Relativistic spin dynamics for vector mesons

Abstract

We propose a relativistic theory for spin density matrices of vector mesons based on Kadanoff-Baym equations in the closed-time-path formalism. The theory puts the calculation of spin observables such as the spin density matrix element <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>ρ</a:mi><a:mn>00</a:mn></a:msub></a:math> for vector mesons on a solid ground. Within the theory we formulate <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>ρ</c:mi><c:mn>00</c:mn></c:msub></c:math> for <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>ϕ</e:mi></e:math> mesons into a factorization form in separation of momentum and spacetime variables. We argue that the main contribution to <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>ρ</g:mi><g:mn>00</g:mn></g:msub></g:math> at lower energies should be from the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>ϕ</i:mi></i:math> fields that can polarize the strange quark and antiquark in the same way as electromagnetic fields. The key observation is that there is correlation inside the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>ϕ</k:mi></k:math> meson wave function between the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>ϕ</m:mi></m:math> field that polarizes the strange quark and that polarizes the strange antiquark. This is reflected by the fact that the contributions to <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>ρ</o:mi><o:mn>00</o:mn></o:msub></o:math> are all in squares of fields that are nonvanishing even if the fields may strongly fluctuate in spacetime. The fluctuation of strong force fields can be extracted from <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>ρ</q:mi><q:mn>00</q:mn></q:msub></q:math> of unflavored vector mesons as links to fundamental properties of quantum chromodynamics. Published by the American Physical Society 2024