One-loop effects on MSSM parameter determination via chargino production at the LC

At a future linear collider, very precise measurements, typically with errors of<1%, are expected to be achievable. Such an accuracy yields sensitivity to quantum corrections, which therefore must be incorporated into theoretical calculations in order to determine the underlying new physics parameters from linear collider measurements. In the context of the chargino--neutralino sector of the minimal supersymmetric standard model, this involves fitting one-loop predictions to prospective measurements of cross sections, forward-backward asymmetries and the accessible chargino and neutralino masses. Taking recent results from LHC SUSY and Higgs searches into account, we consider three phenomenological scenarios, each displaying characteristic features. Our analysis demonstrates how an accurate determination of the desired parameters is possible, and could additionally provide access to the stop masses and mixing angle.


Introduction
A linear collider (LC) [1][2][3][4][5] will be an ideal environment for high precision studies of physics beyond the standard model (BSM). A particularly wellmotivated description of BSM physics is provided by the minimal supersymmetric standard model (MSSM), offering the lightest supersymmetric particle, often the lightest neutralino, as a candidate to explain the evidence for dark matter in the universe [6,7]. Naturalness arguments (see e.g. ref. [8]) support the possibility that higgsino-like charginos and neutralinos are light, as also predicted by GUT motivated SUSY models [9]. Further, due to the challenges involved in detecting electroweakinos at the LHC, current bounds from ATLAS and CMS only exclude small regions of parameter space, see e.g. refs. [10,11]. Charginos and neutralinos could therefore be within reach of a first stage linear collider.
One approach to determine the fundamental MSSM parameters is to consider constrained models such as the constrained minimal supersymmetric standard model (CMSSM), and perform a global fit of this reduced set of parameters to all relevant experimental results available, see e.g. ref. [12]. On the other hand, in order to precisely determine the nature of the underlying SUSY model, we wish to determine the fundamental parameters in the most model-independent way possible. The determination of the U(1) parameter M 1 , the SU(2) parameter M 2 , the higgsino parameter µ and tan β, the ratio of the vacuum expectation values of the two neutral Higgs doublet fields, at the percent level via chargino and neutralino pair-production has been shown to be possible at LO (see ref. [13] and references therein). However, due to the expected high precision of mass and coupling measurements at the LC, as well as the fact that one-loop effects in the MSSM may be sizeable, higher order effects have to be considered. Taking these corrections into account additional MSSM parameters become relevant, such as the masses of the stops and sleptons, which, like the electroweakinos, are also weakly constrained by the LHC.
In this paper we demonstrate that the determination of the fundamental parameters of the chargino and neutralino sector at the LC would be possible, even on including the complications arising due to higher order effects. This requires the calculation of the next-to-leading order (NLO) corrections to the cross-section (σ) and forward-backward asymmetry (A F B ) for chargino production, as well as to the chargino and neutralino masses. A number of next-to-leading order (NLO) calculations of chargino and neutralino pair production at the LC can be found in the literature [14][15][16][17][18]. We perform our calculations in the on-shell (OS) scheme such that, as far as possible, the mass parameters can be interpreted as the physical masses. Recent work on the OS renormalization of the chargino-neutralino sector can be found in refs. [18][19][20][21][22][23][24].
By fitting these loop corrected predictions to the projected experimental results, we show that it would be possible to extract the fundamental parameters of the MSSM Lagangian. However due to the greater number of parameters, performing the fit is more involved than for the LO analysis. Choosing three potential MSSM scenarios, we assess the impact of the loop corrections and the feasibility of such an extraction in each. We further investigate the impact of obtaining masses of the charginos and neutralinos from threshold scans rather than the continuum (see ref. [1]) on the resulting accuracy of the parameters obtained from the fit.
The paper is organised as follows. In sec. 2 we introduce the process studied and define necessary notation. We then provide details of the calculation of the loop corrections in sec. 3, including details of the renormalization scheme used. In sec. 4 we further discuss the method employed in order to fit to the MSSM parameters, define the scenarios considered, and present our results. Finally in sec. 5 we discuss the implications of the results of the fits.

