A generalized picture of colour decoherence in dense QCD media

A bstract We revisit the calculation of the soft gluon emission probability off a colour-singlet $$ q\overline{q} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> <mml:mover> <mml:mi>q</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> system that evolves in a quark-gluon plasma. The $$ q\overline{q} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> <mml:mover> <mml:mi>q</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> antenna is created in the presence of a medium and then emits a soft gluon outside. The gluon emission probability is modified with respect to the vacuum baseline due to interactions with the medium during the formation of the antenna and its propagation. Previous studies disregarded the former effect and found that the medium modification to the interference pattern of the antenna was controlled by the so-called critical angle θ c , that exclusively depends on medium properties. We find that accounting for medium interactions during the antenna formation enhances the total rate of emissions off the $$ q\overline{q} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> <mml:mover> <mml:mi>q</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> antenna. Interestingly, it also promotes the notion of a critical angle to a dynamic quantity, denoted $$ {\overset{\sim }{\theta}}_c $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>θ</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mi>c</mml:mi> </mml:msub> </mml:math> , that depends on both the medium and the antenna properties and is thus different for every splitting. As a consequence, depending on the region of parameter space, colour decoherence can either be delayed or accelerated with respect to previous estimates.