C or relation interferometry of small systems and f emtoscopy scales in pp collisions at LHC

1. Correlation interferometry ofsmallsystemsandfemtoscopyscales in ppcollisionsat LHC Yu.M. Sinyukov, BITP, Kiev In collaboration with V. Shapoval, Iu.Karpenko WPCF-2012 September 09 – 15 2012 FIAS Frankfurt

2. First attempts to apply hydro for both types of high energy collisions: A+A and p+p Slope of pion pT spectra Tf.o.μ Interferometry radii RT, τfrom RL,Tf.o Experiment. data for

3. The simplest estimate for p+p collisions at Freeze-out at τ: transversally , longitudinally: boost-invar. Experiment (ALICE): T=0.170 GeV , τ=1.5 – 2.1 fm/c • Disagreement with the data: Transverse flow smaller homogeneity length (?)

4. 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.

5. HKM results The simulations of p+p 7 TeV within HKM model gives the minimalinterferometry volume by the factor 1.2-1.5 more then the experiment.

6. Yu.S., V. Shapoval: arXiv1209.1747 (this Tuesday) The correlation femtoscopy of small systems(R~1 fm)

7. The idea of the correlation femtoscopyis based onan impossibility to distinguish between registered particles emitted from different points because of their identity. R a b x3 x3 t=0 xb p1 p2 xa x2 x2 D x1 x1 1 2 Momentum representation + symmetrization detector Interferometry microscope (Kopylov / Podgoretcky - 1971) 2 Probabilities: q 1/Ri 1 0 |qi|

8. Probabilities of one- and two- identical bosons emitted independently from distinguishable/orthogonal quantum states with points of emission x1 and x2 (x1 - x2 = ∆x) HBT (Glauber, Feynman, 1965) Double accounting!

9. If the states with different emission points and are not independent at all (full coherence), the phases are equal : Both cases (independent- and fully non-independentemitters) can be described in the formalism of the partially coherent phases (Yu.S. , A. Tolstykh, Z.Phys. 1991):

10. Uncertainty principle and distinguishability of emitters 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 Indistinguishable emitters The states are not orthogonal 1/Δp Distinguishable emitters The states are orthogonal 1/Δp Wave function for emitters Criterion : overlapping of the wave packages: Spectrum: Phase correlations

11. The measurement of the particle momenta phas 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 milestones Femtoscopy for partially indistinguishable and so partially non-independent emitters (for small systems where the uncertainty principle is important) Femtoscopy for independent distinguishable emitters (standard model) The uncertainty principle for momenta measurement. Overlapping integral 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 correlatorsGij and contains also term that eliminate the double accounting.

12. The correlation femtoscopy in the Gaussian approximation 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

13. 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.

14. The results for the Gaussian part of B.-E. correlation functions The reduction of the interferometry radii: R_st means interferometry radii in the (standard) model of independent distinguishable emitters. In the region of the source sizes 0.5 - 2 fmα = 1.5 - 0.4

15. The Bose-Einstein correlation function for small systems 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.

16. RESUME • The effects of the reduction of the interferometry radii and suppression of the correlation function are caused by not complete distinguishabityof 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.

17. BACK TO p+p collisions

18. Interferometry volume vs multiplicity in HKM after corrections for partial indistinguishability of the emitters

19. Femtoscopy scales vs multiplicity in the HKM after corrections

20. Femtoscopy scales vsp_T in the HKM after corrections

21. Femtoscopy scales vsp_T in the HKM after corrections

22. Interferometry volume vs multiplicity for p+p and A+A central collisions in HKM + corrections for partial indistinguishability of the emitters

23. 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 vsfor 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. CONCLUSIONS

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