2. The idea of the correlation femtoscopy is based on an impossibility to distinguish between registered particles emitted from different points because of their identity. R ab detector 12 p1p1 p2p2 x1x1 x2x2 x3x3 x1x1 x2x2 x3x3 xaxa xbxb t=0 2 1 0 |q i | D Momentum representation Probabilities: q 1/R i

3. Probabilities of one- and two- identical bosons emitted independently from distinguishable/orthogonal quantum states with points of emission x 1 and x 2 (x 1 - x 2 = ∆x) Double account! HBT (Glauber, Feynman, 1965)

4. Both cases (in - and -distinguishable states) can be describe in the formalism of the partially coherent phases:

5. The distance between the centers of emitters is much larger than their sizes related to the widths of the emitted wave packets. Spectrum: Criterion : overlapping of the wave packages: Phase correlations Wave function for emitter

6. Density matrix (x-representation): << 1 classical probability sum ~ 1 quantum probability sum Density matrix (p-representation): Quantum fluctuation of angular momentum: Classical fluctuation of angular momentum: Classical limit allowing one to distinguish between different quantum states: p1-x1, p2-x2 or p2-x1, p1-x2 is: q 1/2

7. Probability averaged over events with different phase distributions φ(x) effect of a violation of smoothness condition

8. q

9. q

10. PROBLEM of DOUBLE ACCOUNT Double account! HBT (random phases) Corrected decomposition in generalized picture:

11. R= 1 fm

12. ? 1 2 3 Soften momentum conservation law Cluster/jet structure of the CF

13. q

15. Modification of the distribution function Weight Soften momentum conservation law

17.  For small systems, R ~ 1 fm, and typical for pp and e+e- slopes of spectra the emission points cannot be completely distinguished because of uncertainty principle, so one have to sum the amplitudes of emission from different points with partially random phases, but not the probabilities. It results in the specific reduction of observed interferometry radii /homogeneity lengths.  The decomposition of the 4-point phase averages into the products of the irreducible 2-point ones have to be accompanied by the elimination of the double account. The correct approach results in decreasing of suppression parameter up to zero when the ratio of mean wave length of the emitted quanta to the system size tends to infty.  If momentum difference |q| becomes much more then the inverse slope of the single- particle spectra, one can distinguish between two passible ways of the pair to detector and interference disappear.  Non-femtoscopic correlations can appear when the clusterization in momentum space takes place (e.g. in the case of mini-jets) or when specific fluctuation of emission function appears (e.g. when ICs for hydro fluctuate). These two reasons can be discriminated by means of the comparison of pi+pi+ and pi+pi- non-femtoscopic correlations.