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DESY-11-105 Measurement of CP asymmetries in neutralino production at the ILC 2 1 O. Kittela,1, G. Moortgat-Pickb,c,2, K. Rolbieckic,3, P. Schadec,d,4, 0 M. Terwortc,5 2 n a Departamento de F´ısica Teórica y del Cosmos and CAFPE, a Universidad de Granada, E-18071 Granada, Spain J 6 b University of Hamburg, Luruper Chaussee 149, D-22761 Hamburg, Germany 2 c DESY, Notkestrasse 85, D-22607 Hamburg, Germany ] d CERN, CH-1211 Geneve 23, Switzerland h p - p e Abstract h [ We study the prospects to measure the CP-sensitive triple-product asym- 2 metries in neutralino production e+e− χ˜0χ˜0 and subsequent leptonic two- 0v body decays χ˜0i → ℓ˜Rℓ, ℓ˜R → χ˜01ℓ, f→or ℓi=1e,µ, within the Minimal Su- 2 persymmetric Standard Model. We include a full detector simulation of the 2 International Large Detector for the International Linear Collider. The simu- 3 . lation was performed at a center-of-mass energy of √s = 500 GeV, including 8 0 the relevant Standard Model background processes, a realistic beam energy 1 spectrum, beam backgrounds and a beam polarization of 80% and 60% for 1 − theelectron andpositronbeams,respectively. Inordertoeffectively disentan- : v gle different signal samples and reduce SM and SUSY backgrounds we apply i X a method of kinematic reconstruction. Assuming an integrated luminosity r of 500 fb−1 collected by the experiment and the performance of the current a ILD detector, we arrive at a relative measurement accuracy of 10% for the CP-sensitive asymmetry in our scenario. We demonstrate that our method of signal selection using kinematic reconstruction can be applied to a broad class of scenarios and it allows disentangling processes with similar kinematic properties. 1 [email protected] 2 [email protected] 3 [email protected] 4former address, [email protected] 5 [email protected] 1 Introduction Supersymmetry (SUSY) [1,2] is one of the best motivated candidates for physics beyond the Standard Model (SM). Besides providing a unification of the strong and electroweak gauge couplings and a suitable cold dark matter candidate, the lightest stable SUSY particle, SUSY could offer new sources of CP violation [3–6]. In the Minimal Supersymmetric Standard Model (MSSM), the complex parameters are conventionally chosen to be the Higgsino mass parameter µ, the U(1) and SU(3) gaugino mass parameters M and M , respectively, and the trilinear scalar coupling 1 3 parameters A of the third generation sfermions (f = b,t,τ), f µ = µ eiφµ, M1 = M1 eiφ1, M3 = M3 eiφ3, Af = Af eiφAf. (1) | | | | | | | | The sizes of these phases are constrained by experimental bounds from the electric dipole moments (EDMs). Such experimental limits generally restrict the CP phases to be small, in particular the phase φ [7]. However, the extent to which the EDMs µ can constrain the SUSY phases depends strongly on the considered model and its parameters [7–13]. Duetocancellations amongdifferent contributionstotheEDMs, largeCPphases can give CP-violating signals at colliders, as shown for example in Ref. [13]. It is important to search for these signals, since the cancellations could be a consequence of an unknown underlying structure that correlates the phases. In addition, the existing EDM bounds could also be fulfilled by including lepton flavor violating couplings in the slepton sector [9]. Thus, direct measurements of SUSY CP-sensitive observables are necessary to determineorconstrainthephasesindependently ofEDMmeasurements. Thephases can change SUSY particle masses, their cross sections, branching ratios [14–18], and longitudinal polarizations of final fermions [19]. Although such CP-even observables can be very sensitive