Electroproduction of <Emphasis Type="Italic">J/ψ</Emphasis> mesons within the semihard QCD approach and the color-singlet model

The deep-inelastic production of J/ψ mesons in electron-proton interactions at the HERA collider is considered within the semihard (k_T-factorization) QCD approach and within the color-singlet model. The dependence of the Q², p _T ² , z, y* and W distributions of J/ψ mesons on various sets of unintegrated gluon distributions and the dependence of the spin parameter α on p _T ² and Q² are investigated. The results of the calculations are compared with the latest experimental data obtained by the H1 and ZEUS Collaborations at the HERA collider. It is shown that experimental investigations of the polarization properties of J/ψ mesons over the kinematical region Q²<1 GeV² may provide an additional test of the statement that the dynamics of gluon distributions is governed by the Balitsky-Fadin-Kuraev-Lipatov equations.     

Electroproduction of <Emphasis Type="Italic">D</Emphasis>*<Superscript>±</Superscript> mesons at high energies

A comparative analysis of the predictions of the collinear parton model and the k _T -factorization approach is performed for the case of the D*-meson electroproduction at the HERA ep collider. It is shown that, owing to effectively taking into account, in noncollinear distributions, next-order corrections in the strong coupling constant α _s , the k _T -factorization approach increases, in contrast to the predictions of the collinear parton model, the absolute value of the cross sections for charmed-meson electroproduction by approximately a factor of 1.5 to 2. As a result, the agreement with experimental data is improved. This is not so only for the pseudorapidity spectrum, whose shape differs considerably from the experimental one and depends greatly on the choice of parametrization of the noncollinear gluon distribution within the proton.     

Hadroproduction of heavy quarkonia at high energies within the <Emphasis Type="Italic">k</Emphasis><Subscript><Emphasis Type="Italic">T</Emphasis></Subscript>-factorization approach

On the basis of the k _T -factorization approach, heavy-quarkonium \((c\bar c,b\bar b)\) hadroproduction at high energies is considered within nonrelativistic QCD in the leading order in α _s and v. The p _T spectra of various S-and P-wave quarkonium states at the Tevatron collider energies (run I and run II) are fitted, and sets of octet nonperturbative matrix elements are obtained for three different versions of the noncollinear gluon distribution in the proton.     

Condensates in quantum chromodynamics

The paper presents a short review of our knowledge today on vacuum condensates in quantum chromodynamics (QCD). The condensates are defined as vacuum averages of the operators which arise due to nonperturbative effects. The important role of condensates in determining physical properties of hadrons and of their low-energy interactions in QCD is underlined. The special value of the quark condensate, connected to the existence of baryon masses, is mentioned. Vacuum condensates induced by external fields are discussed. QCD at low energy is checked on the basis of the data on hadronic τ decay. In theoretical analysis, the terms of perturbation theory (PT) up to α _s ³ are accounted for; in the operator product expansion (OPE), those up to dimension 8. The total probability of the decay τ → hadrons (with zero strangeness) and of the τ-decay structure functions are best described at α _s (m _τ ² )=0.330±0.025. It is shown that the Borel sum rules for τ-decay structure functions along the rays in the q ²-complex plane are in agreement with experiment, having an accuracy of ～2% at the values of the Borel parameter |M ²|>0.8 GeV². The magnitudes of dimension 6 and 8 condensates were found, and the limitations on gluon condensates were obtained. The sum rules for the charmed-quark vector-current polarization operator were analyzed in three loops (i.e., in order α _s ² ). The value of the charmed-quark mass (in an \(\overline {MS} \) regularization scheme) was found to be \(\bar m_c (\bar m_c^2 ) = 1.275 \pm 0.015\) GeV, and the value of gluon condensate was estimated as 〈0|(α _s/π)G ²|0〉=0.009±0.007 GeV⁴. The general conclusion is that the QCD described by PT + OPE is in good agreement with experiment at Q ²?1 GeV².     

