Extraction Of CKM Angle ? From B⁰?a₁^±?1260??^?Decays

The Standard Model of particle physics can describe the interactions between elementary particles,such as the strong interactions between quarks and gluons,weak interactions between fermions and W± bosons,and the electromagnetic interactions between photons and charged particles.The Standard Model has become the most beautiful theory to describe these funda-mental interactions,after the discovery of Higgs bosons in 2012.Nevertheless,there are some experimental observations that the Standard Model cannot account for,including the neutrino oscillation,dark matter and dark energy,as well as the anomalous magnetic moment of muon.These phenomena imply that,there may be a New Physics theory beyond the Standard Model.Through systematical studies of the CKM unitary triangle,we can,on the one hand,perform precise tests of the Standard Model and,on the other hand,probe indirectly New Physics signals by looking for the discrepancy between experiment and theory.In the Standard Model,the phase? can be extracted through the quark-level transition b?sqq,the phase-? can be extracted through the B?DK decay,and the phase a can be extracted through the transition b? uud.In this thesis,we will study how to extract the weak phase a in the CKM unitary triangle.According to the definition of the phase ? in the CKM unitary triangle,B???,B???,B??? and B??1? processes can be used to extract the phase ?.It can be seen from the Feynman diagram of b?uud that these decays contain tree and penguin amplitudes.When the penguin amplitude is taken into account,the interference between the tree and the penguin amplitudes will generate additional phase.The additional phase can render the extraction of CKM angle a sufficiently challenging.Reducing the impact from penguin contribution therefore becomes the key to tackle the issue.To this end,technically,one can use either isospin or flavor SU(3)symmetry to perform the analyses.In this thesis,we will adopt the flavor SU(3)symmetry to extract the phase ?.In addition,We select the decay B??1? in the above decay modes to extract the phase ?.Compared with other decays above,the final states of B??1? consist of four charged pions,which are more easily detected at experiments.Based on this,our work will extract the phase ? from the decay modes B0(B0)??1±(1260)?(?).In this thesis,we begin with the decay amplitudes and the time-dependent decay rates for B0(B0)??1±(1260)?(?)involving B-B mixing in terms of tree and penguin amplitudes.And then,given that ?eff is correlated to four detectable CP violation parameters(S,?S,C,?C),we define ?eff in the limit of vanishing penguin amplitudes,so as to reduce the tree-loop inference.Next,the corrections |?-?eff| caused by the penguin amplitudes p± can be bounded by relating the decays B0??1±?(?) with corresponding ?S=1 decays,B??1K and B?K1A? by flavor SU(3)symmetry.Then,we perform numerical analysis for the model parameters by using the error transfer formula and extract the weak phase a thereby.The thesis is composed of the following chapters:The first Chapter is the introduction.In Chapter 2,we briefly review the Standard Model and the theoretical basis involved in this thesis.In Chapter 3,we introduce the theoretical model to extract the phase ? by flavor SU(3)symmetry from the decays B0(B0)??1±(1260)?(?).In Chapter 4,we perform numerical analysis in terms of the model parameters given by different experimental collaborations,and then obtain the phase?.Finally,we give our conclusions and outlooks in Chapter 5.