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Introduction to Heavy Quark Production

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. Outline. How heavy is a heavy quark?. Heavy quarks and heavy quark mesons.

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Introduction to Heavy Quark Production

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  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

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  24. Color evaporation model vs data Jianwei Qiu, ISU

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  26. Difficulties of these models Jianwei Qiu, ISU

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

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  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

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