Gluon Radiation of the Heavy Quark in Nuclei

Gluon Radiation of the Heavy Gluon Radiation of the Heavy QuarkQuark

in Nucleiin Nuclei

Ben-Wei ZhangBen-Wei ZhangInstitute of Particle PhysicsInstitute of Particle Physics

Central China Normal UniveristyCentral China Normal Univeristy

Weihai, Shandong --- Augest 4, 2004Weihai, Shandong --- Augest 4, 2004

Ben-Wei Zhang @ Weihai Ben-Wei Zhang @ Weihai 22

OutlineOutline

MotivationMotivationTwist expansion approachTwist expansion approachModified heavy quark fragmentation functionModified heavy quark fragmentation functionHeavy quark energy lossHeavy quark energy loss

------ ------ Heavy Heavy VSVS.. LightLightConclusionsConclusions


Jet QuenchingJet Quenching

Jet quenching has been observed as a Jet quenching has been observed as a new nuclear phenomenon at RHIC.new nuclear phenomenon at RHIC.

hadrons

ph

parton

E


From Light to HeavyFrom Light to Heavy

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

calculations of the energy loss of a light quark.calculations of the energy loss of a light quark. For massive quarks, the formalism of medium-induced For massive quarks, the formalism of medium-induced

gluon radiation is not developed to the same extent.gluon radiation is not developed to the same extent.

Experiment: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.


Heavy Quark Energy Loss Heavy Quark Energy Loss

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

Dokshitzer and KharzeevDokshitzer and Kharzeev

Djordjevic and GyulassyDjordjevic and Gyulassy

Armesto, Salgado and WiedemannArmesto, Salgado and Wiedemann

…… ……Twist Expansion approach in pQCDTwist Expansion approach in pQCD

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


Jet quenching with pQCDJet quenching with pQCD

How to measure the parton energy loss?How to measure the parton energy loss?Direct measurement is impossibleDirect measurement is impossibleParticle distributions within a jetParticle distributions within a jetModification to Fragmentation FunctionModification to Fragmentation FunctionObtain the energy loss indirectly from Obtain the energy loss indirectly from

measuring the modification of FFmeasuring the modification of FF


Heavy QuarkHeavy Quark In parton model, for the heavy quark production we In parton model, for the heavy quark production we

obtain :obtain :


Fragmentation FunctionFragmentation Function

Charm quark fragmentation function in Peterson form:Charm quark fragmentation function in Peterson form:


Mutiple Scattering in NucleiMutiple Scattering in Nuclei

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

factorizingfactorizing..


Factorization of Twist-4Factorization of Twist-4

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


Generalized FactorizationGeneralized Factorization


Quark-Gluon Double ScatteringQuark-Gluon Double Scattering


Collinear ApproximationCollinear Approximation

Make a collinear approximation:Make a collinear approximation:

The tensor structure can be factorized:The tensor structure can be factorized:


LPM EffectLPM Effect

LMP interference effect.

The formation time of gluon radiation.


Other ProcessesOther Processes


Hard Partonic PartHard Partonic Part

Dead-Cone effect of heavy quark propagatingDead-Cone effect of heavy quark propagating


Modified FF of Heavy Quark 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


Twist-4 Parton CorrelationTwist-4 Parton Correlation


Two-parton Correlation FunctionTwo-parton Correlation Function

Twist-4 parton correlation Twist-4 parton correlation

function is in principle function is in principle

not calculable.not calculable.

With some approximations we can estimate

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


Heavy Quark Energy LossHeavy Quark Energy Loss

Twist-4 correlation functions approximated as:Twist-4 correlation functions approximated as:

Heavy quark energy loss can be derived as:


Two LimitsTwo Limits

(1) When (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


Nuclear Size DependenceNuclear Size Dependence


Heavy Quark Heavy Quark VS.VS. Light Quark Light Quark

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


ConclusionsConclusions

Heavy quark energy loss induced by gluon radiation Heavy quark energy loss induced by gluon radiation is derived in terms of Modified FF with pQCD.is derived in terms of Modified FF with pQCD.

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

Heavy quark energy loss is significantly suppressed Heavy quark energy loss is significantly suppressed relative to a light quark due to mass effect. relative to a light quark due to mass effect.

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


Thank you very much!

谢谢 !

Thank you very much!

谢谢 !

Gluon Radiation of the Heavy Quark in Nuclei

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