Heavy quarks

Accurate theoretical prediction of mass spectra and other properties of hadrons containing heavy quarks is important for mass spectra of hadrons for forthcoming experiments on the study of their properties. At present such facilities as Tevatron, LHC and JHF will have the opportunity to produce hadrons with one or more heavy quarks. The successful experiments at the Collider Detector at Fermilab Collaboration on the observation of the Bc meson (Abe et. ah, 1998) gives some hope to observe heavy quarkonia, also. 

Despite the considerable progress made in the spectroscopy of hadrons containing heavy quarks within the framework of potential models and other approaches, most of the work on the calculation of mass spectra... 

At low energy, the typical momentum transfer by quarks near the Fermi surface is much smaller than the Fermi momentum. Therefore, similarly to the heavy quark effective theory, we may decompose the momentum of quarks near the Fermi surface as... 

G.G. Barnafoldi, P. Levai, and B. Lukacs, Heavy quarks or compactified extra dimensions in the core of hybrid stars , in Proceedings of the 4th Int. Workshop on New Worlds in Astroparticle Physics, Faro, Portugal, Worlds Scientific, Singapore, 2003. (astro-ph/0312330). 

The original fireball created by the big bang expanded and cooled very rapidly. Within a few microseconds, the temperature had dropped to less than 1013 K, an environment in which heavy quarks... 

The U-, d-, and s-quark masses are estimates of so-called current-quark masses, in a mass-independent subtraction scheme such as MS at a scale /r 2 GeV. The c-and 6-quark masses are the running masses in the MS scheme. For the 6-quark we also quote the IS mass. These can be different from the heavy quark masses obtained in potential models. 

As opposed to the other two interactions, the weak interaction does not respect the kind of the quark (called flavor) either heavy quarks can decay into lighter ones via emitting a or... 

First, the weak interaction quanta became massive at the temperature scale of 100 GeV. Since then, weak reactions have only occurred in contact interactions of the particles. At about the same time the t-quark and the Higgs quanta also decoupled from the soup. The same decoupling happened for the other heavy quark species (b-quark, c-quark) and for the heaviest of the leptons (r-particle) in the range 1-5 GeV (a few times lO K) of the average energy density. The x-neutrinos remain in thermal equilibrium via weak neutral interactions. 

The study of heavy quark production is an important research area at the LHC. Heavy quarks will be produced with a large cross section at a yet unreached center-of-mass energy, enabling precision measurements to improve our understanding of heavy flavor physics. In the context of this work the term heavy quark stands for charm and beauty quarks since the mass of the up, down and strange quark are significantly lower. The heavier top quark has a very short lifetime and does therefore not form bound states of heavy hadrons. 

Heavy quark production is interesting on its own as it presents a key process for the study of the theory of strong interactions. Quantum Chromodynamics (QCD). Furthermore, a well-established theory of heavy quark production is needed for many searches at the LHC. 

In this chapter the theoretical concepts relevant to describe the physics of heavy quarks at the LHC are introduced. The main ideas of Quantum Chromodynamics are reviewed, before their appUcation to high-energy hadron-hadron collisions is discussed. This includes the factorization ansatz, the evolution of the parton distribution functions, the partonic processes important for beauty quark production and the phenomenological treatment of heavy quark fragmentation. A further section is dedicated to the description of the decay of -hadrons via the weak interaction. The Monte Carlo event generators which are used in this analysis to generate full hadronic events within the QCD framework are presented in the last section. 

Soft processes resulting in the production of low momentum hadrons will be the most common events in proton-proton collision at the LHC. Although these processes are QCD related, they cannot be calculated by pQCD. Perturbative approaches only lead to reliable results if a hard scale is present in the interaction. In the case of heavy flavor physics, the hard scale is provided by the mass of the heavy quark, its transverse momentum or the virtuality of the process. 

The leading-order (LO) process for the production of a heavy quark Q with mass mq in hadronic collisions is flavor creation, i.e. quark-antiquark annihilation and gluon-gluon fusion... 

Fig. 3.6 Reading order diagrams for heavy-quark pair production (a) quark-antiquark annihilation (b)-(d) gluon-gluon fusion gg -> QQ...

In gluon splitting events the heavy quark occurs in QQ events in the initial- or final-state shower. The resulting heavy flavored final state can carry a large combined transverse momentum and thus be concentrated within a small cone of angular separation. The contribution of the different processes to the total Z -quark production cross section predicted by PYTHIA (see Sect. 3.6) is shown in Fig. 3.8 as a function of the center of mass energy. 

The probability to produce a hadron h from a heavy quark Q can be split in a short- and a long-range part [26] ... 

The most widely used formula for modeling the fragmentation of heavy quarks is the Peterson fragmentation function. The probability that the hadron receives a momentum fraction z from the quark is given by [27]... 

The presence of hadrons containing heavy quarks is deduced by the observation of their decay products. In a first approximation of fc-fiavored hadron decays, only the beauty quark participates in the transition while the other quark acts as a specta-... 

M. L. Mangano, Two lectures on heavy quark production in hadronic collisions. CERN-TH/97-328 (1997)... 

The Higgs decay into two gluons can be obtained from the above formulae (6.2.5-6.2.8) keeping just the quark loop contributions and replacing by (note, however, that the one-loop calculation can only be trusted in this case if the Higgs is suflSciently heavy, say above 1 GeV, so that is suflSciently small). Keeping only the main contribution (coming from heavy quarks), a reasonable estimate for T H — GG) is then... 

The same convenient representation of hadronic states in terms of quark and antiquark hues will be carried over to the new sector of heavy quarks (charm c, bottom or beauty b, top f,...). 

Fig. 11.1 shows the ratio R = hadrons )/ (discussed in Section 6.2.5) up to about 30 GeV (i.e. where electroweak effects can be neglected). As shown in Fig. 11.1, the new pm-ticles appear as very narrow spikes in the e+e" cross-section. Much effort on the theoretical side has been expended in understanding these particles. The dust has long settled and it seems convincingly demonstrated that the J/ is the first manifestation of particles built out of the heavy quark (mass ci 1.5 GeV/c ), i.e. the charm quark introduced in Chapter 9, and whose existence was demanded for the gauge theory of weak interactions to make sense (Glashow, Iliopoulos and Maiani, 1970). The J/ is visualized as a loosely bound state of cc. Similarly, the T(9.46) particle is interpreted as the first manifestation of a 66 bound state. 

To describe the second ingredient that makes the non-relativistic approach a practical tool for numerical computation in the heavy quark sector, we have to briefly review here some of the basic characteristics of QCD, the candidate theory of strong interactions which will be used to describe the interaction potential between quarks. QCD will be discussed in detail in Chapters 20-23. 

The term quarkonium is used to denote any qq bound state system in analogy to positronium in the e+e system. But it is only for heavy quarks that a non-relativistic approach can be justified. In this chapter we deal with the charmonium and bottomonium states whose data was analysed in Chapter 11. We also briefly consider glueballs. There exist several good reviews on the subject (Berkelman, 1986 Kwong et al., 1987 Lichtenberg, 1987 Schindler, 1986). 

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