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Isospin Analysis in Decay Processes: Advancements and Historical Context

This paper presents a comprehensive overview of isospin analysis in the context of decay processes, focusing on the historical developments from early methods in decay extraction like Gronau, London, and Wyler (1991) to more recent advancements in the GLW and GGSZ methods. The nuances of mixing induced CP violation and the challenges posed by discrete ambiguity are examined in detail. We outline the extraction of key parameters and angles through isospin relations and quark diagram approaches, showcasing how nine measurements converge to enhance our understanding of these complex decay systems.

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Isospin Analysis in Decay Processes: Advancements and Historical Context

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  1. CKM EXTRACTION OF VIA ISOSPIN ANALYSIS OF DECAYS Yeo Woong Yoon Collaboration with C. S. Kim and Sechul Oh

  2. HISTORY OF EXTRACTING • decays Weak phase Gronau, London, Wyler (1991) u Color suppressed But the triangles are quite squashed ! Color allowed

  3. HISTORY OF EXTRACTING • GLWFrom and their CP conjugates The triangles are quite squashed • ADSImprovement of GLW method by seeing and . Enhancement of since • GGSZDalitz analysis from Gronau, Wyler (1991), Gronau, London (1991) Atwood, Dunietz, Soni (1997) Giri, Grossman, Soffer, Zupan (2003) Combined all methods : UTfit, Winter 2007

  4. HISTORY OF EXTRACTING • and SU(3) Flavour Symmetry Gronau, Rosner, London (1994); Buras Fleischer (1995); Deshpande, He (1995) Gronau, Hernandez, London, Rosner (1995); Fleischer (1996); NeubertRosner (1998); Buras, Fleischer (1999); Gronau, Rosner (2002)

  5. HISTORY OF EXTRACTING • Fleischer – Mannel Bound Fleischer, Mannel (1998) = 72° = 0.90 ± 0.05

  6. ISOSPIN ANALYSIS IN DECAYS • Isospin Relation for Decays One can make two quadrangle in complex plane from these two relations RemindGronau, London (1990)

  7. ISOSPIN ANALYSIS IN DECAYS Determination of a quadrangle: 4 lengths + 1 angle • All lengths can be obtained by 4 Br’s and 4 Acp’s. • gives one constrains on angles • from gives one another constrains on angles  Two quadrangles are determined Mixing induced CPV is a function of θ

  8. ISOSPIN ANALYSIS IN DECAYS • Mixing induced CPV Middle value Error

  9. DISCRETE AMBIGUITY A B 4 ambiguity C D A ambiguity for two quadrangle A1 A2 A3 A4

  10. DISCRETE AMBIGUITY A1 A2 B1 B2 A3 A4 B3 B4 C1 C2 D1 D2 C3 C4 D3 D4 Totally Sixteen-fold Discrete Ambiguity occurs

  11. EXTRACTION OF A1: A4: B2 and C2: B3: Dashed line : (unreasonable)

  12. EXTRACTION OF Fleischer and Mannel Bound Sharply consistent to the graph Dashed line : (unreasonable)

  13. CONCLUSION • We adopt①Isospin relation in decays. ②Quark Diagram Approach in and it’s charge conjugate modes. • All nine measurements of is requiredto extract in this framework. Mixing inducedCP asymmetry plays a crucial role. • We extract from only decay system without using SU(3) flavor sym. as follows

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