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Difference: ConstraintDeltaMd (1 vs. 5)

Revision 5

30 Jun 2010 - Main.AdrianBevan

   Constraint from
-<
<
+In the Standard Model,  oscillations occur through a second order process (a box diagram) with a loop containing W and up-type quarks. The box diagram with the top quark gives the dominant contribution. The  oscillation frequency, which is related to the mass difference between the light and the heavy mass eigenstates of the system is expressed, in the Standard Model, as function of %$(\bar{\rho},~\bar{\eta})  and the other elements of CKM matrix:
->
>
+In the Standard Model,  oscillations occur through a second order process (a box diagram) with a loop containing W and up-type quarks. The box diagram with the top quark gives the dominant contribution. The  oscillation frequency, which is related to the mass difference between the light and the heavy mass eigenstates of the system is expressed, in the Standard Model, as function of  and the other elements of CKM matrix:
-<
<
+where  is the Inami-Lim function and ,  is the  top mass and   is the perturbative QCD short distance NLO correction. The remaining factor   encodes the information of non-perturbative QCD. The experimental values we use are summarized in the Table of Inputs. The representation of this constraint in the  plane is given below.
->
>
+where  is the Inami-Lim function and ,  is the  top mass,  is the W mass, and  is the perturbative QCD short distance NLO correction. The remaining factor  encodes the information of non-perturbative QCD. The experimental values we use are summarized in the Table of Inputs. The representation of this constraint in the  plane is given below.
  Set plot = DeltaMdRhoEta?
 
-->
-<
<
+EPS - PDF -  PNG - JPG - GIF
->
>
+  EPS - PDF - PNG - JPG - GIF

Revision 4

09 May 2010 - Main.AdminUser

Line: 1 to 1
	Constraint from $\Delta m_d$
Line: 10 to 10
	& = & \frac {G_F^2} {6 \pi^2} m_W^2 \eta_b S(x_t) m_{B_d} f_{B_d}^2 \hat{B}_{B_d} \left \| V_{cb} \right \| ^2 \lambda^2 [(1-\bar{\rho})^2 + \bar{\eta}^2]
Changed:
< <	where is the Inami-Lim function and $x_t=m_t^2/M_W^2), is the $\overline{\mathrm{MS}}$ top mass and $\eta_c$ is the perturbative QCD short distance NLO correction. The remaining factor $f_{B_d}^2 \hat{B}_{B_d}$ encodes the information of non-perturbative QCD. 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.
> >	where is the Inami-Lim function and , is the $\overline{\mathrm{MS}}$ top mass and $\eta_c$ is the perturbative QCD short distance NLO correction. The remaining factor $f_{B_d}^2 \hat{B}_{B_d}$ encodes the information of non-perturbative QCD. 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.

Changed:
< <	[EPS format] [JPG format]
> >	<-- Set plot = DeltaMdRhoEta? --> EPS - PDF - PNG - JPG - GIF

Revision 3

04 Apr 2010 - Main.VincenzoVagnoni

Line: 1 to 1

Added:
> >	Constraint from $\Delta m_d$
	In the Standard Model, $B^0-\bar{B}^0$ oscillations occur through a second order process (a box diagram) with a loop containing W and up-type quarks. The box diagram with the top quark gives the dominant contribution. The $B^0-\bar{B}^0$ oscillation frequency, which is related to the mass difference between the light and the heavy mass eigenstates of the system is expressed, in the Standard Model, as function of %$(\bar{\rho},~\bar{\eta}) and the other elements of CKM matrix:

Revision 2

02 Apr 2010 - Main.VincenzoVagnoni

Line: 1 to 1
Changed:
< <	-- VincenzoVagnoni - 01 Apr 2010
> >	In the Standard Model, $B^0-\bar{B}^0$ oscillations occur through a second order process (a box diagram) with a loop containing W and up-type quarks. The box diagram with the top quark gives the dominant contribution. The $B^0-\bar{B}^0$ oscillation frequency, which is related to the mass difference between the light and the heavy mass eigenstates of the system is expressed, in the Standard Model, as function of %$(\bar{\rho},~\bar{\eta}) and the other elements of CKM matrix: $\Delta m_d & = & \frac {G_F^2} {6 \pi^2} m_W^2 \eta_b S(x_t) m_{B_d} f_{B_d}^2 \hat{B}_{B_d} \left \| V_{tb} \right \| ^2 \left \| V_{td} \right \| ^2 =\\ & = & \frac {G_F^2} {6 \pi^2} m_W^2 \eta_b S(x_t) m_{B_d} f_{B_d}^2 \hat{B}_{B_d} \left \| V_{cb} \right \| ^2 \lambda^2 [(1-\bar{\rho})^2 + \bar{\eta}^2]$ where is the Inami-Lim function and $x_t=m_t^2/M_W^2), is the $\overline{\mathrm{MS}}$ top mass and $\eta_c$ is the perturbative QCD short distance NLO correction. The remaining factor $f_{B_d}^2 \hat{B}_{B_d}$ encodes the information of non-perturbative QCD. 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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