1-loop effects of MSSM particles in Higgs productions at the ILC

Within the framework of the MSSM (Minimal Supersymmetric Standard Model), we investigate the 1-loop effects of SUSY (supersymmetric) particles on the Z, higgs production at the ILC. Three sets of the SUSY parameters are proposed which are consistent with the observed higgs mass, the muon g-2, the dark matter (DM) abundance and the decay branching ratio of B meson. In addition, We investigate the 1-loop effects on νν̄h production using W-fusion approximation at the ILC. We discuss on the possibility of discovering the signals consistent with SUSY as well as of experimentally distinguishing the proposed sets of SUSY parameters.


Introduction
The supersymmetric (SUSY) model [1] is considered as one of the promising candidates for the theory beyond the standard model. The experimental confirmation of the SUSY particles (sparticles) is an important subject of the present and future collider experiments. Since high luminosity is expected at the ILC experiments [2], we should calculate the physical observables with the accuracy better than the experimental data. We have calculated several cross sections and decay branching ratios at 1-loop level with GRACE/SUSY-loop system [3,4,5]. In this paper we report numerical results of the cross section of e − e + → Zh. (The same observable calculated in the previous work [6], and we confirmed almost same numerical results at the same assumption for the MSSM input parameters. We also calculeted the W fusion approximation of e − e + → ν eνe h, where the SM 1-loop correction has already been calculated with using GRACE [7]).

Selection of the MSSM parameter sets
We have considered the experimental constraints ( Table 1) in selection of the typical sets of MSSM parameters. We selected three sets [19] which consistent with next constraints. We have calculated the cross section of e + e − → Zh at the 1-loop level in these sets. We used MicrOMEGAs [11] in the estimation of the MSSM prediction for the dark matter (DM) thermal relic density(1), [8,9,10]. The program package SuSpect2 [18] are used for the muon g-2 anomalous magnetic moment (2), [12,13], the B meson rare decay branching ratio (3), [14] and the observed higgs mass (4), [15,16]. Moreover, we set the sparticle masses which meet the recent LHC bound (5), [17].
In Table 2, we show the set which is adopted for the calculation of e + e − → ν eνe h cross section with the W fusion approximation . It is noted that the set is consistent with the constraints (1),(3),(4), (5). In other words, we have not considered the muon g-2 constraint (2) in table 2. We have shown in the previous work [19] that the anomaly (2)

Numerical Results
We show total cross sections for associate higgs particle production processes at future linear collider in Figure 1. √ s = 250 GeV is adopted for the precision verification of e − e+ → Zh. Since σ(e − e + → ν eνe h) is larger than σ(e − e + → Zh) and σ(e − e + → ν eνe h) via the W-fusion are dominant contribution for √ s > ∼ 500 GeV.
! " " " [TeV] * * * * We define the ratio of the differential cross sections [20], We show δ susy in Figure 3. δ susy is 1∼2% in the entire region and is larger than the statistical error. It means that the 1-loop contribution of the MSSM could be measured at both √ s =250 GeV and 500 GeV. In addition, the difference between set2 and set3 is also larger than the statistical error at √ s=250 GeV.  We confirmed cancellation of ultraviolet and infrared divergences, and the photon cut-off energy independence. The Energy distribution and correction ratio δ susy in W fusion are shown in Figure 5. Where, E h is single generation energy of higgs particle. The  = 22%. In the entire region, δ susy = 11% ∼ 17%. It is larger than the error of the Monte Carlo integration. It means that the MSSM signal is verifiable, but this results are preliminary and necessary to be scrutinized more.

Summary
We selected sets that are consistent with higgs mass, B physics, DM relic density, LHC direct search of sparticles, and muon g-2(only in Zh production). We have probed statistical significance at the ILC. In the results of Zh, the MSSM 1-loop effects are statistically significant at both of √ s= 250 GeV and 500 GeV. At √ s =250 GeV, three sets are distinguishable. The results of W fusion approximation in e − e+ → ν eνe h are preliminary, but the 1-loop effect of supersymmetry would be verifiable at √ s = 500 GeV in the future linear collider.