Principal problems of intensity interferometry for small systems

Yuri SinyukovBITP Kiev

in collaboration with V. Shapoval

Tokyo WPCF 20 – 24 September 2011

Interferometry microscope (Kopylov / Podgoretcky - 1971 )

The idea of the correlation femtoscopy is based on an impossibility to distinguish between registered particles emitted from different points because of their identity.

Ra b

detector 1 2

p1 p2

x1

x2

x3

x1

x2

x3

xa

xb

t=0

2

1

0 |qi|

D

Momentum representation

Probabilities:

q

1/Ri

Probabilities of one- and two- identical bosons emitted independently from distinguishable/orthogonal

quantum states with points of emission x1 and x2 (x1 - x2 = ∆x)

Double account!

HBT (Glauber, Feynman, 1965)

Wx1;x2 (p) =½1 jA1(p)j2+½2 jA2(p)j

2 = 1

If the states with different emission points and are indistinguishable, one have to sum the amplitudes, not probabilities:

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

x1 x2

Indications of distinguishability of quantum states radiating at and

The distance between the centers of emitters is much larger than their sizes related to the widths of the emitted wave packets .

Δ𝑥

Spectrum:

Criterion : overlapping of the wave packages:

Phase correlations

Wave function for emitter

Classical and quantum probability sum

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

Analytical approach

Probability averaged over events with different phase distributions φ(x)

effect of a violation of smoothness condition

CF for two- and five- particles emission for

q

CF for two particle emission for

q

PROBLEM of DOUBLE ACCOUNT

Double account!

HBT (random phases)

Corrected decomposition in generalized picture:

The behavior of CF accounting for a smooth transition from matrix density of pure quantum states to the density matrix of mixed states and eliminating the double account in expression for probability of boson pair registration

R= 1 fm

Deciphering non-femtoscopic two-pion correlations in small systems with simple analytical models

?

12

3

Soften momentum conservation law

Cluster/jet structure of the CF

The CF with cluster/jet formation

q

Non-femtoscopic CF for p+p collisions in simple cluster/jet model (Akkelin, Yu.S. , 2011)

The non-femtoscopic correlations caused by the fluctuating emission function/hydro IC

Modification of the distribution function

Weight

Soften momentum conservation law

Non-femtoscopic CF at the imitation of fluctuating initial conditions for Hydro

Conclusions 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.