Difference: ConstraintEpsK (1 vs. 6)

Revision 6
30 Jun 2010 - Main.AdrianBevan
Line: 1 to 1
 

Constraint from
\varepsilon_K

Changed:
<
<
Indirect CP violation in the Kaon system is usually expressed in terms of | \varepsilon_K | parameter which is the fraction of CP violating component in the mass eigenstates and which is usually defined as:
>
>
Indirect CP violation in the Kaon system is usually expressed in terms of | \varepsilon_K | parameter which is the fraction of the CP violating component in the mass eigenstates and which is usually defined as:
 

\varepsilon_K = \frac{e^{i\pi/4}}{\sqrt{2}\Delta M_K} \left( \Im{M_{12}}+2\xi\Re{M_{12}} \right ),
Line: 14 to 14
  Top and charm quarks contribute to the expression of the mixing in K0-K0 system. The calculation of the box diagram gives

Changed:
<
<
M_{12} = \frac{G_F^2}{12\pi^2} F_K^2 B_K M_K M_W^2 \left [ \lambda_c^{*2} \eta_t S_0 (x_c) + \lambda_t^{*2} \eta_2 S_0 (x_t)+2\lambda_t^* \lambda_c^* \eta_3 S(x_c,~x_t) \right ] with
\lambda_i^*=V^*_{is}V_{id},
>
>
M_{12} = \frac{G_F^2}{12\pi^2} F_K^2 B_K M_K M_W^2 \left [ \lambda_c^{*2} \eta_t S_0 (x_c) + \lambda_t^{*2} \eta_2 S_0 (x_t)+2\lambda_t^* \lambda_c^* \eta_3 S(x_c,~x_t) \right ] where
\lambda_i^*=V^*_{is}V_{id},
 

which allows one to write
Line: 26 to 26
  C_\epsilon = \frac{G_F^2 F_K^2 M_K M_W^2}{6\sqrt{2}\pi^2 \Delta M_K } = 3.84 \cdot 10^4.
Changed:
<
<
The expression actually used in the UT fit is obtained writing | \varepsilon_K | in terms of (\bar{\rho},~\bar{\eta}) and the other elements of CKM matrix:
>
>
The expression actually used in the UT fit is obtained by writing | \varepsilon_K | in terms of (\bar{\rho},~\bar{\eta}) and the other elements of CKM matrix:
 

| \varepsilon_K | = C_\epsilon B_K A^2 \lambda^6 \bar{\eta} \left \{ -\eta_1 S_0(x_c) (1-\lambda^2/2) + \eta_3 S_0 (x_c,~x_t) + \eta_2 S_0(x_t) A^2 \lambda^4 (1-\bar{\rho}) \right \}.
Line: 38 to 38
 
  • Set plot = EpsKRhoEta?
-->
Changed:
<
<

EPS - PDF - PNG - JPG - GIF
>
>

EPS - PDF - PNG - JPG - GIF
 

Revision 5
09 May 2010 - Main.AdminUser
Line: 1 to 1
 

Constraint from
\varepsilon_K

Line: 34 to 34
 

Changed:
<
<

[EPS format] [JPG format]
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>
<-- 
  • Set plot = EpsKRhoEta?
-->


EPS - PDF - PNG - JPG - GIF
 

Revision 4
06 Apr 2010 - Main.VittorioLubicz
Line: 1 to 1
 

Constraint from
\varepsilon_K

Line: 14 to 14
  Top and charm quarks contribute to the expression of the mixing in K0-K0 system. The calculation of the box diagram gives