to the CP phases, CP-odd (T-odd) observables have to be measured for a direct evidence of CP violation. CP asymmetries in particle decay chains can be defined with triple products of final particle momenta [20,21]. Due to spin correlations, such asymmetries show unique hints for CP phases already at tree level. Thus, triple product asymmetries have been proposed in many theoretical papers. For the Large Hadron Col- lider (LHC), triple product asymmetries have been studied for the decays of neutralinos [22–24], stops [13,25–27], sbottoms [28,29], and staus [30]. In a Monte Carlo (MC) analysis for stop decays [26,27], it could be shown that the decay chain can be reconstructed and asymmetries be measured at a 3σ level for luminosi- ties of the order of 300 fb−1. At the International Linear Collider (ILC) [31–34] a clearer identification and a more precise measurement is expected to be achievable. However, in this context only theoretically-based papers exist: for instance, neutralino production with two- [22,35–42] and three-body decays [43–47], charginos with two- [48–53] and three-body decays [54,55], also with transversely polarized beams [56–61], have been studied. 2 e− ℓ N χ˜0 χ˜0 1 i ˜ ℓ e+ ℓ F χ˜0 1 Figure 1: Schematic picture of neutralino production and decay. Therefore, we present in this paper the first experimentally-oriented analysis with regard to the observation of CP asymmetries on the basis of a full detector simulation. To show the feasibility of a measurement of triple product asymmetries, we focus on neutralino production [35,39] e+ +e− χ˜0 +χ˜0 (2) → i 1 with longitudinally polarized beams and the subsequent leptonic two-body decay of one of the neutralinos into the near lepton χ˜0 ℓ˜ +ℓ , (3) i → R N and that of the slepton into a far lepton ℓ˜ χ˜0 +ℓ ; ℓ = e,µ. (4) R → 1 F Fig. 1 shows a schematic picture of neutralino production and its decay chain. The CP-sensitive spin correlations of the neutralino in its production process allow us to probe the phase of the Higgsino mass parameter µ, and the gaugino parameter M . 1 In order to effectively disentangle different signal samples and reduce SM and SUSY backgrounds we apply a method of kinematic reconstruction. A similar ap- proach has been studied successfully for the LHC [27]. The kinematic reconstruction was also considered to study selectron and neutralino properties at the ILC [62–64]. Here, we demonstrate that it can be used as an effective signal selection method, greatly improving the sensitivity to the effects of CP violation. In particular, compared tothe previous studies ofprocess (2), Ref. [39], we areable to suppress slepton and WW contamination to (10%) level. O To investigate in detail the prospect of measuring CP-sensitive observables at the ILC we perform a full detector simulation of the International Large Detec- tor (ILD) concept. We include all relevant SM and SUSY background processes in our study, simulated with a realistic beam energy spectrum (beamstrahlung and initial state radiation (ISR)), beam backgrounds and a beam polarization of 3 (Pe−,Pe+) = (0.8, 0.6), which enhances the cross section of our signal and the size − oftheasymmetry. Weapplythemethodofkinematic reconstruction toapreselected sample of signal event candidates in order to efficiently reject any background and to disentangle the decays of χ˜0 from χ˜0. We determine the CP asymmetries with 2 3 the selected signal events and study the sensitivity to determine the values of the CP phases via a fit. The paper is organized as follows. In Sec. 2 we introduce the theoretical framework for the used CP-sensitive observable and we apply it for the studied process in the chosen benchmark scenario. Section 3 discusses the kinematic aspects of signal versus background selection. Section 4 treats the full detector simulation. Finally in Sec. 5 the SUSY parameters including the CP phases are derived via a fit of the CP-odd asymmetries together with masses and cross sections. Appendix A provides ˜ details for the reconstruction of W and ℓ production and App. B recapitulates the neutralino mixing and its parameters. 