Properties of quark matter governed by quantum chromodynamics (II). Renormalization schemes in quark matter

Renormalization schemes are examined (in the Coulomb gauge) for quantum chromodynamics in the presence of quark matter. We demand that the effective coupling constant for all schemes become congruent with the vacuum QCD running coupling constant as the matter chemical potential, μ, goes to zero. Also, to enable us to standardize with the vacuum QCD running coupling constant at some asymptotic momentum transfer, $\text{|}\text{p}{}_0\text{|,}\text{we keep}\text{μ ? ¦}\text{p}{}_0\text{¦}$, to ensure that the matter contribution is negligible at this point. This means all schemes merge with vacuum QCD at $\text{|}\text{p}{}_0\text{|}$ and beyond. Two renormalization group invariants are shown to emerge: (i) the effective or invariant charge, g_inv², which is, however, scheme dependent and (ii) g²(M)/S(M), where S(M)^?1 is the Coulomb propagator, which is scheme independent. The only scheme in which g_inv² is scheme independent and identical to g²(M)/S(M) is the screened charged scheme (previous paper) characterised by the normalization of the entire Green function, S^?1, to unity. We conclude that this is the scheme to be used if one wants to identify with the experimental effective coupling in perturbation theory. However, if we do not restrict to perturbation theory all schemes should be allowed. Although we discuss matter QCD in the Coulomb gauge, the above considerations are quite general to gauge theories in the presence of matter.     

Heavy meson spectra for heavy quark potential in quantum chromodynamics with dilaton

For heavy meson systems, we study the heavy quark potential, which emerges from the effective dilaton－gluon coupling inspired from the superstring theory. We put emphasis on the new confinement generating mechanism of this potential through the investigation of the spin-averaged energy levels of the heavy meson systems. By using a unified approach to the solutions of the Schr?dinger and the spinless Salpeter equations, we can examine in a realistic way the effects of using a relativistic kinetic energy. The obtained results agree favourably with other predictions, and the relativistic equation can better account for the observed energy levels.     

Photon structure functions in quantum chromodynamics: (II). Feynman diagram method

We compute the strong interaction corrections to the polarized photon structure functions using perturbative chromodynamics. The results agree with those of our previous calculations with the operator product expansion method.     

The quark form factor in quantum chromodynamics

It is shown how leading logarithmic predictions of certain quark form factor effects in QCD, such as the suppression of the Drell-Yan process at small transverse momenta and of the collinear energy-energy correlation in e⁺e^? annihilation, are invalidated by non-leading logarithms corresponding to the vectorial cancellation of gluon transverse momenta. Simple improved expressions incorporating this phenomenon are presented.     

The role of instantons in quantum chromodynamics: (II). Hadronic structure

The “constituent quark” (or “valon”) substructure of ordinary hadrons is the consequence of small instanton radius $\text{?}{}_{\mathrm{<mtext>c</mtext>}}\text{?}\text{1}\text{3}\text{fm}$ in the QCD vacuum. The same parameter determines hadronic masses and other parameters, in particular the unusually large mass scale for “exceptional” hadrons with zero spin.     

Heavy quark effects on the parameters of quantum chromodynamics defined by minimal subtraction

We report a complete two-loop calculation of the relations for matching the parameters of MS renormalized QCD below and above a certain heavy quark threshold and we investigate the implications of these relations for the QCD scale Λ and the scale-invariant quark masses.     

Heavy quarkonium production in the regge limit of quantum chromodynamics

Heavy quarkonium \((c\bar c,b\bar b)\) hadronic production at Tevatron (run I and run II) and LHC energies is considered in the framework of nonrelativistic quantum chromodynamics in the leading order with respect to α _s and v using the quasi-multi-Regge kinematics approach. Fitting of p _T spectra of different S and P wave heavy quarkonium states at Tevatron (run I and run II) energies is carried out. The obtained set of octet nonperturbative matrix elements is used for prediction of heavy quarkonium production at LHC energies. The results obtained in the framework of quasi-multi-Regge kinematics are compared with predictions of the collinear parton model.     