Process studied and tree-level relations
In this paper we study the determination of the fundamental parameters in the chargino-neutralino sector of the MSSM, via chargino production at a LC. The charginos,χ ± , and neutralinos,χ 0 , are the mass eigenstates of the gauginos and higgsinos, as seen from the relevant part of the MSSM Lagrangian [25], where P L/R = 1/2(1 ∓ γ 5 ). The mass matrix for the charginos is given by where s β /c β ≡ sin β/ cos β, and M W is the mass of the W boson. This matrix is diagonalised via the bi-unitary transformation Mχ+ = U * XV † , where U and V are complex unitary matrices. The mass matrix for the neutralinos in Figure 1: Tree-level diagrams for the production of charginosχ + 1 andχ − 1 at the LC. the (B,W ,H 1 ,H 2 ) basis is given by where s W (c W ) is the sin(cos) of the weak mixing angle θ W . Since Y is complex symmetric, its diagonalisation requires only one unitary matrix N , via Mχ0 = N * Y N † . As described in detail in sec. 4, in addition to the experimental determination of the masses of the charginos and neutralinos the parameter determination relies on the measurement of the polarised cross-section for the pair production of charginos,χ − 1 , and the forward-backward asymmetry defined by, for the unpolarised cross-section, where θ is the angle of the momentum of the charginoχ − 1 with respect to the momentum of the incoming electron e − . Neglecting the electron-Higgs couplings, the relevant process occurs at leading order via three diagrams, as seen in fig. 1.
The transition matrix element can be written as [26], where Q αβ denotes the bilinear charges, α = L, R refers to the chirality of the e + e − current and β = L, R to that of theχ + iχ − j current. The summation over α and β is implied. In our notation, the bilinear charges are comprised of the propagators and couplings for which the required MSSM couplings for theχ + iχ − j γ,χ + iχ − j Z and eν eχ + i vertices are given by and G L , G R , D Z and Dν are defined via In the equations above, e denotes the electric charge, m e and M Z are the masses of the electron and Z boson. D Z and Dν refer to the propagators of the Z boson and sneutrino (of mass mν), in terms of the Mandelstam variables s and t. Therefore in order to express the transition matrix element eq. (6) at leading order, the necessary MSSM parameters are M 2 , µ, tan β and mν. However, the expected accuracy of the measurements at the linear collider is such that one-loop corrections become relevant, and we shall see in the following section that at higher orders eq. (6) depends on many additional MSSM parameters.

NLO contributions and renormalization
We have calculated the full one-loop corrections to the forward-backward asymmetry for process e + e − →χ + 1χ − 1 , within the complex MSSM; the corre-sponding corrections to the cross section were calculated in ref. [18]. Examples for the contributing self-energy, vertex and box diagrams are shown in fig. 2. As in ref. [18], for the calculation we have used the program FeynArts [27][28][29][30][31], which allowed an automated generation of the Feynman diagrams and amplitudes. Together with the packages FormCalc [32][33][34] and LoopTools [32] we derived the final matrix elements and loop integrals. We assume a unit CKM matrix. We regularise using dimensional reduction [35][36][37], which ensures that SUSY is preserved, via the implementation described in refs. [32,38]. A number of one-loop calculations in the gaugino-higgsino sector can be found in the literature, mainly in the CP-conserving MSSM [14,[39][40][41][42][43][44][45][46], but some of which apply a renormalization scheme that is also applicable for complex parameters [14,45]. CP-odd observables have also been calculated at the one-loop level, for instance in refs. [48][49][50], but no dedicated renormalization scheme was required in these cases as the observables studied were UV-finite. Since we intend to extend the current study to the case of complex parameters, we follow the approach of refs. [18,20] closely, where a dedicated on-shell renormalization scheme for the chargino and neutralino sector of the MSSM with complex parameters was developed. In the following we will therefore only briefly discuss the parameter renormalization of the chargino and neutralino sector, relevant for the definitions of the parameters at loop level, and for further details about the chargino field renormalization and the renormalization of other sectors refer the reader to refs. [18,20,21,24].
