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Probing Flavor Structure in Supersymmetric Theories

Probing Flavor Structure in Supersymmetric Theories. Shaaban Khalil Ain Shams University, Cairo, Egypt. I. Introduction. The recent results on the mixing-induced asymmetries of B → φ K and B → ή K are:. Belle. BaBar. The direct CP violation in B 0 → K - π + and B - → K - π 0 :.

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Probing Flavor Structure in Supersymmetric Theories

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  1. Probing Flavor Structure in Supersymmetric Theories Shaaban Khalil Ain Shams University, Cairo, Egypt

  2. I. Introduction • The recent results on the mixing-induced asymmetries of B → φ K and B →ή K are: Belle BaBar • The direct CP violation in B0→ K-π+ and B-→ K-π0 : • These observations are considered as signals to new physics.

  3. To accommodate the CP asymmetries of B decays, SUSY models with flavor non-universal soft breaking terms are favored. • The squark mixings are classified as i) LL and RR mixings given by (δu,dLL)ij and (δu,dRR)ij. ii) LR and RL mixings given by (δu,dLR)ij and (δu,dRL)ij. • Constraints are more stringent on the LR (RL) mass insertions than the LL (RR) mass insertions. • MIs between 1st & 2nd generations are severely constrained more than MIs between 1st or 2nd & 3rd generations. • This gives the hope that SUSY contributions to the B-system.

  4. II. Squark Mixing: LL versus LR • The EDM constraints severely restrict the LL and RR mass insertions: (δdLR)22eff ≈ (δdLR)22 +(δdLL)23 (δdLR)33 (δdRR)32 ≈ 10-2 (δdLL)23 (δdRR)32 (for neg. (δdLR)22). • From Hg EDM:Im(δdLR)22 < 5.6 x 10-6 . • The SUSY contributions to the decay amplitudes B → φ K and ή K: Rφ = -0.14 e-i0.1(δdLL)23 -127 e-i0.08(δdLR)23 +(L ↔ R), Rή = -0.07 e-i0.24(δdLL)23 - 64 (δdLR)23 -(L ↔ R).

  5. The CP asymmetries SφK and SήK can not be accommodated simultaneously by dominant (δdLL)23 or(δdRR)23. • Combining the effects of LL and RR MIs, we can fit the exp. data of SφK and SήK. • However, the Hg EDM exceeds with many order of magnitudes its exp. Bound.

  6. Thus, SUSY models with dominant LR and RL may be the most favorite scenario. • However, it is difficult to arrange for (δdLR)23 ≈ O(10-2) whilst (δdLR)12 remains small: From ΔMK and έ/ε:Re (δdLR)12 <O(10-4) & Im (δdLR)12 < O(10-5).

  7. The MI (δdLR)ij are given by • (δdLR)ij≈ [Vd+L . (Yd Ad). VdR]ij . • The factorizableA-term is an example of a specific texture to satisfy this hierarchy between (δdLR)12 and (δdLR)23. • With intermediate/large tanβ, an effective (δdLR)23can be obtained: (δdLR)23eff = (δdLR)23 + (δdLL)23 (δdLR)33 • For negligible (δdLR)23, we find

  8. Thus if (δdLL)23≈ 10-2, we get(δdLR)23eff≈O(10-2 – 10-3). • These contributions are considered as LL (or RR). • The main effect is still due to the Wilson coefficient C8g of the chromomagnetic operator. • Although (δdLL)23≈ 10-2 is not enough to explain the CP asymmetries of B-decays. • Still it can induce an effective LR mixing that accounts for these results.

  9. Suggested supersymmetric flavor model • As an example, we consider the following SUSY model: M1=M2 =M3 = M1/2 Au = Ad = A0 MU2 = MD2 = m02 mH12 = mH22 = m02 • The masses of the squark doublets are given by tan β=15, m0=M1/2=A0=250 → a ≤5

  10. The Yukawa textures play an important rule in the CP and flavour supersymmetric results. Yu=1/v sinβdiag(mu,mc,mt) Yd=1/vsinβ V+CKM. diag(md ,ms,mb) . VCKM • Although, it is hierarchical texture, it lads to a good mixing between the second and third generations. • The LL down MIs are given by: (δdLL)ij =1/mq2 [VLd+ (Md) 2LL VdL]ij Witha=5 →(δdLL)23 ~ 0.08 e0.4 I • Thus, one gets:(δdLR)23eff ~O (10-2-10-3). • The corresponding single LR MI is negligible due to the degeneracy of the A-terms.

  11. Contribution to SφK and SήK • Gluino exchanges give the dominant contribution to the CP asymmetries: SφK and SήK . • 1 σ constraints on SήK leads to a lower bound on a: a ≥ 3. • With a large a, it is quite possible to account simultaneously for the experimental results SφK and SήK .

  12. Contribution to B→ K π • The direct CP asymmetries of B→ Kπ are given by: ACPK-π+ ~ 2 rT sin δT sin(θP + γ) + 2rEWC sin δEWC sin(θP -θEWC), ACPK-π0 ~ 2 rT sin δT sin(θP + γ) - 2 rEW sin δEWsin(θP -θEW). • The parameters θP , θEWC , θEW and δT , δEW,δEWCare the CP violating and CP conserving phases respectively. • The parameter rT measures the relative size of the tree and QCD penguin contributions. • The parameter, rEW ,rEWCmeasure the relative size of the electroweak and QCD contributions.

  13. P eθP= Psm (1+k eθ’P), rEW eδEWeθEW= rEWsm eδEW(1+ l eθ’EW ),rEWCeδEWCeθEWC=(rEWC)sm eδEWC(1+m eθ’EWC), rT eδT=(rT eδT)sm/|1+ k eθ’P| • k,l,m are given by (mg= mq =500, M2=200, μ=400): k eθ’P= -0.0019 tan β (δuLL)32 - 35.0 (δdLR)23 +0.061 (δuLR)32 l eθ’EW= 0.0528 tan β (δuLL)32 - 2.78 (δdLR)23 +1.11(δuLR)32 m eθ’EWC =0.134 tan β (δuLL)32 + 26.4 (δdLR)23 +1.62 (δuLR)32. a=5, m0=M1/2=A0=250 GeV → (δdLR)23 ~ 0.006xe-2.7i. Thus: K~0.2, l~ 0.009, m ~0.16 →rEW ~ 0.13, rcEW ~ 0.012, rT ~ 0.16 → ACPK-π+ ~ -0.113 and ACPK-π0<ACPK-π+

  14. Conclusions • We studied the possibility of probing SUSY flavor structure using K, B CP asymmetries constraints & EDM. • One possibility: large LR and/or RL sector. • Second possibility: large LL combined with a very small RR and also intermediate or large tan β. • Large LR requires a specific pattern for A terms. • Large LL seems quite natural and can be obtained by a non-universality between the squark masses. • As an example, a SUSY model with a non-universal left squark masses is considered. • one gets effective (δdLR)23 that leads to a significant SUSY contributions to the CP asymmetries of B decays.

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