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10 11-2014 -sokolskii science and progress
- 1. Vladimir Sokolskii (St. Petersburg State University) Influence of radial flow fluctuations on mean transverse momentum correlations in AA collisions Science and Progress, Saint Petersburg November 10, 2014 1 10/11/2014, Science and Progress Vladimir Sokolskii 1Influence of radial flow fluctuations on mean transverse momentum correlations in AA collisions Influence of radial flow fluctuations on mean transverse momentum correlations in AA collisions 110/11/2014, Science and Progress Vladimir Sokolskii Scientific advisor - Igor Altsybeev (St. Petersburg State University)
- 2. Influence of radial flow fluctuations on mean transverse momentum correlations in AA collisions 210/11/2014, Science and Progress Vladimir Sokolskii Outline •Introduction •Blast-wave model •Monte-Carlo toy •Definition of the FB correlation coefficient •Results •Conclusions
- 3. 3 10/11/2014, Science and Progress Vladimir Sokolskii 1 3 Influence of radial flow fluctuations on mean transverse momentum correlations in AA collisions 310/11/2014, Science and Progress Vladimir Sokolskii We will consider the case with b=0. b is the impact parameter. "Introduction: collision of relativistic nuclei"
- 4. 4 10/11/2014, Science and Progress Vladimir Sokolskii 1 4 Influence of radial flow fluctuations on mean transverse momentum correlations in AA collisions 410/11/2014, Science and Progress Vladimir Sokolskii Appearance of a radial flow Radial flow is modification of transverse momentum spectrum cased by collectivity effects. RZ
- 5. 5 10/11/2014, Science and Progress Vladimir Sokolskii 1 5 Influence of radial flow fluctuations on mean transverse momentum correlations in AA collisions 510/11/2014, Science and Progress Vladimir Sokolskii Blast-wave model Module of the velocity vector Velocity profile R r Surface T (E. Schnedermann, J. Sollfrank, U. Heinz, Thermal phenomenology of hadrons from 200-A/GeV S+S collisions, Phys.Rev. C48 (1993) 2462-2475; nucl-th/9307020.)
- 6. Fitting function (blast-wave function) 6 10/11/2014, Science and Progress Vladimir Sokolskii 1 6 Influence of radial flow fluctuations on mean transverse momentum correlations in AA collisions 610/11/2014, Science and Progress Vladimir Sokolskii Blast-wave model. Analytical solution Fit parameters are: 𝑇𝑘𝑖𝑛, β 𝑠, n
- 7. 7 10/11/2014, Science and Progress Vladimir Sokolskii 1 7 Influence of radial flow fluctuations on mean transverse momentum correlations in AA collisions 710/11/2014, Science and Progress Vladimir Sokolskii Fitting of experimental data with blast wave model (Centrality dependence of π , K, p production in Pb-Pb collisions at s =2.76 TeV, Phys. Rev. C 88, 044910 (2013))
- 8. 8 10/11/2014, Science and Progress Vladimir Sokolskii 1 8 Influence of radial flow fluctuations on mean transverse momentum correlations in AA collisions 810/11/2014, Science and Progress Vladimir Sokolskii Blast-wave in Monte-Carlo toy Event 𝑝𝑖 ~𝑒𝑥𝑝 − 𝑝 𝑇𝑘𝑖𝑛 𝑇𝑘𝑖𝑛=0,45GeV Boltzmann distribution y Each event: • 100 particles are randomly placed in a circle • 𝑝 𝑇for each particle is randomly oriented, value is given by Boltzmann distribution • 𝑝 𝑇 is modified by Lorentz boost 𝛽 𝑇 𝑟 =𝛽𝑠 𝑟 𝑅 1
- 9. 9 10/11/2014, Science and Progress Vladimir Sokolskii 1 9 Influence of radial flow fluctuations on mean transverse momentum correlations in AA collisions 910/11/2014, Science and Progress Vladimir Sokolskii Pt spectrum Protons βsurface=0.5c Simulation was done with different particles: pions, kaons, protons.