The mass matrix in the chargino sector, eq. (2), is renormalized via where δX is defined by and contains the renormalization constants δM 2 and δµ, as well as renormalization constants (RCs) from other sectors, δc β , δs β (which can be expressed in terms of δ tan β), and δM W , defined in ref. [18]. The neutralino mass matrix, eq. (3), is similarly renormalized via where δY is defined analogously to δX in eq. (11) and contains the additional RC δM 1 , cf. eq. (3). Following e.g. ref. [20], δM 1 , δM 2 and δµ are determined by choosing three out of the total six physical masses of the charginos and neutralinos to be on-shell, i.e. the tree-level masses, mχ i , coincide with the one-loop renormalized masses, We define the coefficients Σ and define the left and right handed vector and scalar coefficients of the renormalized self-energy analogously viaΣ respectively. As stated earlier, we consider the parameter renormalization as for the complex MSSM, such that our setup is easily adaptable for future extensions. In ref. [18,21], it was shown that in the CP violating case, the 1-loop corrections to the phases of M 1 and µ, i.e. φ M 1 and φ µ respectively 1 are UV finite, and it is argued that these phases can therefore be left unrenormalized. Adopting this approach, one can determine expressions for δ|M 1 |, δ|M 2 | and δ|µ|, depending on which three physical masses are chosen to be on-shell. As we have two external charginos, and in order to easily extend our setup to the case ofχ + 1χ − 2 production, we assume the NCC scheme withχ 0 1 ,χ ± 1 andχ ± 2 on-shell [18,[20][21][22]. Note that in choosing a scheme, it is desirable that the on-shell particles should contain significant bino, wino and higgsino components, in order that the M 1 , M 2 and µ parameters are accessible [18,[20][21][22]. For the above choice, these conditions are satisfied for all the scenarios defined in sec. 4, in which the lightest neutralino always has a sizeable bino-like component. The parameters in question of the chargino mass matrix can then be renormalized via expressions given in refs. [18,21,24], which we list here for completeness, where F , C i and N i are defined by and the subscripts ± and 0 identify the coefficients of the chargino and neutralino self-energy respectively. Finite results for the process of interest at one-loop are obtained by adding the counterterm diagrams shown in fig. 3. Although FeynArts generates these diagrams, expressions for the counterterms which renormalize the couplings defined at tree-level in eq. (6), calculated in ref. [18], are required as input, and therefore, again for completeness, we provide expressions for these explicitly. For the γχ + iχ − j , Zχ + iχ − j and eν eχ + i vertices, these can be expressed as follows, where the analogous right-handed parts are obtained by the replacement L → R, and Note that the renormalization constants of the SM fields, i.e. Z V V (V = γ, Z) and δZ L e for the vector bosons and electron, and parameters, i.e. δZ e and δc W (s W ) for the electric charge and cos(sin) of the weak mixing angle respectively, can be found in ref. [18]. The renormalization for the chargino fields is performed in the most general manner, making use of separate RCs for the incoming and outgoing fields, i.e. coefficients δZ L/R ±,ij and δZ L/R ±,ij respectively for left and right-handed charginos as given in ref. [18]. Finally, the counterterm for the sneutrino self energy takes the form forν i =ν e ,ν µ ,ν τ , where the sneutrino field and mass RCs, δZ * ν i and δmν i , are also defined following ref. [18].
Inital and final state soft radiation must also be included to obtain an infra-red finite result as the incoming and outgoing particles are charged, and this is done as described in detail in ref. [18], using the phase-space slicing method to define the singular soft and collinear contributions in the regions E < ∆E and θ < ∆θ respectively. In the soft and collinear limit, the results are regularised using electron and photon masses, respectively, and factorised into analytically integrable expressions proportional to the tree-level cross-section σ tree (e + e − →χ + 1χ − 1 ). However the result is cut-off dependent (i.e. on ∆E and ∆θ), and removing this dependence requires a calculation of the cross section for the three body final state, excluding the soft and collinear regions, which we perform using FeynArts and FormCalc. We further require that soft photon radiation is included in the cross-section obtained from FormCalc. Finally we obtain a complete IR safe and cut-off independent result by adding the collinear contribution, which is calculated following the procedure outlined in ref. [14].

Obtaining MSSM parameters from the fit
With the loop corrections calculated as in section 3, we can determine the fundamental parameters of the MSSM at NLO. From now on, we will restrict our study to the case of real parameters. In the chargino and neutralino sectors there are four real parameters, see sec. 2, which we fit to, We additionally fit to the sneutrino mass, as this enters at tree level and will therefore significantly affect cross sections and forward-backward asymmetries. However in those scenarios where the sneutrino would already have been observed at the LC, its mass is assumed to be known. At the loop level, a large number of MSSM parameters will contribute. Depending on the scenario, only limited knowledge about some of these may be available.
