Violation in Mixing

168 Analysis of the time-dependent �È -violating asymmetry in � � � � decays
time-dependent measurement is therefore expected to be dominated by statistical uncertainty and, ignoring
systematic uncertainties and assuming zero asymmetry in the background, the analysis that optimizes the
effective Ë� Ô Ë � will also minimize the error on the �È asymmetry. The �È asymmetries, as well
as the signal and background yields, are determined simultaneously from a global maximum likelihood fit
using both tagged and untagged � � events.
There are two �È observables in the time-dependent analysis: ��� and ÁÑ�: it would be most convenient to
fit for ��� and ÁÑ�� ���, since the latter provides a direct measurement of ×�Ò «�«. However, it was found
that this fit produces non-Gaussian pull distributions in detailed toy Monte Carlo studies. Moreover, from
Eq. 7.2 it is seen that using ��� as a fit parameter implicitly constrains the coefficient of the cosine term to
be in the physical region � , while there is no such constraint in the data. So there are also conceptual
problems associated with using ��� as a fit parameter. In contrast, fitting for �� and ��� is found to be very
robust and does not bias the fit. The current analysis therefore uses �� and ��� as fit parameters.
7.4 Data samples and event selection
Results in this analysis are based on a greater luminosity with respect to the one described in Sec 4.1:
¯ Run 1 on-resonance data ( �� fb , ��� million �� pairs).
¯ Run 2 1 on-resonance data (���� fb , � million �� pairs).
¯ �� million (���� fb ) ÙÙ, �� and ×× Monte Carlo.
¯ � million (���� fb ) Monte Carlo.
¯ ��� million (���� fb ) � � Monte Carlo.
¯ �k each of � � , à � , and à à signal Monte Carlo.
Candidate � mesons are reconstructed by combining pairs of charged tracks using four-vector addition,
where we assume the pion mass for both tracks. The two-track vertex position is obtained with the standard
BABAR vertex algorithm, like the tag-side vertex is obtained with default BABAR algorithm using the charged
track and the loose à Ëcandidate selection lists as input. For comparison, ¡Ø is calculated with and without
the beam constraints. The BABAR tagging algorithm is used to identify the opposite � meson as a � or � .
We use all the four standard BABAR tagging categories [4, 69]: lepton, kaon, neural network NT1 and NT2.
Except for a tighter background suppression cut and the addition of ¡Ø quality cuts, the selection criteria
used in this analysis are identical to those in Chapter 4. The cut on Ó× �Ë that was at �� is tightened at
� Ó× �Ë� � ��.
The Ñ�Ë and ¡� 2-dimensional side-bands are defined as �¡�� � �� ��Î and �� � Ñ�Ë �
�� ��Î� . The signal band which is the fit region is defined with �¡�� � � � ��Î and �� �Ñ�Ë �
�� ��� ��Î� , while the Ñ�Ë side-band is �¡�� � �� ��Î and �� � Ñ�Ë � �� � ��Î� . The
1 This data-set corresponds to data taken in the first half of year 2001
MARCELLA BONA