Matching between collinear twist-3 and TMD fragmentation function contributions to polarized hyperon production in SIDIS

We investigate the consistency between the collinear twist-3 factorization and the transverse-momentum-dependent (TMD) factorization for the transversely polarized hyperon production in semi-inclusive deep inelastic scattering, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>e</a:mi> <a:mi>p</a:mi> <a:mo stretchy="false">→</a:mo> <a:mi>e</a:mi> <a:msup> <a:mrow> <a:mi mathvariant="normal">Λ</a:mi> </a:mrow> <a:mrow> <a:mo stretchy="false">↑</a:mo> </a:mrow> </a:msup> <a:mi>X</a:mi> </a:mrow> </a:math> . In particular, we focus on the contributions from the twist-3 fragmentation functions (FFs) and the TMD polarizing FF in the region of the hyperon’s intermediate transverse momentum <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msub> <f:mi>P</f:mi> <f:mi>T</f:mi> </f:msub> </f:math> , <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msub> <h:mi mathvariant="normal">Λ</h:mi> <h:mi>QCD</h:mi> </h:msub> <h:mo>≪</h:mo> <h:msub> <h:mi>P</h:mi> <h:mi>T</h:mi> </h:msub> <h:mo>≪</h:mo> <h:mi>Q</h:mi> </h:math> , where both frameworks are valid. In this region the polarizing FF can be expressed in terms of the twist-3 FFs including the purely gluonic ones, and the resulting TMD factorization formula in the Ji-Ma-Yuan scheme for <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>e</k:mi> <k:mi>p</k:mi> <k:mo stretchy="false">→</k:mo> <k:mi>e</k:mi> <k:msup> <k:mi mathvariant="normal">Λ</k:mi> <k:mo stretchy="false">↑</k:mo> </k:msup> <k:mi>X</k:mi> </k:math> agrees with the small- <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:msub> <p:mi>P</p:mi> <p:mi>T</p:mi> </p:msub> </p:math> limit of the corresponding twist-3 cross section. This matching of the two calculations indicates that the two frameworks describe the same effect in quantum chromodynamics (QCD) and provide complementary frameworks for the process in different kinematic regions.