Estimation of electric field in intermediate-energy heavy-ion collisions

We estimate the spacetime profile of the electric field in head-on heavy-ion collisions at intermediate collision energies <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msqrt><a:msub><a:mi>s</a:mi><a:mrow><a:mi>N</a:mi><a:mi>N</a:mi></a:mrow></a:msub></a:msqrt><a:mo>=</a:mo><a:mi mathvariant="script">O</a:mi><a:mrow><a:mo>(</a:mo><a:mn>3</a:mn><a:mo>–</a:mo><a:mn>10</a:mn><a:mspace width="0.28em"/><a:mi>GeV</a:mi><a:mo>)</a:mo></a:mrow></a:mrow></a:math>. Using a hadronic cascade model (JAM; Jet AA Microscopic transport model), we numerically demonstrate that the produced field has strength <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>e</d:mi><d:mi>E</d:mi><d:mo>=</d:mo><d:mi mathvariant="script">O</d:mi><d:mrow><d:mo>(</d:mo></d:mrow><d:msup><d:mrow><d:mo>(</d:mo><d:mn>30</d:mn><d:mo>–</d:mo><d:mn>60</d:mn><d:mspace width="0.28em"/><d:mi>MeV</d:mi><d:mo>)</d:mo></d:mrow><d:mn>2</d:mn></d:msup><d:mrow><d:mo>)</d:mo></d:mrow></d:mrow></d:math>, which is supercritical to the Schwinger limit of QED and is non-negligibly large compared even to the hadron/QCD scale, and survives for a long time <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>τ</g:mi><g:mo>=</g:mo><g:mi mathvariant="script">O</g:mi><g:mo>(</g:mo><g:mn>10</g:mn><g:mspace width="0.28em"/><g:mi>fm</g:mi><g:mo>/</g:mo><g:mi>c</g:mi><g:mo>)</g:mo></g:mrow></g:math> due to the baryon stopping. We show that the produced field is nonperturbatively strong in the sense that the nonperturbativity parameters (e.g., the Keldysh parameter) are sufficiently large. This is in contrast to high-energy collisions <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:msqrt><j:msub><j:mi>s</j:mi><j:mrow><j:mi>N</j:mi><j:mi>N</j:mi></j:mrow></j:msub></j:msqrt><j:mo>≳</j:mo><j:mn>100</j:mn><j:mspace width="0.28em"/><j:mi>GeV</j:mi></j:mrow></j:math>, where the field is extremely short-lived and hence is perturbative. Our results imply that the electromagnetic field may have phenomenological impacts on hadronic/QCD processes in intermediate-energy heavy-ion collisions and that heavy-ion collisions can be used as a new tool to explore strong-field physics in the nonperturbative regime. Published by the American Physical Society 2024