2 Theoretical framework 2.1 CP-odd observables CP-violating observables in collider-based experiments are based on the invariance under CPT , where C is charge conjugation, P stands for parity transformation and N T for time reversal. The index N denotes ’naive’ time reversal, i.e. time reversal but without interchanging initial with final states and therefore can be tested in collider-based experiments. At tree level of perturbation theory, observables odd under T transformations are also odd under the ’true’ time reversal T. N Therefore, it is useful to categorize CP-violating observables in two classes [65]: those that are even under T and those that are odd under T operation. Under N N the absence of final state interactions (FSI), CPT -even operators relate T -odd N N symmetries uniquely with CP-odd transformations [20]. Contrary, CPT -odd op- N erators (i.e. CP-odd but T -even) can have nonzero expectation values only if FSI N are present that give a non-trivial phase (absorptive phase) to the amplitude. Such a phase can arise for instance in loop diagrams. Examples for T -odd observables are triple products that arise from the terms N ǫ[p ,p ,p ,p ], where p are 4-vectors representing spins or momenta and ǫ is the 1 2 3 4 i antisymmetric Levi-Civita tensor. Consequently, such T -odd signals can only be N observed in processes where at least four independent momenta (or their spin ori- entations) are involved. The ǫ-tensor can then be expanded in a series of four triple products ǫ[p ,p ,p ,p ] = E p (p p ) ... that can be evaluated in a suitable 1 2 3 4 1 2 3 4 · × ± and specific kinematical system. The T -odd asymmetries are then composed by N the corresponding triple products. 2.2 Neutralino production and decay processes Neutralinos are mixed states of the supersymmetric partners of the neutral gauge and Higgs bosons and depend on the phases φ and φ , see App. B. CP-violating 1 µ 4 effects in the neutralino production and decay arise at tree level and can lead to CP-sensitive asymmetries due to neutralino spin correlations. In neutralino production effects from CP-violating phases can only occur if two different neutralinos are produced, e+e− χ˜0χ˜0, i = j. Each of the produced → i j 6 neutralinos has a polarizationwith a component normal to the production plane [44, 66,67]. This polarization leads to asymmetries in the angular distributions of the decay products. In our process the only T -odd contribution originates from the production pro- N cess. It is proportional to ǫ[pe+pe−sχ˜0ipχ˜0i] leading to ǫ[pe+pe−pℓNpℓ˜R] due to spin correlations caused by the mentioned neutralino polarization normal to the production plane. Applying momentum conservation p = p +p allows one to extract ℓ˜R χ˜01 ℓF the T -odd triple product of the beam and the final lepton momenta [35], N T = (pe− ×pℓ+N)·pℓ−F ≡ (pe−,pℓ+N,pℓ−F), (5) which projects out the CP-sensitive parts. The corresponding T -odd asymmetry N is then σ( > 0) σ( < 0) ( ) = T − T , (6) A T σ( > 0)+σ( < 0) T T where σ is the cross section for neutralino production and decay, Eqs. (2)-(4). Note: in the case of the 3-body neutralino decay, χ˜0 ℓ+ℓ−χ˜0, one also obtains T -odd i → 1 N contributions originating only from the decay process [26,47]. Therefore further T - N odd