CP Violation in B Meson Decays: Experimental Results Page: 3 of 20
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j W+
b ib
Figure 2: The 'CP mirror' effect on the Vub CKM matrix element in a b ->+ u transition: the complex-conjugate Vu*b has
opposite phase.
is carried by the two elements Vub and Vd. From decay rates and branching fraction measurements, constraining the
absolute values IV4l1, A ~ 0.82, representing the deviation of VbI from A2, is known with an uncertainty of about
t5%, while p2 + 72 ~ 0.4 is less well known.
CP violation in the SM corresponds to 7 $ 0. Observable CP rate asymmetries are generated by interfering
amplitudes, whose relative phase changes sign under CP. Figure 2 shows how the 'CP mirror' changes the sign of
the CKM phase in a charged-current transition coupling the b and a quarks to the W weak boson.
The most effective way of comparing experimental results to SM expectations in the CKM sector is by means of
the unitarity relations between CKM matrix elements that can be represented by Unitarity Triangles (UT) in the
complex plane. The amount of CP violation is linked to the equal areas of these different triangles. When studying
Bu = (bu) and B2 = (bd) meson decays, the relevant triangular relation is between the first and third column of the
matrix:
VbVud + VbVC + VtbVd = 0. (2)
When normalized to VVd, this relation corresponds to the resealed triangle shown in Figure 3; its Unitarity Angles
or relative phases are labelled in different notations a (#2), , (#1), and 'y (#3).
In contrast with the other much flatter triangles that can be constructed from unitarity relations, the three sides
of this UT have comparable sizes, all of the same order ~ A3; they can be measured from decay rates. As a result,
the angles are all expected to be significantly different from zero and lead to the SM expectation of large CP
asymmetries in some B decays. Recalling that Vcd = A and Vud ~ V b ~ 1, the same unitarity relation can be written
approximately:
Vub +1+ Vd =0, (3)
A V~ A VS
and shows that, in this parameterization:
- _ argVub ~ - arg Vd a = 7r - (,+y). (4)
For precision tests of the CKM mechanism, one can take into account unitarity at all orders in A. Defining the
so-called 'standard' parameters [15], [14] in terms of A, A, p, and 7, one obtains a modified Wolfenstein parameteri-
zation [16], where the apex of the resealed UT (Figure 3) is given to all orders in A by:
__ KVud*Vu
p + z -- -dVcb (5)
where p = p(1 - A2/2 + O(A4)) and 4 = 7(1 - A2/2 + 0(A4)).
4. EXPERIMENTAL CHALLENGES
The importance of the Unitarity Triangle as a bookkeeping device is clear from Figure 3. The SM predicts that
the lines, representing constraints from many different measurements of decay rates and asymmetries, all intersect
at the apex (p, q) of the Unitarity Triangle.
WET004 3
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Lanceri, Livio & /Trieste U. /INFN, Trieste. CP Violation in B Meson Decays: Experimental Results, article, August 30, 2005; [Menlo Park, California]. (https://digital.library.unt.edu/ark:/67531/metadc878539/m1/3/: accessed April 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.