HBT two-pion correlations at LHC

HBT two-pion correlations at LHC

Qingfeng Li ( 李庆峰 )(Huzhou Teachers College)

Q.Li for 14th NCNS in Huzhou 2

Outline

• LHC physics and QGP phase• UrQMD updates (cascade & dynamic modes)• HBT Correlations and EoS status• Calculation Results at LHC• Some words of onset of QGP at SPS• Summary and Outlook

Q.Li, G. Graef, M. Bleicher, PRC 85, 034908 (2012);G. Graef, M. Bleicher, Q.Li, PRC, 85, 044901 (2012); G. Graef, Q.Li, M. Bleicher, JPG 39, ?(2012); arXiv:1203.4421


LHC physics

• TeV physics• http://lhc.web.cern.ch/lhc/• To find: Higgs;micro black holes; extra dimensions (Kalu

za–Klein Theory); dark matters

• …a large number of unsolved questions in fundamental physics

CERN

http://lhc.web.cern.ch/lhc/


QGP phase

• Onset/order of the QGP phase/QCD phase transition• Properties of the QGP phase

• Problems, problems…


What to do now…

• The extracted bulk properties of the high temperature fireball created in such ultrarelativistic collisions have provided unprecedented information for fundamental investigations of the phase diagram of quantum chromodynamics.

1. to explore collective features of the strong interaction in high multiplicity pp events;

2. to explore expansion properties of the created matter by investigating the spatial shape of the fireball from AA collisions;

3. to explore the spatial structure of the source created in collisions of various heavy ions at different energies and centralities to shed light on the observed scaling violation when going from pp to AA collisions at the LHC.


UrQMD

• a microscopic many-body approach to p-p, p-A, and A-A interactions at energies ranging from SIS up to LHC.

• It is based on the covariant propagation of mesons and baryons. Furthermore it includes rescattering of particles, the excitation and fragmentation of color strings, and the formation and decay of hadronic resonances.

• At LHC, the inclusion of hard partonic interactions in the initial stage is important and is treated via the PYTHIA model.

• The model can be downloaded from http://urqmd.org……


Main updates in recent years

1. In cascade mode: the newest version is 3.3 (to include LHC physics); Phys. Rev. C 84, 034912 (2011);

2. In the Boltzmann+hydrodynamics hybrid mode: the newest version is 2.3p1 (can be downloaded from the website); Phys. Rev. C 78, 044901 (2008);

3. In the “mean-field potential” version: based on v2.1, adding mean field potentials for hadrons.

• V1.3+PYTHIAV2.1+hydrodynamicsV2.3+LHC collisionsV3.3

Q.Li version

SPS RHIC LHC


Explorations of EoS stiffness

• At INDRA/SIS/CSR energies: soft!?...

• At AGS/SPS/FAIR energies: ?...

• At RHIC/LHC energies: …

2002 2009 2011


The “pre-formed” hadronic potential

• To modify the interactions at early stage, more collisions (by considering a shorter formation time or larger cross sections for “pre-formed” particles) or a mean-field potential for “pre-formed” hadrons might be taken into account. The former idea has been checked in the AMPT and the HRM models. Here we would like to consider the latter idea.

• As the first step, ① the density dependent term used for formed baryons is used for “pre-formed” particles. ② The “pre-formed” mesons act like “pre-formed” baryons but with a reduction factor (2/3) due to the quar

k-number difference.③ The potential interaction between formed and “pre-formed” particles is neglected.④ The “pre-formed” particles also contribute to the hadronic density (for “pre-formed” mesons, the 2/3 fact

or is considered).

See:PLB659, 525(2008)PLB663, 395(2008)For more details


HBT, half century in NP

• HBT=Robert Hanbury-Brown and Richard Q. Twiss In 1950’s, in order to measure stellar radii through the angle subtended by nearby st

ars, Robert invited Richard to develop the mathematical theory of intensity interference. They found by astro-observation that two-photons arriving to the correlators behaved as a consequence of B-E statistics.

• In 1959, during the measurements of the ρ0 resonance (by means of ρ0-+), Goldhaber etc (Berkeley) found an angular correlation among identical pions, which were also explained by the B-E. What’s more, they parameterized the observed correlation as:

• C(Q2)=1+exp(-Q2r2) • The subsequential HBT researches in nuclear physics are based on this Ga

ussian form.