asymmetries can be composed that contribute also in case of same-neutralino pair production and can offer tools for disentangling the different phases. The CP- sensitive asymmetries, Eq. (6), depend on the charge of the leptons [13] and the following relations are given: A(pe−,pℓ+N,pℓ−F) = −A(pe−,pℓ−N,pℓ+F) = −A(pe−,pℓ−F,pℓ+N) = +A(pe−,pℓ+F,pℓ−N), (7) neglecting FSI contributions. Note that a true CP-odd asymmetry, where also an absorptive phase from FSI or finite-width effects is automatically eliminated, can be defined as 1 CP = ( ¯), (8) A 2 A−A where ¯ denotes the T -odd asymmetry for the CP-conjugated process [68]. In our N A case this leads to a separate measurement of asymmetries for a positive (ℓ+) and N negative (ℓ−) near lepton. If CP = 0 holds than we observe a genuine CP-violating N A 6 effect. Therefore, it is important to tag the charge of the near and far leptons in order to establish CP violation in the process (2)-(4). 5 10 10 8 8 A[%] 6 A[%] 6 4 4 2 2 0 0 -2 -2 -4 -4 -6 -6 -8 -8 -10 -10 0 0.5 1 1.5 2 0 0.5 1 1.5 2 φ1[π] φµ[π] (a) (b) Figure 2: Dependence of the asymmetry , Eq. (6), (a) on the phase φ (with 1 A φ = 0), (b) the phase φ (with φ = 0), for neutralino production e+e− χ˜0χ˜0 (sµolid), and e+e− χ˜0χ˜0µ(dashed)1, and subsequent decay χ˜0 ℓ˜ ℓ , ℓ˜ →χ˜01ℓ 2, → 1 3 i → R N R → 1 F (for ℓ = e or µ), at √s = 500 GeV and polarized beams (Pe−,Pe+) = (0.8, 0.6). − The other MSSM parameters are given in Tab. 1. In the left panel, along the flat line of the asymmetry (solid) the decay χ˜0 ℓ˜ ℓ is closed. 2 → R M M µ φ φ tanβ M M 2 | 1| | | 1 µ E˜ L˜ 300 GeV 150 GeV 165 GeV 0.2π 0 10 166 GeV 280 GeV Table 1: MSSM parameters of the benchmark scenario at the electroweak scale, see Sec. 2.3. 2.3 Benchmark scenario Forourfull simulation study, we have chosen abenchmark scenario withtherelevant MSSM parameters given in Tab. 1. Since the phase of the Higgsino mass parameter is strongly constrained by EDM bounds, we have set it to zero. The value of the gaugino phase φ = 0.2π approximately corresponds to the maximum of the CP 1 asymmetries, see Fig. 2. The scenario was chosen to have an enhanced neutralino mixing close to a level-crossing of the neutralino states χ˜0 and χ˜0 for φ = 0, and of 2 3 1 χ˜0 and χ˜0 for φ = π, which leads to large CP asymmetries. 1 2 1 Further, we have assumed beampolarizationsof (Pe−,Pe+) = (0.8, 0.6) enhanc- − ing slightly the SUSY cross section and the asymmetries. At the same time, this choice suppresses the background from WW-pair production, σ(e+e− WW) = → 0.7 pb (compared with 7 pb for unpolarized beams), and also chargino pair produc- 6 masses m = 117 GeV m = 166 GeV χ˜01 ℓ˜R m = 169 GeV m = 280 GeV χ˜02 ℓ˜L m = 181 GeV m = 165 GeV χ˜03 τ˜1 m = 330 GeV m = 280 GeV χ˜04 τ˜2 mχ˜± = 146 GeV mν˜ = 268 GeV 1 mχ˜±2 = 330 GeV mν˜τ = 268 GeV cross sections σ(e+e− χ˜0χ˜0) = 244 fb σ(e+e− e˜+e˜−) = 304 fb → 1 2 → R R σ(e+e− χ˜0χ˜0) = 243 fb σ(e+e− µ˜+µ˜−) = 97 fb → 1 3 → R R branching ratios BR(χ˜0 ℓ˜ ℓ) = 55% BR(χ˜0 τ˜ τ) = 45% 2 → R 2 → 1 BR(χ˜0 ℓ˜ ℓ) = 64% BR(χ˜0 τ˜ τ) = 36% 3 R 3 1 → → asymmetries ( ) = 9.2% ( ) = 7.7% χ˜0χ˜0 χ˜0χ˜0 A T 1 2 − A T 1 3 Table2: Masses, productioncrosssections, neutralinobranchingratiosandasymme- tries, Eq. (6), for the benchmark scenario, see Tab. 1, calculated using the formulas presented in[42]. The ILC cross sections are for √s = 500 GeVand polarized beams (Pe−,Pe+) = (0.8, 0.6). The branching ratios are summed over ℓ = e,µ and both − slepton charges. tion σ(e+e− χ˜±χ˜∓) = 110 fb (410 fb, respectively). Thus, the scenario is opti- → i j mized to yield large asymmetries, large cross sections and sizable neutralino branching ratiosinto electrons andmuons, aslisted in Tab. 2. We have set A = 250 GeV τ − in the stau sector, which has low impact on the neutralino branching ratios. Also we have chosen the slepton masses such that χ˜0 is close in mass with the slepton ℓ˜ . 