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Simple metho d for measuring of prop erties of Dark Matter particles at ILC for different mo dels of DM
I. F. Ginzburg, Sob olev Inst. of Mathematics, SB RAS and Novosibirsk State University Novosibirsk, Russia

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Dark matter. Candidates
Ab out 20% of the Universe is made from Dark Matter (DM). Different candidates for particles of DM: Fermion. Lightest sup erparticle -- LSP. Scalar. Higgs-like field -- Inert Dark Mo del, IDM ..... They are usually memb ers of families of particles (called here as Dparticles), having some additional quantum numb er, which conservation guarantees stability of lightest memb er of this family. For SUSY this quantum numb er is R-parity, for IDM that is sp ecific D-parity

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Most probable: Dark matter particle is neutral D0, Mass < 60 - 70 GeV,(to prevent annihilation D0D0 W +W - even slightly b elow threshold) The charged particles having the same quantum numb er DБ are heavier than 100 GeV (LEP), In the scalar case the counterpart with opp osite P-parity DA also exists, they are lighter than ab out 120 GeV(LEP). Perhaps, more strong limitations can b e obtained for separate mo dels. Main (or single) decay channels:

D Б D 0W Б,

D A D 0Z
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where W and Z are represented their decay pro ducts either on mass shell or with lower effective mass.


In the estimates we assume MDБ s/2 = Ee. + + - Main pro duction channel e e D D (e+e- ЕЕ)/4 f or scalars Cross section is ab out (e+e- ЕЕ) f or f ermions. Than -- decay D+ W +D with branching close to 1.

Pro duction. Decay. Signature

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MD Б > M D 0 + M W
: Two dijets with effective mass close to MW (observed cross section (2/3)2 (e+e- D+D-) = 0.44 (e+e- D+D-) --or 1 dijet +e or Е (observed cross section 2 з (2/3) з 2[(1/9)(1 + 0.17] (e+e- D+D-) 0.35 (e+e- D+D-). Pro cesses of SM with the same kinematics demand pro duction additional or something else. Their cross sections contains additional factor - two orders lower. Even rough measurement

Signature

Large missing energy and p

of cross section gives value of spin of DM

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We denote (s; s1, s2) = s2 + s2 + s2 - 2ss1 - 2ss2 - 2s1s2. 1 2 + the energy and momentum of W Б from decay In the rest frame of D 2 2 2 2 (M 2 + , MW , MD0 ) M 2 + + MW - Md0 D r D+ DW + are EW = D , pr + = . W 2M D + 2M D + In the lab system energy of DБ is equal to b eam energy E and velo city 2 of DБ is v = 1 - MDБ /E 2, = E /MDБ . Denoting W escap e angle in D+ rest frame relative to direction of D+ motion in the lab system by and c = cos we have energy of W + L r in the lab system EW = (EW + cv pr ). W's are distributed within W r - v pr ), E (+) = (E r + v pr )). interval (E (-) = (EW W W W Boundary values E (Б) give two equations for determination of masses DБ and D0 with accuracy b etter 10 GeV (preliminary estimate). The distribution of these dijets in energy is uniform. dN (E ) dE since there is no correlation b etween escap e angle of W in the rest frame of DБ and pro duction angle of DБ.
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After determining of MDБ , cross section of e+e- D+D- pro cess is calculated precisely for each D-particle spin value. It allows to determine spin of D particles more definite via measuring of cross sections (factor ab out 4 difference).

Observation of determine sign allows to study for checking on

pro cess e+e- D+D- D0D0j j + 's allow to of charge of 2-jets W = q q in each separate case. It ? charge and p olarization asymmetries (like at Z -p eak) more detail prop erties of D-particles.

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MD Б < M D 0 + M W
In this case single decay channel is D+ D0W +, where W + means dijet (q q ) or system having effective mass w < Mw . (w < ? MD+ - MD0 ). All ab ove results are valid for each separate value w with the change in all equations MW w. The energy distributions for each pair of dijets are indep endent from each other.

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MD Б MD 0 + MW
In this case prop er width of DБ is large so that we can observe nonuniform energy distribution of dijets which will b e convolution of uniform distribution for narrow DБ with Breit-Wigner mass distribution. One can hop e that the measuring of violation of the observed energy distribution from uniform will allow to determine b oth mass of DБ and its width.

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Axial D-particle DA
For scalar D-particles, the pseudoscalar DA also exists, it has interaction Z D AD0. +- 0A 00 Therefore the pro cess e e Z D D D D Z has only cross section of the same order as e+e- Е+Е- and observable either dilepton (e+e- or Е+Е-) or dijet with effective mass equal to MZ (with accuracy to Z width). Almost entire ab ove discussion is valid in this case. The observation of these dilepton or dijet with large missed energy and p.

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The case of very light D0 (few GeV) demands additional simulation to determine its sensitivity.

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