Physics Letters B 579 (2004) 371–376 www.elsevier.com/locate/physletb Impact of CP phases on a light sbottom and gluino sector Chuan-Hung Chen Department of Physics, National Cheng-Kung University, Tainan 701, Taiwan, ROC Received 25 September 2003; received in revised form 3 November 2003; accepted 5 November 2003 Editor: T. Yanagida Abstract We study a scenario in which light bottom squarks and light gluinos with masses in the range 2–5.5 GeV and 12–16 GeV, respectively, can coexist in the MSSM, without being in conflict with flavor-conserving low-energy observables. We find that in − such a scenario, the anomalous magnetic moment of a muon could be as large as 10 9, if the theory conserves CP. However, if the theory violates CP, we conclude that not both, the gluino and bottom squark, can be light at the same time, after the neutron electric dipole moment constraint on Weinberg’s 3-gluon operator has been taken into account. 2003 Elsevier B.V. All rights reserved. Inspired by the unforeseen excess of the bottom- decaying to a pair of light bottom squarks [6], radiative → ˜∗ ˜ + ¯ ˜ ˜ quark production observed at the hadronic collider of B meson decays [7], the decays Z bb1g bb1g Fermilab [1], Berger et al. [2] proposed a solution followed by g˜ → bb˜∗/b¯b˜ and e+e− → qq¯g˜g˜ [8], as ˜ 1 1 with light sbottom b (m ˜ 2.0–5.5 GeV) and light 1 b1 well as the running of strong coupling constant αs [9]. gluino g˜ (mg˜ 12–16 GeV). Interestingly, various To further explore more impacts on other processes, problems can easily be avoided, such as by adopting it is necessary to investigate different systems instead ˜ ˜ the proper mixing angle of two sbottoms bL and bR, of those in which the final states are directly associated the Z-peak constraint can be evaded; and also, the with the light sbottom and gluino. It is known that Rb contribution, arisen from sbottom-gluino loop, can supersymmetric models not only supply an elegant ˜ be suppressed by considering the second sbottom b2 mechanism for the electroweak symmetry breaking being lighter than 180 GeV for the CP conserved and a solution to the hierarchy problem, but also ˜ case [3], while the mass of b2 can be heavier in guarantee the unification of gauge couplings at the the CP violating one [4]. The amazing thing is that scale of GUTs [10]. Therefore, besides the effects such light supersymmetric particles, so far, have not mentioned above, other contributions will also appear been excluded by experiments, even after including when considering different phenomena. Inevitably, the data of precise measurements [5]. Moreover, for new parameters will come out. To avoid introducing searching the signals of the light sbottom and gluino, the irrelevant parameters, such as the mixing angles many testable proposals are raised, e.g., the rate of χb among different flavors of squark, we have to consider the processes in which the dependent parameters are still concentrated on the minimal set. The best E-mail address: [email protected] (C.-H. Chen). candidates are the flavor-conserving processes. 0370-2693/$ – see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physletb.2003.11.020 372 C.-H. Chen / Physics Letters B 579 (2004) 371–376 One of the mysteries in the standard model (SM) is to CPV. Since the results must be proportional to the ˜ ˜ whether the Higgs mechanism plays an essential role mixing of bL and bR, for generality, we describe the for the symmetry breaking and the resultant of Higgs relationship between weak and physical eigenstates as particle can be captured in future colliders. Based ˜ ˜ bL = 10 cos θb sin θb b1 on the same philosophy of the symmetry breaking, ˜ iδ ˜ , b 0 e b − sin θb cosθb b the minimal supersymmetric standard model (MSSM) R 2 needs the second Higgs doublet field to balance the (1) anomaly of quantum corrections, i.e., there are three where δb is the CP violating phase which could arise ∗ − neutral Higgs particles in MSSM, one of them is CP- from the off-diagonal mass matrix element mb(Ab ˜ ˜ odd (A0) and the remains are CP-even (h and H ). It µ tanβ). To suppress the coupling Zb1b1,weset is obvious that besides the mixing angle of sbottoms sin 2θb = 0.76 in our discussions. In the following and the masses of sbottom (gluino), the essential analyses, we separate the problem into CPC and CPV parameters in MSSM are At(b), the trilinear SUSY soft cases. breaking terms, µ, the mixing parameter of two Higgs 1. CPC (δb = 0) superfields, mA0(h,H), the masses of