2 R This leads to soft leptons from the decay χ˜0 ℓ˜ ℓ, as can be seen in Fig. 3, which 2 R → has to be taken care of in the lepton identification described in Sec. 4.2. In general, our analysis is relevant for scenarios with strong gaugino-higgsino mixingintheneutralinosector, usuallyleadingtosizableasymmetries. Inparticular, for µ < M < 300 GeV the asymmetries can reach several percent, the neutralino 2 | | | | pair-pr∼oduction∼cross sections reach more than 50 fb, and the neutralino branching ratios into electrons and muons are of the order of several 10%, see also Ref. [35] for more details. In any case, the selectron and smuon masses should fulfil m < χ˜0 1 m < m , so that at least one relevant decay channel remains open. Decreasing ℓ˜R χ˜02 the selectron mass will result in larger asymmetries and production cross sections. 7 0.16 0.035 1] χ˜02 → ℓN ℓF χ˜01 1] 0.03 χ˜03 → ℓN ℓF χ˜01 − − V V 0.12 e e G G ℓ N [ [ dσdE dσdE 0.02 σ σ 0.08 ℓ N 0.01 0.04 ℓ F ℓ F 0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 E[GeV] E[GeV] (a) (b) Figure 3: Energy distributions (each normalized to 1) of the near lepton ℓ (solid), N and the far lepton ℓ (dashed), from neutralino production e+e− χ˜0χ˜0 for (a) i = 2, and (b) i = 3, wiFth subsequent decay χ˜0 ℓ˜ ℓ , ℓ˜ χ˜0ℓ , →for t1heibenchmark i → R N R → 1 F scenario as given in Tabs. 1 and 2. 3 Kinematic selection of signal and background In order to measure the CP asymmetries, Eq. (6), we have to separate the signal lepton pairs originating from χ˜0χ˜0 and χ˜0χ˜0 production, respectively. This is essen- 1 2 1 3 tial, since inour scenario the corresponding CP asymmetries, (χ˜0χ˜0) = 9.2%and A 1 2 − (χ˜0χ˜0) = 7.7%, have opposite sign. Large CP asymmetries naturally occur when 1 3 A the neutralinos are mixed states of gauginos and Higgsinos, which often implies that they are close in mass. In addition we need an efficient method for background separation. The CP-even backgrounds will reduce the asymmetries, since they contribute to the denominator, but cancel out in the numerator of the asymmetries, see Eq. (6). Among the most severe SM and SUSY background processes are W pair production and slepton pair production. Owing to a known center-of-mass energy and a well-defined initial state one may attempt to perform a full kinematic reconstruction of the events at the ILC. Unlike in the case of the LHC [24,27], this is already possible with very short decay chains. Assuming that the masses of intermediate and invisible particles are known from other measurements, the full reconstruction can be performed even when only two particles are visible in the final state. In the following, we extend the method of Ref. [58] to reconstruct the pair of signal leptons from the neutralino decay, Eq. (2). We show that even for two neu- tralinostatesthatarecloseinmass, hereχ˜0 andχ˜0, thefinalleptonscanbecorrectly 2 3 8 assigned totheir mother particle. Asimilar procedure to identify andsuppress back- groundfromW andsleptonpairproductionisdescribed inApp.A,seealsoRef.[69]. Finally, we discuss how well the kinematic selection and reconstruction works at the MC level. 