What Is the Renormalized Gluon Dressing Function?

[RicardoMP]

Consider, for example, the gluon propagator $$D^{\mu\nu}(q)=-\frac{i}{q^2+i\epsilon}[D(q^2)T^{\mu\nu}_q+\xi L^{\mu\nu}_q]$$

What exactly is the renormalized gluon dressing function ##D(q^2)## and what is its definition? My interest is in knowing if I can then write the bare version of this function simply as ##D_B(q^2)=Z_AD(q^2)##, where ##Z_A## is the renormalization constant for the gluon field (##A_B=Z_A^{\frac{1}{2}}A##).

 

[azntoon]

The renormalized gluon dressing function ##D(q^2)## is defined as the inverse of the renormalized gluon propagator, which can be written as: $$D^{\mu\nu}(q)=-i[D(q^2)T^{\mu\nu}_q+\xi L^{\mu\nu}_q]$$where ##T^{\mu\nu}_q## and ##L^{\mu\nu}_q## are the transverse and longitudinal tensors, respectively, and ##\xi## is the gauge parameter. The renormalized gluon dressing function is then defined as$$D(q^2)=\frac{1}{-i(T^{\mu\nu}_q+\xi L^{\mu\nu}_q)D^{\mu\nu}(q)}$$Yes, you can write the bare version of the function as ##D_B(q^2)=Z_AD(q^2)##, where ##Z_A## is the renormalization constant for the gluon field (##A_B=Z_A^{\frac{1}{2}}A##).