1. Effects of minijet degradation on hadron observables in heavy-ion collisions Lilin Zhu Sichuan University QPT2013, Chengdu

2. Outline  Introduction  Physics ideas of the recombination model  New property of minijet distribution  Hadronic spectra  Conclusion Lilin Zhu2

3. QPT2013, Chengdu3 Transverse momentum spectra pTpT 26 lowintermediatehigh pQCD hydro no rigorous theoretical framework At intermediate p T recombination model has been successful. That is where abundant experimental data exist.

4. Lilin ZhuCPOD2011, Wuhan4 ReCo models  Duke group: I. 6-dimensional phase space II. using Wigner function from density matrix  Texas A&M/Budapest I. Monte Carlo implementation II. Soft and hard partons III. Soft-hard coalescence is allowed  Oregon group: I. one-dimensional momentum space II. using phenomenological recombination function PRL90,202301(03), PRC68,044902(03), ArXiv:1102.5723. PRL90,202302(03), PRC68,034904(03). PRC67,034902(03), PRC70,024905(04). Hwa, QGP4, p.267.

5. QPT2013, Chengdu Oregon recombination model p T distributions of and p Recombination functions Hwa, Phys. Rev. D (1980). S : shower parton T : thermal parton = T T + T S + SS =T T T + T T S + T SS + SSS fragmentation Lilin Zhu 5 Parton distributions before recombination

6. QPT2013, Chengdu Parton distributions Thermal partons: Shower distribution Lilin Zhu6 SPD, Obtained from FF, Hwa-Yang (04) T is the inverse slope parameter, not the hydro temperature let’s see how to take parton momentum degradation into account hard and semihard parton distributions at the medium surface. Integrated over all initial creation points.

7. Lilin Zhu p2p2 dynamical path length Fries, et al PRC(03) The process of momentum degradation parton distribution at creation point Calculation in pQCD is not reliable at intermediate q and difficult to account for the nuclear complications at various c and The degradation of momentum from k to q can be written as a simple exponential Hwa-Yang(10) Nuclear complicatioin is in the determination of 7 QPT2013, Chengdu

8. Lilin ZhuQPT2013, Chengdu8 The probability of having at and c in the medium Since depends on the nuclear medium and the azimuthal angle, so we could express in terms of angle and centrality c. That is contained in the probability function in relating to

9. Mean dynamical path length Lilin ZhuQPT2013, Chengdu9 As the system expands, the density D decreases but t 1 increases, so is not very sensitive to the expansion dynamics. probability of production of a (semi)hard parton at creation point x 0 and y 0 The dynamical effect of energy loss per unit length i=g, q. Whereas depends on, c implicitly, the mean depends on them explicitly. determined by fitting nuclear modification factor The geometrical path length is weighted by the local density along the trajectory marked by t. not time Hwa-Yang(10)

10. Lilin ZhuQPT2013, Chengdu10 Mean dynamical path length Points determined from calculation that account for nuclear complications.

11. Lilin ZhuQPT2013, Chengdu11 For calculating the p T spectra of any hadron produced later, we make averaged over No momentum degradation More suppression for gluons than for quarks throughout the whole region. Minijet distribution at RHIC minijet distribution, averaged over, initial creation points.

12. Minijet Degradation Factor QPT2013, ChengduLilin Zhu Increase is rapid at low q. R g is roughly half of R q, but q and c dependencies are similar in shape. 12 It is analogous to the nuclear modification factor R AA for, but for minijets.

13. parametrization for Lilin ZhuQPT2013, Chengdu13 Tsallis distribution could fit the minijet distribution very well T t =0.32 is universal; n i depends on parton type.

14. pion production Lilin ZhuQPT2013, Chengdu14 The formalism for recombination of thermal and shower partons has been developed previously. Hwa-Yang, PRC(04) Hwa-Zhu, PRC(11) Now we generalize to non-central collisioins, especially show the contributions from various species of semihard partons Zhu-Hwa, 1307.3328 The two shower partons are from the same minijet with momentum q TT TS SS

15. proton production Lilin ZhuQPT2013, Chengdu15 TTT TTS SSS TSS

16. pion at central collision Lilin ZhuQPT2013, Chengdu16 The inverse slope is adjusted to fit the low p T behavior. T=0.283 GeV. It’s the same value for all hadrons at low p T. The p T of TS and SS are fixed by minijets, whose magnitudes depend on. TT TS SS

17. QPT2013, ChengduLilin Zhu Zhu-Hwa, 1307.3328 17 pion Only vary C(N part ) for the thermal partons. No parameters are adjusted for the shape of the p T distribution at intermediate and high p T region at all centralities.

18. proton Lilin ZhuQPT2013, Chengdu18 It is our prediction for proton p T >5 for c > 20%. Quark minijets are more influential than gluons in the proton distribution at high p T.

19. Kaon Lilin ZhuQPT2013, Chengdu19 Good fit out to 9 GeV/c for all centralities.

20. p/pi at RHIC QPT2013, Chengdu  For 0-10% the ratio is very well reproduced.  For 20-40% not as well around the peak. Lilin Zhu20

21. Lilin ZhuQPT2013, Chengdu21 at LHC

22. pion Hwa-Zhu, PRC (11) Lilin Zhu QPT2013, Chengdu 22 Pb-Pb collisions at 2.76 TeV  At LHC minijets are pervasive and their effects dominate the spectra at the low and intermediate p T range.  TS>TT at p T >0.5 GeV/c. RHIC TT TS SS Zhu-Hwa, 1307.3328

23. Lilin ZhuQPT2013, Chengdu23 K/p/Λ spectra (0-5% Central) T=0.38 for thermal partons is higher than 0.283 at RHIC. For p and Λ, TTS>TTT 0-5 ％ Hwa-Zhu, PRC(11)

24. Lilin ZhuQPT2013, Chengdu effect of minijets at LHC T=0.38 GeV at LHC T=0.283 GeV at RHIC 24 Due to the abundant production of minijet, TS is elevated going from RHIC to LHC

25. QPT2013, Chengdu Summary & outlook  new features of momentum degradation of minijets produced at intermediate q before hadronization.  p T and c dependencies of hadronic observables are well reproduced-- by the minijet approach in the framework of the recombination model  Extension of the study to hyperons production, such as: Omega.  Hadron production at LHC. Lilin Zhu25

26. QPT2013, Chengdu Thank you! Lilin Zhu26

27. QPT2013, Chengdu backup Lilin Zhu27

28. Hwa-Zhu, (12) QPT2013, ChengduLilin Zhu28 The good fits support our minijet approach to the treatment of azimuthal anisotropy.

29. Lilin ZhuCPOD2011, Wuhan29 Determining RFs  R p was determined from CTEQ  From the parton distributions in proton  a=b=1.755, c=1.05 at Q 2 =1GeV 2  R  was determined from Drell-Yan processes  a=b=0  See Phys. Rev. C 66, 025204

30. Lilin ZhuCPOD2011, Wuhan30 Recombination functions Given by the valon distribution of the hadrons

31. Lilin ZhuCPOD2011, Wuhan31 Recombination model for fragmentation Fragmentation function known from fitting e+e- annihilation data S  V  G  S K G K Biennewies, Kniehl, Kramer Kniehl, Kramer, Pötter Recombination function known in the recombination model Hwa, Phys. Rev. D (1980). Shower parton distributions K, L, G, L s, G s Hwa and Yang, PRC70,024904(2004)