There is serious disagreement between the predictions of Non-Relativistic Quantum Chromodynamics (NRQCD) and the data on $J/ψ$ polarisation which has persisted for almost a quarter of a century. We find that if we account for the effect of perturbative soft gluons on the intermediate charm-anticharm octet states in NRQCD then the polarisation problem can be resolved. In addition, this model, when used to fit the Run 1 data on $J/ψ$ and $ψ'$ production from the CDF experiment at Tevatron, gives good fits and yields values of (energy-independent) non-perturbative parameters. These, in turn, can be used to make parameter-free predictions for $J/ψ$ and $ψ'$ data from the CMS experiment at the Large Hadron Collider and the predictions are in excellent agreement with the CMS data.
We discuss correlations between two particles in jets at high energy colliders and exactly solve the MLLA evolution equations in the small x limit. We thus extend the Fong-Webber analysis to the region away from the hump of the single inclusive energy spectrum. We give our results for LEP, Tevatron and LHC energies, and compare with existing experimental data.
It is shown that the Lagrangian of Quantum Chromodynamics can be modified by the adding gluon masses. On mass-shell renormalizability of the resulting theory is discussed.
The MLLA single inclusive distribution inside one high energy (gluon) jet at small x is estimated by the steepest descent method. Its analytical expression is obtained outside the "limiting spectrum". It is then used to evaluate 2-particle correlations at the same level of generality. The dependence of both observables on the ratio between the infrared cutoff Q\_0 and Lambda\_QCD is studied. Fong & Webber's results for correlations are recovered at the limits when this ratio goes to 1 and when one stays close to the peak of the single inclusive distribution.
We adopt a non-perturbative relativistic constituent-quark model for the pi-meson electromagnetic form factor, which have successfully predicted experimental results, and supplement it with the effective momentum-dependent quark mass to study quantitatively the transition to the perturbative QCD asymptotics. The required asymptotical behaviour (including both the Q^{-2} fall-off and the correct coefficient) settles down automatically when the quark mass is switched off; however, the present experimental data on the form factor suggest that this cannot happen at the values of the momentum trans…
After demonstrating their general expressions valid at all x, double differential 1-particle inclusive distributions inside a quark and a gluon jet produced in a hard process, together with the inclusive k-transverse distributions, are calculated at small x in the Modified Leading Logarithmic Approximation (MLLA), as functions of the transverse momentum of the outgoing hadron. Results are compared with the Double Logarithmic Approximation (DLA) and a naive DLA-inspired evaluation; sizable corrections are exhibited which, associated with the requirement to stay in a perturbative regime, set the…
It has been previously shown that a particular nonperturbative constituent-quark model of hadrons describes experimental measurements of electromagnetic form factors of light charged mesons through a small number of common phenomenological parameters, matching at the same time the Quantum-Chromodynamics (QCD) asymptotics for the pi-meson form factor at large momentum transfer. Here we start with the determination of the K0 electromagnetic form factor in this approach. Precise measurement of the K0 charge radius makes it possible to constrain model parameters with high accuracy. Then, with all …
We calculate the cross section of inclusive direct J/psi photoproduction at next-to-leading order within the factorization formalism of nonrelativistic quantum chromodynamics, for the first time including the full relativistic corrections due to the intermediate ^1S_0^[8], ^3S_1^[8], and ^3P_J^[8] color-octet states. A comparison of our results to recent H1 data suggests that the color octet mechanism is indeed realized in J/psi photoproduction, although the predictivity of our results still suffers from uncertainties in the color-octet long-distance matrix elements.
