Femtoscopic scales in $p+p$ and $p+$Pb collisions in view of the uncertainty principle

A method for quantum corrections of Hanbury-Brown/Twiss (HBT) interferometric radii produced by semi-classical event generators is proposed. These corrections account for the basic indistinguishability and mutual coherence of closely located emitters caused by the uncertainty principle. A detailed analysis is presented for pion interferometry in $p+p$ collisions at LHC energy ($sqrt{s}=7$ TeV). A prediction is also presented of pion interferometric radii for $p+$Pb collisions at $sqrt{s}=5.02$ TeV. The hydrodynamic/hydrokinetic model with UrQMD cascade as afterburner is utilized for this aim. It is found that quantum corrections to the interferometry radii improve significantly the event generator results which typically overestimate the experimental radii of small systems. A successful description of the interferometry structure of $p+p$ collisions within the corrected hydrodynamic model requires the study of the problem of thermalization mechanism, still a fundamental issue for ultrarelativistic $A+A$ collisions, also for high multiplicity $p+p$ and $p+$Pb events.