In particular LHC data may only provide limited information about the parameters of the stop sector, and direct production at the LC might not be possible. However, our analysis also offers good sensitivity to these parameters at the LC, as stops could significantly contribute to chargino/neutralino observables at NLO. At the LC, the accessible masses are expected to be measured with high precision using different methods [1]. In the following we adopt the experimental precision which could be achieved using the threshold scan method, however we also investigate how the fit precision would change if the masses were obtained from the continuum. In case of the cross sections, the experimental uncertainty is dominated by the statistical uncertainty [51], where S and B are the signal and background contributions, respectively. In addition, we assume that the statistical uncertainties for the cross sections correspond to an integrated luminosity of L = 200 fb −1 per polarisation assuming the efficiency of = 15%, which includes branching ratios for semileptonic final states and a selection efficiency of 50% [51]. Similarly, for the forward-backward asymmetry we have and the total number of events N = N + + N − [51]. In order to estimate the theoretical uncertainty on the masses, crosssections and forward backward asymmetries, we consider the size of possible effects due either to neglected higher order corrections or to unknown MSSM parameters not included in the fit. NNLO corrections are an important source of theoretical uncertainty, however, at present, corrections of this kind are only known for chargino and neutralino masses, for which the leading SUSY-QCD NNLO corrections were calculated in ref. [46]. Based on these results we estimate the uncertainty on the masses due to NNLO corrections to be of the order of 0.5 GeV, i.e. comparable to the expected experimental uncertainty. Note that the masses chosen on-shell are assigned no theoretical uncertainty. We further neglect the currently unknown uncertainties arising due to NNLO corrections to the cross-sections and forward backward asymmetries, assuming that in the future NNLO results for these could be incorporated. However, we do include the additional uncertainty arising due to any unknown MSSM parameters which are not included in the fit, dominated by the contribution from the heavy pseudoscalar Higgs boson mass m A 0 . We perform a multi-dimensional χ 2 fit using Minuit [52,53] where the sum runs over the input observables O i , depending on the scenario, with their corresponding experimental uncertainties δO i .

Scenarios studied and motivation
We carry out the fit for three scenarios, S1, S2 and S3, shown in tab. 1, chosen in order to realistically assess the sensitivity to the desired parameters in a variety of possible situations. Due to the current status of direct LHC searches [54,55], in all scenarios we require heavy first and second generation squarks and gluinos, while the stop sector is assumed to be relatively light. 2 In S1 and S2 we take the masses of the stops, mt 1 and mt 2 , to be 400 GeV and 800 GeV respectively, and the mixing angle to be cos θ t = 0. The sbottom sector is then obtained by defining mb 1 = 400 GeV and cos θ b = 0. On the other hand in S3, in order to obtain m h = 125 GeV, calculated using FeynHiggs 2.9.1 [56][57][58][59], such that it is compatible with the recent Higgs results from the LHC [60,61], the stop sector parameters are chosen to be m u 3 = 450 GeV, m q 3 = 1500 GeV and A t = −1850 GeV, ensuring large mixing between the stops, such that cos θ t = 0.148. The sbottom sector is then obtained by defining mb 1 = 450 GeV and cos θ b = 0. In fig. 4 the mass corrections for neutralinosχ 0 2 andχ 0 3 are seen to be sensitive to the stop mixing angle for each of the studied scenarios.
As a result of indirect limits (checked using micrOmegas 2.4.1 [62,63]), we have chosen mixed gaugino higgsino scenarios favoured by the relic density measurements [64] and relatively high pseudoscalar Higgs masses in light of flavour physics constraints, e.g. due to the dependence of the branching ratio B(b → sγ) on the charged Higgs mass. We also check that our scenarios agree with the experimental results for branching ratio B(b → sγ) and the anomalous magnetic moment of the muon ∆(g µ − 2)/2. Further, in S2 we study the sensitivity of the fit to large values of M 2 , such that the wino-like Scenario 3 125 M e 3 106 Table 1: Parameters for scenarios 1/2 and 3 (S1/S2 and S3), in GeV with the exception of tan β. Here M (l/q) i (M (e/u/d) i ) represent the left (right) handed mass parameters for a slepton/squark of generation i respectively, and A f is the trilinear coupling for a sfermionf . See text for stop and sbottom parameter definitions.