3.1 Kinematic constraints from neutralino production Inthecenter-of-masssystemofneutralinopairproductionthemomentaandenergies are fixed [67] : E = s+mχ2˜0i −mχ2˜0j, E = s+mχ2˜0j −mχ2˜0i , p = λ21(s,m2χ˜0i,mχ2˜0j), (9) χ˜0i 2√s χ˜0j 2√s | χ˜0i,j| 2√s with the beam energy E = √s/2, the neutralino masses m ,m , and λ(x,y,z) = χ˜0 χ˜0 i j x2+y2+z2 2(xy+xz+yz). The neutralino production is followed by the two-body − decay chain of one of the neutralinos χ˜0 via a slepton, i χ˜0 ℓ˜ +ℓ χ˜0 +ℓ +ℓ , ℓ = e,µ. (10) i → R N → 1 F N In our signal process, Eqs. (2)-(4), we have χ˜0 = χ˜0 and it escapes undetected. j 1 In the following, we assume that the near and far leptons can be distinguished via their different energy distributions.6 For our scenario, the leptons from χ˜0χ˜0 1 2 production and decay have distinct energy ranges, see Fig. 3(a). The leptons from χ˜0χ˜0 production and decay only have a small overlap in the energy window E 1 3 ℓ ∈ [18,38] GeV, see Fig. 3(b). Events are discarded if both leptons happen to fall into this energy range. We now choose a coordinate system such that the measured momenta are p = p (0,0,1), (11) ℓN | ℓN| p = p (sinθ , 0, cosθ ), θ [0,π], (12) ℓF | ℓF| NF NF NF ∈ where θ is the angle between the near and the far leptons. In order to fully NF reconstruct the event, the decay angles of the sleptons need to be resolved p = p (sinbcosB, sinbsinB, cosb), b [0,π], B [0,2π]. (13) ℓ˜ | ℓ˜| ∈ ∈ The slepton momentum, p2 = E2 m2, is already fixed due to energy conservation, ℓ˜ ℓ˜− ℓ˜ E = E E . Using also momentum conservation, p2 = (p +p )2, the polar ℓ˜ χ˜0i − ℓN χ˜0i ℓN ℓ˜ angle, b = (cid:30)(p ,p ), can be determined ℓN ℓ˜ p2 p2 p2 cosb = χ˜0i − ℓN − ℓ˜, sinb = +√1 cos2b. (14) 2 p p − | ℓN|| ℓ˜| 6This is not needed for the determination of the asymmetry, see Eq. (7), but will be exploited for the event selection. 9 Using also momentum conservation in the slepton decay, p = p +p , a similar ℓ˜ ℓF χ˜01 relation can be obtained for the azimuthal angle p2 +p2 p2 cosB = 1 ℓF ℓ˜− χ˜01 cosbcosθ , (15) NF sinbsinθ 2 p p − NF | ℓF|| ℓ˜| ! and p2 = E2 m2 is obtained from energy conservation E = E E E . χ˜01 χ˜01 − χ˜01 χ˜01 χ˜0i − ℓN − ℓF The kinematic variables cosb and cosB solely depend on the center-of-mass energy s, the lepton energies, E and E , the angle between the leptons, p p , and ℓN ℓF ℓN · ℓF finally on the contributing particle masses, m , m , and m . Thus, there only χ˜0i χ˜01 ℓ˜R remains an ambiguity for sinB, since for B [0,2π] we have sinB = √1 cos2B. ∈ ± − This ambiguity in the azimuthal angle is irrelevant for the efficiency of the event selection7. 3.2 Method of kinematic event selection For a given lepton pair, we apply the following kinematic selection method. The aim is to assign the correct origin of the lepton pair, which can be signal, e+e− χ˜0χ˜0, or background e+e− W+W−, ℓ˜+ℓ˜−. Thus, we have four systems of eq→uatioin1s, → R R one for each possible production process. For each candidate event we employ the following kinematic selection: We apply the reconstruction procedure from Sec. 3.1, assuming χ˜0χ˜0 and χ˜0χ˜0 • 1 2 1 3 production. Thus, we calculate cosb and cosB, Eqs. (14) and (15), with m = m (m = m ) for χ˜0χ˜0 (χ˜0χ˜0) production. χ˜0 χ˜0 χ˜0 χ˜0 1 2 1 3 i 2 i 3 We apply the reconstruction procedure from App. A, assuming WW and slep- • ton pair production. Thus, we calculate two values of y2, Eq. (A.9). The event solves the system of equations if • cosb < 1 and cosB < 1 , (17) | | | | when neutralino production has been assumed, and y2 > 0 , (18) when W/slepton production has been assumed. 7Theambiguityisrelatedtotheneutralinomomentum,forwhichwehavetwopossiblesolutions |pℓ˜|sinbcosB pχ˜0i =pℓN +pℓ˜= ±|pℓ˜|sinbsinB . (16) |pℓN|+|pℓ˜|cosb   For this reason, the neutralino production plane cannot be resolved in e+e− χ˜0χ˜0 processes → i j for j = 1. For j 2, the decay of χ˜0 could be included in order to reconstruct the production ≥ j plane [58]. In that case larger triple product asymmetries can be studied, which include the neutralino momentum itself [35]. 10