Momentum distribution of charged particles in jets in dijet events and comparison to perturbative QCD predictions

Inclusive momentum distributions of charged particles are measured in dijet events. Events were produced at the AMY detector with a centre of mass energy of 60 GeV. Our results were compared, on the one hand to those obtained from other e⁺e^?, ep as well as CDF data, and on the other hand to the perturbative QCD calculations carried out in the framework of the modified leading log approximation (MLLA) and assuming local parton–hadron duality (LPHD). A fit of the shape of the distributions yields Q_eff = 263±13 MeV for the AMY data. In addition, a fit to the evolution of the peak position with dijet mass using all data from different experiments gives Q_eff = 226±18 MeV. Next, α_s was extracted using the shape of the distribution at the Z⁰ scale, with a value of 0.118 ± 0.013. This is consistent, within the statistical errors, with many accurate measurements. We conclude that it is the success of LPHD + MLLA that the extracted value of α_s is correct. Possible explanations for all these features will be presented in this paper.     

Generating QCD amplitudes in the color-flow basis with MadGraph

We propose to make use of the off-shell recursive relations with the color-flow decomposition in the calculation of QCD amplitudes on MadGraph. We introduce colored quarks and their interactions with nine gluons in the color-flow basis plus an Abelian gluon on MadGraph, such that it generates helicity amplitudes in the color-flow basis with off-shell recursive formulae for multi-gluon sub-amplitudes. We demonstrate calculations of up to 5-jet processes such as gg→5g, \(u\overline{u}\rightarrow5g\) and uu→uuggg. Although our demonstration is limited, it paves the way to evaluate amplitudes with more quark lines and gluons with MadGraph.     

Deep-inelastic heavy-quark production at the HERA collider within the QCD semihard approach

Deep-inelastic heavy-quark production in electron-proton interactions at the HERA collider energies is considered within the QCD semihard (k _T-factorization) approach. The dependence of the total and differential cross sections for the production of b quarks (and for muons arising in the subsequent semileptonic decay of B mesons) on the choice of unintegrated distributions of gluons in the proton is investigated. In particular, the gluon distributions obtained by solving the Catani-Ciafaloni-Fiorani-Marchesini evolution equation and the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-Balitsky-Fadin-Kuraev-Lipatov combined equation are used in numerical calculations. The results of the theoretical calculations are compared with latest experimental data obtained by the H1 and ZEUS Collaborations at the HERA collider.     

Measurement of polarization angular coefficients in <Emphasis Type="Italic">Z</Emphasis> boson leptonic decays with ATLAS at the LHC

This paper presents the complete set of polarization angular coefficients A _0?7 describing lepton angular distributions in Z boson decay, which were measured at the ATLAS experiment in proton–proton collisions with the energy √s = 8 TeV. Theoretical values for the difference A ₀ ? A ₂ calculated in the fixed-order QCD perturbation theory O(α _s ² ), demonstrate significant deviation from the measured data, which indicates the necessity of taking into account higher order corrections. The evidence of nonzero coefficients A _5,6,7 was obtained for the first time, in accordance with theoretical calculations in O(α _s ² ) approximation. Measurement of the polarization angular coefficients A _i is important for subsequent precision measurement of parameters of the electroweak model at the LHC, such as the sine of Weinberg electroweak mixing angle sin² θ _W and the W boson mass.     

Nonperturbative phenomena in QCD at finite temperature in a magnetic field

The norperturbative QCD vacuum at finite temperature in a external magnetic field is studied. Equations that relate nonperturbative QCD condensates at finite temperature to the thermodynamic pressure at T ≠ 0 and H ≠ 0 are obtained, and low-energy theorems are derived. The free energy of the QCD vacuum in the hadronic phase at H ≠ 0 is calculated, and expressions for the quark and gluon condensates are obtained. Various limiting cases for the behavior of the condensates at low and high temperatures and in weak and strong magnetic fields are investigated. A new interesting phenomenon that consists in the freezing of the quark condensate by a magnetic field is found. The character of spontaneous chiral-symmetry breaking in finite-temperature QCD in a magnetic field is studied. For this purpose, the Gell-Mann-Oakes-Renner formula relating the pion mass M _π and the axial-vector coupling constant F _π to the quark condensate is derived at T ≠ 0 and H ≠ 0. It is shown that this formula preserves its form at finite temperature after taking into account a magnetic field—that is, no additional terms independent of T and H appear. Thus, the scheme of soft chiral-symmetry breaking remains unchanged. The quark-hadron phase transition in QCD in a magnetic field is studied. It is shown that the phase-transition temperature becomes lower than that in the case of zero magnetic field.     

