Small x phenomenology on gluon evolution through the BFKL equation in light of a constraint in multi-Regge kinematics

We investigate the impact of so-called kinematic constraint on gluon evolution at small x.Implanting the constraint on the real emission term of the gluon ladder diagram, we obtain an integro-differential form of the Balitsky-Fadin-Kuraev-Lipatov(BFKL) equation. Later we solve the equation analytically using the method of characteristics. We sketch the Bjorken x and transverse momentum k_t~2 dependence of our solution of unintegrated gluon distributions f (x,k_t~2) in the kinematic constraint supplemented BFKL equation and contrasted the same with the original BFKL equation. Then we extract the integrated gluon density xg(x, Q~2) from unintegrated gluon distributions f (x,k_t~2) and compared our theoretical prediction with that of global data fits, namely NNPDF3.1 sx and CT14. Finally we illustrate the phenomenological implication of our solution for unintegrated gluon distribution f (x,k_T~2) towards exploring high precision HERA DIS data by the theoretical prediction of proton structure functions(F_2 and F_L).     

Transport coefficients of a gluon plasma

Transport coefficients of gluon plasma are calculated for an SU(3) pure gauge model by lattice QCD simulations on 16(3) x 8 and 24(3) x 8 lattices. Simulations are carried out at slightly above the deconfinement transition temperature T(c), where a new state of matter is currently being pursued in BNL RHIC experiments. Our results show that the ratio of the shear viscosity to the entropy is less than one and the bulk viscosity is consistent with zero in the region 1.4 < or = T/T(c) < or = 1.8.     

Shadowing correction to the gluon distribution behavior at small x

We determined the saturation exponent of the gluon distribution using the solution of the QCD nonlinear Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (NLDGLAP) evolution equation at small x . The very small-x behavior of the gluon distribution is obtained by solving the Gribov, Levin, Ryskin, Mueller and Qiu (GLR-MQ) evolution equation with the nonlinear shadowing term incorporated. The form of the initial condition for the equation is determined. We find, with decreasing x , the emergence of a singular behavior and the eventual taming (at R = 5 GeV^-1) and the essential taming (at R = 2 GeV^-1) of this singular behavior by the shadowing term. The nonlinear gluon density functions are calculated and compared with the results for the integrated gluon density from the Balitsky-Kovchegov (BK) equation for the different values of Q². It is shown that the results for the gluon density function are comparable with the results obtained from the BK equation solution. Also we show that for each x , the Q²-dependence of the data is well described by gluon shadowing corrections to the GLR-MQ equation. The resulting analytic expression allows us to predict the logarithmic derivative \( {\frac{{\partial F^{s}_{2} (x,Q^{2})}}{{\partial \ln Q^{2}}}}\) and to compare the results with H1 data and a QCD analysis fit.     

胶子遮蔽和末态作用对p—A碰撞中粲偶素和b夸克偶素产额压低的贡献

本文用胶子结构函数的遮蔽效应和末态作用分析了在ｐ－Ａ碰撞中粲偶素和ｂ夸克偶素产额压低的实验数据，较好地描述了粲偶素和ｂ夸克偶素产额的压低与Ａ和Ｘ２的关系．     

Non-Perturbative Propagators in QCD

We have derived the gluon and quark complete propagators under chain approximation in the presence of gluon condensation <Ω│G²│Ω> and quark condensation <Ω│ψψ│Ω>.The nonvanishing vacuum average value for gluon composite operator <Ω│Aαμ(x)Abv(y)│Ω> is expanded into a series in terms of two point distance (x—y) in Lorentz gauge condition.The series is of translation invariance as compared with the series in fixed gauge condition.<Ω│G²│Ω> is introduced as the series coefficient when we take into account the correction of <Ω│Aαμ(x)Abv(y)│Ω> to quark propagator.     

An Analysis of the Proton Structure Function and the Gluon Distributions at Small x

Recently, we reported an analysis of Proton structure function at small x based on Taylor approximated DGLAP equations assuming a plausible relationship between the singlet and the gluon distributions. In this paper, we report a generalised version of the previous work. A corresponding study of the suggested gluon distribution is also made.The present generalised version of the model for the structure function results in a wider x range of phenomenological validity than the earlier one. A comparison of both the models of the proton structure function and the gluon distribution is made with exact result as well as with the Froissart saturated models of Block, Durand and Mckay.     

