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<p>In 1998, it was shown that, if flavor SU(3) symmetry [SU(3)<sub><i>F</i></sub>] is assumed in charmless <i>B</i> → <i>PP</i> decays (<i>P</i> is a light pseudoscalar meson), some reduced matrix elements involving electroweak penguin (EWP) operators are related to those involving tree operators. Similarly, EWP diagrams are related to tree diagrams. These SU(3)<sub><i>F</i></sub> EWP-tree relations were recently used in global analyses of <i>B</i> → <i>PP</i> decays. They have also been used over the years in analyses of the <i>B</i> → <i>πK</i> puzzle, even though the <i>B</i> → <i>πK</i> amplitudes are related by isospin symmetry [SU(2)<sub><i>I</i></sub>], and not the full SU(3)<sub><i>F</i></sub>. In this paper, we show that, even if only SU(2)<sub><i>I</i></sub> is assumed, there are still EWP-tree relations. In ∆<i>S</i> = 0 decays, these relations are similar to those of SU(3)<sub><i>F</i></sub>, and can be used to take into account the EWP contributions in the extraction of the CP phase <i>α</i> from <i>B</i> → <i>ππ</i> decays. In ∆<i>S</i> = 1 decays, the SU(2)<sub><i>I</i></sub> EWP-tree relations are quite different from those of SU(3)<sub><i>F</i></sub>; when these are used to analyze the <i>B</i> → <i>πK</i> puzzle, one now finds a 4–5<i>σ</i> discrepancy with the Standard Model, much larger than what was previously found. We argue that, if one analyzes a set of hadronic <i>B</i> decays whose amplitudes are related by isospin, one must use the SU(2)<sub><i>I</i></sub> EWP-tree relations for that set of decays in the analysis.</p>

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Isospin-based EWP-tree relations

  • 期刊论文

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  • 发表日期：

    2026年5月18日

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  • Bhubanjyoti Bhattacharyay,
  • Marianne Bouchard,
  • Alexandre Jean,
  • David London,
  • Ipsita Ray

摘要

In 1998, it was shown that, if flavor SU(3) symmetry [SU(3)F] is assumed in charmless B → PP decays (P is a light pseudoscalar meson), some reduced matrix elements involving electroweak penguin (EWP) operators are related to those involving tree operators. Similarly, EWP diagrams are related to tree diagrams. These SU(3)F EWP-tree relations were recently used in global analyses of B → PP decays. They have also been used over the years in analyses of the B → πK puzzle, even though the B → πK amplitudes are related by isospin symmetry [SU(2)I], and not the full SU(3)F. In this paper, we show that, even if only SU(2)I is assumed, there are still EWP-tree relations. In ∆S = 0 decays, these relations are similar to those of SU(3)F, and can be used to take into account the EWP contributions in the extraction of the CP phase α from B → ππ decays. In ∆S = 1 decays, the SU(2)I EWP-tree relations are quite different from those of SU(3)F; when these are used to analyze the B → πK puzzle, one now finds a 4–5σ discrepancy with the Standard Model, much larger than what was previously found. We argue that, if one analyzes a set of hadronic B decays whose amplitudes are related by isospin, one must use the SU(2)I EWP-tree relations for that set of decays in the analysis.