Spectrum of heavy-light mesons in the QCD string picture

We describe in detail predictions of the QCD string approach for the masses of the heavy—light D, D _s , B, and B _s mesons, including orbitally and radially excited states. We discuss the role of the proper dynamics of the QCD string in the formation of the spectrum of the heavy—light mesons, with quark self-energy corrections calculated self-consistently in the same picture. We give our predictions in terms of the current quark masses; the string tension—the only dimensional parameter describing the interquark interaction; and the strong coupling constant, which differs for the fine and the hyperfine interactions. The results are compared with the predictions of other models and with the experimental and lattice results.     

<Emphasis Type="Italic">K</Emphasis><Superscript>±</Superscript><Emphasis Type="Italic">p</Emphasis> elastic scattering in the QCD inspired eikonalized model

Based on our previous study of the QCD inspired eikonalized model for describing vector meson photoproduction, pp, and \(\bar p\) p elastic scattering at high energies, we apply the mode to high energy K ^± p elastic scattering. The total cross section σ _tot(s), differential cross section dσ/dt, the ratio of the real part to imaginary part of the forward scattering amplitude ρ(s), and nuclear slope parameter function β(s) are calculated in the model. Our results show that the theoretical prediction for σ _tot(s) is in a good agreement with the experimental data within error bars of the data. For the other theoretical predictions there are no data to test the predictive power of the model. We need the corresponding experimental data to examinate the validity of our QCD inspired eikonalized model. However, our calculations clearly show that the Odderon exchange in the process makes a significant contribution to the observable of ρ(s) and β(s). Therefore, we may conclude that there is a good opportunity to find the QCD Odderon in the K ^± p elastic scattering at high energies.     

Investigation of the Balitsky-Fadin-Kuraev-Lipatov dynamics of gluon distributions in the inelastic production of <Emphasis Type="Italic">J/ψ</Emphasis> mesons at the HERA collider

The inelastic photo-and electroproduction of J/ψ mesons at the HERA collider are considered within the semihard (k _T -factorization) QCD approach and the color-singlet model. The total, differential, and double-differential cross sections for the inelastic production of J/ψ mesons are investigated versus the Pomeron intercept Δ, which is the basic parameter of low-x physics; also studied here is the spin alignment parameter α versus the square of the transverse momentum, p _ψT ² , and the variable z. The theoretical results obtained in the present study are compared with the latest experimental data of the H1 and ZEUS Collaborations. It is shown that experimental investigations of the polarization properties of J/ψ mesons at the HERA collider for Q²<1 GeV² may provide an additional test of the Balitsky-Fadin-Kuraev-Lipatov dynamics of gluon distributions.     

Heavy-quark production in p $$\bar p$$ collisions and unintegrated gluon distributions

The inclusive production of heavy (c and b) quarks in high-energy p\(\bar p\) collisions are considered within the semihard approach in QCD. The dependence of the cross section for heavy-quark production, σ(p_T>p _T ^min ), on unintegrated gluon distributions is studied. The results of this consideration are compared with experimental data obtained by the D0 and CDF Collaborations at Tevatron.     

