Regularization dependence of pion generalized parton distributions

Pion generalized parton distributions are calculated within the framework of the Nambu–Jona-Lasinio model using different regularization schemes, including the proper time regularization scheme, the three-dimensional (3D) momentum cutoff scheme, the four-dimensional momentum cutoff scheme, and the Pauli-Villars regularization scheme. Furthermore, we check the theoretical constraints of pion generalized parton distributions required by the symmetries of quantum chromodynamics in different regularization schemes. The diagrams of pion parton distribution functions are plotted, in addition, we evaluate the Mellin moments of generalized parton distributions, which are related to the electromagnetic and gravitational form factors of pion. Pion generalized parton distributions are continuous but not differential at begin{document}$ x=pm ,xi $end{document}, when considering the effect of the contact contribution term, generalized parton distributions become not continuous at begin{document}$ x=pm ,xi $end{document} in all the four regularization schemes. Generalized parton distributions in impact parameter space are considered, the width distribution of u quark in the pion and the mean-squared begin{document}$ langle {boldsymbol{b}}_{bot}^2rangle_{pi}^u $end{document} are calculated. The light-front transverse-spin distributions are studied when quark polarized in the light-front-transverse begin{document}$ +,x $end{document} direction, the transverse-spin density is no longer symmetric around begin{document}$ (b_x=0,b_y=0) $end{document}, the peaks shift to begin{document}$ (b_x=0,b_y>0) $end{document}, we compare the average transverse shift begin{document}$ langle b_{bot}^yrangle_1^u $end{document} and begin{document}$ langle b_{bot}^yrangle_2^u $end{document} in different regularization schemes. The light-cone energy radius begin{document}$ r_{E,LC} $end{document} and the light-cone charge radius begin{document}$ r_{c,LC} $end{document} are also evaluated, we found that in the proper time regularization scheme the values of these quantities were the largest, in the 3D momentum cutoff scheme they were the smallest.     

Helicity-dependent generalized parton distributions in constituent quark models

Helicity-dependent generalized parton distributions of the nucleon are derived from the overlap representation of generalized parton distributions using light-cone wave functions obtained in constituent quark models. Results from two different quark models are used also to study the angular momentum sum rule and the spin asymmetry in polarized electron scattering.     

Drawing insights from pion parton distributions

A symmetry-preserving continuum approach to the two valence-body bound-state problem is used to calculate the valence,glue and sea distributions within the pion;unifying them with,inter alia,electromagnetic pion elastic and transition form factors.The analysis reveals the following momentum fractions at the scale ζ2:=2GeV:〈xvalence〉=0.48(3),〈xglue〉=0.41(2),〈xsea〉=0.11(2);and despite hardening induced by the emergent phenomenon of dynamical chiral symmetry breaking,the valence-quark distribution function,q^π(x),exhibits the x≈1 behaviour predicted by quantum chromodynamics(QCD).After evolution to ζ=5.2 GeV,the prediction for q^π(x)matches that obtained using lattice-regularised QCD.This confluence should both stimulate improved analyses of existing data and aid in planning efforts to obtain new data on the pion distribution functions.     

Revealing pion and kaon structure via generalised parton distributions

Clear windows onto emergent hadron mass(EHM)and modulations thereof by Higgs boson interactions are provided by observable measures of pion and kaon structure,many of which are accessible via generalised parton distributions(GPDs).Beginning with algebraic GPD Ans?tze,constrained entirely by hadron-scaleπand K valence-parton distribution functions(DFs),in whose forms both EHM and Higgs boson influences are manifest,numerous illustrations are provided.They include the properties of electromagnetic form factors,impact parameter space GPDs,gravitational form factors and associated pressure profiles,and the character and consequences of allorders evolution.The analyses predict that mass-squared gravitational form factors are stiffer than electromagnetic form factors;reveal that K pressure profiles are tighter than profiles,with both mesons sustaining near-core pressures at magnitudes similar to that expected at the core of neutron stars;deliver parameter-free predictions for and K valence,glue,and sea GPDs at the resolving scale l=2GeV;and predict that at this scale the fraction of meson mass-squared carried by glue and sea combined matches that lodged with the valence degrees-of-freedom,with a similar statement holding for mass-squared radii.     