We investigate a new ``renormalization invariant analytic formulation'' of calculations in quantum chromodynamics, where the renormalization group summation is correlated with the analyticity with respect to the square of the transferred momentum $Q^2$. The expressions for the invariant charge and matrix elements are then modified such that the unphysical singularities of the ghost pole type do not appear at all, being by construction compensated by additional nonperturbative contributions. Using the new scheme, we show that the results of calculations for a number of physical processes are st…
The exact nonperturbative confining solutions of the SU(3)-Yang-Mills equations recently obtained by author in Minkowski spacetime with the help of the black hole theory techniques are analysed and on the basis of them the gluon propagator corresponding to linear confinement at large distances (small momenta) is constructed in a nonperturbative way. At small distances (large momenta) the resulting propagator passes on to the standard (nonperturbative) gluon propagator used in the perturbative quantum chromodynamics (QCD). The results suggest some scenario of linear confinement for mesons and q…
The perturbative quantum chromodynamics (pQCD) has been extremely successful in the prediction and description of main properties of quark and gluon jets. There are, however, some problems of the jet calculus with the higher order corrections of the modified perturbative expansion which should be resolved to get more precise statements. Some of them are discussed here.
We give a selection of results on spectrum and decay constants of light and heavy-light hadrons. Effective field theories relevant for their lattice calculation, namely non-relativistic QCD (NRQCD) for heavy quarks on the lattice and Chiral Perturbation Theory for light quarks, are briefly discussed.
We exactely calculate the inclusive transverse momentum (kt) distributions and the 2-particle momentum correlations in high energy hadronic jets at the Modified Leading Logarithmic Approximation (MLLA) of QCD (Quantum Chromodynamics). We first obtain the exact solution of the evolution equations at "small x", which we calculate at the so called "limiting spectrum". We then go beyond this approximation by performing the steepest descent evaluation, which allows to generalize the preceeding results. Our predictions are in good agreement with the data (LEP, Tevatron) and improve those which have …
Because quarks and gluons are confined within hadrons, they have a maximum wavelength of order the confinement scale. Propagators, normally calculated for free quarks and gluons using Dyson-Schwinger equations, are modified by bound-state effects in close analogy to the calculation of the Lamb shift in atomic physics. Because of confinement, the effective quantum chromodynamic coupling stays finite in the infrared. The quark condensate which arises from spontaneous chiral symmetry breaking in the bound state Dyson-Schwinger equation is the expectation value of the operator $\bar q q$ evaluated…
We propose a model for Quantum Chromodynamics, obtained by ignoring the angular dependence of the gluon fields, which could qualitatively describe systems containing one heavy quark. This leads to a two dimensional gauge theory which has chiral symmetry and heavy quark symmetry. We show that in a light cone formalism, the Hamiltonian of this spherical QCD can be expressed entirely in terms of color singlet variables. Furthermore, in the large $N_c$ limit, it tends to a classical hadron theory. We derive an integral equation for the masses and wavefunctions of a heavy meson. This can be interpr…
Heavy quarkonium production in the framework of the non-relativistic quantum chromodynamics and leading order of the parton Reggeization approach at the Tevatron and LHC is discussed. In this note, we compare our predictions for the bottomonium production at the LHC due to the color-singlet approximation of the non-relativistic quantum chromodynamics with CMS and LHCb data. It is found, that in the production of Upsilon(1S) states, the color-singlet mechanism is dominating, whereas to describe the data for the inclusive Upsilon(2S) and Upsilon(3S) production, the color- octet contributions sho…
Relativistic corrections to the pair $B_c$-meson production in $e^+e^-$-annihilation are calculated. We investigate a production of pair pseudoscalar, vector and pseudoscalar+vector $B_c$-mesons in the leading order perturbative quantum chromodynamics and relativistic quark model. Relativistic expressions of the pair production cross sections are obtained. Their numerical evaluation shows that relativistic effects in the production amplitudes and bound state wave functions three times reduce nonrelativistic results at the center-of-mass energy s=22 GeV.
We discuss the light-cone quantization of gauge theories as a calculational tool for representing hadrons as QCD bound-states of relativistic quarks and gluons, and also as a novel method for simulating quantum field theory on a computer. The light-cone Fock state expansion of wavefunctions provides a precise definition of the parton model and a general calculus for hadronic matrix elements. We present several new applications of light-cone Fock methods, including calculations of exclusive weak decays of heavy hadrons, and intrinsic heavy-quark contributions to structure functions. Discretized…
The new relativistic Coulomb-like threshold resummation $S$-factor in quantum chromodynamics is obtained. The consideration is given within the framework of quasipotential approach in quantum field theory which is formulated in relativistic configuration representation for two particles of unequal masses.
