Anomalies in hadronic B decays: An update

Recently, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>B</a:mi><a:mo stretchy="false">→</a:mo><a:mi>P</a:mi><a:mi>P</a:mi></a:math> decays (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>B</d:mi><d:mo>=</d:mo><d:mo stretchy="false">{</d:mo><d:msup><d:mi>B</d:mi><d:mn>0</d:mn></d:msup><d:mo>,</d:mo><d:msup><d:mi>B</d:mi><d:mo>+</d:mo></d:msup><d:mo>,</d:mo><d:msubsup><d:mi>B</d:mi><d:mi>s</d:mi><d:mn>0</d:mn></d:msubsup><d:mo stretchy="false">}</d:mo></d:math>, <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>P</h:mi><h:mo>=</h:mo><h:mo stretchy="false">{</h:mo><h:mi>π</h:mi><h:mo>,</h:mo><h:mi>K</h:mi><h:mo stretchy="false">}</h:mo></h:math>) were analyzed under the assumption of flavor SU(3) symmetry (<l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mrow><l:msub><l:mrow><l:mi>SU</l:mi><l:mo stretchy="false">(</l:mo><l:mn>3</l:mn><l:mo stretchy="false">)</l:mo></l:mrow><l:mrow><l:mi>F</l:mi></l:mrow></l:msub></l:mrow></l:math>). Although the individual fits to <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi mathvariant="normal">Δ</p:mi><p:mi>S</p:mi><p:mo>=</p:mo><p:mn>0</p:mn></p:math> or <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi mathvariant="normal">Δ</s:mi><s:mi>S</s:mi><s:mo>=</s:mo><s:mn>1</s:mn></s:math> decays are good, it was found that the combined fit is very poor: there is a <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mn>3.6</v:mn><v:mi>σ</v:mi></v:math> disagreement with the <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mrow><x:msub><x:mrow><x:mi>SU</x:mi><x:mo stretchy="false">(</x:mo><x:mn>3</x:mn><x:mo stretchy="false">)</x:mo></x:mrow><x:mrow><x:mi>F</x:mi></x:mrow></x:msub></x:mrow></x:math> limit of the standard model (<bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:mrow><bb:msub><bb:mrow><bb:mi>SM</bb:mi></bb:mrow><bb:mrow><bb:msub><bb:mrow><bb:mi>SU</bb:mi><bb:mo stretchy="false">(</bb:mo><bb:mn>3</bb:mn><bb:mo stretchy="false">)</bb:mo></bb:mrow><bb:mrow><bb:mi>F</bb:mi></bb:mrow></bb:msub></bb:mrow></bb:msub></bb:mrow></bb:math>). One can remove this discrepancy by adding <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:mrow><fb:msub><fb:mrow><fb:mi>SU</fb:mi><fb:mo stretchy="false">(</fb:mo><fb:mn>3</fb:mn><fb:mo stretchy="false">)</fb:mo></fb:mrow><fb:mrow><fb:mi>F</fb:mi></fb:mrow></fb:msub></fb:mrow></fb:math>-breaking effects, but 1000% <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mrow><jb:msub><jb:mrow><jb:mi>SU</jb:mi><jb:mo stretchy="false">(</jb:mo><jb:mn>3</jb:mn><jb:mo stretchy="false">)</jb:mo></jb:mrow><jb:mrow><jb:mi>F</jb:mi></jb:mrow></jb:msub></jb:mrow></jb:math> breaking is required. In this paper, we extend this analysis to include decays in which there is an <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:mi>η</nb:mi></nb:math> and/or <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"><pb:msup><pb:mi>η</pb:mi><pb:mo>′</pb:mo></pb:msup></pb:math> meson in the final state. We now find that the combined fit exhibits a <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"><rb:mn>4.1</rb:mn><rb:mi>σ</rb:mi></rb:math> discrepancy with the <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"><tb:mrow><tb:msub><tb:mrow><tb:mi>SM</tb:mi></tb:mrow><tb:mrow><tb:msub><tb:mrow><tb:mi>SU</tb:mi><tb:mo stretchy="false">(</tb:mo><tb:mn>3</tb:mn><tb:mo stretchy="false">)</tb:mo></tb:mrow><tb:mrow><tb:mi>F</tb:mi></tb:mrow></tb:msub></tb:mrow></tb:msub></tb:mrow></tb:math>, and 1000% <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"><xb:mrow><xb:msub><xb:mrow><xb:mi>SU</xb:mi><xb:mo stretchy="false">(</xb:mo><xb:mn>3</xb:mn><xb:mo stretchy="false">)</xb:mo></xb:mrow><xb:mrow><xb:mi>F</xb:mi></xb:mrow></xb:msub></xb:mrow></xb:math>-breaking effects are still required to explain the data. These results are rigorous, group-theoretically—no theoretical assumptions have been made. But when one adds some theoretical input motivated by QCD factorization, the discrepancy with the <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"><bc:mrow><bc:msub><bc:mrow><bc:mi>SM</bc:mi></bc:mrow><bc:mrow><bc:msub><bc:mrow><bc:mi>SU</bc:mi><bc:mo stretchy="false">(</bc:mo><bc:mn>3</bc:mn><bc:mo stretchy="false">)</bc:mo></bc:mrow><bc:mrow><bc:mi>F</bc:mi></bc:mrow></bc:msub></bc:mrow></bc:msub></bc:mrow></bc:math> grows to <fc:math xmlns:fc="http://www.w3.org/1998/Math/MathML" display="inline"><fc:mn>4.9</fc:mn><fc:mi>σ</fc:mi></fc:math>.