June 25, 2004 Jianwei Qiu, ISU 1 Introduction to Heavy Quark Production Jianwei Qiu Iowa State University CTEQ Summer School on QCD Analysis and Phenomenology June , 2004 University of Wisconsin, Madison, WI

June 25, 2004 Jianwei Qiu, ISU 2 Outline  Summary and outlook  Heavy quarks and heavy quark mesons  How heavy is a heavy quark?  Production of heavy flavors  Hidden heavy flavors - Quarkonia  Heavy quark distribution and intrinsic quark

June 25, 2004 Jianwei Qiu, ISU 3 Six quark flavors in SM   Quark families:   Quark masses:  Quark charges Quark masses span a wide kinematical range: Light quarks < GeV Heavy quarks > GeV Particle data book

June 25, 2004 Jianwei Qiu, ISU 4 How heavy is a heavy quark? Heavy quarks are those that we can calculate their production rate perturbatively   A simple criterion:   QCD running coupling constant:  Minimum pair production energy required ~ 2m Q  Reliable perturbative calculation in QCD requires   Renormalization scale  order of the hard scale Heavy quark mass > GeV But, …

June 25, 2004 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:   bb mesons: nonperturbative binding is involved Nonperturbative physics is always involved in charm and bottom quark production

June 25, 2004 Jianwei Qiu, ISU 6 Top quark is a better heavy quark   Charm and bottom quarks decay slowly and leave enough time to form charm and bottom mesons   Top quark decays very fast, likely before any top meson can be formed Top quark should be a better candidate for studying heavy quark production, and heavy quark properties Much more in Tim Tait’s lecture m c and m b << M W Charm and bottom decay via a virtual W into light qq or ℓ Semi-leptonic decay width:    MeV m t > M W + m b t → W + + b → ℓ + +  or q + q )

June 25, 2004 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  Double counting: Requires heavy flavor parton distributions A part of the heavy flavor creation was included In the evolution of the heavy flavor distributions Only relevant when energy exchange is much larger than heavy quark masses

June 25, 2004 Jianwei Qiu, ISU 8 Heavy flavor creation (pair production)   e+e- annihilation:   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 No machine had enough energy to produce the top/anti-top pairs

June 25, 2004 Jianwei Qiu, ISU 9 Heavy flavor creation (pair production)   Hadron-hadron collision: Dominates if 2m Q /√S >> 0.1 Discovery channel   light quark annihilation to heavy quarks:  gluon fusion to heavy quarks: Dominates if 2m Q /√S << 0.1 Massive production channel

June 25, 2004 Jianwei Qiu, ISU 10 Lowest order pair production   Light quark annihilation: k1k1 p2p2 k2k2 p1p1   Partonic cross section: Threshold constraint More see Ellis’ lecture

June 25, 2004 Jianwei Qiu, ISU 11 From heavy quark to heavy meson   Heavy quark fragmentation is different 2003 CTEQ SS - Cacciari Massless limit Normal DGLAP Heavy quark mass Suppress radiation in a cone of Θ < m Q /E Dead cone effect No collinear divergence

June 25, 2004 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

June 25, 2004 Jianwei Qiu, ISU 13 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: Normalization condition Treated as a free parameter This is just one of many possible models! zPzP

June 25, 2004 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

June 25, 2004 Jianwei Qiu, ISU 15 b-quark at Tevatron We cannot really measure b-quark momentum

June 25, 2004 Jianwei Qiu, ISU 16 b-mesons at Tevatron Peterson fragmentation functions More see Ellis’ lecture Better fragmentation function Cacciari, Nason, PRL 89 (2002)

June 25, 2004 Jianwei Qiu, ISU 17 Heavy quark parton distributions  Heavy flavor excitation:  Subtraction scheme to avoid double counting:  Total heavy quark cross section: + - Heavy quark mass dependence here should be Consistent with DGLAP Aivazis et al Phys. Rev. D50, 3102 (1994)

June 25, 2004 Jianwei Qiu, ISU 18 Hidden heavy flavors - Quarkonia  Heavy quark pairs are produced locally:  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: 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 Q Q H A B meson antimeson Open flavor threshold for the quarkonium production

June 25, 2004 Jianwei Qiu, ISU 19 Hidden heavy flavors - Quarkonia  Quarkonium production: Q Q H h A B  Production models: Different assumptions on the non-perturbative transition from the QQ pair to a quarkonium lead to different production models With  maximum heavy quark velocity in QQ rest frame: Charm: Bottom: Depend on choice of heavy quark mass

June 25, 2004 Jianwei Qiu, ISU 20 Color evaporation model

June 25, 2004 Jianwei Qiu, ISU 21 Non-relativistic QCD (NRQCD) model Quantum states [O] separated by spin and color

June 25, 2004 Jianwei Qiu, ISU 22 NRQCD model vs CDF data

June 25, 2004 Jianwei Qiu, ISU 23

June 25, 2004 Jianwei Qiu, ISU 24 Color evaporation model vs data

June 25, 2004 Jianwei Qiu, ISU 25

June 25, 2004 Jianwei Qiu, ISU 26 Difficulties of these models

June 25, 2004 Jianwei Qiu, ISU 27 NRQCD model vs CDF data on polarization

June 25, 2004 Jianwei Qiu, ISU 28

June 25, 2004 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!