CP VIOLATION in b ? s l l- Transition

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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?

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This shows that the effect will vanish if the two
coupling constants can be made relatively real.
And also if strong phase be zero.
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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
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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.
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• 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(qd,s,b), Vub
• 3. CP- Violation

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b ? s l l-

• Vub Vus Vtb Vts Vcb Vcs 0
• Using unitary condition of CKM matrix and
• neglecting VubVus in comparison to
• VtbVts and VcbVcs Indicate that such decay
  involves only
• CP Violation in this channel is suppressed by
  SM.

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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.

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The formalism

• Using general form of 4-Fermi interactions in SM.
  

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• Minimal Extension of the SM

We extend the matrix element of the b ? s l
l- where C9 get a new weak phase.
?new Can be parameterized as
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Using the expression of the matrix element and
neglecting the s-quark mass(ms), we obtain the
expression for the differential decay rate as
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• is the velocity of the final lepton
• ? is expression in terms of masses , Wilson
  coefficients.

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CP-Violation asymmetry

• CP-Violation differential decay width asymmetry
  is defined

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The differential decay width for the CP
conjugated process can be obtain by making the
replacements
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• CP-asymmetry is evaluated to be

Since for any allowed region of s, ? ltlt ?, So, we
can ignore the term proportional to ? in the
dominator of equation
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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

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In order to eliminate the s dependence, instead
of CP asymmetry in the differential decay width,
we study CP asymmetry in the total decay width by
doing numerical integration over s in ACP(s)
equation
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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 .
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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
C9eff received 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.
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