Spin relaxation rate for baryons in a thermal pion gas

We study the relaxation dynamics of the spin polarization of baryons (nucleon and <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi mathvariant="normal">Λ</a:mi></a:math> baryon), in a thermal pion gas as a simple model of the hadronic phase of the QCD plasma produced in relativistic heavy-ion collisions. For this purpose, we formulate the quantum kinetic theory for the spin density matrix of baryons in the leading order of the gradient expansion. Considering the baryon-pion elastic scattering processes as the dominant interaction between baryons and thermal pions, we compute the spin relaxation rate of nucleons and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi mathvariant="normal">Λ</c:mi></c:math> baryons in a pion gas up to temperature 200 MeV. In the case of nucleons, we evaluate the spin relaxation rate in the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>s</e:mi></e:math>-channel resonance approximation, based on the known experimental data on <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi mathvariant="normal">Δ</f:mi></f:math> resonances. We also estimate the spin relaxation rate for <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mi mathvariant="normal">Λ</h:mi></h:math> baryons, based on experimental inputs and theoretical models for the low-energy <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:mi mathvariant="normal">Λ</j:mi><j:mi>π</j:mi></j:mrow></j:math> scattering, including the chiral perturbation theory. Published by the American Physical Society 2024