Difference: ConstraintEpsK (r6 vs. r5)

r6 - 30 Jun 2010 - 20:28 - AdrianBevan r5 - 09 May 2010 - 18:30 - AdminUser
  

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 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 ),
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 ]
where
\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}\pi^2 \Delta M_K } = 3.84 \cdot 10^4.
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 \}.
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 - PDF - PNG - JPG - GIF

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 ),
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}\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:
| \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 - PDF - PNG - JPG - GIF
r6 - 30 Jun 2010 - 20:28 - AdrianBevan r5 - 09 May 2010 - 18:30 - AdminUser

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