Transverse spin polarization as a novel probe of the medium-induced transverse-momentum-broadening effect

The transverse polarization of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi mathvariant="normal">Λ</a:mi> </a:mrow> </a:math> hyperons within unpolarized jets is encoded in the transverse-momentum-dependent fragmentation function <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:msubsup> <d:mi>D</d:mi> <d:mrow> <d:mn>1</d:mn> <d:mi>T</d:mi> </d:mrow> <d:mo>⊥</d:mo> </d:msubsup> <d:mo stretchy="false">(</d:mo> <d:mi>z</d:mi> <d:mo>,</d:mo> <d:msub> <d:mi mathvariant="bold-italic">p</d:mi> <d:mo>⊥</d:mo> </d:msub> <d:mo>,</d:mo> <d:msup> <d:mi>μ</d:mi> <d:mn>2</d:mn> </d:msup> <d:mo stretchy="false">)</d:mo> </d:math> . In the vacuum environment, the QCD evolution of this transverse-momentum-dependent fragmentation function is governed by the Collins-Soper equation. However, in the presence of the quark-gluon plasma medium, the jet-medium interaction induces the transverse-momentum-broadening effect that modifies the QCD evolution. As a result, the transverse spin polarization of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi mathvariant="normal">Λ</i:mi> </i:math> hyperons in relativistic heavy-ion collisions differs from that in <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mi>p</l:mi> <l:mi>p</l:mi> </l:math> collisions. We demonstrate that this difference serves as a sensitive probe for studying jet-medium interaction, offering a novel perspective through the spin degree of freedom.