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/Math/MathML" display="inline"> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>−</mml:mo> </mml:msup> </mml:math> annihilation: Consequences for the muon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>g</mml:mi> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:math> and conserved vector current tests

Abstract

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.

Topics & Concepts