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## CP VIOLATION in b → s l + l - Transition

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**Direct CP-Violation**CP non-conservation shows up as a rate difference between two processes that are the CP conjugates of one-another. How can such a rate difference appear?**This shows that the effect will vanish if the two coupling**constants can be made relatively real. And also if strong phase be zero.**CP violation in SM.**4 parameters : Euler angles: ½ n(n-1)=3 Complex Phase: ½ (n-1)(n-2)=1 Unitarity and Properties of CKM**physics beyond the Standard Model will have, in general,**possible additional CP-violating parameters. Any further fields, such as any additional Higgs fields, can introduce further CP-violating couplings. Such effects may then enter into B decay physics.**FCNC IN b s(d) TRANSITION :**1 . As a test of SM and beyond SM 2. As a tool to Det. CKM elements such as Vtq(q=d,s,b), Vub 3. CP- Violation**b → s l+ l-**Vub Vus* + Vtb Vts* + Vcb Vcs* = 0 Using unitary condition of CKM matrix and neglecting |VubV*us| in comparison to |VtbV*ts| and |VcbV*cs| Indicate that such decay involves only CP –Violation in this channel is suppressedby SM.**Beyond the SM**• The possibility of CP violation the b → s transition has been studied in supersymmetry by [Kruger, et al]. • The SM with fourth generation [Arhrib et al]. • In another study, this has been studied with the addition of CP odd phases to Wilson coefficients [Aliev, et al].**The formalism**• Using general form of 4-Fermi interactions in SM.**We extend the matrix element of the**b → s l+ l- where C9get a new weak phase. Minimal Extension of the SM: ΛnewCan be parameterized as :**Using the expression of the matrix element and neglecting**the s-quark mass(ms), we obtain the expression for the differential decay rate as:**is the velocity of the final lepton &**∆ is expression in terms of masses , Wilson coefficients.**CP-Violation asymmetry**• CP-Violation differential decay width asymmetry is defined:**The differential decay width for the CP conjugated process**can be obtain by making the replacements:**CP-asymmetry is evaluated to be**Since for any allowed region of s, << , So, we can ignore the term proportional to in the dominator of equation:**Numerical analysis**• we examine the dependence of ACP on new .. • ACP depends on both magnitude and phase of new . • The first measurement of the b → s l+ l- decay reported by BELLE help us to get an idea about magnitude of new. We assume that:**In order to eliminate the sdependence, instead of CP**asymmetry in the differential decay width, we study CP asymmetry in the total decay width by doing numerical integration over sin ACP(s) equation:**The figure depicts that ACP is sensitive to the new weak**phase and can reach about 4.5% which is quite measurable at future colliders such as LHCb, BTeV, ATLAS CMS or ILC .**In conclusion, this study has presented the CP asymmetry in**the b → s l+ l- transition in the minimal extension of the standard model where C9effreceived extra weak phase new due to the new physics effects. We imposed 10% of uncertainty to the SM branching ratio of the b → s l+ l- transition and obtained the bound on a new parameter new . Our predictive model showed that the CP-violation asymmetry could reach to the order of 4.5% which was not only entirely measurable in experiments, but also indicated the new physics effects, since in the SM, this CP asymmetry is near zero.