- 10. 10 10/11/2014, Science and Progress Vladimir Sokolskii 1 10 Influence of radial flow fluctuations on mean transverse momentum correlations in AA collisions 1010/11/2014, Science and Progress Vladimir Sokolskii Comparison P, m=0.938MeVK, m=0.494MeVπ, m=0.140MeV Stronger momentum modification for heavier particles βsurface=0.5c
- 11. 11 10/11/2014, Science and Progress Vladimir Sokolskii 1 11 Influence of radial flow fluctuations on mean transverse momentum correlations in AA collisions 1110/11/2014, Science and Progress Vladimir Sokolskii Definition: Mean transverse momentum correlation coefficient ForwardBackward PtB 1-1 0 PseudorapidityPtF Overline means average in event Angle brackets means averaging over events 𝑏 𝑐𝑜𝑟𝑟 is sensitive to different initial-state effects such as quark-gluon strings interactions.
- 12. 12 10/11/2014, Science and Progress Vladimir Sokolskii 1Influence of radial flow fluctuations on mean transverse momentum correlations in AA collisions 1210/11/2014, Science and Progress Vladimir Sokolskii Independent modeling for each type: π, K, P 100 000 events with 100 particles βsurfaceδβsurface bcorr δβ - range of surface velocity fluctuations
- 13. 13 10/11/2014, Science and Progress Vladimir Sokolskii 1 13 Influence of radial flow fluctuations on mean transverse momentum correlations in AA collisions 1310/11/2014, Science and Progress Vladimir Sokolskii Influence of radial flow fluctuations on mean transverse momentum correlations δβsurface=0.1 𝑏 𝑐𝑜𝑟𝑟 increase with 𝑏 𝑐𝑜𝑟𝑟 for protons is larger then for lighter particles. β 𝑠𝑢𝑟𝑓𝑎𝑐𝑒
- 14. 14 10/11/2014, Science and Progress Vladimir Sokolskii 1 14 Influence of radial flow fluctuations on mean transverse momentum correlations in AA collisions 1410/11/2014, Science and Progress Vladimir Sokolskii Comparison δβsurface=0.05 δβsurface=0.15 Larger surface velocity fluctuations lead to larger 𝑏 𝑐𝑜𝑟𝑟.
- 15. 15 10/11/2014, Science and Progress Vladimir Sokolskii 1 15 Influence of radial flow fluctuations on mean transverse momentum correlations in AA collisions 1510/11/2014, Science and Progress Vladimir Sokolskii Conclusions • In toy Monte-Carlo model, it is shown that event-by-event fluctuations in surface velocity of the fireball lead to transverse momentum correlations. • It is found that correlation coefficient rises with increasing surface velocity and its fluctuations. • 𝑏𝑐𝑜𝑟𝑟 is higher for heavier particles. We conclude that the impact of the radial flow should be taken into account in interpretation of the experimental measurements of mean transverse momenta correlations.
- 16. Thank you for your attention
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- 19. 24 10/11/2014, Science and Progress Vladimir Sokolskii 1 24 Influence of radial flow fluctuations on mean transverse momentum correlations in AA collisions 2410/11/2014, Science and Progress Vladimir Sokolskii Conclusions
Editor's Notes
- Good evening . My name is Vladimir Sokolskii . I am a fourth year student of the Faculty of Physics .I take part in HEP group. My work called Influence of radial flow fluctuations on mean transverse momentum correlations in nuclear-nuclear collisions. //What are the benefits for us from exploring this issue?
- Here is an Outline for my talk. I will start with short introduction, then describe blast-wave model for nucleus-nucleus collisions and our toy monte-carlo realization of it. Then I will introduce correlation coefficient between mean transverse momentum and its values obtained in our monte-carlo model. I will finish with conclusions. let's get started
- We see central collisions of two nucleus Impact parameter is a distance between the centers of the nuclei
- Radial flow is a modification of transverse momentum spectrum caused by collectivity effects. Collectivity means that final state in nucleus-nucleus collision is not just a simple superposition of products from individual nucleon collisions, but a more complex system with new properties. In the right cartoon, RF exists in a plane which is transverse to z-axis.
- We simulate RF according to blast-wave model. In the framework of this model, expansion velocity of the (quark-gluon) medium depends on the radius. We have transverse velocity field like what is shown on this pic. When hadrons appear after freeze-out of the medium, their transverse momentum spectrum is modified by expansion velocity at radius r (IF WE LOOK AT THE SYSTEM FROM THE LABORATORY FRAME). Transverse velocity of the ELEMENTARY VOLUME OF THE MEDIUM IS determinED by this formula . Here R is radius of fireball r is a radial distance in the transverse plane, beta_t is transverse expansion velocity, beta_s is transverse expansion velocity at the surface, n is just a coefficient which determines a velocity profile.
