CP -odd window into long distance dynamics in rare semileptonic B decays

We consider the combined measurements of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>C</a:mi><a:mi>P</a:mi></a:math>-averaged decay rates and direct <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>C</c:mi><c:mi>P</c:mi></c:math> asymmetries of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>B</e:mi><e:mo>±</e:mo></e:msup><e:mo stretchy="false">→</e:mo><e:msup><e:mi>K</e:mi><e:mo>±</e:mo></e:msup><e:msup><e:mo>ℓ</e:mo><e:mo>+</e:mo></e:msup><e:msup><e:mo>ℓ</e:mo><e:mo>−</e:mo></e:msup></e:math> and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msup><h:mi>B</h:mi><h:mo>±</h:mo></h:msup><h:mo stretchy="false">→</h:mo><h:msup><h:mi>π</h:mi><h:mo>±</h:mo></h:msup><h:msup><h:mo>ℓ</h:mo><h:mo>+</h:mo></h:msup><h:msup><h:mo>ℓ</h:mo><h:mo>−</h:mo></h:msup></h:math> to probe (nonlocal) four-quark operator matrix element contributions to rare semileptonic <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>B</k:mi></k:math> meson decays. We also explore how their effects could be in principle disentangled from possible local new physics effects using <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>U</m:mi></m:math>-spin relations. To this end, we construct a ratio of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>C</o:mi><o:mi>P</o:mi></o:math>-odd decay rate differences which are exactly predicted within the standard model in the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>U</q:mi></q:math>-spin limit, while the leading <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>U</s:mi></s:math>-spin breaking effects can also be systematically calculated. Our results motivate binned measurements of the direct <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>C</u:mi><u:mi>P</u:mi></u:math> asymmetry in <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msup><w:mi>B</w:mi><w:mo>±</w:mo></w:msup><w:mo stretchy="false">→</w:mo><w:msup><w:mi>π</w:mi><w:mo>±</w:mo></w:msup><w:msup><w:mo>ℓ</w:mo><w:mo>+</w:mo></w:msup><w:msup><w:mo>ℓ</w:mo><w:mo>−</w:mo></w:msup></w:math> as well as dedicated theoretical estimates of <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mi>U</z:mi></z:math>-spin breaking both in local form factors as well as in four-quark matrix elements.