The complete next-to-next-to-leading order (i.e. $O(v^2)$, $O(v α_s)$ and $O(α_s^2)$) relativistic corrections to the total photon mediated $t\bar t$ production cross section at threshold are presented in the framework of nonrelativistic quantum chromodynamics. The results are obtained using semi-analytic methods and ``direct matching''. The size of the next-to-next-to-leading order relativistic corrections is found to be comparable to the size of the next-to-leading order ones.
This paper is a slightly modified version of the introductory part of a doctoral dissertation also containing the articles hep-ph/0303076, hep-ph/0409328 and hep-ph/0409058. The paper focuses on the calculation of particle production in a relativistic heavy ion collision using the McLerran-Venugopalan model. The main part of the paper summarizes the background of these numerical calculations. First we relate this calculation of the initial stage af a heavy ion collision to our understanding of the whole collision process. Then we discuss the saturation physics of the small x wavefunction of a …
This Resource Letter provides a guide to the literature on Quantum Chromodynamics (QCD), the relativistic quantum field theory of the strong interactions. Journal articles, books, and other documents are cited for the following topics: quarks and color, the parton model, Yang-Mills theory, experimental evidence for color, QCD as a color gauge theory, asymptotic freedom, QCD for heavy hadrons, QCD on the lattice, the QCD vacuum, pictures of quark confinement, early and modern applications of perturbative QCD, the determination of the strong coupling and quark masses, QCD and the hadron spectrum…
We review the present status of the search for a phase transition and critical point as well as anomalous transport phenomena in Quantum Chromodynamics (QCD), with an emphasis on the Beam Energy Scan program at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory. We present the conceptual framework and discuss the observables deemed most sensitive to a phase transition, QCD critical point, and anomalous transport, focusing on fluctuation and correlation measurements. Selected experimental results for these observables together with those characterizing the global properties o…
The axial charges of the nucleon and the well-established N* resonances are studied within a consistent framework. For the first time the axial charges of the N* resonances are produced for the relativistic constituent quark model. The axial charge of the nucleon is predicted close to experiment, and the ones of N*(1535) and N*(1650), the only cases where such a comparison is possible, agree well with results from quantum chromodynamics on the lattice that have recently become available. The relevance of the magnitudes of the N* axial charges for the low-energy behavior of quantum chromodynami…
We consider two approaches to estimate and characterise the theoretical uncertainties stemming from the missing higher orders in perturbative calculations in Quantum Chromodynamics: the traditional one based on renormalisation and factorisation scale variation, and the Bayesian framework proposed by Cacciari and Houdeau. We estimate uncertainties with these two methods for a comprehensive set of more than thirty different observables computed in perturbative Quantum Chromodynamics, and we discuss their performance in properly estimating the size of the higher order terms that are known. We fin…
A range of quantum field theoretical phenomena driven by external magnetic fields and their applications in relativistic systems and quasirelativistic condensed matter ones, such as graphene and Dirac/Weyl semimetals, are reviewed. We start by introducing the underlying physics of the magnetic catalysis. The dimensional reduction of the low-energy dynamics of relativistic fermions in an external magnetic field is explained and its role in catalyzing spontaneous symmetry breaking is emphasized. The general theoretical consideration is supplemented by the analysis of the magnetic catalysis in qu…
We investigate the interparticle potential between spin-0, -1/2 and -1 sources interacting in modified electrodynamics in the non-relativistic regime. By keeping terms of $\mathcal{O}( |{\bf p}|^2/m^2 )$ in the amplitudes, we obtain spin- and velocity-dependent interaction energies. We find well-known effects such as spin-orbit couplings, as well as spin-spin (dipole-dipole) interactions. For concreteness, we consider the cases of electrodynamics with higher derivatives (Podolsky-Lee-Wick) and hidden photons.
Instead of the often used Foldy-Wouthuysen-Tani (FWT) transformation in non-relativistic quantum chromodynamics (NRQCD), we take a more general relation between the relativistic and non-relativistic on-shell spinors to recalculate the quark-quark-gluon vertex for heavy quarks. In comparison with the previous result using FWT, the recalculated coefficients in the NRQCD Lagrangian are different at order $1/m^3$ and new at order $1/m^4$ and $1/m^5$, where $m$ is the heavy quark mass.
