## Constraint from

The oscillation frequency, which is related to the mass difference between the light and the heavy mass eigenstates of the system, is proportional to in the Standard Model. Neglecting terms giving small contributions, is independent of and . Instead, the ratio is proportional to and and the advantage of using this ratio instead of only is that the ratio is expected to be better determined from the theory than the individual quantities entering its expression. The measurement of gives a similar constraint as :

In practice a problem arises in the (possible) use of the information from twice in the fit: in the constraint itself and in the ratio . The correlation has to be taken into account. One should recall that alone would give a constraint on and so . It should also be considered that due to the error coming from chiral extrapolations the quantities which are best known and which are effectively calculated are and while is derived from the other two. For this reason we write the constraints in the following way :

Here the quantities entering in the expression of are the calculated ones: and . To make the constraint on more effective both quantities have to be improved. The constraint on helps in improving the knowledge of one of those: . We implemented this bound using directly the information from the experimental likelihood provided by CDF. The representation of this constraint in the plane is given below.

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