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Violation in Mixing

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4 Strategy and Tools for Charmless Two-body � Decays Analysis 97<br />

4.1 Data samples . . ....................................... 97<br />

4.2 Event selection . ....................................... 98<br />

4.2.1 Topological Variables ................................100<br />

4.2.2 � candidate selection: k<strong>in</strong>ematic Variables . . . .................102<br />

4.2.2.1 Control Sample � ¦ � � � ¦ ....................103<br />

4.3 Background fight<strong>in</strong>g . . . ..................................104<br />

4.4 PID selection . . .......................................107<br />

4.4.1 � � £ � control sample ............................107<br />

4.4.2 Selector-based PID .................................109<br />

4.5 Track<strong>in</strong>g Corrections . . . ..................................111<br />

4.6 Analysis methods .......................................111<br />

4.6.1 Sample def<strong>in</strong>itions .................................112<br />

4.6.2 Beam energy-substituted mass Ñ�Ë ........................113<br />

4.6.3 Energy difference ¡� ...............................114<br />

4.6.4 Fisher output � ...................................116<br />

4.6.5 Pion and kaon � ..................................117<br />

4.6.6 Correlations between PDFs . ............................119<br />

5 Measurement of Branch<strong>in</strong>g Fractions for � ¦ � Ã � ¦ decays 121<br />

5.1 Data samples and event selection . . . ............................121<br />

5.2 Ã Ë reconstruction .......................................122<br />

5.3 Analysis Strategy .......................................125<br />

5.4 Background Suppression and PDF Parameterization .....................126<br />

5.4.1 ¡� PDF and Def<strong>in</strong>ition of Signal and Side-band Regions . ...........126<br />

5.4.2 Parameterizations of Ñ�Ë Distributions ......................128<br />

5.4.3 Fisher Discrim<strong>in</strong>ant .................................128<br />

5.4.4 Particle ID Selection ................................129<br />

iii

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