Heavy Quark Energy Loss with Twist Expansion

Approach

Ben-Wei ZhangInstitute of Particle Physics

Central China Normal Univeristy

CCAST, Beijing --- Augest 10, 2004

Thanks to my collaborators: Xin-Nian Wang and Enke Wang

2-------------------------------------------Ben-Wei Zhang @ CCAST, Beijing

Outline

• Motivation

• Twist expansion approach

• Modified heavy quark fragmentation function

• Heavy quark energy loss

------ Heavy VS. Light

• Conclusion

3-------------------------------------------Ben-Wei Zhang @ CCAST, Beijing

Jet QuenchingJet Quenching

Jet quenching has been discovered at RHIC as a good probe of the hot/dense matter.

hadrons

ph

parton

E

X.N. Wang, nucl-th/0405017

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From Light to Heavy

Theory:• A lot of theoretical studies have been devoted to the

calculations of the energy loss of a light quark.

• For massive quarks, the formalism of medium-induced gluon radiation is not developed to the same extent.

Experiment:• Open charm suppression, which can now be measured at

RHIC by comparing pt distributions of D-mesons in D-Au and Au-Au collisions, is a novel probe of QGP dynamics.

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Heavy Quark Energy Loss

• There are several theoretical calculations to obtain the heavy quark energy loss:

Yu.L. Dokshitzer and D.E. Kharzeev M. Djordjevic and M. Gyulassy B.W.Zhang, E. Wang and X.N. Wang N. Armesto, C. Salgado and U. Wiedemann

……• Twist Expansion approach in pQCD

B.W. Zhang, E. Wang and X.N. Wang, PRL 93(2004) in press

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Jet quenching with pQCD

• How to measure the parton energy loss?

• Direct measurement is impossible

• Particle distributions within a jet

• Modification to Fragmentation Function

• Obtain the energy loss indirectly from measuring the modification of FF

hadrons

ph

parton

E

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Heavy QuarkHeavy Quark In eA DIS, for the heavy quark production we obtain :In eA DIS, for the heavy quark production we obtain :

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Multiple Scattering in NucleiMultiple Scattering in Nuclei

In order to calculate the heavy quark energy loss induced by gluon radiation in pQCD, we should separate the ‘hard’ part from the ‘soft’ part:

factorizing.

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Generalized Factorization

Luo, Qiu, Sterman, PLB 279(1992)377;Luo, Qiu, Sterman, PRD 49(1994)4493; PRD 50(1994)1951

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Quark-Gluon Double Scattering

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Tensor Structure

• Making a collinear approximation:

• The tensor structure can be factorized as:

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LPM Effect

LMP interference effect.

The formation time of gluon radiation.

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Other ProcessesOther Processes

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Hard Partonic Part

Dead-cone effect of heavy quark propagating will suppress gluon radiation at small angles.

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Modified FF of Heavy Quark With the generalized factorization theorem we With the generalized factorization theorem we

obtain the semi- inclusive hadronic tensor:obtain the semi- inclusive hadronic tensor:

The modified effective fragmentation function is

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Two-parton Correlation FunctionTwist-4 parton correlation function is in principle not calculable.

With some approximations we can estimate the twist-4 correlation functions approximated as

J. Osborne and Xin-Nian Wang, NPA 710(2002)281

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Heavy Quark Energy Loss

Heavy quark energy loss can be derived as:

Xiao-fen Guo, Xin-Nian Wang, PRL 85(2000)3591;

Xin-Nian Wang, Xiao-fen Guo, NPA 696(2001) 788

Ben-Wei Zhang, Xin-Nian Wang, NPA 720(2003) 429

When M=0, we will recover the result of the light quark energy loss.

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Two Distinct Limits

(1) When

2QQ^2

(2) For large values of Q(2) For large values of Q2 2 or small xor small xBB, we have, we have

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Nuclear Size Dependence

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Heavy Quark VS. Light Quark

Energy loss of heavy quark is significantly suppressed due to mass effect, in particular, the dead-cone effect.

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Conclusion• Heavy quark energy loss induced by gluon radiation is

derived in terms of Modified FF with pQCD.

• Two mass effects:

(I) Gluon formation time of the heavy quark is reduced relative to that of a light quark:

Medium size dependence of heavy quark enegy loss is found to change from a linear to a quadratic form when the initial energy and momentum scale are increasing.

(II) Dead-cone effect: Heavy quark energy loss is significantly suppressed

relative to a light quark.

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Thank you very much!

谢谢 !

Thank you very much!

谢谢 !

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Backup

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Factorization of Twist-4

Luo, Qiu, Sterman, PLB 279(1992)377;Luo, Qiu, Sterman, PRD 49(1994)4493; PRD 50(1994)1951

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Twist-4 Parton Correlation

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Factorization of Twist-4 Matries