Quasiclassical Gluon Fields and Low’s Soft Theorem at Small Momentum-Fraction x

In the high-energy limit, soft gluons can be approximately described by quasiclassical gluon fields. It is well known that the gluon field is a pure gauge field on the transverse plane at eikonal order. We derived the complete next-to-eikonal order solutions of the classical Yang-Mills equations for soft gluons in the dense nuclear regime. Utilizing these solutions, it is shown that Low’s soft theorem at small <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>x</a:mi></a:math> can be obtained by considering off-diagonal matrix elements of quasiclassical chromoelectric field between single-gluon states in the dilute regime. We further propose on extending Low’s soft theorem at small <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>x</c:mi></c:math> to incorporate the effects of gluon saturation in the dense regime. Published by the American Physical Society 2024