Quarks In Quantum Chromodynamics Research Articles

Quantum information with top quarks in QCD

Top quarks represent unique high-energy systems since their spin correlations can be measured, thus allowing to study fundamental aspects of quantum mechanics with qubits at high-energy colliders. We present here the general framework of the quantum state of a top-antitop (tt¯) quark pair produced through quantum chromodynamics (QCD) in a high-energy collider. We argue that, in general, the total quantum state that can be probed in a collider is given in terms of the production spin density matrix, which necessarily gives rise to a mixed state. We compute the quantum state of a tt¯ pair produced from the most elementary QCD processes, finding the presence of entanglement and CHSH violation in different regions of phase space. We show that any realistic hadronic production of a tt¯ pair is a statistical mixture of these elementary QCD processes. We focus on the experimentally relevant cases of proton-proton and proton-antiproton collisions, performed at the LHC and the Tevatron, analyzing the dependence of the quantum state with the energy of the collisions. We provide experimental observables for entanglement and CHSH-violation signatures. At the LHC, these signatures are given by the measurement of a single observable, which in the case of entanglement represents the violation of a Cauchy-Schwarz inequality. We extend the validity of the quantum tomography protocol for the tt¯ pair proposed in the literature to more general quantum states, and for any production mechanism. Finally, we argue that a CHSH violation measured in a collider is only a weak form of violation of Bell's theorem, necessarily containing a number of loopholes.

Thermodynamic potential for quark-qluon plasma with finite quark mass and chemical potential

We summarize the derivation of the finite temperature, finite chemical potential thermodynamic potential in the bag-model approximation to quantum chromodynamics (QCD) that includes a finite s-quark mass in the Feynman diagram contributions for both zero-order and two-loop corrections to the quark interaction. The thermodynamic potential for quarks in QCD is a desired ingredient for computations of the equation of state in the early universe, supernovae, neutron stars, and heavy-ion collisions. The 2-loop contributions are normally divergent and become even more difficult in the limit of finite quark masses and finite chemical potential. We describe various means to interpolate between the low and high chemical potential limits. Although physically well motivated, we show that the infinite series Padé rational polynomial interpolation scheme introduces spurious poles. Nevertheless, we show that lower order interpolation schemes such as polynomial interpolation reproduce the Padé result without the presence of spurious poles. We propose that in this way one can determine the equation of state for the two-loop corrections for arbitrary chemical potential, temperature and quark mass. This provides a new realistic bag-model treatment of the QCD equation of state. We compute the QCD phase diagram with up to the two-loop corrections. We show that the two-loop corrections decrease the pressure of the quark-gluon plasma and therefore increase the critical temperature and chemical potential of the phase transition. We also show, however, that the correction for finite s-quark mass in the two-loop correction serves to decrease the critical temperature for the quark-hadron phase transition in the early universe.

Vortices and vortex states in Rashba spin-orbit-coupled condensates

The Rashba spin-orbit coupling is equivalent to the finite Yang-Mills flux of a static SU(2) gauge field. It gives rise to the protected edge states in two-dimensional topological band insulators, much like magnetic field yields the integer quantum Hall effect. An outstanding question is which collective topological behaviors of interacting particles are made possible by the Rashba spin-orbit coupling. Here we address one aspect of this question by exploring the Rashba SU(2) analogs of vortices in superconductors. Using the Landau-Ginzburg approach and conservation laws, we classify the prominent two-dimensional condensates of two- and three-component spin-orbit-coupled bosons, and characterize their vortex excitations. There are two prominent types of condensates that take advantage of the Rashba spin-orbit coupling. Their vortices exist in multiple flavors whose number is determined by the spin representation, and interact among themselves through logarithmic or linear potentials as a function of distance. The vortices that interact linearly exhibit confinement and asymptotic freedom similar to quarks in quantum chromodynamics. One of the two condensate types supports small metastable neutral quadruplets of vortices, and their tiles as metastable vortex lattices. Quantum melting of such vortex lattices could give rise to non-Abelian fractional topological insulators, SU(2) analogs of fractional quantum Hall states. The physical systems in which these states could exist are trapped two- and three-component bosonic ultracold atoms subjected to artificial gauge fields, as well as solid-state quantum wells made either from Kondo insulators such as ${\mathrm{SmB}}_{6}$ or conventional topological insulators interfaced with conventional superconductors.