- This model has an analytical solution. "in this formula, rho is so-called 'velocity profile' which is determined by this definition: rho=tanh-1(beta)“ Io and K1 is the modified Bessel function m_t is transverse mass We have 3 free parameters for fitting there is freeze-out temperature T_kin surface velocity profile n Blast-wave function is used to fit transverse momentum spectra.
- For example, this MODEL describes well the transverse momentum spectra of PIONS, KAONS AND PROTONS, MEASURED BY the ALICE collaboration.
- Simple toy Monte-Carlo model simulates only CENTRAL collisions. In our toy MC model, we choose n=1. We have a hundred particles in every event. Particles are UNIFORMELY distributed in a circle. Each particle has randomly oriented momentum in a transverse plane. The module of momenta of particles is distributed according to Boltzmann distribution. As your already now, in the framework of Blast-wave model, in a medium we have transverse velocity field like on this pic. ,so, each particles which was born in the medium, gaines transverse Lorentz boost according it’s radial position. Thus (поэтому),we modify particle momentum by going into laboratory reference frame. Monte-Carlo model simulates centrality collisions. We have hundred particles(this is quite enough for owe goals) Which are evenly distributed in the circle. Each particle has randomly oriented momentum in a transverse plane. In the rest frame of the medium the module momenta of particles distributed according Boltzmann formula . As your already now , we attributed to medium velocity field like on this pic. Each particles was boned in the medium gained transverse velocity according it’s position and within setting velocity fluctuations interval. We modify Spector momentum going into laboratory reference system by Lorentz boost. Further we need to catch particles…//next slide
- This HISTOGRAM illustrates the influence of a boost on transverse momenta spectrum . I choose proton because it is the heaviest in three given type of particles.
- Now you can see the difference in shift of the spectrum depend of particle mass: stronger momentum modification for heavier particles
- Correlations between observables measured in separated rapidity intervals provide important information about the initial states of proton-proton and nucleus-nucleus collisions at high energies. Different observables can be used in correlation method. In particular, correlations between mean transverse momenta of particles produced in two rapidity intervals The correlation strength is conventionally characterized by the correlation FB coefficient bcorr. 𝑏 𝑐𝑜𝑟𝑟 is sensitive to different initial-state effects such as quark-gluon strings interactions. We have two disjoint pseudorapidity windows. Backward in the range from minus one to zero and forward in the range from zero to one Particles have equal chance go to forward of backward windows. OVERLINE means average in event angle brackets means averaging over events. In our toy MC model we show, that mean transverse momentum correlations are sensitive to fluctuations of surface velocity
- For a set of statistics we carry out hundred of thousands events with 100 particles. From the obtained data we extract the correlation coefficient bcorr We consider Bcoor as a function of three parameters there are: 1)type of particle(we use particle mas as parameter in Lorentz boost) 2)βsurface 3) δβsurface -it is a RANGE, in which surface velocity uniformely fluctuates EVENT-by-EVENT" (событие-за-событием, термин такой, когда в разных событиях что-то разное происходит) deltaBeta - range of surface velocity fluctuations) Please note that δβsurface set each time in each event it is really important point , else the correlations coefficient remains stable .
- Let’s look at that line graph .It represents the changes in correlation coefficient depend on surface velocity. We see significantly increased of correlation coefficient from two-tenths to eight-tenths the speed of light.
- here are two plots, they differ in a (delta beta). We can therefore conclude that larger surface velocity fluctuations lead to larger 𝑏 𝑐𝑜𝑟𝑟 .
- - In toy Monte-Carlo model, it is shown that event-by-event fluctuations in surface velocity of the fireball lead to transverse momentum correlations. - It is found that correlation rises with increasing surface velocity and its fluctuations. - bcorr are higher for heavier particles. We conclude that the impact of radial flow should be taken into account in interpretation of the experimental measurements of mean transverse momenta correlations.
- Please look wright at the picture, it demonstrate on fingers stages of the nuclear-nuclear collision. In the collision occurs confinement. The strings are stretched and torn .They produced particles until they have enough energy to it. On the left side you can see proportions of produced products in AA collisions .