A DYNAMICAL MODEL FOR THE GLUON DISTRIBUTION FUNCTION

In this paper the forms of the gluon distribution function at different Q² are discussed with the aid of the three-quarks model associated with dynamical calculations of QCD (the LLA approximation). The Buras-Gaemers parametrization is improved and the gluon distribution functions are obtained. It can be described by a simple parameter form: xG(x, Q²)=xG₁(x, Q²)+xG₂(x, Q²)=[1+B(s)]1(Q²)>2(1-x)^[B(s)]+[1+D(s)]2)>(1-x)^D(s), The form satisfies the QCD evolution equations and does not contradict evidently with existing experimental data. Then the properties of the constituent gluons in a nucleon are analyzed on these basis and it is indicated that the gluon distribution function could be considered as to be made of two different parts-soft and hard parts.     

Can a Chaotic Solution in the QCD Evolution Equation Restrain High-Energy Collider Physics？

We indicate that the random aperiodic oscillation of the gluon distributions in a modified Balitsky -Fadin-Kurae- Lipatov （BFKL） equation has positive Lyapunov exponents. This first example of chaos in QCD evolution equations raises the sudden disappearance of the gluon distributions at a critical small value of the Bjorken variable x and may stop the increase of the new particle events in an ultra high energy hadron collider.     

Nonperturbative gluon radiation and energy dependence of elastic scattering

The energy dependence of the total hadronic cross sections is caused by gluon bremsstrahlung which we treat nonperturbatively. It is located at small transverse distances about 0.3 fm from the valence quarks. The cross section of gluon radiation is predicted to exponentiate and rise with energy as s(delta) with delta = 0.17+/-0. 01. The total cross section also includes a large energy independent Born term which corresponds to no gluon radiation. The calculated total cross section and the slope of elastic scattering are in good agreement with the data.     

Comparisons Between Additional Parton Evolution and Q2-Rescaling Models Based on Recombination Effect

Comparisons between the additional parton evolution (APE) model and Q²-rescaling (QR) model based on the recombination effect are made by means of investigating deep-inelastic (DIS) structure functions F₂^A, nuclear Drell-Yan process and nuclear gluon distributions. While explaining experimentally measured F₂^A(x) structure functions, the difference in the recombination results of the two models mainly lies in their sensitivity to input parton distributions and Q²-dependence. In predicting the nuclear Drell-Yan ratio, the APE model gives more reasonable results in the small x region than those of the QR model. The two motlels offer similar predictions of the nuclear gluon ratio G_sn(x)/G_c(x) which are extracted from the inelastic J/ψ production process.     

A candidate for strangeonium hybrid

We propose that the recently observed structure at 2175 MeV by the Babar Collaboration is a 1⁻⁻ strangeonium hybrid, and we investigate this interpretation from both the flux tube model and the constituent gluon model. The decay patterns and decay width in the flux tube model and the constituent gluon model (for the “gluon excited” hybrid) are very similar. The crucial test of our scenario is suggested.     

Diffraction at HERA, Color Opacity and Nuclear Shadowing in DIS off nuclei

The QCD factorization theorem for diffractive processes in DIS is used to derive formulae for the leading twist contribution to the nuclear shadowing of parton distributions in the low thickness limit (due to the coherent projectile (photon) interactions with two nucleons). Based on the current analyzes of diffraction at HERA we find that the average strength of the interactions which govern diffraction in the gluon sector at x≤ 10⁻³, Q ₀= 2 GeV is ∼50mb. This is three times larger than in the quark sector and suggests that applicability of DGLAP approximation requires significantly larger Q ₀ in the gluon sector. We use this information on diffraction to estimate the higher order shadowing terms due to the photon interactions with N≥ 3 nucleons which are important for the scattering of heavy nuclei and to calculate nuclear shadowing and Q ² dependence of gluon densities. For the heavy nuclei the amount of the gluon shadowing: G _A(x,Q ₀ ²) /AG _N(x,Q ₀ ²)_{|x ≤ 10−3}∼ 0.25–0.4 is sensitive to the probability of the small size configurations within wave function of the gluon “partonometer” at the Q ₀ scale. At this scale for A∼ 200 the nonperturbative contribution to the gluon density is reduced by a factor of 4–5 at x≤ 10⁻³ unmasking PQCD physics in the gluon distribution of heavy nuclei. We point out that the shadowing of this magnitude would strongly modify the first stage of the heavy ion collisions at the LHC energies, and also would lead to large color opacity effects in eA collisions at HERA energies. In particular, the leading twist contribution to the cross section of the coherent J/ψ production off A≥ 12 nuclei at s ⁻²≥ 70 GeV is strongly reduced as compared to the naive color transparency expectations. The Gribov black body limit for F _2A(x,Q ²) is extended to the case of the gluon distributions in nuclei and shown to be relevant for the HERA kinematics of eA collisions. Properties of the final states are also briefly discussed. Received: 12 March 1999     

Jet quenching versus jet enhancement: a quantitative study of the BDMPS-Z gluon radiation spectrum

