Survival of Back-to-Back Correlations for Finite Expanding Fireballs

In the late 1990’s, Back-to-Back Correlations (BBC) of boson-antiboson pairs were predict to exist if the particles masses were modified in the hot and dense medium[ 1], expected to be formed in high energy nucleus-nucleus collisions. The BBC are related to in-medium mass-modification and squeezing of the quanta involved. Not much longer after that, it was also shown that an analogous BBC existed between fermion-antifermion pairs with medium-modified masses[ 2]. A similar formalism is applicable to both BBC cases, related to the Bogoliubov-Valatin transformations of in-medium and asymptotic operators. Both the bosonic (bBBC) and the fermionic (fBBC) Back-to-Back Correlations are positive and have unlimited magnitude, thus differing from the identical-particle correlations, also known as HBT (Hanbury Brown & Twiss) correlations, which are limited for both cases, being negative in the fermionic sector. BBC were expected to be significant for pT < 2 GeV/c. Nevertheless, already in the Ref.[ 1], it was shown that, if the emission process is not sudden, even a short duration of particle emission significantly suppresses the BBC magnitude. On the other hand, the effects of finite system sizes and of collective phenomena had not been studied yet. Thus, for testing the survival and magnitude of the effect in more realistic situations, we study the BBC when mass-modification occurs in a finite sized, thermalized medium, considering a non-relativistically expanding fireball with short emission duration, and evaluating the width of the back-to-back correlation function. We show that the BBC signal indeed survives the expansion and flow effects, with sufficient magnitude to be observed at RHIC. Some preliminary results are discussed here and illustrated for particular cases. Our analysis assumes the validity of local thermalization and hydrodynamics up to the system freeze-out. We also consider H = H0− ∫ dxdyφ(x)δM(x−y)φ(y) as an effective in-medium Hamiltonian, where the first term is the asymptotic (free) Hamiltonian in the rest frame of the matter, and the second term describes the medium modifications. The