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Current knowledge of the CKM Matrix Elements

Wolfenstein suggested a rather convenient approximate parameterization of hte CKM matrix [9],

equation90

where there are four parameters, tex2html_wrap_inline606 and tex2html_wrap_inline608 , that have to be obtained from experiment. Of the four, tex2html_wrap_inline610 and A are relatively well determined; less is know about tex2html_wrap_inline614 and tex2html_wrap_inline608 .

The parameter tex2html_wrap_inline610 , which is the sine of the Cabibbo angle, tex2html_wrap_inline620 is determined from strange particle decays ( tex2html_wrap_inline622 ) [10, 11], nuclear tex2html_wrap_inline624 decay ( tex2html_wrap_inline626 ) [12], and the production of charm in tex2html_wrap_inline628 interactions ( tex2html_wrap_inline630 ) [13, 14] to be

equation107

The semileptonic width of the B meson, determined from its lifetime tex2html_wrap_inline634 and semileptonic branching ratio tex2html_wrap_inline636 , yields the best measurement of A [15],

equation112

The relative strength of tex2html_wrap_inline638 and tex2html_wrap_inline640 transition in semileptonic B decays [16] determines the ratio

equation117

In addition, there are three other constraints on tex2html_wrap_inline614 and tex2html_wrap_inline608 . The strength for tex2html_wrap_inline646 mixing, tex2html_wrap_inline648 , dominated by the t-quark exchange diagram and can be expressed in terms of tex2html_wrap_inline596 as [17]

equation130

Here tex2html_wrap_inline654 is the tex2html_wrap_inline656 decay constant and tex2html_wrap_inline658 is the so-called bag parameter--both have theoretical uncertainties. The observed CP violation in the tex2html_wrap_inline660 mass matrix, tex2html_wrap_inline662 , is proportional to tex2html_wrap_inline608 [18],

equation156

where tex2html_wrap_inline666 and tex2html_wrap_inline668 are tex2html_wrap_inline670 and tex2html_wrap_inline672 , respectively, and expressions for the functions S and F are given in ref [18]. Limits on direct CP violation in tex2html_wrap_inline674 S = 1 tex2html_wrap_inline676 decays ( tex2html_wrap_inline678 ) can be translated to limits on tex2html_wrap_inline608 given by [19],

equation184



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Thu Oct 24 14:23:05 KST 1996