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Bs Mixing and Its Implication for B → S Transitions in Supersymmetry Richard Arnowitt A, Bhaskar Dutta A,Bohub, Sechul Oh C,∗

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Bs Mixing and Its Implication for B → S Transitions in Supersymmetry Richard Arnowitt A, Bhaskar Dutta A,Bohub, Sechul Oh C,∗ View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Physics Letters B 641 (2006) 305–309 www.elsevier.com/locate/physletb ¯ Bs–Bs mixing and its implication for b → s transitions in supersymmetry Richard Arnowitt a, Bhaskar Dutta a,BoHub, Sechul Oh c,∗ a Department of Physics, Texas A&M University, College Station, TX 77845, USA b Department of Physics, Nanchang University, Jiangxi 330047, China c Natural Science Research Institute, Yonsei University, Seoul 120-479, South Korea Received 17 June 2006; received in revised form 17 July 2006; accepted 3 August 2006 Available online 18 September 2006 Editor: M. Cveticˇ Abstract We investigate the effect of the current measurement of the neutral Bs meson mass difference, MBs , on SUGRA models which have non-zero 2 u,d → values of the soft breaking terms (mLL,RR)23 and A23 at the GUT scale. We use non-zero values of these parameters to explain the B Kπ puzzle and find that even after satisfying the experimental result on MB and the branching ratio (BR) of b → sγ we still can explain the puzzle. s Further we show that in this parameter space it is possible to accommodate the large BR of B → η K and the current experimental data for CP → 0 → 0 eff asymmetries of B η K and B φK . The predicted value of sin(2β )ηK0 is about 0.52–0.67. © 2006 Published by Elsevier B.V. Open access under CC BY license. ¯ Flavor changing b → s transitions are particularly interest- characterizes the Bs–Bs mixing phenomenon. The CDF result ing for new physics (NP) searches using B meson decays. In is [6] the Standard Model (SM) these transitions can occur only at the = +0.42 ± −1 loop-level so that they are particulary sensitive to NP effects. So MBs 17.33−0.21(stat) 0.07(syst) ps . (1) far, a few possible indications to NP effects through b → s tran- The D∅ Collaboration has also recently provided a new result sitions have been reported by experimental collaborations such [7]: as BaBar and Belle. Among them is the recent B → Kπ puzzle: −1 −1 i.e., discrepancies between the SM predictions and the experi- 17 ps <MBs < 21 ps (90% C.L.). (2) mental results for the direct and mixing-induced CP asymme- These experimental results are consistent with the SM estima- → tries and the branching ratios (BRs) in B Kπ modes whose tion. Therefore, these new experimental results are expected to → ¯ = dominant quark level processes are b sqq(q u, d) [1–4]. provide important constraints on NP beyond the SM [8].Moti- → The measurements of the CP asymmetries in Bd η K and vated by these new results, some theoretical studies have been → → Bd φK modes as well as the rather large BR for B η K done to search for NP effects [9–20]. and B → ηK also have drawn a lot of attention, due to their In the SM, the mass difference in the Bs system is given by possible deviation from the SM predictions [1,5]. The (domi- → ¯ 2 2 nant) subprocess of these modes is the b sss transition. SM GF MW ˆ 2 ∗ 2 M = MB ηˆB BB f |VtbV | S (xt ), (3) Recently, the CDF Collaboration has reported a new result Bs 6π 2 s s Bs ts 0 for another interesting observable relevant to the b → s tran- where the NLO short-distance QCD correction gives ηˆB = sition: The mass difference between the neutral Bs states that 0.552 and S0(xt ) = 2.463 [21]. The non-perturbative quanti- ˆ ties BBs and fBs are the bag parameter and the decay constant, respectively. The best fit for MSM is given by [22,23] Bs * Corresponding author. E-mail addresses: [email protected] (R. Arnowitt), SM = ± −1 [ ] MB 21.5 2.6ps UTfit , [email protected] (B. Dutta), [email protected] (B. Hu), s SM +5.9 −1 [email protected] (S. Oh). M = 21.7 ps [CKMfitter]. (4) Bs −4.2 0370-2693 © 2006 Published by Elsevier B.V. Open access under CC BY license. doi:10.1016/j.physletb.2006.08.065 306 R. Arnowitt et al. / Physics Letters B 641 (2006) 305–309 Table 1 (the gaugino masses for the U(1), SU(2) and SU(3) groups, B¯ −6 iα iθ Experimental data on the CP-averaged branching ratios ( in units of 10 ), i = 1, 2, 3), A0 =|A0|e A and μ =|μ|e μ . However, we can the direct CP asymmetries (A ), and the effective