Impacts of the CP-odd phase of the chargino mass matrix in light chargino-pair production at LEP II
Introduction
The Minimal Supersymmetric Standard Model (MSSM) [1]is a well-defined quantum theory of which the Lagrangian form is completely known, including the general R-parity preserving, soft supersymmetry (SUSY) breaking terms.
The full MSSM Lagrangian has 124 truly independent parameters – 79 real parameters and 45 CP-noninvariant complex phases [2]. The number of parameters in MSSM is too large compared to 19 in the Standard Model (SM). Therefore, many studies on possible direct and indirect SUSY effects have been made by making several assumptions and investigating the variation of only a few parameters 3, 4, 5. Recently, it has, however, been shown [6]that limits on sparticle masses and couplings are very sensitive to the assumptions and need to be re-evaluated without making any of the simplifying assumptions that have been standard.
Despite the large number of phases in the model as a whole, just one CP-odd rephase-invariant phase [7], stemmed from the chargino mass matrix, takes part in chargino production [9]. In light of this aspect, the analyses with the general parameter set in the chargino system are not so much more difficult than those with parameters assumed real. The CP-noninvariant phase may be constrained indirectly by the electron or neutron electric dipole moment [7]and may be small, but the constraints on its actual size depends strongly on the assumptions in those analyses. Moreover, as has been recently shown [8], cancellations between different terms contributing to the dipole moments can allow for values of the phases very different from zero even the sparticle masses are relatively light. Consequently, unless there exist any concrete demonstrations for a small value of the phase, it will be more reasonable to take the CP-odd phase as a free parameter.
Charginos are produced in e+e− collisions, either in diagonal or in mixed pairs. However, the second chargino is generally expected to be significantly heavier than the first state. At LEP2 [10], and potentially even in the first phase of e+e− linear colliders (see e.g. Ref. [11]), the chargino may be, for some time, the only chargino state that can be studied experimentally in detail. In the present note, we will focus on the diagonal pair production of the light chargino in e+e− collisions,and investigate in detail the phenomenological impacts of the CP-odd complex phase in the determinations of the relevant SUSY parameters in the production process.
The production of the light chargino-pair is completely described by the chargino mass , the cosines of two rotation angles determining the size of the wino and higgsino components in the charginos, and the sneutrino mass5. First of all, in Section 2, we recapitulate the elements of the mixing formalism and quantitatively discuss the dependence of the chargino masses and the cosines of the two rotation angles on the CP-noninvariant phase. In Section 3 the cross section for chargino production along with the light chargino mass is mapped over the parameter space, especially for the gaugino mass M2 and the higgsino mass parameter |μ|, by varing the CP-noninvariant phase. Then, we examine the phenomenological impacts of the CP-odd phase in constraining the parameter space. Conclusions are given in Section 4.
Section snippets
Chargino masses and mixing angles
In the MSSM, the spin-1/2 partners of the W boson and charged Higgs boson, and , mix to form chargino mass eigenstates . The mass eigenvalues and the mixing angles and phases are determined by the elements of the chargino mass matrix in the basis [1]which is built up by the fundamental SUSY parameters; the gaugino mass M2, the higgsino mass parameter μ, and the ratio tanβ=v2/v1 of the vacuum expectation values of the two neutral Higgs fields
Production cross-section
The process is generated by the three mechanisms: s-channel γ and Z exchanges, and t-channel exchange. The transition matrix element, after a Fierz transformation of the -exchange amplitude,can be expressed in terms of four bilinear charges, classified according to the chiralities α,β=L,R of the associated lepton and chargino currents
Conclusions
We have analyzed how the parameters of the chargino system, the masses of the charginos and the size of the wino and higgsino components in the chargino wave functions, parametrized in terms of the two angles φL and φR, are affected by the CP-noninvariant phase Φμ in the chargino mass matrix. In addition, we have studied the dependence of the production cross section of the light chargino-pair in e+e− collisions on the phase and have determined the dependence of the minimal cross section as
Acknowledgements
This work was supported by Korean Science and Engineering Foundation in part through KOSEF-DFG large collaboration project, Project No. 96-0702-01-01-2 and in part through the Center for Theoretical physics, Seoul National University.
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2000, Physical Review D - Particles, Fields, Gravitation and Cosmology
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