*R. Hanbury Brown and R.Q. Twiss, Philos. Mag. 45, 663 (1954).*G. Goldhaber, S. Goldhaber, W. Lee, and A. Pais, Phys. Rev. 120, 300 (1960)


The HBT correlation and paramerization

32

3

31

3

32

31

6

),(

dpNd

dpNddpdpNd

KqC 21 ppq 2/)( 21 ppK

The quotient of two-particle and one-particle spectra

The two-particle correlator C(q,K) is related to the emission function s(x,K), which is the Wigner phase-space density of the particle emitting system and can be viewed as the probability that a particle with average momentum K is emitted from the space-time point x in the collision region. the two-particle relative wave function.

222111

2

221121

,,

,,),(

pxsdxpxsdx

pxspxsdxdxKqC

Experimentally:

Theoretically:

The correlator is constructed with the help of the CRAB program


Cont’d

• CRAB analyzing program: http://www.nscl.msu.edu/~pratt/freecodes/crab/home.html

• Three-dimensional Gaussian parameterization

• LCMS is employed in usual calculations• Coulomb effect in FSI is considered for charged tw

o-kaon correlation with a Bowler-Sinyukov method• non-Gaussian effect can be discussed under th

e Edgeworth expansion

)2exp(1),,( 2222222LOOLLLSSOOLSO qqRqRqRqRqqqC

))2exp(1)((

)1(),,(2222222

LOOLLLSSOOinvcoul

LSO

qqRqRqRqRqK

qqqC

The fitting work can be done by the ROOT or the ORIGIN software (using -squared method)


One task of HBT: to probe the QGP fireball

• A non-trivial structure in the excitation function of HBT probes might be seen IF there is a (phase) transition.

Energy density

Predictions by

Rischke, Gyulassy, in Nucl.Phys.A608:479-512,1996

long life times in the mixed phase?


Effects of EOS and freeze-out criteria on the RO/RS ratio

Note:Different hydro freeze-out criteria affects slightly the ratio, if one considers HR.The BG-EoS is too soft to explain the ratio.

From PLB674,111(2009)From PLB674,111(2009)


Calculation Results at LHC

1. Q1: p+p collisions at √sNN=7 TeV

2. Q2: : Pb+Pb collisions at √sNN=2.76 TeV

3. Q3: Examination of scaling of HBT radii with charged particle multiplicity


Q1: p+p collisions at √sNN=7 TeV

• It seems like in massive nucleus-nucleus collisions, a strongly interacting medium is created even in pp collisions, that exhibits similar bulk properties such as space momentum correlations and collective behaviour;

• While it is often argued, that the particle emitting system in p+p collisions is too small to create a medium that exhibits bulk properties, this should be different at a center of mass energy of √s= 7 TeV.

• an essential quantity that influences the particle freezeout radii is the formation time in flux tube fragmentation

• the recent LHC data on pp collisions allows to determine the formation time in the flux tube break-up

From JPG; arXiv:1203.4421


Formation time in UrQMD

• For the Lund model the formation times are proportional to the transverse mass of the created hadron and inversely proportional to the string tension.

• For simplicity UrQMD uses a constant formation time of tf = 0.8 fm/c for hard collisions.

The average dNch/d from UrQMD is 15% smaller than ALICE data


Projections of Correlation function

Non-Gaussian effect is visible in out and long directions and at large q


KT dependence of HBT radii for diff. dN classess and diff. formation times

the present ALICE data allows to constrain the formation timeto values of tf ≈ 0.3-0.8 fm/c.

An additionalmomentum dependence in tf isneeded.


Q2: : Pb+Pb collisions at √sNN=2.76 TeV

Non-Gaussian effect is stronger at LHC than at lower energiesCalculated non-Gaussian effect is more obvious than data

From PRC 85, 034908 (2012)


KT dependence of HBT radii

1,Strong kT dependencesubstantial expansion of the source2,As RHICLHC, HBT radii (esp. RL) rise.3,At LHC, RL and RO are larger than data, separately & RO/RS ratio is larger than data.


x-t correlation

• even in the cascade calculation, there exists a visibly positive correlation between the emission time and position.