chargino and neutralino are heavy and decoupled from the bino and higgsinolike particles. Finally, in S1/S2 we consider the case that the sleptons (with the exception of the light stau) and pseudoscalar Higgs bosons are at the TeV scale, and in S3 the case that they are relatively light. Therefore, while S1/S2 are not in keeping with the 125 GeV Higgs boson, they provide illustrative examples of the potential of the LC in scenarios complementary to S3. 3

Results for scenario 1
In this scenario, only the charginos and three neutralinos will be accessible at the LC. As input for the fit we therefore use: • the masses of the charginos (χ ± 1 ,χ ± 2 ) and three lightest neutralinos  Table 2: Observables (masses in GeV, cross sections in fb) used as input for the fit in S1, tree-level values and loop corrections are specified. Here the superscript on σ and A F B denotes √ s in GeV, and the subscript on σ denotes the beam polarisation (P(e − ), P(e + )). Errors in brackets are for masses obtained from the continuum. The central value of the theoretical prediction, B(b → sγ) = 3.3 · 10 −4 GeV is also included in the fit. See text for details of the calculation and error estimation. from ref. [65], is adopted. We found that the impact of the muon anomalous magnetic moment is negligible in this scenario, mainly due to the heavy smuon sector. It should be possible to probe the supersymmetric QCD sector, with sqark masses of ∼1.5 TeV and the gluino mass of ∼ 700 GeV, at the LHC, such that the theoretical uncertainty arising due to these parameters is small in comparison to that due to the unknown m A 0 . We therefore include the small dependence on the A 0 mass as an additional source of error, having explicitly checked that the impact of all other parameters is negligible. Note that there are no theoretical errors for masses chosen to be on-shell. Even at one loop, these masses are related to the fundamental parameters via the tree level relations, and are included in the fit.
In S1 we fit 8 MSSM parameters: M 1 , M 2 , µ, tan β, mν, cos θ t , mt 1 , and mt 2 . The results of the fit are given in tab. 3. We find that the gaugino and higgsino mass parameters are determined with an accuracy better than 1%, while tan β is determined with an accuracy of 5%. Excellent precision of 2-3% is obtained for the mass of the otherwise unobservable sneutrino. Including NLO effects even allows us to constrain the parameters of the stop sector. Although the precision shown in tab. 3 is rather limited, this could lead to an important hint concerning the masses of the stops, which, if not already seen, might allow for a well-targeted search at the LHC. This could be another example of LC-LHC interplay [66].
Finally, in tab. 3 we compare the fit results using masses of the charginos and neutralinos obtained from threshold scans and from the continuum. For the latter, the accuracy at which the parameters can be determined is seen to deteriorate, with errors on the fundamental parameters almost doubling, clearly indicating the need to measure chargino and neutralino masses via threshold scans.

Results for scenario 2
In this scenario, where the M 2 parameter is set to 2 TeV, only the light chargino and three lightest neutralinos will be accessible at the LC. As input Observable Tree value Loop corr. Error exp. Error th. for the fit we therefore use: • the masses of the lighter chargino (χ ± 1 ) and neutralinos (χ 0 1 ,χ 0 2 ,χ 0 3 ) • the light chargino production cross section σ(χ + 1χ − 1 ) with polarised beams at √ s = 400 and 500 GeV • the forward-backward asymmetry A F B at √ s = 400 and 500 GeV • the branching ratio B(b → sγ).
As we again find that the muon anomalous magnetic moment has a negligible impact, it is not used in the fit. The input variables, together with errors, namely the assumed experimental precision of the prospective LC measurements as well as the theoretical uncertainties, are listed in tab. 4. While A F B is negligible at LO, the NLO corrections to it are again found to be large. We again fit 8 MSSM parameters: M 1 , M 2 , µ, tan β, mν, cos θ t , mt 1 , and mt 2 . The impact of other parameters, except the heavy Higgs boson mass, can be neglected. The results from the fit are given in tab. 5  and bino mass parameters are well constrained in this scenario since bino-like neutralino and all higgsinos are directly accessible. Even though the winos are not directly accessible, the wino mass parameter M 2 can be constrained with 10% accuracy at 1σ level. An accuracy of 20% is achieved for tan β, significantly worse than in S1. This can be understood by the fact that the mixing in S2 between chargino states is weak due to M 2 being heavy, and the constraint on tan β is dependent on this mixing. No limits can be derived on the sneutrino mass, due to the Yukawa suppressed coupling of the higgsinolikeχ ± 1 to the electron and sneutrino. We are however, as shown in tab. 5, still able to derive limits on the stop masses and mixing angle.