We study the gluon radiation spectrum off a hard in-medium produced quark in the multiple soft-rescattering formalism of Baier–Dokshitzer–Mueller–Peigné–Schiff and of Zakharov (BDMPS-Z). Its dependence on the quark and gluon energy, on the gluon transverse momentum, on the in-medium pathlength and on the rescattering properties of the nuclear medium is analyzed quantitatively. The two components of gluon radiation, the hard vacuum radiation associated to the quark production vertex, and the medium-induced rescattering contribution interfere destructively. For small spatial extensions of the medium, this destructive interference overcompensates the hard vacuum radiation, and the total medium-induced radiative energy loss decreases as ΔE∝− L³. Medium-induced gluon production dominates only above a finite critical length L>L_crit which varies between 3 and more than 6 fm depending on the rescattering properties of the medium. Deviations from the BDMPS-L²-behaviour persist above L_crit. The medium-dependence of the angular gluon distribution is dominated by transverse brownian k-broadening. This results in a depletion of the low transverse momentum part of both the hard and the medium-induced contribution. As a consequence, the medium-induced energy loss outside a finite angular cone size Θ can be more than a factor two larger than the total medium-induced radiative energy loss. We discuss implications of these results for the jet quenching signal in relativistic heavy-ion collisions at RHIC and LHC.     

模拟锆(Zr) 的基体效应对Ni3Al-x atoms % Zr晶界内聚性的影响(英文)

利用双粒子模型研究微量元素锆(Zr)的基体效应对Ni3Al x atoms % Zr晶界内聚性的影响. 模型显示， x\[锆(Zr)的基体浓度\]从0.1增加到0.5， 在晶界Zr富集是增加的； Ni富集和Al贫乏在x=0.3时趋于最大. 模型还显示， Ni3Al x atoms % Zr晶界的内聚性在x=0.3时为最佳.     

Distribution Function of Polarized Proton

The region of allowed values of quark and gluon spin densities in a proton is discussed. The helicity difference distributions of the constituents which can fit the existent data for g₁^p are constructed and the significant differences between the results fiom our distributions and from other models at small x region (< 10^-1) are shown.     

Calculation of the Gluon Distribution Function Using Alternative Method for the Proton Structure Function

A calculation of the proton structure function F2(x,Q2) is reported with an approximation method that relates the reduced cross section derivative and the F2(x, Q2) scaling violation at low x by using quadratic form for the structure function. This quadratic form approximation method can be used to determine the structure function F2 (x, Q2)from the HERA reduced cross section data taken at low x. This new approach can determine the structure functions F2(x,Q2) with reasonable precision even for low x values which have not been investigated. We observe that the Q2 dependence is quadratic over the full kinematic covered range. To test the validity of our new determined structure functions, wefind the gluon distribution function in the leading order approximation with our new calculation for the structure functions and compare them with the QCD parton distribution functions.     

A Lower Bound on Longitudinal Structure Function at Small x from a Self-Similarity Based Model of Proton

Self-similarity based model of proton structure function at small x was reported in the literature sometime back. The phenomenological validity of the model is in the kinematical region 6.2 × 10-7 ≤ x ≤ 10-2 and 0.045 ≤ Q2 ≤ 120 GeV2. We use momentum sum rule to pin down the corresponding self-similarity-based gluon distribution function valid in the same kinematical region. The model is then used to compute bound on the longitudinal structure function FL（X, Q2） for A1tarelli-Martinelli equation in QCD and is compared with the recent HERA data.     

Low-x QCD with CMS at the LHC

The physics of gluon saturation and non-linear evolution at small values of parton momentum fraction x in the proton and nucleus is discussed in the context of experimental results at HERA and RHIC. The rich physics potential of low-x QCD studies at the LHC is discussed and some measurements in pp, pA and AA collisions accessible with the compact muon solenoid (CMS) experiment are presented. PACS 12.38.-t; 24.85.+p; 25.75.-q     

High-density QCD and cosmic-ray air showers

We discuss particle production in the high-energy, small-x limit of QCD where the gluon density of hadrons is expected to become nonperturbatively large. Strong modifications of the phase-space distribution of produced particles as compared to leading-twist models are predicted, which reflect in the properties of cosmic-ray induced air showers in the atmosphere. Assuming hadronic primaries, our results suggest a light composition near Greisen-Zatsepin-Kuzmin cutoff energies. We also show that cosmic-ray data are sensitive to various QCD evolution scenarios for the rate of increase of the gluon density at small x, such as fixed-coupling and running-coupling Balitsky-Fadin-Kuraev-Lipatov evolution. There are clear indications for a slower growth of the gluon density as compared to RHIC and HERA, due, e.g., to running-coupling effects.