Abstract
I am reporting results of two papers, written together with W.Florkowski and K.Zalewski [1, 2], discussing the consequences of the observation [3] that, due to their composite nature and thus finite size, hadrons observed in the HBT measurements must be correlated in space-time. Using the blast-wave model [4] adjusted [1] to ALICE data on the measured HBT radii in pp collisions at 7 TeV [5], the full Bose-Einstein correlation functions in three direction (out, side, long) are evaluated. The results are presented together with some additional comments.
Highlights
Interpretation of the measurements of Bose-Einstein correlation function is usually discussed using the formula C(P12, Q) ≡N(p1, p2) N ( p1 )N ( p2 ) = 1+dx1dx2eiQxw(P12, x) 2 dx1w(p1, x1) dx2w(p2, x2) Cu(P12, Q) ≥ (1)where p1, x1 and p2, x2 are momenta and positions of particles, w(p, x) is their corresponding distribution (Wigner function)
The second term gives only a small correction at Q ≈ 0, it may dominate at large Q, where the data show that the inequality (1) is violated
This observation allows to formulate the approximate procedure to estimate the magnitude of the effects we are discussing: STEP ONE: Choose a model describing the considered process and fix its parameters by adjusting to data at small Q, ignoring the correction from the space-time correlation
Summary
Where p1, x1 and p2, x2 are momenta and positions of particles, w(p, x) is their corresponding distribution (Wigner function). That this formula does not describe correctly the existing data [6,7,8] because the inequality on the R.H.S. of (1) is not satisfied The explanation of this problem can be found by observing that (1) is only an approximation to the general formula [9, 10]. Where W(P12, P12; x1, x2) is the distribution in momentum and in space-time (Wigner function) of the two particles. Violation of the inequality (1) implies that the produced particles must be correlated It was suggested in [3] that such correlations in space-time must be necessarily present because observed hadrons are not point-like particles but rather systems composed of a certain number of more elementary constituents. One sees from (6) that the inequality (1) is no longer compulsory
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