Isospin breaking corrections in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mi>π</mml:mi></mml:mrow></mml:math> production in tau decays and <mml:math xmlns:mml="http://www.w3.org/1998/Ma

We revisit the isospin-breaking corrections relating the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>e</a:mi><a:mo>+</a:mo></a:msup><a:msup><a:mi>e</a:mi><a:mo>−</a:mo></a:msup></a:math> hadronic cross section and the tau decay spectral function, focusing on the dipion channel, that gives the dominant contribution to the hadronic vacuum polarization piece of the muon <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>g</c:mi><c:mo>−</c:mo><c:mn>2</c:mn></c:math>. We test different types of electromagnetic and weak form factors and show that both, the Gounaris-Sakurai and a dispersive-based approach, describe accurately <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>τ</e:mi></e:math> lepton and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi>e</g:mi><g:mo>+</g:mo></g:msup><g:msup><g:mi>e</g:mi><g:mo>−</g:mo></g:msup></g:math> data (less when KLOE measurements are included in the fits) and comply reasonably well with analyticity constraints. From these results we obtain the isospin-breaking contribution to the conserved vector current (CVC) prediction of the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi>BR</i:mi></i:mrow><i:mo stretchy="false">(</i:mo><i:mi>τ</i:mi><i:mo stretchy="false">→</i:mo><i:mi>π</i:mi><i:mi>π</i:mi><i:msub><i:mi>ν</i:mi><i:mi>τ</i:mi></i:msub><i:mo stretchy="false">)</i:mo></i:math> and to the <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mn>2</n:mn><n:mi>π</n:mi></n:math> hadronic vacuum polarization (HVP) contribution to the muon <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi>g</p:mi><p:mo>−</p:mo><p:mn>2</p:mn></p:math>, in agreement with previous determinations and with similar precision. Our results abound in the utility of using tau data-based results in the updated data-driven prediction of the muon <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>g</r:mi><r:mo>−</r:mo><r:mn>2</r:mn></r:math> in the Standard Model.