sin(2β) (β is the angle of CP set one of the gaugino phases to zero and we choose θ2 = 0. The the unitarity triangle) for B → PP decays [1] electric dipole moments (EDMs) of the electron and neutron BR Average CP asymmetry Average can now allow the existence of large phases in the theory [26]. B¯ ± → 0 ± ± A 0 ± − ± (B K π ) 24.1 1.3 CP(K π ) 0.02 0.04 In our calculation, we use O(1) phases but calculate the EDMs ± ± ± B¯(B → K π0) 12.1 ± 0.8 A (K π0) +0.04 ± 0.04 −27 CP to make sure that current bounds (|de| < 1.2 × 10 ecm[27] B¯ 0 → ± ∓ ± A ± ∓ − ± (B K π ) 18.9 0.7 CP(K π ) 0.108 0.017 | | × −26 ¯ 0 0 0 0 0 and dn < 6.3 10 ecm[28]) are satisfied. B(B → K π ) 11.5 ± 1.0 ACP(K π ) −0.02 ± 0.13 sin(2βeff) +0.31 ± 0.26 We evaluate the squark masses and mixings at the weak scale Ks π0 ¯ ± ± +2.8 by using the above boundary conditions at the GUT scale. The B(B → η K ) 69.7 sin(2βeff) +0.50 ± 0.09 −2.7 η K0 RGE evolution mixes the non-universality of type LR (A terms) B¯ ± → ± ± A ± ± (B φK ) 8.30 0.65 CP(φK ) 0.037 0.050 via dm 2 /dt ∝ A† A terms and creates new LL and sin(2βeff) +0.47 ± 0.19 QLL,RR u(d) u(d) φK0 RR contributions at the weak scale. We then evaluate the Wil- son coefficients from all these new contributions. We have both In a recent paper [15], this mass difference is found to be 23.4± chargino and gluino contributions arising due to the LL, LR, − RR up type and down type squark mixing. These contributions 3.8ps 1 using HPQCD and JLQCD data for f Bˆ . Bs Bs affect the following Wilson coefficients C3–C9, C and C . In this Letter, we study the neutral B meson mixing ef- 7γ 8g s The chargino contributions affect mostly the electroweak pen- fect in supersymmetry (SUSY): Specifically in the supergrav- guins (C7 and C9) and the dipole penguins, where as the gluino ity (SUGRA) model. Then, using the constraints obtained penguin has the largest contribution to the dipole penguins due from MBs , we focus on how to resolve all the possible cur- to the presence of an enhancement factor m ˜ /m (the gluino rent anomalies observed in hadronic B → PP (P denotes a g b contribution also affects the QCD penguins). We include all pseudoscalar meson) decays through the b → s transitions, contributions in our calculation. such as B → Kπ, B → η K. The current experimental data For calculation of the relevant hadronic matrix elements, we are listed in Table 1. adopt the QCD improved factorization. This approach allows We consider the SUGRA model with the simplest possible us to include the possible non-factorizable contributions, such non-universal soft terms which is the simplest extension of the as vertex corrections, penguin corrections, hard spectator scat- minimal SUGRA (mSUGRA) model. In the SUGRA model, tering contributions, and weak annihilation contributions [29]. the superpotential and soft SUSY breaking terms at the grand The relevant end point divergent integrals are parameterized unified theory (GUT) scale are given by 1 as X ≡ dx ≡ (1 + ρ eiφA ) ln mB [29]. φ are arbitrary, A 0 x A Λh H,A W = U + D + L + 0◦ φ 360◦, ρ are of order 1. Y QH2U Y QH 1D Y LH1E μH1H2, H,A H,A 1 The neutral B meson mass difference involves gluino and L =− m2|φ |2 − M λ¯ λ + BμH H soft i i 2 α α α 1 2 chargino diagrams in SUSY [30]. In mSUGRA, with univer- i α sal boundary condition, the chargino diagram has the dominant + U + D + L + contribution. Once we introduce mixing in the (2, 3)-sector of A QH2U A QH1D A LH1E H.c. , (5) 2 the mLL,RR or ALR soft breaking terms, the mass difference gets enhanced and we get large contributions from the gluino where E, U and D are respectively the lepton, up-quark and diagrams. down-quark singlet superfields, L and Q are the SU(2) dou- L The B → πK puzzle cannot be solved using just the blet lepton and quark superfields, and H are the Higgs dou- 1,2 mSUGRA boundary condition. In the conventional prediction blets. φ and λ denote all the scalar fields and gaugino fields, + +− i α of the SM, A 0 is expected to be almost the same as A :In respectively. CP CP particular, they would have the same sign. However, the current The SUSY contributions appear at loop order. In our calcula- + +− data show that A 0 differs by 3.5σ from A . Further, the re- tion, we do not use the mass insertion approximation, but rather CP CP cent experimental data for the CP-averaged BRs of B → Kπ do a complete calculation [24,25].
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