The production cross sections of $e^+e^- $ to a heavy quarkonium with $C$-parity even $S-$wave and $P-$wave associated with a photon are analyzed in the framework of non-relativistic Quantum Chromodynamics(NRQCD) factorization formalism. The short-distance coefficients are determined up to the next-to-leading order(NLO) QCD radiative corrections for $S-$ and $P-$wave and NLO relativistic corrections for $S-$wave in analytical forms. Applying the results to estimate the cross sections we find that both the radiative and relativistic corrections are considerable.
Generalizing the collision term in the relativistic Boltzmann equation to include nonlocal effects, and using Grad's 14-moment approximation for the single-particle distribution function, we derive evolution equations for the relativistic dissipative fluid dynamics and compare them with the corresponding equations obtained in the standard Israel-Stewart and related approaches. Significance of this generalization on hydrodynamic evolution is demonstrated in the framework of one-dimensional scaling expansion.
We study the pair production of $B_c$ mesons in the photon-photon interaction in the framework of perturbative quantum chromodynamics and the relativistic quark model. The production amplitudes of a pair of pseudoscalar and vector $B_c$ mesons are constructed in the nonrelativistic approximation and taking into account relativistic effects. Relativistic corrections related to the relative motion of heavy quarks in the production amplitude, as well as in the wave function of the bound state of heavy quarks, are taken into account. Analytical expressions are constructed for the relativistic diff…
By single-time reduction technique of Bethe-Salpeter formalism for two-fermion systems analytical expressions for the quasipotential of quark-quark interactions in QCD have been obtained in one-gluon exchange approximation. The influence of infrared singularities of gluon Green`s functions on the character of quark-quark forces in QCD has been investigated. The way the asymptotic freedom manifests itself in terms of two-quark interaction quasipotential in quantum chromodynamics is shown. Consistent relativistic consideration of quark interaction problem by single-time reduction technique in QF…
In the weak-field limit of General Relativity, gravitational waves obey linear equations and propagate at the speed of light. These properties of General Relativity are supported by the observation of ultra high energy cosmic rays as well as by LIGO's recent detection of gravitation waves. We argue that two existing relativistic generalizations of Modified Newtonian Dynamics, namely Generalized Einstein-Aether theory and BIMOND, display fatal inconsistencies with these observations.
In this work, we present the calculation of the production cross sections of bottomonia states using Non-Relativistic Quantum Chromodynamics (NRQCD) formalism. The direct production cross-section of a resonance can be factorised in terms of short distance Quantum Chromodynamics (QCD) cross sections and long distance matrix elements (LDMEs) under NRQCD. We use a large set of measured $Υ$(nS) production data at Tevatron and LHC energies in both central and forward rapidity regions to extract the LDMEs with better precision. The feed down contributions from the higher states including the $χ_{b}$…
The suppression of heavy quarkonia e.g. $J/ψ$, $Υ$ etc. is considered as a suitable probe to identify the nature of the matter created in heavy ion collisions. Recently we have presented a modified colour screening model for $J/ψ$ suppression in the quark gluon plasma (QGP) using quasiparticle model as the equation of state. In this paper, we extend our model to calculate the anomalous suppression of various states of $Υ$ arising due to QGP medium alone. We obtain the suppression patterns of different bottomonia states with respect to centrality at various available collision energies and comp…
Based on the non-relativistic quantum chromodynamics factorization framework, we study the inclusive $J/ψ$ photoproduction at the future high energy $e^+e^-$ collider, International Linear Collider(ILC), where the initial photons come from the back-scattering of laser and electron (positron). The intermediate states, $c\bar{c}$$({}^3\!S_1^{[\textbf{1}]}$,${}^1\!S_0^{[\textbf{8}]}$,${}^3\!S_1^{[\textbf{8}]}$,${}^3\!P_{0,1,2}^{[\textbf{8}]})$, and resolved photoproduction processes are considered. Numerical results show that the cross section of $J/ψ$ photoproduction at the ILC could be very lar…
Within the nonrelativistic quantum chromodynamics (NRQCD) factorization formalism, we compute the relativistic corrections to the exclusive decays of bottomonia with even charge conjugation parity into $S$-wave charmonium pairs at leading order in the strong coupling constant. Relativistic corrections are resummed for a class of color-singlet contributions to all orders in the charm-quark velocity $v_c$ in the charmonium rest frame. Almost every process that we consider in this work has negative relativistic corrections ranging from -20 to -35,%. Among the various processes, the relativistic c…
We consider the dynamics of tensor and scalar gravitational fields in the Relativistic Theory of Gravitation with the Minkowskian vacuum metric and generalize the formulation to the massless graviton. The potential of scalar field is determined in the presence of cosmological term under clear physical motivations. We find cosmological inflationary solutions and analyze conditions providing the transition to the regime of hot expanding universe.
