A Novel Feature of Valence Quark Distributions in Hadrons

Examining the evolution of the maximum of valence quark distribution, qV, weighted by Bjorken x, h(x,t)≡xqV(x,t), it is observed that h(x,t) at the peak becomes a one-parameter function; h(xp,t)=Φ(xp(t)), where xp is the position of the peak, t=logQ2, and Q2 is the resolution scale. This observation is used to derive a new model-independent relation which connects the partial derivative of the valence parton distribution functions (PDFs) in xp to the quantum chromodynamics (QCD) evolution equation through the xp derivative of the logarithm of the function Φ(xp(t)). A numerical analysis of this relation using empirical PDFs results in an observation of the exponential form of the Φ(xp(t))=h(xp,t)=CeDxp(t) for leading to next-to-next leading order approximations of PDFs for the range of Q2, covering four orders in magnitude. The exponent, D, of the observed “height-position” correlation function converges with the increase in the order of approximation. This result holds for all the PDF sets considered. A similar relation is observed also for the pion valence quark distribution, indicating that the obtained relation may be universal for any non-singlet partonic distribution. The observed “height-position” correlation is used also to indicate that no finite number of exchanges can describe the analytic behavior of the valence quark distribution at the position of the peak at fixed Q2.

Saturation effects in SIDIS at very forward rapidities

Using the dipole picture for electron-nucleus deep inelastic scattering at small Bjorken x, we study the effects of gluon saturation in the nuclear target on the cross-section for SIDIS (single inclusive hadron, or jet, production). We argue that the sensitivity of this process to gluon saturation can be enhanced by tagging on a hadron (or jet) which carries a large fraction z ≃ 1 of the longitudinal momentum of the virtual photon. This opens the possibility to study gluon saturation in relatively hard processes, where the virtuality Q2 is (much) larger than the target saturation momentum $$ {Q}_s^2 $$ Q s 2 , but such that z(1 − z)Q2 ≲ $$ {Q}_s^2 $$ Q s 2 . Working in the limit z(1 − z)Q2 ≪ $$ {Q}_s^2 $$ Q s 2 , we predict new phenomena which would signal saturation in the SIDIS cross-section. For sufficiently low transverse momenta k⊥ ≪ Qs of the produced particle, the dominant contribution comes from elastic scattering in the black disk limit, which exposes the unintegrated quark distribution in the virtual photon. For larger momenta k⊥ ≳ Qs, inelastic collisions take the leading role. They explore gluon saturation via multiple scattering, leading to a Gaussian distribution in k⊥ centred around Qs. When z(1 − z)Q2 ≪ Q2, this results in a Cronin peak in the nuclear modification factor (the RpA ratio) at moderate values of x. With decreasing x, this peak is washed out by the high-energy evolution and replaced by nuclear suppression (RpA< 1) up to large momenta k⊥ ≫ Qs. Still for z(1 − z)Q2 ≪ $$ {Q}_s^2 $$ Q s 2 , we also compute SIDIS cross-sections integrated over k⊥. We find that both elastic and inelastic scattering are controlled by the black disk limit, so they yield similar contributions, of zeroth order in the QCD coupling.

An analysis of parton distribution functions of the pion and the kaon with the maximum entropy input

We present pion and kaon parton distribution functions from a global QCD analysis of the experimental data within the framework of dynamical parton model. We use the DGLAP equations with parton–parton recombination corrections and the valence input of uniform distribution which maximizes the information entropy. At our input scale $$Q_0^2$$ Q 0 2 , there are no sea quark and gluon distributions. All the sea quarks and gluons of the pion and the kaon are completely generated from the parton splitting processes. The mass-dependent parton splitting kernel is applied for the strange quark distribution in the kaon. The obtained valence quark and sea quark distributions at high $$Q^{2}$$ Q 2 ($$Q^2>5$$ Q 2 > 5 GeV$$^2$$ 2 ) are compatible with the existed experimental measurements. Furthermore, the asymptotic behaviours of parton distribution functions at small and large x have been studied for both the pion and the kaon. Lastly, the first three moments of parton distributions at high $$Q^{2}$$ Q 2 scale are calculated, which are consistent with other theoretical predictions.

The Collins asymmetry in electroproduction of Kaon at the electron ion colliders within TMD factorization

We apply the transverse momentum dependent factorization formalism to investigate the transverse single spin dependent Collins asymmetry with a $$\sin (\phi _h+\phi _s)$$sin(ϕh+ϕs) modulation in the semi-inclusive production of Kaon meson in deep inelastic scattering process. The asymmetry is contributed by the convolutions of the transversity distribution function $$h_1(x)$$h1(x) of the target proton and the Collins function of the Kaon in the final state. We adopt the available parametrization of $$h_1(x)$$h1(x) as well as the recent extracted result for the Kaon Collins function. To perform the transverse momentum dependent evolution, the parametrization of the nonperturbative Sudakov form factor of the proton and final state Kaon are utilized. We numerically predict the Collins asymmetry for charged Kaon production at the electron ion colliders within the accuracy of next-to-leading-logarithmic order. It is found that the asymmetry is sizable and could be measured. We emphasize the importance of planned electron ion colliders in the aspect of constraining sea quark distribution functions as well as accessing the information of the nucleon spin structure and the hadronization mechanism.

The role of transverse momentum on the nuclear valence and sea quark distribution functions

We investigate the transverse momentum dependence of valence and sea quark distribution functions of light asymmetric nuclei ($$^{3}He$$3He and $$^{7}Li$$7Li). To this end, we first calculate the valence and sea distributions of these nuclei applying a parametrization method in which the parton distribution functions (PDFs) of nucleus are related to those of free nucleon via a weight function that contains the nuclear modifications. Then we obtain the unpolarized transverse momentum dependent (TMD) PDFs of the nucleus using the covariant parton model (CPM) approach. We also compute the valence and sea quark distributions ratios of $$^{3}He$$3He and $$^{7}Li$$7Li to those of deuteron and present the results with respect to x (Bjorken variable) at fixed values of transverse momentum. It is found that these ratios shift to the larger values of x by increasing the transverse momentum value as expected and they are not transverse momentum dependent in large x region.