 200 GeV provides excellent opportunity for these tasks in the process e+e– → D+D– [7, 8]. Main process e+e– → D+D–. Energies, γfactors and velocities of D± are s/2, γ + = E/M + , β + =
E± = E =
2
2
1 – M + /E .(1)
Neglecting terms ∝ (1/4 – sin2θW), the cross sec tion of process is a sum of model independent QED term (photon exchange) and axial Z exchange term— Fig. 1: ⎧ ⎪ β+ ⎪ σ = σ0 ⎨ ⎪ 3 ⎪ β+ ⎩
2
2M 2 1 + + + r Z β + ⎛ s D = 1⎞ , ⎝ 2⎠
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