In the present work, we perform systematic estimations for the radiative decays of the charmed mesons in a modified relativistic quark model. Our estimations indicate that the branching ratios of the process of $D_2^0(1^3P_2) \to D^{\ast 0}(1^3S_1) γ$, $D_3^0(1D_3) \to D_2^0(1^3P_2) γ$, $D_2^0(2D_2^\prime) \to D_1^{0}(2P_1) γ$, $D_3^0(2^3D_3) \to D_2^0(2^3P_2) γ$, and $D^{\ast 0}(1^3S_1) \to D^0(1^1S_0) γ$ are of the order of $10^{-2}$, which are sizable to be detected experimentally. Moreover, the branching ratios of some channels, for example, $D_1^0(1P_1) \to D(1^1S_0)^0 γ$, $D^0(3^1S_0) \t…
We determine the leading-order nonrelativistic quantum chromodynamics (NRQCD) matrix element < O_1 >_Upsilon and the ratio < q^2>_Upsilon, for Upsilon=Upsilon(nS) with n=1, 2, and 3 by comparing the measured values for Gamma[Upsilon -> e^+ e^-] with the NRQCD factorization formula in which relativistic corrections are resummed to all orders in the heavy-quark velocity v. The values for < q^2 >_Upsilon, which is the ratio of order-v^2 matrix element to < O_1 >_Upsilon, are new. They can be used for NRQCD predictions involving Upsilon(nS) and eta_b(nS) with relativistic corrections. As an applic…
We construct the five loop anomalous dimensions of the basic fields in Quantum Chromodynamics in a linear covariant gauge in the modified Regularization Invariant (RI') scheme. Using these core results we also compute the four loop Green's function where the quark mass operator and vector current are separately inserted in a quark 2-point function. These are necessary for measurements of the same quantities on the lattice. The Green's functions are provided in both the modified Minimal Subtraction (MSbar) and RI' schemes. All the results are available for a general Lie group.
A causal, non-Hermitian, renormalizable, local, unitary and Lorentz convariant formulation of Quantum Theory (QT) (= Quantum Mechanics (QM) and Quantum Field Theory (QFT)) is developed which is free of formalistic problems we face in the commonly used Hermitian formulation of QT. Side effects of the new formulation of QT are the derivation of a consistent (anti)causal neutrino Lagrangian, the enrichment of chiral symmetries, the removal of the Dirac sea, the separation of positive and negative energy states including a reformulation of the anti-particle concept and a critical analysis of the c…
derivation of the effective lagrangian for non-relativistic quantum chromodynamics and the heavy quarks effective field theory is given. Our calculation provides of a simple and systematic method of calculation of the full off shell effective lagrangian at tree level including all the $1/m$ corrections.
