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In collaboration with V. Shapoval, Iu.Karpenko
Correlation interferometry of small systems and
femtoscopy scales in pp collisions at LHC
Yu.M. Sinyukov, BITP, Kiev
WPCF-2012 September 09 – 15 2012 FIAS Frankfurt
First attempts to apply hydro for both types of high energy collisions: A+A and p+p
Interferometry radii RT, τ from RL, Tf.o
Experiment. data for
Slope of pion pT spectra Tf.o.μ
T=0.170 GeV , τ=1.5 – 2.1 fm/c
The simplest estimate for p+p collisions at
Freeze-out at τ: transversally , longitudinally: boost-invar.
Experiment (ALICE):
Disagreement with the data:
Transverse flow smaller homogeneity length (?)
Fast forward Twenty Years Later
The modern dynamical models are too complicated to use analytics .
To check validity of the model of space-time evolution of the matter in hadron and nuclear collisions one should do the following:
Select initial time from which the model can be applied (for thermal or hybrid ones it is 1~2 fm/c; pre-thermal models are related to the interval: 0.1 – 1÷1.5 fm/c).
Select initial profile of the energy (or entropy) density (e.g., MC Glauber-like one, CGC, EPOS, etc…).
Select parameters of IC (e.g., maximal initial energy density) from the condition of description of and observed transverse spectra of pions, kaons, protons…
Select EoS from, e.g., lattice QCD.
Then the model, fixed as above, has to describe observed femtoscopy scales (interferometry radii), otherwise it does not catch the real evolution of the system and, so, cannot pretend to be the space-time model of the reactions of hadronic or nuclear collisions.
HKM results
The simulations of p+p 7 TeV within HKM model gives the minimal interferometry volume by the factor 1.2-1.5 more then the experiment.
The correlation femtoscopy of small systems
(R~1 fm)
Yu.S., V. Shapoval: arXiv 1209.1747 (this Tuesday)
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 + symmetrization
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 accounting!
HBT (Glauber, Feynman, 1965)
Both cases (independent- and fully non-independent emitters) can be described in the formalism of the partially coherent phases (Yu.S. , A. Tolstykh, Z.Phys. 1991):
x1 x2 If the states with different emission points and are not independent at all (full coherence), the phases are equal :
The distance between the centers of emitters is larger than their sizes related to the widths of the emitted wave packets 1/Δp .
=x1 – x2
-
1/Δp
Spectrum:
Criterion : overlapping of the wave packages:
Phase correlations
Wave function for emitters
Uncertainty principle and distinguishability of emitters
1/Δp Distinguishable emitters The states are orthogonal
1/Δp Indistinguishable emittersThe states are not orthogonal
The uncertainty principle for momenta measurement. The measurement of the particle momenta p has accuracy depending on
the duration of the measurement Δt: Δp ~ 1/Δt [Landau, Lifshitz, v. IV]. So one can measure the time of particle emission without noticeable violation of the momentum spectra with accuracy not better than 1/ Δp
The 4-points phase correlator for maximally possible chaotic and independent emitters permitted by uncertainty principle is decomposed into the sum of products of the two-point correlators Gij and contains also term that eliminate the double accounting.
Overlapping integral
Femtoscopy for independent distinguishable emitters (standard model)
Femtoscopy for partially indistinguishable and so partially non-independent emitters
(for small systems where the uncertainty principle is important)
The milestones
single-particle amplitude
wave-function of emitter
emitter’s spectrum spatiotemporal distr. of emitters
overlapping integral
approximation for two-point phase average
two-particle amplitude
The correlation femtoscopy in the Gaussian approximation
The accuracy of the approximation for the overlapping integral
The comparison of the correlation function without subtraction of the double accounting with corresponding analytical approximations. The alpha- parameters, which give a good agreement with the exact results, are presented for different system sizes. The momentum dispersion k=m=0.14 GeV, p_T=0, T=R.
The results for the Gaussian part of B.-E. correlation functions
R_st means interferometry radii in the (standard) model of independent distinguishable emitters.
In the region of the source sizes 0.5 - 2 fm α = 1.5 - 0.4
The reduction of the interferometry radii:
The behavior of the two-particle Bose-Einstein correlation function ( side-projection) where the uncertainty principle and correction for double accounting are utilized. The momentum dispersion k=m=0.14 GeV, p_T=0, T=R.
The Bose-Einstein correlation function for small systems
The effects of the reduction of the interferometry radii and suppression of the correlation function are caused by not complete distinguishabity of the emitting points of the source because of the uncertainty principle:
Δp ~ 1/Δt, Δx ~ 1/Δp
The elimination of the double accounting leads also to the reduction of the intercept of the correlation function when the system size shrinks. So, there is the positive correlation between observed interferometry radii and the intercept when the system size is changing.
The effects are practically absent for A+A collisions where
effective sizes (homogeneity lengths) more then 3 fm.
RESUME
BACK TO p+p collisions
Interferometry volume vs multiplicity in HKM after corrections for partial indistinguishability of the emitters
Femtoscopy scales vs multiplicity in the HKM after corrections
Femtoscopy scales vs p_T in the HKM after corrections
Femtoscopy scales vs p_T in the HKM after corrections
Interferometry volume vs multiplicity for p+p and A+A central collisions in HKM + corrections for partial
indistinguishability of the emitters
Vi nt(A;dN=dy)
CONCLUSIONS
Our preliminary results on p+p collisions at the LHC energy demonstrates that the
uncertainty principle may play an important role for such small systems and allows
one to explain the observed overall femtoscopy scale (interverometry volume) and its
dependence on multiplicity.
An analysis of the p_T – dependence of the femtoscopic scales corrected for uncertainty
principle does not exclude the possibility of the hydrodynamic interpretation of p+p
collisions at the LHC energies.
The comparison of vs for pp and AA collisions conforms probably the
result of Akkelin, Yu.S. : PRC 70 064901 (2004); PRC 73 034908 (2006) that the
interferometry volume depends not only on multiplicity but also on the initial size of
colliding systems.
Vi nt dN=d́
THANK YOU FOR ATTENTION!
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