The parton bubble model compared to central Au Au collisions (0% to 5%) at √ s $_{NN}$=200 GeV. arXiv:1001.1132v1 [nucl-th] 7 Jan 2010 R.S. Longacre 1 $^{1}$Brookhaven National Laboratory, Upton, New York 11973 (Dated: November 13, 2018) In an earlier paper we developed a Parton Bubble Model (PBM) for RHIC, high-energy heavy-ion collisions. PBM was based on a substructure of a ring of localized bubbles (gluonic hot spots) which initially contain 3-4 partons composed of almost entirely gluons. The bubble ring was perpendicular to the collider beam direction, centered on the beam, at midrapidity, and located on the expanding fireball surface of Au Au central collisions (0-10%) at √ s NN =200 GeV. The bubbles emitted cor- related particles at kinetic freezeout, leading to a lumpy fireball surface. For a selection of charged particles (0.8 GeV/c < p t < 4.0 GeV/c), the PBM reasonably quantitatively (within a few percent) explained high precision RHIC experimental correlation analyses in a manner which was consistent with the small observed HBT source size in this transverse momentum range. We demonstrated that surface emission from a distributed set of surface sources (as in the PBM) was necessary to obtain this consistency. In this paper we give a review of the above comparison to central Au Au collisions. The bubble formation can be associated with gluonic objects predicted by a Glasma Flux Tube Model (GFTM) that formed longitudinal flux tubes in the transverse plane of two colliding sheets of Color Glass Condensate (CGC), which pass through one another. These sheets create boost invariant flux tubes of longitudinal color electric and magnetic fields. A blast wave gives the tubes near the surface transverse flow in the same way it gave transverse flow to the bubbles in the PBM. In this paper we also consider the equivalent characteristics of the PBM and GFTM and connect the two models. In the GFTM the longitudinal color electric and magnetic fields have a non-zero topological charge density $_{F}$˜ F . These fields cause a local strong CP violation which effects charged particle production coming from quarks and anti-quarks created in the tube or bubble. PACS numbers: 25.75.Nq, 11.30.Er, 25.75.Gz, 12.38.Mh them. Our interest in and the eventual development of the PBM goes back many years to the early nineteen eighties. Van Hove’s work[1] in the early eighties considered the bubbles as small droplets of quark- gluon plasma (QGP) assumed to be produced in ultra-relativistic collisions of hadrons and/or nu- clei. His work recognized that experimental detec- tors only see what is emitted in the final state at kinetic freezeout. Therefore final state predictions of his string model work on plasma bubbles or any other theory required specific convincing predictions that are observable in the final state which can be measured by experiment. His work predicted that the final state rapidity distribution dn/dy of hadrons would exhibit isolated maxima of width Δ y ∼ 1 (sin- gle bubble) or rapidity bumps of a few units (due to those cases producing a few bubbles). These rapid- ity regions would also contain traditional signals of QGP formation. Even this early work by Van Hove needed his bubbles near the surface of the final state fireball in order to experimentally measure the par- ticles emitted in the final state at kinetic freezeout. We and other searched for these Van Hove bubbles, but no one ever found any significant evidence for When we considered the RHIC quantum interfer- ence data in 2000[4] it became clear that the fire- ball surface was rapidly moving outward. This im- plied a very large phase space region covered by the fireball, and also implied that it would be very un- likely for there to be only one isolated bubble (small source size) with a large amount of energy sitting on the surface. It seemed more likely that there Our next paper[2] was our final attempt to make a theoretical treatment of the single bubble case (sim- ilar to the Van Hove case) which could be experi- mentally verified. It is possible that with enough statistics one in principle could find single to a few bubble events. We developed a number of event gen- erators which could possibly provide evidence for striking signals resulting from these bubbles. One should note that in that paper we had included in Sec. 11 mathematical expressions describing how charged pions are effected by strong color electric and color magnetic fields which are present and par- allel in a CP-odd bubble of metastable vacuum. This section was motivated by the work of Kharzeev and Pisarski[3]. For example eq. 3-4 of the section show the boosts of the π + and the π − we estimated. Thus in 2000 we were already interested in and were in- vestigating and publishing predictions for this phe- nomenon. I. PARTON BUBBLE MODEL DEVELOPMENT