Understanding Large Localized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>C</mml:mi> <mml:mi>P</mml:mi> </mml:math> Violation in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:ms

We utilize the universality of pion-pion ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>π</a:mi> <a:mi>π</a:mi> </a:math> ) final-state interactions at small invariant masses to understand the enhanced localized <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mi>C</c:mi> <c:mi>P</c:mi> </c:mrow> </c:math> violation in <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:mi>π</e:mi> <e:mo>+</e:mo> </e:msup> <e:msup> <e:mi>π</e:mi> <e:mo>−</e:mo> </e:msup> </e:math> , using a dispersive approach. From a fit to the integrated <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mrow> <h:mi>C</h:mi> <h:mi>P</h:mi> </h:mrow> </h:math> -asymmetry data, we successfully predict the Dalitz-plot kinematic distribution of the asymmetry in the low-energy <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mi>π</j:mi> <j:mi>π</j:mi> </j:math> region, including the large localized <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mrow> <l:mi>C</l:mi> <l:mi>P</l:mi> </l:mrow> </l:math> violation recently observed by LHCb. An essential role is played by the contributions of isospin 2. This formalism, whose parameters have a physical meaning, can be adapted straightforwardly to other systems with <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mrow> <n:mi>C</n:mi> <n:mi>P</n:mi> </n:mrow> </n:math> violation enhanced by final-state interactions.