Phase-space integrals through Mellin-Barnes representation

This letter introduces a novel analytical approach to calculating phase-space integrals, crucial for precision in particle physics. We develop a method to compute angular components using multifold Mellin-Barnes integrals, yielding results in terms of Goncharov polylogarithms for integrals involving three denominators. Our results include expressions for massless momenta to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="script">O</a:mi><a:mo stretchy="false">(</a:mo><a:msup><a:mi>ε</a:mi><a:mn>2</a:mn></a:msup><a:mo stretchy="false">)</a:mo></a:math> and for massive momentum to <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi mathvariant="script">O</f:mi><f:mo stretchy="false">(</f:mo><f:mi>ε</f:mi><f:mo stretchy="false">)</f:mo></f:math>. We derive recursion relations that reduce integrals with higher powers of denominators to simpler ones. We detail how to combine the angular part with the radial one which requires a careful handling of singularities.