Dynamics of Relativistic Heavy Ion Collisions and the Quark Gluon Plasma

The standard theory of strong interaction is quantum chromodynamics (QCD) which governs dynamics of color charged particles such as quarks and gluons. Like photons in quantum electrodynamics, gluons are gauge bosons which mediate the strong force among matter particles (namely quarks in QCD). Contrary to photons which do not have electric charges, gluons carry color charges. Hence, gluons interact among themselves. This kind of self-interaction is manifestation of QCD as a non-Abelian gauge theory. It was shown that the coupling “constant” among color charges decreases with increasing energy scale in non-Abelian gauge theory. Then one can expect that quarks and gluons, which are ordinary confined into hadrons, are freed at extremely high temperature. The matter in which the quarks and gluons are thermally equilibrated is called the quark gluon plasma (QGP).1) Let us suppose that a sort of transition from a hadron gas to the QGP takes place when the lightest hadrons, pions, are close-packed. The number density of close-packed system is

Photon structure and quantum fluctuation

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Dainton John 2001Photon structure and quantum fluctuationPhil. Trans. R. Soc. A.359279–308http://doi.org/10.1098/rsta.2000.0727SectionRestricted accessPhoton structure and quantum fluctuation John Dainton John Dainton Oliver Lodge Laboratory, Department of Physics, University of Liverpool, Oxford Street, Liverpool L69 7ZE, UK () Google Scholar Find this author on PubMed Search for more papers by this author John Dainton John Dainton Oliver Lodge Laboratory, Department of Physics, University of Liverpool, Oxford Street, Liverpool L69 7ZE, UK () Google Scholar Find this author on PubMed Search for more papers by this author Published:15 February 2001https://doi.org/10.1098/rsta.2000.0727AbstractPhoton structure derives from quantum fluctuation in quantum field theory to fermion and anti-fermion, and has been an experimentally established feature of electrodynamics since the discovery of the positron. In hadronic physics, the observation of factorizable photon structure is similarly a fundamental test of the quantum field theory quantum chromodynamics (QCD). An overview of measurements of hadronic photon structure in e+e− and ep interactions is presented, and comparison made with theoretical expectation, drawing on the essential features of photon fluctuation into quark and antiquark in QCD. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetails This Issue15 February 2001Volume 359Issue 1779Discussion Meeting Issue ‘The quark structure of matter’ organized by I. Butterworth, J. Ellis and E. Gabathuler Article InformationDOI:https://doi.org/10.1098/rsta.2000.0727Published by:Royal SocietyPrint ISSN:1364-503XOnline ISSN:1471-2962History: Published online15/02/2001Published in print15/02/2001 License: Citations and impact KeywordsstructureQCDtwo–photon physicsphotoproductionjetsphoton

Pole masses of quarks in-dimensional reduction

Pole masses of quarks in quantum chromodynamics are calculated to two-loop order in the framework of the regularization by dimensional reduction. For the diagram with a light quark loop, the non-Euclidean asymptotic expansion is constructed with the external momentum on the mass shell of a heavy quark.

On the Importance of Self-interaction in QCD

The electromagnetic self-energy of charged particles has remained a problem in classical as well as in quantum electrodynamics. In contrast here, in a review of the analysis of the chromodynamic self-energy of quarks in quantum chromodynamics (QCD), we see that the quark self-energy is a finite and a dominant effect in determining the structure of hadrons.