• The most important contribution to RO comes from the emission duration term


Contribution of emission duration to the HBT radii

• To lead to smaller RO values in all kT bins but leaves RS unchanged;

• Overall it results in an improved agreement with the data of the ratio.


Some hints

1. The overestimation of both RO and RL can be attributed to the known fact that the pressure in the early stage is not strong enough in the cascade model calculations.

2. A higher pressure would lead to a more explosive expansion, a stronger phase-space correlation, and a faster decoupling of the system, thus leading to smaller regions of homogeneity.

3. A more satisfactory solution is possible in the near future by improving the dynamic processes for both QGP and HG phases.


Q3: Examination of scaling of HBT radii with charged particle multiplicity

• Same: 1) charged particle multiplicity at midrapidity: ||<1.2 for pp; ||<0.8 for other classes. 2) KT bin: 300-400 MeV/c.

• Different solutions:• To change: a) beam energy: Pb+Pb at √s=2760, 200, 1

30, 62.4 GeV and Elab = 158 GeV; b) centrality: Pb+Pb within 0-5%, 5-20%, 20-50% and 50-80% centralities; c) colliding system: Pb+Pb, Cu+Cu, C+C, p+p.

From PRC, 85, 044901 (2012)


Scaling of the HBT radii

1,The scaling is good if the change in Nch is caused by a change of centrality at a fixed energy. 2,A small offset on the order of 2-3 fm is visible for different system sizes, due to the finite size of the nuclei.3,Increasing the center-of-mass energy leads to a reduction of the radii at a given fixed Nch-bin.


Some hints

1. The scaling of the source size with (dNch/d)1/3 for different centralities is a hint that the underlying physics, e.g. pion production via resonance decay versus production via string fragmentation, is nearly unchanged by changes in the collision geometry.

2. A change in √s on the other hand results not only in different weights of the production mechanisms, but also in changed expansion dynamics towards a more violent expansion with increased energy.

• Different pp and AA result is attributed to the strongly different particle production mechanisms in AA and pp. I.e., bulk emission vs. string/jet dominated emission.


Volume of the homogeneity region

1. A good agreement between experiment and theory is observed for the quantity R2

SRL while the experimental results for RORSRL are slightly overestimated.

2. A steeper slope with decreasing energy.


Freeze-out time

• By fitting the hydrodynamic expression:

1, a shorter decoupling time with increased energy2, UrQMD overestimates the source lifetime by a factor of 2–3∼ when compared to LHC data back to the duration time


Some words of onset of QGP at SPS

• Currently a more detailed study on the onset of QGP at SPS is more urgent.

– Extracting EoS of QGP based on lQCD calculations (potentials of preformed hadrons, like PHSD).

– Extracting potentials of different formed hadrons in HG via RMF, Chiral, etal., (like AMPT)

• Comparison with cascade and hybrid mode calculations and with RHIC-BES/ SPS-SHINE/ FAIR data in the near future.


Summary and Outlook

• Two-pion HBT correlations at LHC are calculated by using the UrQMD v3.3.

1. the present ALICE pp data allows to constrain the formation time to values of tf ≈ 0.3-0.8 fm/c.

2. The overestimation of both RO and RL from Pb+Pb central collisions can be attributed to the known fact that the pressure in the early stage is not strong enough in the cascade model calculations.

3. The scaling of the source size with (dNch/d)1/3 for different centralities is a hint that the underlying physics, e.g. pion production via resonance decay versus production via string fragmentation, is nearly unchanged by changes in the collision geometry, while change in √s on the other hand results not only in different weights of the production mechanisms, but also in changed expansion dynamics towards a more violent expansion with increased energy.

4. Different pp and AA result is attributed to the strongly different particle production mechanisms in AA and pp. I.e., bulk emission vs. string/jet dominated emission.

• Call for a better dynamics for both phases, which, currently, might be concentrated in the SPS energy region, as the RHIC-BES/ SPS-SHINE/ FAIR data come forth.


Thank you for your concern!

Using the e-mail: [email protected] for more discussions.

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HBT two-pion correlations at LHC

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