Spontaneous $CP$ violating quark scattering from asymmetric $Z(3)$ interfaces in the quark-gluon plasma

In this paper, we extend our earlier study of the spontaneous $CP$ violating scattering of quarks and antiquarks from QCD $Z(3)$ domain walls for the situation when these walls have asymmetric profiles of the Polyakov loop order parameter $l(x)$. Dynamical quarks lead to the explicit breaking of $Z(3)$ symmetry, which lifts the degeneracy of the $Z(3)$ vacua arising from spontaneous breaking of the $Z(3)$ symmetry in the quark-gluon plasma phase. The resulting domain walls have an asymmetric profile of $l(x)$ (under the reflection $x\to -x$ for a domain wall centered at the origin). We calculate the background gauge field profile $A_0$ associated with this domain wall profile. Interestingly, even with the asymmetric $l(x)$ profile, quark-antiquark scattering from the corresponding gauge field configuration does not reflect this asymmetry. We show that the expected asymmetry in scattering arises when we include the effect of the asymmetric profile of $l(x)$ on the effective mass of quarks and antiquarks and calculate the resultant scattering. We discuss the effects of such asymmetric $Z(3)$ walls in generating quark and antiquark density fluctuations in cosmology, and in relativistic heavy-ion collisions, e.g., event-by-event baryon fluctuations.

Figure 1

Plot of $|l(x)|$ obtained from an energy minimization for $b_1=0.0$ and $T=400\mathrm{MeV}$. The corresponding $A_0$ configuration is on the right. The $A_0$ profile fits well with a tanh function.

Figure 2

Plot of $|l(x)|$ obtained from the energy minimization for $b_1=0.645$ (the solid curve). On the left is the initial trial configuration. The final configuration is on the right.

Figure 3

Plot of the calculated $A_0$ and the fitted profile [$A_0(x)=p\tanh (qx+r)+s$] for $b_1=0.03$ and 0.645.