Results for scenario 3
This final scenario features the richest phenomenology of the studied benchmark scenarios. As input for the fit we therefore use: • the masses of the charginos (χ ± 1 ,χ ± 2 ) and neutralinos (χ 0 1 ,χ 0 2 ,χ 0 3 ) • the light chargino production cross section σ(χ + 1χ − 1 ) with polarised beams at √ s = 400 and 500 GeV • the forward-backward asymmetry A F B at √ s = 400 and 500 GeV • the Higgs boson mass, m h • the branching ratio B(b → sγ) • the anomalous muon magnetic moment Compared to the previous scenarios, these observables are supplemented by the Higgs boson mass, m h , calculated using FeynHiggs 2.9.1 [56][57][58][59]. The estimated experimental precision at the LC for m h , taken from ref. [1], is adopted. We further assume the future theoretical uncertainty on the Higgs boson mass to be 1 GeV [59]. As before, the remaining two observables, the branching ratio B(b → sγ) and the anomalous muon magnetic moment are calculated using micrOmegas 2.4.1 [62,63], and a projected experimental error on the anomalous muon magnetic moment of 3.4·10 −10 is employed [67], which we assume would dominate over the theoretical uncertainty. The input variables, together with errors, namely the assumed experimental precision of the prospective LC measurements and the theoretical uncertainties, are summarised in tab. 6. As the sneutrino is now directly accessible, we assume that its mass has been measured and it is therefore not included in the fit. On the other hand, due to the stronger dependence of the NLO cross-section and forward-backward asymmetry on m A 0 , this is now used as an additional fit prameter. We neglect the remaining theoretical uncertainty on the crosssections, as it is found to be negligible in comparison to the experimental error. This means that in scenario 3, we fit to M 1 , M 2 , µ, tan β, cos θ t , mt 1 , mt 2 and m A 0 . The results of the fit are collected in tab. 7. The parameters of the electroweak gaugino-higgsino sector are determined with high precision. Due to a significant mixing in the stop sector, and the improvement in the fit quality due to the inclusion of the higgs mass, we find that the fit is now also more sensitive to the mass of the heavy stop. The accuracy is better than 20% for this particle even though it is far beyond the reach of the LC and also most likely of the LHC. In addition, in this scenario an upper limit on the mass of the heavy Higgs boson can be placed at 1000 GeV, at the 2σ level. It is the particular sensitivity of the NLO corrections to m A 0 which presents this unique opportunity to set such an upper bound.

Conclusions
The evidence for the Higgs boson and dark matter, when examined in the context of supersymmetry, suggests the possibility of a light µ and M 1 . We have extended previous analyses, which fitted observables for chargino production at the LC to extract fundamental MSSM parameters, by incorporating NLO corrections. The loop corrections are calculated for all observables Observable Tree value Loop corr. Error exp. Error th. fitted, namely the polarised cross-sections and forward backward asymmetry for chargino production as well as theχ ± 1 ,χ ± 2 andχ 0 1 ,χ 0 2 ,χ 0 3 masses, in an on-shell scheme which facilitates the extension to the complex case. We have fitted these observables in three complementary scenarios.
On including NLO corrections, we found that when M 1 , M 2 and µ are light they can be determined to percent-level accuracy, and tan β to < 5%. Further we showed that if masses of the charginos and neutralinos are obtained from the continuum as opposed to via threshold scans, the uncertainty on the fundamental parameters would almost double, reinforcing the importance of threshold scans for mass measurements. As a heavy M 2 is still a viable possibility, we also considered M 2 = 2000 GeV, and found that the sensitivity to M 2 is approximately 10%. However in this case the error on tan β, dependent on the degree of mixing in the chargino sector, increases to ∼ 20%. Note that the inclusion of B(b → sγ) in the fit, in combination with the use of masses determined via threshold scanning, was seen to improve cos θ t 0.15 +0.08 −0.06 ( +0.16 −0.09 ) mt 1 430 +200 −130 ( +300 −400 ) mt 2 1520 +200 −300 ( +300 −400 ) m A 0 < 650 (< 1000) Table 7: Fit results (in GeV with the exception of tan β and cos θ t ) for S3, including results for the masses of the heavier stop mass (mt 2 ) and the pseudoscalar higgs boson (m A 0 ). the sensitivity to the stop sector. The final scenario we considered was compatible with the latest Higgs results. Here we found that including B(b → sγ), ∆(g µ − 2)/2 and m h in the fit, as well as the fact that there was significant mixing in the stop sector, helped to obtain an accuracy better than 20% on the mass of the heavy stop, even though this particle is far beyond the reach of the LC and also most likely of the LHC. We also included m A 0 in the fit, and found that, due to the particular sensitivity of the NLO corrections to m A 0 , it would even be possible to place a 2σ upper bound on this parameter of 1000 GeV. In summary, we have shown that incorporating NLO corrections is required for the precise determination of the fundamental parameters of the chargino and neutralino sector at the LC, and could further provide sensitivity to the parameters describing particles which contribute via loop corrections.