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Charm as a probe of QGP

Che-Ming KoTexas A&M University

Charm flow and energy loss Charmed baryon-to-meson ratiosCharmonium regeneration and flow Charm production Charm exotics

Collaborators: Su Houng Lee (Yonsei Univ.), Yongseok Oh (TAMU), Shigehiro Yasui (KEK), Ben-wei Zhang (Huazhong Normal Univ.), Bin Zhang (Arkansas State Univ.) …..

Supported by National Science Foundation and The Welch Foundation

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Importance of charm production in HIC

Essential for understanding charmonium production: Braun-Munzinger, Thews, Greco ….

Charmed exotics:

- Yield depends quadratically on the charm quark number in statistical,kinetic, and coalescence models

- Possible stable charmed tetraquark meson and pentaquark baryon (Lee, Yasui, Liu & Ko, EPJC 54, 259 (2007))

)cc(udTcc)cudus(scΘ

Probe of charm interactions in quark-gluon plasma: Moore, Teaney …

- DsJ (2317) as a tetraquark meson ( ) (Chen, Liu, Nielsen, Ko,PRC 76, 014906 (2007))

qqsc

Probe of diquarks in QGP- Enhanced Λc production (Lee, Ohnishi, Yasui, Yoo & Ko, PRL100, 222301 (2008); Oh et al.)

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Greco, Rapp, Ko, PLB595, 202 (04)

S. Kelly,QM04

Charmed meson elliptic flow

v2 of electrons

Data consistent with thermalizedcharm quarks with similar v2 as lightquarks

Smaller charm v2 than light quarkv2 at low pT due to mass effectQuark coalescence

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Charm quark elliptic flow from AMPT

PT dependence of charm quark v2 is different from that of light quarksAt high pT, charm quark has similar v2 as light quarksCharm elliptic flow is also sensitive to parton cross sections

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Charm RAA and elliptic flow from AMPTZhang, Chen & Ko, PRC 72, 024906 (05)

Need large charm scattering cross section to explain dataSmaller charmed meson elliptic flow is due to use of current lightquark masses

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Charm suppression and elliptic flow D. MolnarEPJ C49, 181 (2007)

Large parton cross sections are needed to explain data

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Charm elliptic flow from the Langevin model

Moore & Teaney, PRC 71, 064904 (2005)

pQCD gives D≈a/(2πT) in QGP with a=6 but data require a=1.5

a=1.5

a=3

a=6

a=12

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Resonance effect on charm scattering in QGP

Van Hees & Rapp, PRC 71, 034907 (2005)

( ) 4/m-k41J2

91

2D

2D

2/1

2D

2qc→qcΓ+

Γ+=

sπσ

With mc≈1.5 GeV, mq≈5-10 MeV, mD≈2 GeV, ΓD≈0.3-0.5 GeV, and including scalar, pseudoscalar, vector, and axial vector D mesons gives

σcq→cq(s1/2=mD)≈6 mb

Since the cross section is isotropic, the transport cross section is 6 mb, which is about 4 times larger than that due to pQCD t-channel diagrams, leading to a charm quark drag coefficient γ ~ 0.16 c/fm in QGP at T=225 MeV.

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Van Hees, Greco, and Rapp, PRC 73, 034913 (2006)

Langevin simulation with resonance scattering and including both coalescence and fragmentation can explain the data

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Heavy quark energy loss in pQCDa) Radiative energy loss (Amesto et al., hep-ph/0511257)

b) Radiative and elastic energy loss (Wicks et al., nucl-th/0512076)

c) Three-body elastic scattering (Liu & Ko, nucl-th/0603004)

a) +

+ ⋅ ⋅ ⋅

May be important as interparton distance ~ range of parton interactionAt T=300 MeV, Ng~(Nq+Nqbar)~ 5/fm3, so interparton distance ~ 0.3 fmScreening mass mD=gT~600 MeV, so range of parton interaction ~ 0.3 fm

a) +b) + + ⋅ ⋅ ⋅

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Reasonable agreement with data from Au+Au @ 200A GeV after including heavy quark three-body scattering and increasing αs by 2 as given by lattice QCD.

Spectrum and nuclear modification factor of electrons from heavy meson decay

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Sorenson, EJPC 49, 379 (2007)

Enhancement of charmed baryon to meson ratioon non-photonic electrons in HIC

Assuming that same Λc/D0 and Λ/K0 ratios could also explain observed nuclear modification factor for charmed mesons

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Martinez-Garcia, Gadrat & Crotchet, PLB 663, 55 (2008)

Enhanced production of Λc reduces the nuclear modification factorfor charm mesons

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Diquark in sQGP and Λc enhancement Lee, Yasui, Ohnishi, Yoo& Ko, PRL100, 222301 (2008)Diquark mass due to color-spin interaction:

MeV450mm

1ss C-mmmdu

dudu[ud] ≈⋅+≈rr

Coalescence model Statistical model

( ) 24.0emm

2D

c0Dc

0

c T/mm-2/3

D0

c ≈⎟⎟⎠

⎞⎜⎜⎝

⎛≈

Λ −Λ Λ

Enhanced by a factor of 4-8Similar for ΛB/B0

for mu=md= 300 MeV and C/mu2~195 Me V from mΔ-mN

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Inclusion of resonances and fragmentation Oh et al., arXiv:0901,1382 [nucl-th]

Including coalescence contribution enhances Λc/D0 ratio, which isfurther enhanced by the presence of diquarks in QGP

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As for Λc/D0, including coalescence contribution enhances Λb/B0

ratio, and it is further enhanced by the presence of diquarks in QGP

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Charmonium spectra and elliptic flow Zhang, PLB 647, 249 (2007)

AMPT shows that charmonium elliptic flow is appreciable and increases with increasing parton cross sections

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Zhang, PLB 647, 249 (2007)

In AMPT, large (small) charm quark scattering cross section leads to suppressed (enhanced) yield but larger (smaller) elliptic flow.

