Macroscopic Chirality Fluctuations in Heavy Ion Collisions should induce CP forbidden Decays

Abstract

f large fluctuations of quark chirality occur in heavy ion collisions, they result in macroscopic CP-odd "spots" of the so called theta-vacua, with a non-zero $\theta(x)$. We consider particular decays of mesons, CP-forbidden in the vacuum with zero $\theta$, like $\eta\to \pi\pi$. We evaluate their rates for such decays near hadronic freezeout. These rates, as well as charge asymmetries already observed, are proportional to square of the CP-violating parameter $<\theta^2>$ averaged over the fireball and events. With such input, we found that the forbidden decay rates are likely to be orders of magnitude larger than CP-allowed ones. We further estimated that up to about one per mill of $\eta$ mesons produced in heavy ion collisions should decay in this way. We further discuss how those can be observed. We argue using STAR data on charge asymmetries for AuAu and CuCu collisions that the size of CP-odd spots at freezeout is as large as Cu nuclei: this fortunate fact (not explained so far by itself) suggests that the two-pion invariant mass is modified by only about a percent, which is comparable to experimental resolution. If so, we think experimental observation of these decays is within the reach of current dataset. If those decays are found, it would confirm that CP-odd interpretation of charge asyymetry is correct, even without complication related to geometry, impact parameter or magnetic field induced on the fireball.