Gottfried Sum Rule in QCD Nonsinglet Analysis of DIS Fixed-Target Data

Deep-inelastic-scattering data from fixed-target experiments on the structure function F₂ were analyzed in the valence-quark approximation at the next-to-next-to-leading-order accuracy level in the strong-coupling constant. In this analysis, parton distributions were parametrized by employing information from the Gottfried sum rule. The strong-coupling constant was found to be α _s (M²_Z) = 0.1180 ± 0.0020 (total expt. error), which is in perfect agreement with the world-averaged value from an updated Particle Data Group (PDG) report, α^PDG _s (M²_Z) = 0.1181 ± 0.0011. Also, the value of 〈x〉_u?d = 0.187 ± 0.021 found for the second moment of the difference in the u- and d-quark distributions complies very well with the most recent lattice result 〈x〉^LATTICE_u?d = 0.208 ± 0.024.     

Production of heavy quarks on protons within the semihard QCD approach

The inclusive production of heavy quarks in p\(\bar p\) interactions at the Tevatron and LHC energies is considered within the semihard QCD approach. The dependence of the total and differential cross sections for the production of b quarks and B mesons (and of muons originating from the subsequent semileptonic decay B → μν _μ X) on various samples of unintegrated gluon distributions is studied. The results obtained by calculating azimuthal correlations between the transverse momenta of final particles are presented. The theoretical results are compared with the latest experimental data obtained by the D0 and CDF Collaborations at the Tevatron.     

Saturation Approach in Top Production

The reduced cross section for the top production, in deep inelastic scattering, determined when we use the Kharzeev–Levin–Nardi (KLN) model of the low x gluon distributions. With respect to this model, a compact formula for the ratio R^t(τ) provided that it is approximately independent of τ behavior at low- τ values. For the top production where Q_sr_⊥ ? 1, the model reduced to color transparency.     

Parton distribution functions from the precise NNLO QCD fit

We report on the parton distribution functions (PDFs) determined from the NNLO QCD analysis of the world inclusive DIS data with account for the precise NNLO QCD corrections to the evolution equations kernel. The value of the strong coupling constant α _s ^NNLO (M _Z ) = 0.1141 ± 0.0014 (exp.), in fair agreement with the one obtained using the earlier approximate NNLO kernel by van Neerven-Vogt. The intermediate bosons rates calculated in the NNLO using the obtained PDFs are in agreement with the latest Run II results.     

The effect of hadronic rindler horizon on hadronization process

In this study by extending the recent suggested mechanisms to hadronization processes, the information loss for QCD matter in hadronic Rindler horizon is found. We notice that for all finite values of quark and gluon energies, all information from all hadronization processes experiences some degree of loss. Then the effect of hedonic Rindler horizon on three jet cross section is explored. It is found that the three jet cross section is rising at y_cut =?0.0002 exhibits a turn-over at moderate value of y_cut =?0.01 and then rapidly decreases as y_cut increases. This model is consistent with OPAL data. Finally, different channels for producing Higgs boson near hadronic Rindler horizon are studied. It is shown that the cross section of Higgs boson produced via gluon fusion and quark interaction near a single Hadronic Rindler Horizon is much larger for higher center of mass energies. This is because an increase in the energy of hadronic Rindler horizon raises the temperature, thus intensifying the thermal radiation of QCD matter.     

Determination of the scattering coefficient of biological tissue considering the wavelength and absorption dependence of the anisotropy factor

The anisotropy factor g, one of the optical properties of biological tissues, has a strong influence on the calculation of the scattering coefficient μ _s in inverse Monte Carlo (iMC) simulations. It has been reported that g has the wavelength and absorption dependence; however, few attempts have been made to calculate μ _s using g values by taking the wavelength and absorption dependence into account. In this study, the angular distributions of scattered light for biological tissue phantoms containing hemoglobin as a light absorber were measured by a goniometric optical setup at strongly (405 nm) and weakly (664 nm) absorbing wavelengths to obtain g. Subsequently, the optical properties were calculated with the measured values of g by integrating sphere measurements and an iMC simulation, and compared with the results obtained with a conventional g value of 0.9. The μ _s values with measured g were overestimated at the strongly absorbing wavelength, but underestimated at the weakly absorbing wavelength if 0.9 was used in the iMC simulation.