Δmd/Δms

The Bs0- Bs0 oscillation frequency, which is related to the mass difference between the light and the heavy mass eigenstates of the system is proportional, in the Standard Model, to |Vts|2. Neglecting terms, having small contribution, |Vts|2 is independent of ρ and η.
Instead, the ratio Δmd/Δms is proportional to ρ and η and the advantage of using this ratio instead of only Δms is that the ratio ξ= fBdBBd/ fBsBBs is expected to be better determined from the theory than the individual quantities entering into its expression. The measurement of Δmd/Δms gives a similar constraint as Δmd :

Δ_ms formula

In practice a problem arise in the (possible) use of the information from Δmd twice : in the Δmd constraint itself and in the ratio Δmd/Δms. The correlation has to be taken into account. It should be remembered that Δms alone would give a constraint on |Vts|2 and so fBsBBs. It should be also considered that due to the error coming from chiral extrapolations the quantities which are best known and which are effectively calculated are fBsBBs and ξ while fBdBBd is derived from the other two. For this reason we propose to write the constraints in the following way :

Δ_md formula used

Here the quantities entering in the expression of Δmd are the calculated ones : fBsBBs and ξ. To renders the constraint on Δmd more effective both quantities have to be improved. The constraint on Δms helps in improving the knowledge of one of those : fBsBBs.

We implemented this bound using directly the information from the experimental likelihood provided by CDF.


Bound on R_t from Δm_d//Δ m_s
(EPS) [JPG]

Bound on Rt from Δmd/Δ ms
Rt = 0.92 ± 0.04 ([0.85,1.00] @ 95% Prob.)


present bound from Δm_d/Δm_s
(EPS) [JPG]

bound from Δ md/Δ ms on (ρ, η) plane


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