Dynamical Evolution, Hadronization and Angular De-correlation of Heavy Flavor in

Hot and Dense QCD Matter

Shanshan CaoIn collaboration with

Guang-You Qin and Steffen A. BassDuke University

Outline• Heavy flavor initial production: pQCD + shadowing• Heavy flavor evolution inside QGP : Improved

Langevin approach incorporating gluon radiation• Heavy flavor hadronization: a hybrid coalescence

plus fragmentation model• Results of heavy flavor suppression and flow and

comparison with LHC and RHIC data• Angular correlation of heavy flavor pairs• Summary

• Initial production: MC-Glauber for the position space and leading-order pQCD calculation for the momentum space

• Shadowing effect: different PDF’s of nucleon and nuclei lead to different production rate of HQ in pp and AA collisions

K. Eskola, et al., JHEP 0807 (2008) 102

Heavy Flavor Initial Production

Significant shadowing effect for charm quark production at low pT (especially at the LHC energy) impact on RAA

• Two ways for heavy quarks to lose energy:

• Unless in the ultra-relativistic limit (γv >> 1/g), gluon radiation is suppressed by the “dead cone effect”

• Heavy quark inside QGP medium: Brownian motion• Description: Langevin equation

c

q q

g

c

medium

θ

collisional radiative

Heavy Flavor Evolution inside QGP(Energy Loss Mechanisms)

What shall we modify to go from RHIC to LHC?HQ becomes ultra-relativistic – cannot ignore gluon radiation

Heavy Flavor Evolution inside QGP( Improved Langevin Approach )

Modified Langevin Equation:

Fluctuation-dissipation relation between drag and thermal random force:

Transport Coefficients:

Force from gluon radiation:

Gluon distribution taken from Higher Twist calculation:

Guo and Wang, PRL 85, 3591; Majumder, PRD 85, 014023; Zhang, Wang and Wang, PRL 93, 072301.

Heavy Quark Energy Loss

• Collisional energy loss dominates low energy region, while radiative dominates high energy region.

• Crossing point: 6 GeV for c and 16 GeV for b quark.• Collisional energy loss alone may work well to

describe previous RHIC data but is insufficient for LHC.

Heavy Flavor Hadronization: Fragmentation + Recombination

• Most high momentum heavy quarks fragment into heavy mesons: use PYTHIA 6.4

• Most low momentum heavy quarks hadronize to heavy mesons via recombination (coalescence) mechanism: use the sudden recombination model

Y. Oh, et al., PRC 79, 044905 (2009)

The Sudden Recombination Model

Distribution of the i th kind of particle

Two-particle recombination:

Light quark: fermi-dirac distri. in the l.r.f of the hydro cellHeavy quark: the distribution at Tc after Langevin evolution

Probability for two particles to recombine

Variables on the R.H.S. are defined in the c.m. frame of the two-particle system.

Fragmentation dominates D meson production at high pT.

Recombination significantly enhances the D meson spectrum at intermediate pT.

Use f W to calculate Pcoal.(pHQ) for all channels: D/B Λ Σ Ξ Ω

Normalization: Pcoal.(pHQ=0) =1

Use Monte-Carlo to determine the hadronization channel of each HQ: frag. or recomb.? recomb. to D/B or a baryon?

The Hybrid Coal. + Frag. Model

Sum up: Heavy Flavor inside QGP• Generation of QGP medium: 2D viscous hydro from OSU

group (thanks to Qiu, Shen, Song, and Heinz)• Initialization of heavy quarks: MC-Glauber for position

space and pQCD calculation for momentum space• Simulation of heavy quark evolution: the improved

Langevin algorithm in the local rest frame of the medium• Hadronization of HQ into heavy meson: frag. + recomb.

outside the medium(below Tc)hadronize

D=6/(2πT), i.e., qhat around 2~3 GeV2/fm at initial temperature (around 350~400 MeV)

RAA of LHC D meson

• Collisional dominates low pT, radiative dominates high pT.• The combination of the two mechanisms provides a good

description of experimental data.

RAA of LHC D meson

• Shadowing effect reduce RAA significantly at low pT.• Recombination mechanism raise RAA at medium pT.

frag. only: force fragmentation, i.e., fW(q)=0 for any q.recomb. only: force combination, i.e., fW(q)=1 for any q.Recombination mechanism provides larger v2 than fragmentation. However, due to the momentum dependence of the Wigner function, our combined mechanism only slightly raises the D v2 at medium pT.

v2 of LHC D meson

RAA and v2 of RHIC D Meson

Recombination mechanism has a significant contribution to RAA at RHIC energy.With the incorporation of the low energy effect (shadowing and recombination), our improved Langevin framework provides good descriptions of the RHIC data.

Angular Correlation of QQbar

Δθ

At LO: Back-to-back production of initial QQbar with the same magnitude of momentum

Angular De-correlation of CCbar

• Though each energy loss mechanism alone can fit RAA with certain accuracy, they display very different behaviors of angular de-correlation.

• Pure radiative energy loss does not influence the angular correlation significantly; pure collisional leads to peak at collinear distribution because of the QGP flow.

• MCNLO + Herwig radiation for HQ initial production

• Angular correlation function of final state ccbar pairs

• Within each event, loop each D with all Dbar’s

• Similar shape as ccbar pairs, but on top of a large background

More Realistic Analysis

Experimental observations will help distinguish the energy loss mechanisms of heavy quark inside QGP.