Decoupling of heavy quarks in quantum chromodynamics

Decoupling of heavy quarks in quantum chromodynamics (QCD) defined by mass-independent renormalization is investigated. The structure of the relations between the parameters of f flavour QCD and the parameters of the effective f − 1 flavour QCD below a heavy-quark threshold is discussed to all orders in the loop expansion, and the relations are computed to two-loop approximation for the minimal subtraction schemes (MS) and to one-loop approximation for some Weinberg schemes. These matching relations can be used to systematically determine the renormalization group (RG)-invariant parameters of the effective theory in terms of the RG-invariant parameters of the theory which includes the heavy quark, or vice versa. For the MS scheme the connection between Λ f − 1 nad Λ f to two and three loops is given as well as the two-loop connection between the RG-invariant mass parameters of the f − 1 and f flavour theory. The effect of heavy quarks on the evolution of the QCD coupling is of significance for present QCD phenomenology based on next-to-leading-order perturbation theory. This is illustrated with a few examples within the MS scheme.

Decoupling of heavy quarks in Quantum Chromodynamics: W. Bernreuther. Institut für Theoretische Physik der Universität Heidelberg, D-6900 Heidelberg, West Germany

Decoupling of heavy quarks in Quantum Chromodynamics: W. Bernreuther. Institut für Theoretische Physik der Universität Heidelberg, D-6900 Heidelberg, West Germany

Masses of light quarks in quantum chromodynamics

We try to determine light quark masses by considering sum rules for the vacuum expectation value of the time-ordered correlation function of two divergences of the axial vector current. The evaluation is carried out at momenta high enough for the non-perturbative contributions to be negligible. We find that the average mass of the up and down quark at a momentum of 1 GeV lies between 3.3 and 7.9 MeV while that for the strange quark lies between 84 and 212 MeV. The ranges of values reflect predominantly the uncertainty in the absorptive part in the low energy region (⪅1.7 GeV).

Dynamical generation of the spectrum of fermions in non-abelian gauge field theories

The dynamical mechanism of spontaneous breakdown of chiral invariance in non-abelian gauge theories is proposed. The dynamical masses of quarks in quantum chromodynamics are estimated within this framework.

Effective Lagrangian due to heavy quarks in quantum chromodynamics

We extend our previous analysis of heavy-particle effects in the low-energy light-particle sector to quantum chromodynamics. The central technique is the use of the Ward-Takahashi identities due to Becchi-Rouet-Stora transformations. Some discussion of the isolation of mass singularities is given. An important result in our approach, as before, is to give precise meaning to the notion of an effective Lagrangian (which is renormalized) with calculable effective coupling constants. The counterterms for the effective local vertices in the Lagrangian are self-generated by the theory, while the effective coupling constants obey a set of Callan-Symanzik-type equations.

Pion decay constant, electromagnetic form factor, and quark electromagnetic self-energy in quantum chromodynamics

We examine dynamical chiral symmetry breaking in quantum chromodynamics (QCD). To lowest order in a double perturbation expansion in $g$, the gauge coupling, and $\ensuremath{\lambda}=\mathrm{exp}(\ensuremath{-}\frac{1}{b{g}^{2}})$ we obtain exact representations for the pion decay constant ${f}_{\ensuremath{\pi}}$ and electromagnetic form factor ${F}_{\ensuremath{\pi}}({q}^{2})$. Using the experimental values for ${f}_{\ensuremath{\pi}}$ and ${F}_{\ensuremath{\pi}}({q}^{2})$, we estimate the dynamically generated quark mass to be 270-300 MeV, in good agreement with a value obtained from ${e}^{+}{e}^{\ensuremath{-}}$ annihilation data. We also calculate the finite electromagnetic self-energy of a quark in QCD and discuss the implications.

Physical processes and the infrared problem in gauge theories

Some aspects of the perturbative study of the infrared structure of Yang-Mills theories are discussed. First of all, the computational details of a previously reported result are presented. It is shown through lowest non-trivial order that production and detection of massive quarks in quantum chromodynamics is infrared finite in terms of an appropriately defined renormalized coupling constants. This is conjectured to be true to all orders. The implications of this Block-Nordsieck like result for quark confinement are discussed. It is emphasized that there are assumptions implicit in the use of perturbation theory which could be wrong in a non-perturbative solution. The language of the renormalization group is used to elucidate these possibilities.