J/ψ production from charm quark coalescence

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Zhao & Rapp, arXiv:0810.4566 [nucl-th]

Nuclear modification factor for charmonium

Regeneration from coalescence of charm and anticharm quarksis non-negligible at RHIC as first pointed out by Thews

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Charm production in HIC

Direct production: Meuller, Wang (92); Vogt (94); Gavin (96) …..

Pre-thermal production: Lin, Gyulassy (95), Levai, Meuller, Wang (95)…..

Thermal production from QGP: Levai, Vogt (97) …..

Thermal production from hadronic matter: Cassing et al. (99), Liu & Ko (02)- πN→ΛcD and ρN→ΛcD- Small effect on charm production in HIC

- Mainly from initial gluon fusions- About 3 pairs in mid-rapidity at RHIC (from STAR collaboration)- About 20 pairs in mid-rapidity at LHC

- Not important based on minijet gluons - Production from initial strong color field?

- Based on leading-order calculations - Important if initial temperature of QGP is high

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Thermal charm production in QGP Zhang, Liu & Ko,PRC 77, 024901 (08)

Thermal production at LHC non-negligibleNext-leading order and leading order contributions are comparableInsensitive to gluon massesEffect increases by about 2 for initial temperature T0=750 MeV but decreases by ~ 3 for T0=630 MeV

mc=1.3 GeVαs=0.3

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Charm production from three-gluon interaction ggg→cc

( ) ( ) eqc

eqcgggcc54321

)4(2

ccgggiii

5

1i

3 nnvp-p-pppMpfpd31R →→

=

∝++∝ ∫∏ σδ

Determine rate for from via detailed balance

Negligible rate for massivegluons as the threshold becomes larger than the charm pair massWith massless gluons, the rate is comparable to that of two-body processes

ccggg → gggcc →

Gluon density ~ 0.5/fm3 at TCand much larger initially

23Works very well with 3x CB = CM = 635 mu2

u u d

[ ]∑ ⋅ jiji

B ssmm

C

MeV 4700m MeV, 1500m MeV, 500m MeV, 300mm bcsdu =====

Baryon mass differences

Meson mass differences

d u

[ ]∑ ⋅ jiji

M ssmm

C

Diquark

Quark-antiquark

Quark color-spin interaction and hadron massesLee, Yasui, Liu & Ko, EPJC 54, 259 (2007))

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Tetraquark (udq1q2) mesons_ _

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Pentaquark (udusq) baryons_

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Charm tetraquark mesons

- Tcc ( ) is ~ 80 MeV below D+D* according to quark model- Coalescence model predicts a yield of ~5.5X10-6 in central Au+Aucollisions at RHIC and ~9X10-5 in central Pb+Pb collisions at LHCif midrapidity charm quark numbers are 3 and 20, respectively

- Yields increase to 7.5X10-4 and 8.6X10-3, respectively, in the statistical model

ccud

Charmed pentaquark baryons

- Θcs( ) is ~ 70 MeV below D+Σ in quark model- Yield is ~1.2X10-4 at RHIC and ~7.9X10-4 at LHC from the

coalescence model for midrapidity charm quark numbers of 3 and 20, respectively

- Statistical model predicts much larger yields of ~4.5X10-3 at RHIC and ~2.7X10-2 at LHC

cudus

Charm exotics production in HIC Lee, Yasui, Liu & Ko,EPJC 54, 259 (2007)

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Decay modes of Tcc andΘcs

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Mass of 2317 MeV less than those predicted by quark model and QCD sum rule for two-quark state (c ) but comparable to those for four-quark state (c q )

Width of a few (two-quark) to a few tens (four quark) keVfrom decay to isospin violated channel of Dsπ, empirically less than 4.6 MeV limited by experimental resolution.

Observed in elementary reactions: - BABAR: from Ds+π0 inclusive invariant mass distribution

in e+e- annihilation (PRL 90, 242001 (03)) - Belle: from B decay (PRL 91, 262002 (03))

Dsj(2317): Jπ=0+

ss q

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DsJ production at RHIC

Cross sections shown are for four-quark state and are larger by ~9 for two-quark state. Final yield is sensitive to the quark structure of DsJ

Chen, Liu, Nielsen & Ko, PRC 76, 014906 (2007))

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Summary

Charm quarks interact strongly in QGP and including heavy quarkthree-body scattering in QGP helps to explain observed nuclear modification factor of electrons from heavy meson decays.

Existence of diquarks in QGP enhances Λc and Λb production at RHIC and affects the yield of heavy mesons and thus the nuclear modification factor of electrons from cha meson decays.

Charmonium regeneration is non-negligible at RHIC and expect appreciable charmonium elliptic flow.

Thermal charm production could be important at LHC as the production rate increases exponentially with the temperature of QGP.

Enhanced charm production at LHC offers the opportunity to search for possible charmed exotics such as Tcc, Θcs and Dsj.