Summary

• Study the heavy flavor evolution and hadronization in QGP in the framework of the Langevin approach

• Improve the Langevin algorithm to incorporate both collisional and radiative energy loss of heavy quark

• Reveal the significant effect of gluon radiation at high energies and recombination at medium energies, and provide good descriptions of D meson suppression and flow measured at both RHIC and LHC

• Discussed about a potentially measurable quantity – angular correlation function of HF pairs – that may help distinguish the HQ energy loss mechanisms

Thank you!

Numerical Implementation (Ito Discretization)

Drag force:

Thermal random force:

Momentum of gluon radiated during Δt:

Lower cut for gluon radiation: πT

• Balance between gluon radiation and absorption

• Guarantee equilibrium after sufficiently long evolution

Heavy Flavor Evolution inside QGP( Improved Langevin Approach )

Charm Quark Evolution in Static MediumT = 300 MeV, D=6/(2πT), i.e., qhat ~ 1.3 GeV2/fm

Einit = 15 GeV z

Evolution of E distribution

•Before 2 fm/c, collisional energy loss dominates; after 2 fm/c, radiative dominates;•Collisional energy loss leads to Gaussian distribution, while radiative generates long tail.

Prediction for B Meson Measurements

The shadowing effect for b-quark is not as significant as c-quark, but still non-negligible. “Anti-shadowing” at RHIC energy.

Different geometries and flow behaviors of the QGP medium influence heavy flavor v2 while does not significantly impact the overall suppression (SC, Qin and Bass, J. Phys. G40 (2013) 085103 )Currently use smooth initial condition for hydro evolution, an event-by-event study of HQ may result in different final state spectrumNo hadronic interaction yet after the QGP phase

Uncertainties of v2

The Sudden Recombination Model

N: normalization factorgM: statistics factor e.g. D ground state: 1/(2*3*2*3)=1/36 – spin and color D*: 3/(2*3*2*3)=1/12 – spin of D* is 1ΦM: meson wave function – approximated by S.H.O.

Integrating over the position space leads to

μ: reduced mass of the 2-particle systemω: S.H.O frequency – calculated by meson radius 0.106 GeV for c, and 0.059 GeV for b

Can be generalized to 3-particle recombination (baryon)

Questions to be Discussed• How to quantify such distribution functions• How to subtract the large background of non-correlated heavy

meson pairs (Zero Yield at Minimum [ZYAM]? Will over-subtract the background for heavy flavor.)

• Theoretical uncertainties – initial production of QQbar pairs: similar single particle spectra but different angular distribution

pT Dependence of Angular De-correlation

Δθ

π-Δθ

• The de-correlation behavior strongly depends on HQ pT.• Collisional: charm quarks below 2 GeV are close to thermal,

but above 2 GeV are off-equilibrium.• Radiative: CCbar pair remains strongly correlated.

For the limit of uniform distribution between [0,π]:

Prediction for LHC B Meson

The shadowing effect for b-quark is not as significant as c-quark, but still non-negligible.The dip in the B meson v2 results from the transition behavior from the collisional dominating region to the radiative dominating region. (SC, Qin and Bass, Nucl. Phys. A904-905 (2013) 653c-656c)

Prediction for RHIC B Meson

Instead of “shadowing”, RHIC b-quark has “anti-shadowing” effect at low pT.

Check of Detail BalanceModified Langevin Equation:

Gluon radiation only, may break the detail balance

Cut off gluon radiation at low energies where collisional energy loss dominates and detail balance is preserved.

Large enough cut reproduces charm quark thermalization behavior.

More rigorous solution: include gluon absorption term into the higher-twist formalism directly and recalculate term.

Back up: the dip of B meson v2

During the transition from the collisional dominating region the radiative dominating region, a dip may occur in the v2 spectrum, might be more significant for KLN initial condition than Glauber because the former leads to higher peaks of v2.

Glauber for hydro frag. only

RAA and v2 of RHIC Heavy-decay Electron

The b/c ratio in the initial production is tuned to be 0.3% in order to describe the measured RAA – slightly smaller than the usually adopted value (0.5 ~ 1%).

Recombination ProbabilityUse the Wigner function to calculate Pcoal.(pHQ) for all channels: D/B Λ Σ Ξ Ω

Fix N: Pcoal.(pHQ=0) =1

Normalization is tuned in the lab frame with Teff = 175 MeV to mimic the flow (0.6c) effect of 165 MeV (Tc) hydro medium

• Generate random number: frag. or recomb.? recomb. to D/B or baryons?

• If recombine to D/B, pick up a light quark in the cell frame (Monte Carlo according to the Wigner function), boost into the lab frame and combine with the heavy quark.

Consistency between our calculation and the latest ALICE data from Quark Matter 2012

RAA of D meson

Similar trend of competition between the two energy loss mechanisms as revealed by RAA Different geometries and flow behaviors of the QGP medium may have impact heavy flavor v2 while does not significantly influence the overall suppression (SC, Qin and Bass, arXiv:1205.2396)Influence of coalescence mechanism and hadronic interaction

KLN provides larger eccentricity for the QGP profile than Glauber and therefore larger D meson v2

v2 of D meson

Prediction for B Meson

• Similar behaviors as D meson – collisional energy loss dominates low pT region, while radiative dominates high pT.

• The crossing point is significantly higher because of the much larger mass of bottom quark than charm quark.

• B meson has larger RAA and smaller v2 than D meson.