We present a relativistic treatment of the problem of soft electromagnetic structure by the modified instant form of relativistic Hamiltonian dynamics. Our approach uses relativistic parametrization and so picks out the relativistic invariant quantities on each stage of the calculation. The electromagnetic current matrix element satisfies the current conservation law automatically. We use relativistic modified impulse approximation. It is constructed in relativistic invariant way. For composite systems (including the spin 1 case) the approach guarantees the uniqueness of the solution and it do…
Within the framework of intermittency analysis, a search for critical fluctuations is ongoing to locate the possible critical point in the quantum chromodynamics phase diagram. In this study, self-similar critical fluctuations from a critical Monte Carlo (CMC) model have been incorporated into the cascade ultrarelativistic quantum molecular dynamics (UrQMD) model. This hybrid UrQMD+CMC model exhibits a clear power-law behavior of scaled factorial moment for charged particles in Au+Au collisions at $\sqrt{s_\mathrm{NN}}$ = 7.7-200 GeV. By comparing the UrQMD+CMC model results with those from th…
We investigate the spectroscopy and decays of the charm-strange quarkonium system in a potential model consisting of a relativistic kinetic energy term, a linear confining term including its scalar and vector relativistic corrections and the complete perturbative one-loop quantum chromodynamic short distance potential. The masses and wave functions of the various states are obtained using a variational technique, which are then used in a perturbative treatment of the potential to find the mass spectrum of the $c\bar{s}$ system and radiative decay widths. Our results compare well with the avail…
Lattice quantum chromodynamics (QCD) predicts a new state of matter, called quark-gluon plasma (QGP), at sufficiently high temperatures or equivalently large energy densities. Relativistic heavy ion collisions are expected to produce such energy densities, thereby providing us a chance to test the above prediction. After a brief introduction of the necessary theoretical concepts, I present some critical comments on the experimental results with an aim to examine whether QGP has already been observed experimentally.
We derive analytical expressions for external fields of a charged relativistic bunch with a circular cross section. At distances far from the bunch, the field reduces to the relativistic modified Coulomb form and in the near region, reproduce the external fields of a continuous beam. If the bunch is surrounded by conducting surfaces, the bunch self-fields are modified. Image fields generated by a bunch between two parallel conducting planes are studied in detail. Exact summation of image fields by the direct method invented by Laslett allows the infinite series to be represented in terms of el…
We investigate the spectroscopy and decays of the charmonium and upsilon systems in a potential model consisting of a relativistic kinetic energy term, a linear confining term including its scalar and vector relativistic corrections and the complete perturbative one-loop quantum chromodynamic short distance potential. The masses and wave functions of the various states are obtained using a variational technique, which allows us to compare the results for both perturbative and nonperturbative treatments of the potential. As well as comparing the mass spectra, radiative widths and leptonic width…
The aim of this note is to describe the computation of post-Minkwoskian Hamiltonians in modified theories of gravity. Exploiting a recent relation between amplitudes of massive scalars and Hamiltonians for relativistic point-particles, we define a post-Minkowskian potential at second order in Newton's constant arising from $\mathcal{R}^3$ modifications in General Relativity. Using this result we calculate the associated contribution to the scattering angle for binary black holes at second post-Minkowskian order, showing agreement in the non relativistic limit with previous results for the bend…
As the value of the longitudinal momentum carried by partons in a ultra-relativistic hadron becomes small, one observes a growth of their density. When the parton density becomes close to a value of order $1/α_s$, it does not grow any longer, it saturates. These high density effects seem to be well described by the Color Glass Condensate effective field theory. On the experimental side, the LHC provides the best tool ever for reaching the saturated phase of hadronic matter. For this reason saturation physics is a very active branch of QCD during these past and coming years since saturation the…
In light of the forthcoming high precision quasielastic electron scattering data from Jefferson Lab, it is timely for the various approaches to nuclear structure to make robust predictions for the associated response functions. With this in mind, we focus here on the longitudinal response function and the corresponding Coulomb sum rule for isospin-symmetric nuclear matter at various baryon densities. Using a quantum field-theoretic quark-level approach which preserves the symmetries of quantum chromodynamics, as well as exhibiting dynamical chiral symmetry breaking and quark confinement, we fi…
We study the dynamics of color fields as generated by simple configurations of relativistic particles with Abelian and non-Abelian (SU(2)) charges in the classical limit. We find that chromodynamic (non-Abelian) systems generally show Coulomb-like features by analogy with electrodynamics. A peculiar feature in the non-Abelian case is the additional strength of the chromoelectric and chromomagnetic fields caused by the contribution of changing the color charge. This change of color SU(2) charges results in a rotation of the color vector which is getting very fast at close partonic distances. Th…
