Introduction to Heavy Quark Production

1. Introduction to Heavy Quark Production Jianwei Qiu Iowa State University CTEQ Summer School on QCD Analysis and Phenomenology June 22 - 30, 2004 University of Wisconsin, Madison, WI Jianwei Qiu, ISU

2. Outline • How heavy is a heavy quark? • Heavy quarks and heavy quark mesons • Production of heavy flavors • Heavy quark distributionand intrinsic quark • Hidden heavy flavors - Quarkonia • Summary and outlook Jianwei Qiu, ISU

3. Six quark flavors in SM • Quark families: • Quark charges • Quark masses: Quark masses span a wide kinematical range: Light quarks < GeV Heavy quarks > GeV Particle data book Jianwei Qiu, ISU

4. How heavy is a heavy quark? • A simple criterion: Heavy quarks are those that we can calculate their production rate perturbatively • QCD running coupling constant: • Minimum pair production • energy required ~ 2mQ • Reliable perturbative • calculation in QCD • requires a(m) << 1 • Renormalization scale • m ~ order of the hard scale Heavy quark mass > GeV But, … Jianwei Qiu, ISU

5. No free quarks floating around • QCD color confinement Mesons and baryons in the detectors • Charmed mesons: • Charmed, strange mesons: • Bottom mesons: Light quarks and nonperturbative binding are involved • Bottom, charmed mesons: • cc mesons: Nonperturbative physics is always involved in charm and bottom quark production • bb mesons: nonperturbative binding is involved Jianwei Qiu, ISU

6. Charm and bottom decay via a virtual W into light qq or ℓn t → W+ + b → ℓ+ + n ( or q + q ) Top quark is a better heavy quark • Charm and bottom quarks decay slowly and leave enough time to form charm and bottom mesons mc and mb << MW Semi-leptonic decay width: G ~ 10-10MeV • Top quark decays very fast, likely before any top meson can be formed mt > MW + mb Top quark should be a better candidate for studying heavy quark production, and heavy quark properties Much more in Tim Tait’s lecture Jianwei Qiu, ISU

7. Production of heavy flavors • Heavy flavor creation: Heavy flavor is produced in a hard collision, and No heavy flavor in the initial-state • Heavy flavor excitation: Hard collision librates (or excites) the Initial-state (or intrinsic) heavy flavor contents Q Requires heavy flavor parton distributions Only relevant when energy exchange is much larger than heavy quark masses • Double counting: A part of the heavy flavor creation was included In the evolution of the heavy flavor distributions Jianwei Qiu, ISU

8. Heavy flavor creation (pair production) • e+e- annihilation: No machine had enough energy to produce the top/anti-top pairs • Lepton-hadron collision: No machine had enough energy to produce the top/anti-top pairs If the exchange energy is not too much larger than heavy quark masses, we are able to calculate production rate with a set of the fixed flavor parton distributions without introducing the heavy flavor parton distributions Jianwei Qiu, ISU

9. Heavy flavor creation (pair production) • Hadron-hadron collision: • light quark annihilation to heavy quarks: Dominates if 2mQ/√S >>0.1 Discovery channel • gluon fusion to heavy quarks: Dominates if 2mQ/√S <<0.1 Massive production channel Jianwei Qiu, ISU

10. Lowest order pair production p1 k1 • Light quark annihilation: • Partonic cross section: k2 p2 Threshold constraint More see Ellis’ lecture Jianwei Qiu, ISU

11. Suppress radiation in a cone of Θ < mQ/E Dead cone effect No collinear divergence From heavy quark to heavy meson • Heavy quark fragmentation is different Normal DGLAP Massless limit Heavy quark mass 2003 CTEQ SS - Cacciari Jianwei Qiu, ISU

12. Consequences of the dead cone effect • Heavy quark mass cuts off the collinear divergence: Heavy quark cross section are finite in fixed order pQCD • Large logarithmic high order corrections: • Collinear logs: • Soft logs: • Resummation can improve the predictions for the production rate of heavy quarks • For production of charm and bottom hadrons, there is a need for non-perturbative fragmentation functions Jianwei Qiu, ISU

13. zP Treated as a free parameter Normalization condition Heavy quark fragmentation functions • A fast moving heavy quark of momentum P fragments into a heavy hadron H=Qq of momentum zP: Energy difference before and after the fragmentaton • Peterson function: This is just one of many possible models! Jianwei Qiu, ISU

14. Extraction of fragmentation functions • Heavy quarks in e+e- collisions: • ALEPH analysis (Phys. Lett. B512, 30 (2001) as well as the others Jianwei Qiu, ISU

15. b-quark at Tevatron We cannot really measure b-quark momentum Jianwei Qiu, ISU

16. b-mesons at Tevatron Peterson fragmentation functions Better fragmentation function Cacciari, Nason, PRL 89 (2002) More see Ellis’ lecture Jianwei Qiu, ISU

17. - + Heavy quark mass dependence here should be Consistent with DGLAP Heavy quark parton distributions • Heavy flavor excitation: Aivazis et al Phys. Rev. D50, 3102 (1994) • Subtraction scheme to avoid double counting: • Total heavy quark cross section: Jianwei Qiu, ISU

18. Q meson A H antimeson B Q Hidden heavy flavors - Quarkonia • Heavy quark pairs are produced locally: Heavy quark pairs are produced at a distance scale much less than fm A heavy quark pair needs to be coherently self-interacted and expanded before a heavy quarkonium can be formed • A heavy quark pair is likely to become two open flavor heavy mesons if the invariant mass of the pair is larger than the total mass of the two mesons: Open flavor threshold for the quarkonium production Jianwei Qiu, ISU

19. A Q h H With B Q • maximum heavy quark velocity in QQ rest frame: Charm: Bottom: Different assumptions on the non-perturbative transition from the QQ pair to a quarkonium lead to different production models Hidden heavy flavors - Quarkonia • Quarkonium production: Depend on choice of heavy quark mass • Production models: Jianwei Qiu, ISU

20. Color evaporation model Jianwei Qiu, ISU

21. Quantum states [O] separated by spin and color Non-relativistic QCD (NRQCD) model Jianwei Qiu, ISU

22. NRQCD model vs CDF data Jianwei Qiu, ISU

23. Jianwei Qiu, ISU

24. Color evaporation model vs data Jianwei Qiu, ISU

25. Jianwei Qiu, ISU

26. Difficulties of these models Jianwei Qiu, ISU

27. NRQCD model vs CDF data on polarization Jianwei Qiu, ISU

28. Jianwei Qiu, ISU

29. Summary and outlook • Top quark is the only “true” heavy quark • Non-perturbative information are very important for understanding production of charm and bottom quarks from corresponding mesons • Need better information on heavy quark fragmentation functions • Need better understanding of heavy quarkonium production • See Lectures by Dr. Ellis and Dr. LeCompte in this school! Jianwei Qiu, ISU