17 VII. STRONG CP VIOLATIONS OR CHERN-SIMONS TOPOLOGICAL CHARGE A. The Source $_{F}$˜ F . they will pickup or lose transverse momentum after the bubble is boosted radial outwards due to radial flow of the blast wave. These changes in p t will be transmitted to the π + π − pairs. It is important to note that the CP violating asym- metries in π + and π − momenta arise through the Witten-Wess-Zumino [34, 35] term. The quarks and anti quarks which, later form the π + and π − , di- rectly respond to the color electric and color mag- netic fields and receive their boosts at the quark and anti quark level before they are pions. These boosts are transmitted to the pions at hadronization. Thus no external magnetic field is required in the method- ology followed in this paper. The following references demonstrate this: [2, 3, 33, 36]. To represent the color electric field effect we as- sume as the first step for the results being shown in this paper; that we generate bubbles which have an added boost of 100 MeV/c to the quarks in the longitudinal momentum which represents the color electric effect. The π + and the π − which form a pair are boosted in opposite directions along the beam axis. In a given bubble all the boosts are the same but vary in direction from bubble to bubble. For the color magnetic field effect, we give 100 MeV/c boosts to the transverse momentum in an opposite way to the π + and the π − which form a pair. For each pair on one side of a bubble one of the charged pions boost is increased and the other is decreased. While on the other side of the bubble the pion for which the boost was increased is now decreased and the pion which was decreased is now increased by the 100 MeV/c. All pairs for a given bubble are treated in the same way however each bubble is random on the sign of the pion which is chosen to be boosted on a given side. This addition to our model is used in the simulations of the following subsections. C. Color electric field pionic measure. B. Pionic measures of CP violation. Above we saw that pairs of positive and nega- tive pions should show a charge separation along the beam axis due to a boost in longitudinal momen- tum caused by the color electric field. A measure of this separation should be a difference in the pseudo- rapidity (Δ η ) of the opposite sign pairs. This Δ η measure has a well defined sign since we defined this difference measuring from the π − to the π $^{+}$. In or- der to form a correlation we must pick two pairs for comparison. The pairs have to come from the same bubble (a final state of an expanded flux tube) since we have shown by investigating the events generated by the model that pairs originating from different bubbles will not show this correlation. Therefore we require the π + and the π − differ by 20 ◦ or less in φ . The glasma flux tube model (GFTM)[17] consid- ers the wavefunctions of the incoming projectiles, form sheets of CGC[18] at high energies that collide, interact, and evolve into high intensity color electric and magnetic fields. This collection of primordial fields is the Glasma[19, 20]. Initially the Glasma is composed of only rapidity independent longitudi- nal (along the beam axis) color electric and mag- netic fields. These longitudinal color electric and magnetic fields generate topological Chern-Simons charge[21] through the F ˜ F term and becomes a source of CP violation. How much of these longi- tudinal color electric and magnetic fields are still present in the surface flux tubes when they have been pushed by the blast wave is a speculation of this paper for measuring strong CP violation? The color electric field which points along the flux tube axis causes an up quark to be accelerated in one di- rection along the beam axis, while the anti-up quark is accelerated in the other direction. So when a pair of quarks and anti-quarks are formed they separate along the beam axis leading to a separated π + π − pair along this axis. The color magnetic field which also points along the flux tube axis (which is paral- lel to the beam axis) causes an up quark to rotate around the flux tube axis in one direction, while the anti-up quark is rotated in the other direction. So when a pair of quarks and anti-quarks are formed The strong CP problem remains one of the most outstanding puzzles of the Standard Model. Even though several possible solutions have been put for- ward it is not clear why CP invariance is respected by the strong interaction. It was shown however through a theorem by Vafa-Witten[32] that the true ground state of QCD cannot break CP. The part of the QCD Lagrangian that breaks CP is related to the gluon-gluon interaction term F ˜ F . The part of F ˜ F related to CP violations can be separated into a separate term which then can be varied by mul- tiplying this term by a parameter called θ . For the true QCD ground state θ = 0 (Vafa-Witten theo- rem). In the vicinity of the deconfined QCD vacuum metastable domains[33] θ non-zero could exist and not contradict the Vafa-Witten theorem since these are not the QCD ground state. The metastable do- mains CP phenomenon would manifest itself in spe- cific correlations of pion momenta[3, 33].