1、2022-3-17RHIC物理和低能強子物理研討會，威海Combination of Heavy Quarks with Partons from Quark-Gluon Matter: a Scaling Probe山東大學物理系 李世淵 INTRODUCTION : measurement/probe of QGP , via combination processes success of combination models, more rigorous framework needed for measurement FORMULAE for PROCESS heavy + ligh

2、t (from QGP) EXTRACT COMBINATION MATRIX ELEMENTS NUMERICAL ESTIMATES CONCLUSION2022-3-17RHIC物理和低能強子物理研討會，威海Hot dense quark-gluon matter(QGP?) observed at RHIC Quantitatively Measure the Distribution of “QGP” from now onHeinz adds that it is now important to move away from discovery measurements and

3、to begin characterizing the plasmas behaviour. We need to start exploring the details of this new kind of matter, says (Ulrich)Heinz.Nature 430, 498 - 499 (29 July 2004); 2022-3-17RHIC物理和低能強子物理研討會，威海 Can we measure it via combination processes? RC Hwa & CB Yang , Infer the distribution in the fr

4、amework of their model the model nucl-th/0211010, nucl-th/0301004, nucl-th/0302006, nucl-th/0304073, nucl-th/0307112, hep-ph/0312271, nucl-th/0401001, nucl-th/0406072 Key:Final hadron proportional to quark distribution In principle, this can be done by every kinds of QCM How about the combination mo

5、dels? 2022-3-17RHIC物理和低能強子物理研討會，威海QCM(1)Date back to 3 decades ago, In hadronization process V. V. Anisovich et al.,(1973) J. D. Bjorken et al., (1974) K.P. Das & R.C. Hwa(1977) Xie et al. (SDQCM), (1980s) A Bulk of quarks ( Gluons?), Combine accord. to some rulesNow in RHIC, for “QGP” hadroniza

6、tion B. Muller et al., R. Hwa et al., C. Ko et al. (Coalescence), Xie et al., both rate & spectrumboth rate & spectrum Quark Combination Models(QCM) describes hadronization as well as String ,Cluster, Independent Fragmentation, lsy2022-3-17RHIC物理和低能強子物理研討會，威海Combination schemes describe data

7、 in various processes as well as the Fragmentation scheme, which describes inclusive production. PQCD FACTORIZATION They seem succeed the later in RHIC e.g.:),(2zDdkdpddTTh hp pp ph hPerfect scaling for all measured hadrons,some deviation for pions (from decays)The success of combination model also

8、indicates local equilibium 2022-3-17RHIC物理和低能強子物理研討會，威海2M2M33,B33, ,B( ,)( ,(1)( ,)( , )( ,( )( ,(1)2 )(2 )dNP uEddxd PdNPw R xP w Rx Pw R xP w R x PuEddxdxd pwx PxRxxx 2022-3-17RHIC物理和低能強子物理研討會，威海 The success of QCMS for RHIC is “annoyed” by the uncertainties in various models. 2M2M33,B33, ,B( ,)(

9、,(1)( ,)( , )( ,( )( ,(1)2 )(2 )dNP uEddxd PdNPw R xPwRx Pw R xPwR x PuEddxdxd pwx PxRxxx Quark distributionCombination ruleboth by handuncertainties : call for further investigationSo we want to FIX as many as possible.2022-3-17RHIC物理和低能強子物理研討會，威海Theo.: Braaten et al (2002), Phys.Rev.Lett.89:122002

10、,2002 The parton spectra calculated in PQCD, param.:only a probability（more uniform, Ma& Si)QCM(2)Now comes Heavy Quark combinationAsymmetry of D mesons in forward directionExp.: E791: 500GeV -beam on nuclear target2022-3-17RHIC物理和低能強子物理研討會，威海d+Au experiments indicateAt the same time,lspectra ar

11、e harder than PYTHIA extrapolation from low energies! (hard fragmentation function, charm quark recombination ?)2022-3-17RHIC物理和低能強子物理研討會，威海though the light parton spectrum in QGP unknown heavy quark spectrum calculable So We can know more! key: How to describe the combination with one parton from “

12、QGP” in the framework of PQCD factorization Following Qiu and Vitev, start fromFactorization hard proc.+universal param.)(,exqmQCDIAAHNow how about QCM in AA when heavy quarks present?Further step more than nave models2022-3-17RHIC物理和低能強子物理研討會，威海AB1P2PHc21P 22P examplean as , XDBAnDParton Distr. In

13、QGPParton Distr. In QGPCharm Meson ME Hard Inter. Xcba0|0GQhhGQIn principle:More than the nave QCMunknown objects Two2022-3-17RHIC物理和低能強子物理研討會，威海=12qKQz222022-3-17RHIC物理和低能強子物理研討會，威海AB1P2PHc21P 22P nDNormal DGLAPVacuum radiation+medium radiationNo Collinear singularity for heavy!Higher orders factor

14、ization: Infrared cancel between real and virtual everywhere; Collinear for initial parton lead to DGLAP; ANDVR+MR; But collinear absorbed into Evolution2022-3-17RHIC物理和低能強子物理研討會，威海To extract the ME in other processes, e.g., light q frag. into charm meson in e+e-2022-3-17RHIC物理和低能強子物理研討會，威海UNIVERSAL

15、DCM ME, AA 2022-3-17RHIC物理和低能強子物理研討會，威海process? of kindsuch separate Can weSame ME value as Braaten et al.,2022-3-17RHIC物理和低能強子物理研討會，威海Indication of recent data ?!Differences between data and theo. for in e+e-LEP/SLD world average 2001: vs. Theo.:2.007% This diff. leaves space for the recombination

16、process As an first approxi. we can use the value of Braaten More precise measurement: Giga Z!ccg )%38. 096. 2(ccgccg*The MC of the shape of these events indicates that part of which could have been included when measuringDJ Miller et al.,2022-3-17RHIC物理和低能強子物理研討會，威海cDdddShort for TTdpdypdMuch diff.

17、 For various distr.Suit for being probeIn central region, harder than quarkSimple numerical estimation 2022-3-17RHIC物理和低能強子物理研討會，威海CONCLUSION Quark-gluon matter to be measured RHIC &LHC QCM successful in RHIC, can be used for measure Uncertainties both quark distri. and comb. rules In the PQCD f

18、actorization framework, for universal parameters+hard process We have one parameter as “PDF of QGP” & the Simple scaling relation Extract comb. ME from, e.g., light to HM in e+e- Comp. wrt data(RHIC,LHC), we get knowledge on “PDF ”of QGP as well as those of proton, pion photon This is also a good framework for light quark jet combinationAcknowledgementsPart of the work done with 金毅博士金毅博士Topic of D mesons suggested by and discussed many times with 王新年教授王新年教授 Many help