Dynamical parton distributions from DGLAP equations with nonlinear corrections

Determination of proton parton distribution functions is presented under the dynamical parton model assumption by applying DGLAP equations with GLR-MQ-ZRS corrections.We provide two data sets,referred to as IMParton16,which are from two different nonperturbative inputs.One is the naive input of three valence quarks and the other is the input of three valence quarks with flavor-asymmetric sea components.Basically,both data sets are compatible with the experimental measurements at high scale(Q~2 2 GeV~2).Furthermore,our analysis shows that the input with flavor-asymmetric sea components better reproduces the structure functions at high Q~2.Generally,the parton distribution functions obtained,especially the gluon distribution function,are good options for inputs to simulations of high energy scattering processes.The analysis is performed under the fixed-flavor number scheme for nf = 3,4,5.Both data sets start from very low scales,around 0.07 GeV~2,where the nonperturbative input is directly connected to the simple picture of the quark model.These results may shed some lights on the origin of the parton distributions observed at high Q~2.     

Unpolarized structure functions and the parton distributions for nucleon in an independent quark model

Considering the nucleon as consisting entirely of its valence quarks confined independently in a scalar-vector harmonic potential; unpolarized structure functions F ₁(x, μ ²) and F ₂(x, μ ²) are derived in the Bjorken limit under certain simplifying assumptions; from which valence quark distribution functions u _v(x, μ ²) and d _v(x, μ ²) are appropriately extracted satisfying the normalization constraints. QCD-evolution of these input distributions from a model scale of μ ²=0.07 GeV² to a higher Q ² scale of Q ₀ ² =15 GeV² yields xu _v(x, Q ₀ ² ) and xd _v(x, Q ₀ ² ) in good agreement with experimental data. The gluon and sea-quark distributions such as G(x, Q ₀ ² ) and q _s(x, Q ₀ ² ) are dynamically generated with a reasonable qualitative agreement with the available data; using the leading order renormalization group equations with appropriate valence-quark distributions as the input.     

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).     

The generalized parton distribution of the pion in a relativistic Bethe-Salpeter quark model

We present a Poincaré covariant calculation of the generalized parton distribution of the pion. Results for different values of the kinematical parameters are shown and discussed.     

Final state interactions and the transverse structure of the pion using non-perturbative eikonal methods

In the factorized picture of semi-inclusive hadronic processes the naive time-reversal odd parton distributions exist by virtue of the gauge link which renders it color gauge invariant. The link characterizes the dynamical effect of initial/final-state interactions of the active parton due soft gluon exchanges with the target remnant. Though these interactions are non-perturbative, studies of final-state interaction have been approximated by perturbative one-gluon approximation in Abelian models. We include higher-order gluonic contributions from the gauge link by applying non-perturbative eikonal methods incorporating color degrees of freedom in a calculation of the Boer–Mulders function of the pion. Using this framework we explore under what conditions the Boer–Mulders function can be described in terms of factorization of final state interactions and a spatial distribution in impact parameter space.     

QED corrections to the evolution of parton distributions

We study the systematic inclusion of QED corrections in the evolution of parton distributions. corrections modify the evolution equation for parton distributions. They introduce additional parton distributions, like the photon distribution in the nucleon, and lead to additional mixing effects. We discuss the modifications for a realistic model of N_f,up up-type flavours and N_f,down down-type flavours. We have implemented these corrections into a numerical program and we quantify the size of these effects in a toy model. The corrections reach the order of 1%.     

Some numerical studies of the evolution of generalized parton distributions

We study the evolution behavior of generalized parton distributions at small longitudinal momentum fraction. Particular attention is paid to the ratio of a generalized parton distribution and its forward limit, to the mixing between quarks and gluons, and to the dependence on the squared momentum transfer t.     

Multi-component hierarchies of double bracket equations

A new integrable hierarchy, with equations defined by double brackets of two matrix pseudo-differential operators (Lax pairs), is constructed. Some algebraic properties are demonstrated. It is also shown that each equation is equivalent to a certain gradient flow. A new version of the Zakharov-Shabat type equations is proved. Formal solutions of this hierarchy are constructed using a matrix “double bracket bilinear identity”.     

Effects of elliptic flow and resonance decay process on the Kurtosis of net baryon distributions

Kurtosis is regarded as a meaningful and promising observable in searching for the possible critical point predicted by QCD. In this paper, the effects of elliptic flow and resonance decay process on the Kurtosis have been studied with Monte Carlo event generators in Au + Au collisions at √s_NN=200 GeV. The results show that the Kurtosis is not sensitive to elliptic flow and resonance decay process.     

Small <Emphasis Type="Italic">x</Emphasis> behavior of parton distributions: a study of higher twist effects

We review the double asymptotic scaling phenomenon for the structure functions of the deepinelastic scattering process. We present an analytical parameterization of the contributions from the twist-two operators of the Wilson operator product expansion and power suppressed terms. Higher twist corrections to F ₂ at small x are studied for the case of a flat initial condition for the twist-two QCD evolution in the next-to-leading order approximation. Higher twist terms are estimated using two different approaches: one motivated by BFKL and the other motivated by the renormalon formalism. The results of the latter approach are in very good agreement with deep inelastic scattering data from HERA. The text was submitted by the authors in English.     

