Δm _s , ΔГ _s and φ _s Measurements at Tevatron

Abstract

Oscillations of neutral B meson systems have always given a big insight into Standard Model (SM) structure. In particular, for the B _s system, mass and width difference of the two mass eigenstates are related to the matrix elements M ^s₁₂ and Г ^s₁₂ with:

$$ \Delta m_s = 2|M_{12}^s |, \Delta \Gamma _s = 2\left| {\Gamma _{12}^s } \right|\cos \varphi _s $$

(1)

where φ _s is the CP violating phase of the SM and is defined as φ _s ≡ arg $\frac{{V_{ts} V_{tb}^* V_{cs}^* V_{cb} }} {{V_{ts}^* V_{tb} V_{cs} V_{cb}^* }}$ , while M ^s−i/2Г ^s is the effective Hamiltonian matrix governing the system dynamics [3]. A third quantity providing information on the mixing problem is the CP asymmetry in flavor specific decays:

$$ A_{fs}^s = \operatorname{Im} \frac{{\Gamma _{12}^s }} {{M_{12}^s }} = \frac{{\Delta \Gamma _s }} {{\Delta m_s }}\tan \varphi _s $$

(2)