Narrow Results

A review is presented of recent results in QCD from the H1 and ZEUS experiments at HERA, emphasizing the use of higher order calculations to describe the data.

The static properties of protons are useful for understanding the quark structure of the proton. In his work we have introduced the hypercentral constituent quark model and isospin dependent potentials. Here constituent quarks interact with each other via a potential in which we have taken into account the three-body force effect and the standard two-body potential contributions. According to our model the static properties of protons containing u and d quarks are better than the other models and closer to experimental results. The two key ingredients of this improvement are the effective quark–gluon hypercentral potentials, and hyperfine interaction and isospin dependence potential. Recently, Schrödinger equation has been solved by Giannini but we have solved the Dirac equation exact analytically and we have shown that a considerable improvement in the description of the static properties of proton is obtained with an isospin dependent potential and the complete interaction including spin and isospin terms reproduces the position of the quark.

I review lattice QCD calculations of the strong coupling and quark masses.

The octonion algebra is analyzed using a formalism that demonstrates its use in color quark confinement. In this study, we attempt to write a connection between octonion algebra and SU(3)${}_c$ group generators, as well as color quarks representation. We demonstrated the glueballs construction in the extended octonionic color field and also proposed the prerequisite for octonion color confinement of hadrons.

A review is given to pentaquark mass predictions in quark models and QCD. It is pointed out that no successful quark model prediction is available for low-lying pentaquark states. Some new results of direct application of QCD, QCD sum rules and lattice QCD, are also presented.

Within the effective quark model with chiral U(3) × U(3) symmetry we calculate the S-wave and P-wave amplitudes and the partial widths of the nonleptonic decays of the Λ⁰-hyperon, Λ⁰ → pπ^- and Λ⁰ → nπ⁰. The theoretical results agree well with the experimental data. The angular distributions of the decay rates in dependence on the polarizations of baryons are analyzed both in the laboratory frame and in the rest frame of the Λ⁰-hyperon.

Within the effective quark model with chiral U(3) × U(3) symmetry we calculate the S-wave and P-wave amplitudes of the nonleptonic decay Σ⁺ → pπ⁰, the partial width and the dynamical polarization of the proton in the dependence on the polarization of the Σ⁺-hyperon. The theoretical results agree well with the experimental data.

A general expression for the dead cone of gluons radiated by virtual partons has been derived. The conventional dead cone for massive on-shell quarks and the dead cone for the virtual partons have been obtained by using different limits of the general expression. Radiative suppression due to the virtuality of initial parton jets in heavy-ion collisions has been discussed. It is observed that the suppression caused by the high virtuality is overwhelmingly large as compared to that on account of conventional dead cone of heavy quarks.

The Bialas–Bzdak model of elastic proton–proton scattering is generalized to the case when the real part of the parton–parton level forward scattering amplitude is nonvanishing. Such a generalization enables the model to describe well the dip region of the differential cross-section of elastic scattering at the intersecting storage rings (ISR) energies, and improves significantly the ability of the model to describe also the recent TOTEM data at LHC energy. Within this framework, both the increase of the total cross-section, as well as the decrease of the location of the dip with increasing colliding energies, is related to the increase of the quark–diquark distance and to the increase of the "fragility" of the protons with increasing energies. In addition, we present and test the validity of two new phenomenological relations: one of them relates the total p+p cross-section to an effective, model-independent proton radius, while the other relates the position of the dip in the differential elastic cross-section to the measured value of the total cross-section.

Central production of lepton–antilepton pairs (e⁺e^- and μ⁺μ^-) and heavy quark composite states (charmonia and bottomonia) in diffractive proton collisions (proton momenta transferred |q_⊥| ~ m/ln s) are studied at ultrahigh energies (ln s ≫ 1), where σ_tot(pp^±) ~ ln^N s with 1 ≲ N ≲ 2. The pp^±-rescattering corrections, which are not small, are calculated in terms of the K-matrix approach modified for ultrahigh energies. Two versions of hadron interactions are considered in detail: the growth (i) σ_tot(pp^±) ~ ln² s, σ_inel(pp^±) ~ ln² s within the black disk mode and (ii) σ_tot(pp^±) ~ ln² s, σ_inel(pp^±) ~ ln s within the resonant disk mode. The energy behavior of the diffractive production processes differs strongly for these modes, thus giving a possibility to distinguish between the versions of the ultrahigh energy interactions.

The Bialas–Bzdak model of elastic proton–proton scattering assumes a purely imaginary forward scattering amplitude, which consequently vanishes at the diffractive minima. We extended the model to arbitrarily large real parts in a way that constraints from unitarity are satisfied. The resulting model is able to describe elastic pp scattering not only at the lower ISR energies but also at in a statistically acceptable manner, both in the diffractive cone and in the region of the first diffractive minimum. The total cross-section as well as the differential cross-section of elastic proton–proton scattering is predicted for the future LHC energies of , 14, 15 TeV and also to 28 TeV. A nontrivial, significantly nonexponential feature of the differential cross-section of elastic proton–proton scattering is analyzed and the excitation function of the nonexponential behavior is predicted. The excitation function of the shadow profiles is discussed and related to saturation at small impact parameters.