Changed:
<
<
M_{12} = \frac{G_F^2}{12\pi^2} F_K^2 B_K M_K M_W^2 \left [ \lambda_c^{*2} \eta_t S_0 (x_c) + \lambda_t^{*2} \eta_2 S_0 (x_t)+2\lambda_t^* \lambda_c^* \eta_3 S(x_c,~x_t) \right ] with
\lambda_i^*=V^*_{is}V_{id},
>
>
M_{12} = \frac{G_F^2}{12\pi^2} F_K^2 B_K M_K M_W^2 \left [ \lambda_c^{*2} \eta_t S_0 (x_c) + \lambda_t^{*2} \eta_2 S_0 (x_t)+2\lambda_t^* \lambda_c^* \eta_3 S(x_c,~x_t) \right ] with
\lambda_i^*=V^*_{is}V_{id},
 

which allows one to write
Line: 25 to 23
  where

Changed:
<
<
C_\epsilon = \frac{G_F^2 F_K^2 M_K M_W^2}{6\sqrt{2} \Delta M_K } = 3.78 \cdot 10^4.
>
>
C_\epsilon = \frac{G_F^2 F_K^2 M_K M_W^2}{6\sqrt{2}\pi^2 \Delta M_K } = 3.84 \cdot 10^4.
 

The expression actually used in the UT fit is obtained writing | \varepsilon_K | in terms of (\bar{\rho},~\bar{\eta}) and the other elements of CKM matrix:
Line: 36 to 34
 

Changed:
<
<

    [EPS format]   [JPG format]
>
>

[EPS format] [JPG format]
 

Revision 3
04 Apr 2010 - Main.VincenzoVagnoni
Line: 1 to 1
 
Added:
>
>

Constraint from
\varepsilon_K

  Indirect CP violation in the Kaon system is usually expressed in terms of | \varepsilon_K | parameter which is the fraction of CP violating component in the mass eigenstates and which is usually defined as:

\varepsilon_K = \frac{e^{i\pi/4}}{\sqrt{2}\Delta M_K} \left( \Im{M_{12}}+2\xi\Re{M_{12}} \right ),
Revision 2
02 Apr 2010 - Main.VincenzoVagnoni
Line: 1 to 1
Changed:
<
<
-- VincenzoVagnoni - 01 Apr 2010
>
>

Indirect CP violation in the Kaon system is usually expressed in terms of | \varepsilon_K | parameter which is the fraction of CP violating component in the mass eigenstates and which is usually defined as:

\varepsilon_K = \frac{e^{i\pi/4}}{\sqrt{2}\Delta M_K} \left( \Im{M_{12}}+2\xi\Re{M_{12}} \right ),

where

\xi=\frac{\Im{A_{\pi\pi.~I=0}}}{\Re{A_{\pi\pi.~I=0}}}.

Top and charm quarks contribute to the expression of the mixing in K0-K0 system. The calculation of the box diagram gives

M_{12} = \frac{G_F^2}{12\pi^2} F_K^2 B_K M_K M_W^2 \left [ \lambda_c^{*2} \eta_t S_0 (x_c) + \lambda_t^{*2} \eta_2 S_0 (x_t)+2\lambda_t^* \lambda_c^* \eta_3 S(x_c,~x_t) \right ]
with
\lambda_i^*=V^*_{is}V_{id},

which allows one to write

\varepsilon_K=C_\epsilon B_K A^2 \Im{\lambda_t} \left \{ \Re{\lambda_c} \left [ \eta_1 S_0(x_c) - \eta_3 S_0 (x_c,~x_t) A^2 \lambda^4 \right ] - \Re{\lambda_t} \eta_2 S_0(x_t) \right \} e^{i \pi /4},

where

C_\epsilon = \frac{G_F^2 F_K^2 M_K M_W^2}{6\sqrt{2} \Delta M_K } = 3.78 \cdot 10^4.

The expression actually used in the UT fit is obtained writing | \varepsilon_K | in terms of (\bar{\rho},~\bar{\eta}) and the other elements of CKM matrix:

| \varepsilon_K | = C_\epsilon B_K A^2 \lambda^6 \bar{\eta} \left \{ -\eta_1 S_0(x_c) (1-\lambda^2/2) + \eta_3 S_0 (x_c,~x_t) + \eta_2 S_0(x_t) A^2 \lambda^4 (1-\bar{\rho}) \right \}.

The experimental values we use are summarized in the Table of Inputs. The representation of this constraint in the (\bar{\rho},~\bar{\eta}) plane is given below.


    [EPS format]   [JPG format]

 
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