Unlocking time-dependent CP violation without signal vertexing at B factories

We present a method to measure time-dependent <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>C</a:mi><a:mi>P</a:mi></a:mrow></a:math> violation in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>B</c:mi><c:mn>0</c:mn></c:msup></c:math> decays produced in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mrow><e:mi mathvariant="normal">ϒ</e:mi><e:mo stretchy="false">(</e:mo><e:mn>4</e:mn><e:mi>S</e:mi><e:mo stretchy="false">)</e:mo></e:mrow><e:mo stretchy="false">→</e:mo><e:msup><e:mrow><e:mi>B</e:mi></e:mrow><e:mrow><e:mn>0</e:mn></e:mrow></e:msup><e:mrow><e:msup><e:mrow><e:mover accent="true"><e:mrow><e:mi>B</e:mi></e:mrow><e:mrow><e:mo stretchy="false">¯</e:mo></e:mrow></e:mover></e:mrow><e:mrow><e:mn>0</e:mn></e:mrow></e:msup></e:mrow></e:mrow></e:math> events at <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>B</m:mi></m:math> factories without reconstructing the signal decay vertex. The method exploits the sensitivity of the tag <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mover accent="true"><o:mi>B</o:mi><o:mo stretchy="false">¯</o:mo></o:mover><o:mn>0</o:mn></o:msup></o:math> decay time to <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mrow><s:mi>C</s:mi><s:mi>P</s:mi></s:mrow></s:math> violation in the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msup><u:mi>B</u:mi><u:mn>0</u:mn></u:msup></u:math> signal. It relies on a compact <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msup><w:mi>e</w:mi><w:mo>+</w:mo></w:msup><w:msup><w:mi>e</w:mi><w:mo>−</w:mo></w:msup></w:math> interaction region and excellent vertex resolution, which enable precise measurement of the displacement between production and decay vertices of the tag meson. We study an application to <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msup><y:mi>B</y:mi><y:mn>0</y:mn></y:msup><y:mo stretchy="false">→</y:mo><y:msup><y:mi>π</y:mi><y:mn>0</y:mn></y:msup><y:msup><y:mi>π</y:mi><y:mn>0</y:mn></y:msup></y:math> decays using a simplified simulation that approximates the conditions of the Belle II experiment at the SuperKEKB collider. Our approach achieves a sensitivity on mixing-induced <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:mrow><bb:mi>C</bb:mi><bb:mi>P</bb:mi></bb:mrow></bb:math> violation that would require 20 times larger samples with standard approaches. When incorporated into the <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mi>B</db:mi><db:mo stretchy="false">→</db:mo><db:mi>π</db:mi><db:mi>π</db:mi></db:math> isospin analysis, the expected results would reduce the degeneracy of <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msub><gb:mi>ϕ</gb:mi><gb:mn>2</gb:mn></gb:msub></gb:math> solutions and significantly increase precision. This work opens a path to previously inaccessible <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mrow><ib:mi>C</ib:mi><ib:mi>P</ib:mi></ib:mrow></ib:math>-violation studies enhancing and accelerating the reach of Belle II and future flavor physics programs.