On the basis of requirements of unitarity and analyticity we analyze the real and imaginary parts of the scattering amplitude at recent ultrahigh energies, $\text{1–100}\mathrm{\text{TeV}}$. The predictions for the region $\sqrt{s}>100\mathrm{\text{TeV}}$ and $q^2<0.4{\mathrm{\text{GeV}}}^2$ are given supposing the black disk asymptotic regime. It turns out that the real part of the amplitude is concentrated in the impact parameter space at the border of the black disk.

Sometime back, a self-similarity based model of the proton structure function at small $x$ was proposed by Lastovicka. We make reanalysis of this model with most recent HERA data. No significance difference with the earlier analysis is found. Both the analyses have singularity within the kinematical range of $x$: $0\le x\le 1$. We therefore study the model with the additional assumption that it should be singularity free, imposing positivity conditions on the model parameters. This results in a new model which is, however, phenomenologically valid only in a limited low $Q^2$ range. We therefore make further generalization of the defining self-similar unintegrated Parton Density Function (uPDF) and show that the with proper generalizations and initial conditions on them not only remove the undesired singularity but also results in a structure function with logarithmic growth in $Q^2$ closer to QCD. The phenomenological range of validity is then found to be much larger than the earlier versions. We also extrapolate the models to large $x$ in a parameter-free way. The possibility of incorporation of Transverse Momentum Dependent (TMD) PDF in this approach is explored as well.

Froissart bound implies that the total proton–proton cross-section (or equivalently proton structure function) cannot rise faster than ${log}^{2}s\sim {log}^2\frac{1}{x}$. Compatibility of such behavior with the notion of self-similarity in proton structure function was suggested by us sometime back. In the present work, we generalize and improve it further by considering more recent self-similarity based models of proton structure functions and compare with recent data as well as with the model of Block, Durand, Ha and McKay.

Whenever one has witnessed some event and then sees it reported in the media, one’s reaction is the same: it was not quite like that. It is in this spirit of a frequent first-hand witness that I write this article. I discuss a few selected points which — to my judgement — illustrate well the QCD evolution (in time) from the theoretical, phenomenological and experimental points of view.

In this paper, we use the concept of conformable fractional derivative to study the nonrelativistic radial Schrödinger equation. We suggest an extended version of the Cornell potential as the quark–antiquark interaction of light and heavy mesons. We generalize the asymptotic iteration method to the fractional domain. The latter is used to calculate the energy eigenvalues, as well as the effect of the fractional order $\nu$ on energy spectra. To test the applicability of our model, we use the obtained results to reproduce the mass spectra of some light and heavy mesons such as $b\bar{b}$, $c\bar{c}$, $c\bar{s}$, $\bar{b}c$, $b\bar{q}$ and $b\bar{s}$ quarks. The mass spectra are obtained at different values of the fractional order parameter $\nu$ and were compared with experimental results and other relevant theoretical works. Using the wave function, we calculated the decay constants for heavy-light $D^0$, $D^{+}$, $D_s^{+}$, $B^{-}$, ${\bar{B}}^0$ and ${\bar{B}}_s^0$ mesons. Our results are found to be in good agreement with the experimental data, and improved in comparison with other theoretical previsions.

In this work, we use the approach recently introduced by Barros to study hadron spectra and some quark confinement properties in a Schwarzchild-like space–time generated by a nongravitational field. As a starting point, for the nongravitational field, we make the choice of a strong Yukawa-like field whose associated potential is a generalized Yukawa-like potential, typical of strong interactions. Then, from the latter field, the energy momentum tensor is constructed, the Einstein field equations are solved and the curvature function of the Schwarzchild metric is obtained. The correspondence principle applied to the Schwarzchild metric has enable us to construct the Dirac equation in the latter space. The resolution of the coupled differential equations of Dirac made it possible to obtain the energy spectrum of the strong interaction. The latter is obtained in a more general form than in the previous investigations. Then, the energy spectrum, masses and confinement radius of few hadrons are estimated and compared with experimental data and other theoretical studies. In most considered cases, our predictions are found to be in good agreement with experimental data. The good agreement observed between our outcomes and the experiment can be attributed to the choice of our potential, which has more free parameters than in past studies with the same approach.

A dependence of phonon interaction on the interelectronic distance is found for a translation-invariant (TI) strong-coupling bipolaron. It is shown that the charge induced by the electrons in a TI-bipolaron state is always greater than that in a bipolaron with spontaneously broken symmetry.

The phase diagram of quantum chromodynamics is conjectured to have a rich structure containing at least three forms of matter: hadronic nuclear matter, quarkyonic matter and quark–gluon plasma. We justify the origin of the quarkyonic phase transition in a chiral-quark model and describe its formulation in terms of Skyrme crystals.

Wigner distribution functions are the quantum analogue of the classical phase space distribution and being quantum implies that they are not genuine phase space distribution and thus lack any probabilistic interpretation. Nevertheless, Wigner distributions are still interesting since they can be related to both generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) under some limit. We study the Wigner distribution of quarks and also the orbital angular momentum (OAM) of quarks in the dressed quark model.