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Difference: ConstraintDeltaMd (r3 vs. r2)

		r3 - 04 Apr 2010 - 15:52 - VincenzoVagnoni		r2 - 02 Apr 2010 - 11:04 - VincenzoVagnoni


		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: $\Delta m_d & = & \frac {G_F^2} {6 \pi^2} m_W^2 \eta_b S(x_t) m_{B_d} f_{B_d}^2 \hat{B}_{B_d} \left \| V_{tb} \right \| ^2 \left \| V_{td} \right \| ^2 =\\ & = & \frac {G_F^2} {6 \pi^2} m_W^2 \eta_b S(x_t) m_{B_d} f_{B_d}^2 \hat{B}_{B_d} \left \| V_{cb} \right \| ^2 \lambda^2 [(1-\bar{\rho})^2 + \bar{\eta}^2]$ 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]		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]

		r3 - 04 Apr 2010 - 15:52 - VincenzoVagnoni		r2 - 02 Apr 2010 - 11:04 - VincenzoVagnoni

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