Light quark masses in quantum chromodynamics and chiral symmetry breaking

We derive model independent lower bounds for the sums of effective quark masses \(\bar m_u + \bar m_d \) and \(\bar m_u + \bar m_s \) . The bounds follow from the combination of the spectral representation properties of the hadronic axial currents two-point functions and their behavior in the deep euclidean region (known from a perturbative QCD calculation to two loops and the leading non-perturbative contribution). The bounds incorporate PCAC in the Nambu-Goldstone version. If we define the invariant masses \(\hat m\) by $$\bar m_i = \hat m_i \left( {{{\frac{1}{2}\log Q^2 } \mathord{\left/ {\vphantom {{\frac{1}{2}\log Q^2 } {\Lambda ^2 }}} \right. \kern-\nulldelimiterspace} {\Lambda ^2 }}} \right)^{{{\gamma _1 } \mathord{\left/ {\vphantom {{\gamma _1 } {\beta _1 }}} \right. \kern-\nulldelimiterspace} {\beta _1 }}} $$ and <F ²> is the vacuum expectation value of $$F^2 = \Sigma _a F_{(a)}^{\mu v} F_{\mu v(a)} $$ , we find, e.g., $$\hat m_u + \hat m_d \geqq \sqrt {\frac{{2\pi }}{3} \cdot \frac{{8f_\pi m_\pi ^2 }}{{3\left\langle {\alpha _s F^2 } \right\rangle ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} }}} $$ ; with the value <α _u F ²?0.04GeV⁴, recently suggested by various analysis, this gives $$\hat m_u + \hat m_d \geqq 35MeV$$ . The corresponding bounds on \(\bar m_u + \bar m_s \) are obtained replacingm _π ² f _π bym _K ² f _K . The PCAC relation can be inverted, and we get upper bounds on the spontaneous masses, \(\hat \mu \) : $$\hat \mu \leqq 170MeV$$ where \(\hat \mu \) is defined by $$\left\langle {\bar \psi \psi } \right\rangle \left( {Q^2 } \right) = \left( {{{\frac{1}{2}\log Q^2 } \mathord{\left/ {\vphantom {{\frac{1}{2}\log Q^2 } {\Lambda ^2 }}} \right. \kern-\nulldelimiterspace} {\Lambda ^2 }}} \right)^d \hat \mu ^3 ,d = {{12} \mathord{\left/ {\vphantom {{12} {\left( {33 - 2n_f } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {33 - 2n_f } \right)}}$$ .     

The role of instantons in quantum chromodynamics: (III). Quark-gluon plasma

With the increase in density and/or temperature of matter in the quark-gluon plasma phase, suppression of instanton-induced effects takes place. At some critical parameters chiral symmetry is restored. In this first-order transition the massive quasiparticles-valons-are substituted by nearly massless quarks and gluons, while the “instanton liquid” dissociates into “instanton molecules” with zero topological charge.     

Heavy quark production in jets

Zeitschrift für Physik C Particles and Fields - We study possible deviations from the Standard Model in the reactione + e ?→Z?, where ? denotes a spinless neutral boson....     

Gluon and quark jets in a recursive model motivated by quantum chromodynamics

We compute observable quantities like the multiplicity and momentum distributions of hadrons in gluon and quark jets in the framework of a recursive cascade model, which is strongly motivated by the fundamental interactions of QCD. Fragmentation occurs via 3 types of breakups: quark → meson+ quark, gluon→meson+gluon, gluon→quark+ antiquark. In our model gluon jets are softer than quark jets. The ratio of gluon jet to quark jet multiplicity is found to be 2 asymptotically, but much less at lower energies. Some phenomenological consequences for λ decay are discussed.     

On the quark mass dependence of the parameters of quantum chromodynamics

The running coupling constant and quark masses in QCD are calculated in the one-loop approximation using the 3-gluon vertex to define the coupling constant. Our results differ for finite quark masses from those reported previously in the literature. We discuss the origin of this apparent discrepancy. We also make some comments on the gauge dependence of the QCD parameters.     

Spectral function sum rules in quantum chromodynamics: (I). Charged currents sector

The Weinberg sum rules of the algebra of currents are reconsidered in the light of quantum chromodynamics (QCD). We derive new finite-energy sum rules which replace the old Weinberg sum rules. The new sum rules are convergent and the rate of convergence is explicitly calculated in perturbative QCD at the first non-trivial order. Phenomenological applications of these sum rules in the charged current sector are also discussed.     

Photon structure functions in quantum chromodynamics: (I). Operator product expansion method

A study of the polarized photon structure functions is made using the operator product expansion in the framework of perturbative chromodynamics. The non-spin-flip function is corrected as in the unpolarized case but the spin-flip function is unchanged.     

The QCD pomeron in ultraperipheral heavy ion collisions: II. Heavy quark production

The heavy quark production in ultraperipheral heavy ion collisions is investigated, with particular emphasis on the results from the coherent interactions given by the two-photon process. One addresses the heavy quark total cross sections at photon level considering the saturation model and the BFKL dynamics in the color dipole picture. The corresponding cross sections at nuclear level are presented. It is verified that the QCD dynamics implies an enhancement of the cross section in comparison with previous calculations. Received: 30 January 2003 / Revised version: 26 March 2003 / Published online: 13 May 2003 RID="a" ID="a" e-mail: barros@ufpel.tche.br RID="b" ID="b" e-mail: magnus@if.ufrgs.br     

Heavy quark production in heavy ion colliders

We describe updated calculations of $Q\bar Q$ production in pp and π ^- p interactions. We compare these results to total cross section data and discuss how the baseline cross sections extrapolate to heavy ion collider energies. We touch upon the differences between leading and next-to-leading order heavy quark production. Finally, we discuss the implications of our calculations for quarkonium production. Our discussion here focuses on bottom quarks.