corresponding Unlike non-SUSY two-Higgs doublet models, it Higgses, and tan β, defined by the ratio of vu to vd in is well known that besides the enhancement of large with vu(d) being the vacuum expectation of the Higgs tan β or 1/ cosβ, there exists another enhanced factor field that couples to up (down) type quarks. And also, Ab in the couplings of S = h and H to bottom squarks unlike the non-SUSY two-Higgs-doublet model, the [11]. As described early, some novel consequences mixing angle of two neutral Higgs fields, denoted by based on both large factors have been displayed on α, is not an independent parameter and can be related the Higgs hunting. With these factors, we examine to tan β [11]. the implication on aµ by considering the case of a The activity of searching for the Higgs particle and light sbottom. In addition, for convenience, we adopt studying its properties is proceeding continuously [12, ≈ the decoupling limit with mA0 mZ so that tan 2α 13]. In particular, the remarkable results with a large tan 2β. tan β have been investigated enormously because the The effective interaction hγ γ is induced from the exclusive characteristic can give the unification of bot- radiative effects in which sbottoms are the internal tom and tau Yukawa couplings and the realization of particles of the loop, illustrated in Fig. 1(a), and the the top to the bottom mass ratio in GUTs [14]. It has gauge invariant form of the coupling can be obtained been found that if the SUSY soft breaking terms carry the explicit CP violating phases, due to the enhance- ment of large At(b) and µ, radiative effects can in- duce a sizable mixing between scalar and pseudoscalar such that the lightest Higgs boson could be 60–70 GeV and thus escape the detection of detectors [15]. More- over, with the requirements satisfied with electroweak baryogenesis, a novel prediction on the muon electric −24 dipole moment (EDM) of 10 e cm can be reached (a) by the proposed experiment [16]. In sum, it will be more exciting that if the light sbottom and gluino can be compatible with the Higgs physics with or without CP violation (CPV). In order to further pursue the implications of the light sbottom and gluino, in this Letter, we concentrate on two flavor-conserving processes: one is anomalous (b) magnetic moment of muon, aµ, and the other is Fig. 1. (a) Diagram which induces the effective coupling S–γ –γ , EDMs of muon and neutron. The former corresponds where S can be the lightest scalar boson h or pseudo-scalar boson 0 to CP conservation (CPC) while the latter is related A ; (b) loop for aµ. C.-H. Chen / Physics Letters B 579 (2004) 371–376 373 as [tanβ = 50] in Fig. 2(a) and (b) [(c) and (d)], where the solid, dashed and dashed-dotted lines denote the γ = γ 2 · − iΓµν iA (q ) (q k)gµν qµkν , results of Mh = 100, 120 and 140 GeV, respectively. 2 Unlike non-SUSY models, which require the neutral γ 2 αemQbmbAb sin α A (q ) = Nc sin 2θb Higgs to be a few GeV to fit a [11], the lightest 2πvcosβ µ Higgs boson in SUSY models could be the values 1 + x(1 − x) constrained by the current experiments. Interestingly, × (−1)i 1 dx , 2 − 2 − due to the light sbottom, a significant contribution = M ˜ q x(1 x) i 1,2 0 bi to anomalous magnetic moment of muon without (2) extremely tuning Ab is shown up [17]. where Nc = 3 is the color number, αem is the fine structure constant, Qb =−1/3 is the charge of sbot- 2. CPV (δb = 0) tom, and mb(M ˜ ) is the mass of bottom quark bi CP problem has been investigated thoroughly in (squarks). Because we concentrate on the light sbot- the kaon system since it was discovered in 1964 [18]. tom case, we do not discuss the contributions of stops Now, CPV has been confirmed by Belle [19] and by setting their masses being heavy. Since h couples ˜ ˜ Babar [20] with high accuracy in the B system. Al- to different sbottoms bL and bR but γ couples to the though the mechanism of Kobayashi–Maskawa (KM) same sbottoms, it is clearly inevitable to introduce the [21] phase in the SM is consistent with the CP mea- mixing angle θb. In Eq. (2), we already neglect the surements, the requirement of the Higgs mass of smaller contribution related to µ cosα/cosβ.Byus- 60 GeV for the condition of the matter–antimatter ing the result of Eq. (2), via the calculation of the asymmetry has been excluded by LEP. One of candi- loop in Fig. 1(b), the anomalous magnetic moment dates to deal with the baryogenesis is to use the SUSY of muon from two-loop Higgs-sbottom-sbottom dia- theory.