Abstract
Two-particle momentum correlations of $N$ identical bosons are studied in the quantum canonical ensemble. We define the latter as a properly selected subensemble of events associated with the grand canonical ensemble which is characterized by a constant temperature and a harmonic-trap chemical potential. The merits of this toy model are that it can be solved exactly, and that it demonstrates some interesting features revealed recently in small systems created in $p+p$ collisions at the LHC. We find that partial coherence can be observed in particle emission from completely thermal ensembles of events if instead of inclusive measurements one studies the two-boson distribution functions related to the events with particle numbers selected in some fixed multiplicity bins. The corresponding coherence effects increase with the multiplicity.
Highlights
Femtoscopic study results on the two-particle momentum correlations in p þ p collisions at the CERN Large Hadron Collider (LHC) have been presented recently by the ALICE [2], ATLAS [3], CMS [4], and LHCb [5] Collaborations
While there is some evidence that hydrodynamics can be successfully applied to describe particle momentum spectra in highmultiplicity p þ p collisions, it is still unclear whether the reported results on Bose-Einstein momentum correlations can be attributed to hydrodynamic evolution like in A þ A collisions
We assume that m is equal to pion mass and we take the set of parameters corresponding roughly to the values at the system’s breakup in p þ p collisions at the LHC energies: The temperature T
Summary
Femtoscopic study results on the two-particle momentum correlations (see, e.g., Ref. [1]) in p þ p collisions at the CERN Large Hadron Collider (LHC) have been presented recently by the ALICE [2], ATLAS [3], CMS [4], and LHCb [5] Collaborations. In our opinion, observed peculiarities of Bose-Einstein momentum correlations in high-multiplicity p þ p collisions do not indicate inapplicability of hydrodynamics but can be partly associated with quantum coherence effects in small systems, when the effective system size is comparable with typical wavelength of the thermal bosons. It is shown that if one deals (even locally) with a grand canonical ensemble, a nontrivial coherence parameter appears in inclusive two-boson spectra only in the case of coherent condensate formation Without the latter, no coherence-induced suppression of the inclusive correlation function is possible because of the thermal Wick’s theorem. We study the two-boson momentum correlations in small systems with high particle number densities at the moment when the system breaks up Such almost sudden freeze-out can happen due to very fast expansion (when the homogeneity lengths are around 1 fm) of the matter formed in high-multiplicity p þ p collisions at the LHC. We apply the fixed particle number constraint to the corresponding grand-canonical statistical operator and discuss the influence of such constraints on one-particle momentum spectra and twoboson momentum correlations
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