Phase of the electromagnetic form factor of the pion

Abstract

We employ a dispersion relation that allows us to recover the phase of the electromagnetic form factor of the pion from its absolute value above threshold. Compared to alternative approaches building on the phase, this approach builds on experimental input directly accessible at colliders. Employing the precise datasets from the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msup> <a:mrow> <a:mi>e</a:mi> </a:mrow> <a:mrow> <a:mo>+</a:mo> </a:mrow> </a:msup> <a:msup> <a:mrow> <a:mi>e</a:mi> </a:mrow> <a:mrow> <a:mo>−</a:mo> </a:mrow> </a:msup> <a:mo stretchy="false">→</a:mo> <a:msup> <a:mrow> <a:mi>π</a:mi> </a:mrow> <a:mrow> <a:mo>+</a:mo> </a:mrow> </a:msup> <a:msup> <a:mrow> <a:mi>π</a:mi> </a:mrow> <a:mrow> <a:mo>−</a:mo> </a:mrow> </a:msup> </a:mrow> </a:math> reaction, we obtain the phase of the electromagnetic form factor up to 2.5 GeV, well beyond standard dispersive approaches. In addition, we separate the isovector and isoscalar components, that allows us to extract the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi>P</d:mi> </d:math> -wave <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mi>π</f:mi> <f:mi>π</f:mi> </f:math> phase shift. We also provide relevant results, including the radius of the form factor and bounds in the spacelike region. Last, but not least, the study assess potential systematic uncertainties from the interpolation method and potential zeros of the form factor. Published by the American Physical Society 2024

Topics & Concepts