Magnetic interactions and Preisach distributions of nanostructured barium hexaferrite

Barium hexaferrite (phase M) samples with different nanostructures were studied. Sample M1 is composed of nanocrystals of BaFe₁₂O₁₉ produced after milling the elemental oxides (Fe₂O₃ and BaCO₃) and heating in air atmosphere. Two more samples were produced by milling the same oxides and a 20% excess of -Fe. The resulting powder (composed of phase M and a 20% hematite) was heat-treated in different conditions, resulting in samples MF1 (with a partially sintered structure) and MF8 (with almost completely sintered structure).

In order to have an insight into the interactions in each sample, Preisach distributions were obtained using first-order reversion curves (FORCs) measurements. The Preisach distribution corresponding to M1 is a Gaussian-shaped one, with a maximum around 4.1 kOe. The distribution of MF1 has a narrow and high peak at 5.3 kOe, a number of overlapping small peaks down to 2.6 kOe and a distinct and low-intensity peak at 2 kOe. MF8 has a Preisach distribution with a succession of equally spaced distinct peaks from 4.2 to 1.5 kOe.

The found Preisach distributions suggest that the interactions occur among nanocrystals inside conglomerates with different number of particles.     

Effect of parton shadowing on the distributions of global observables

The effect of parton shadowing on the distributions of global observables (total transverse energy E _T and charged-particle multiplicity n _ch) is investigated on the basis of the HIJING model of nucleus-nucleus interactions. It is shown that, for the interaction of lead nuclei at $\sqrt s = 5$ TeV per nucleon, the shadowing effect results in a considerable reduction of the cross section for (mini)jet production (approximately by a factor of 4); this in turn reduces the total transverse energy and the charged-particle multiplicity by a factor of 2.7. Upon taking into account the QCD evolution of nuclear structure functions in Q ², the shadowing effect becomes less pronounced (by a factor of 1.9 for PbPb interactions). It is shown that global observables can be used to test models of parton shadowing.     

A study on the effect of stress state on damage evolution in hot deformation of free cutting steels using double notched bars

The effect of stress state on the initiation of damage for leaded free cutting steel has been investigated under hot rolling conditions. Double notched (DN) circumferential tension samples were designed and used to simulate damage development at different stress states and deformation conditions using a Gleeble (3800) thermal-mechanical testing system. Two DN sample geometries with varying notch profiles were used to account for different states of stress. To simulate the conditions of hot rolling the samples were tested at high temperatures (900–1200 °C) and moderate strain rates (0.1–1 s^?1). After testing to failure, which normally occurs at one notch of the specimen, the unfailed notch of each sample was sectioned to examine the sites where damage occurs since the material has been captured in a state very close to failure. Two of the cases examined have shown definitive damage paths occurring from ‘outside–in’ for a sharp notch deformed at T = 900 °C and from ‘inside–out’ for a blunt notch tested at T = 1200 °C for the same strain rate of 0.1 s^?1. The experimental results of the failure initiation sites were compared with computed values of the stress fields around the notch profiles, obtained from FE analysis using a set of viscoplastic constitutive equations calibrated for free cutting steel. The temperature profiles from high temperature mechanical testing were used in the FE calculations of the stress state.     

微扰QCD演化过程中存在遮蔽效应的一个证据

核子的纵向结构函数F_L以及虚光子吸收的纵向和横向散射截面的比值R_L在小X区域主要取决于胶子的分布函数.而胶子的初始分布函数的形式决定了在演化过程中是否要考虑遮蔽效应.利用新的动力学演化方程分析了F_L和R_L,发现在部分子演化过程中存在遮蔽现象.     

Spin structure of the nucleon—status and recent results

After the initial discovery of the so-called “spin crisis in the parton model” in the 1980s, a large set of polarization data in deep inelastic lepton-nucleon scattering was collected at labs like SLAC, DESY and CERN. More recently, new high precision data at large x and in the resonance region have come from experiments at Jefferson Lab. These data, in combination with the earlier ones, allow us to study in detail the polarized parton densities, the Q² dependence of various moments of spin structure functions, the duality between deep inelastic and resonance data, and the nucleon structure in the valence quark region. Together with complementary data from HERMES, RHIC and COMPASS, we can put new limits on the flavor decomposition and the gluon contribution to the nucleon spin. In this report, we provide an overview of our present knowledge of the nucleon spin structure and give an outlook on future experiments. We focus in particular on the spin structure functions g₁ and g₂ of the nucleon and their moments.