Explore the vast range of titles available.

In this paper, I investigate the gluon distributions for the kaon and pion, as well as the improvement of the valence-quark distributions, in the framework of the gauge-invariant nonlocal chiral quark model (NLχQM), where the momentum dependence is taken into account. I then compute the gluon distributions for the kaon and pion that are dynamically generated from the splitting functions in the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) QCD evolution. In a comparison with the recent lattice QCD and JAM global analysis results, it is found that the results for the pion gluon distributions at Q= 2 GeV, which is set based on the lattice QCD, have a good agreement with the recent lattice QCD data; this is followed up with the up valence-quark distribution of the pion results at Q= 5.2 GeV in comparison with the reanalysis experimental data. The prediction for the kaon gluon distributions at Q=2 GeV is consistent with the recent lattice QCD calculation.

The hadronization of a high-energy parton is described by fragmentation functions which are introduced through QCD factorizations. While the hadronization mechanism per se remains uknown, fragmentation functions can still be investigated qualitatively and quantitatively. The qualitative study mainly concentrates on extracting genuine features based on the operator definition in quantum field theory. The quantitative research focuses on describing a variety of experimental data employing the fragmentation function given by the parameterizations or model calculations. With the foundation of the transverse-momentum-dependent factorization, the QCD evolution of leading twist transverse-momentum-dependent fragmentation functions has also been established. In addition, the universality of fragmentation functions has been proven, albeit model-dependently, so that it is possible to perform a global analysis of experimental data in different high-energy reactions. The collective efforts may eventually reveal important information hidden in the shadow of nonperturbative physics. This review covers the following topics: transverse-momentum-dependent factorization and the corresponding QCD evolution, spin-dependent fragmentation functions at leading and higher twists, several experimental measurements and corresponding phenomenological studies, and some model calculations.

A new type of parametrization for parton distribution functions in the proton, based on their Q2-evolution at large and small x values, is constructed. In our analysis, the valence and nonsinglet parts obey the Gross–Llewellyn–Smith and Gottfried sum rules, respectively. For the singlet quark and gluon densities, momentum conservation is taken into account. Then, using the Kimber–Martin–Ryskin prescription, we extend the consideration to Transverse Momentum Dependent (TMD, or unintegrated) gluon and quark distributions in the proton, which currently plays an important role in a the number of phenomenological applications. The analytical expressions for the latter, valid for both low and large x, are derived for the first time.

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.

Understanding the behavior of large atomic nuclei (heavy ions) in high-energy collisions has been the focus of a concerted research effort over the past 10-15 years. Much of the latest progress in the field has centered around transverse momentum-dependent (or \"unintegrated\") parton distributions: in particular the prediction of the high-energy behavior of these distributions, in the form of the Balitsky-JIMWLK equations, and the development of the hybrid factorization framework, which connects the unintegrated parton distributions to predictions for experimentally measured cross sections. With the advent of high-energy proton-nucleus collisions at RHIC and the LHC, we are able to experimentally test these predictions for the first time. In this dissertation, I show two case studies of these predictions, to illustrate the use of the hybrid factorization at leading and next-to-leading order. First, as a simple example, I analyze the azimuthal angular correlation for a Drell-Yan process, the production of a lepton pair with an associated hadron. The correlation for back-to-back emission turns out to be determined by the low-momentum region of the unintegrated gluon distribution, and the correlation for parallel emission is determined by the high-momentum region. Accordingly, a proper prediction of the correlation at all angles requires a gluon distribution with physically realistic behavior at both high and low momenta. Furthermore, the properties of the central double peak that emerges in Drell-Yan production can provide some insight into the form of the gluon distribution. I'll then describe a numerical calculation of the cross section for inclusive hadron production, which incorporates all corrections up to next-to-leading order in the strong coupling. This calculation illustrates several obstacles presented by subleading terms, including the removal of divergences by renormalizing the integrated and unintegrated parton distributions. The results of the calculation are negative at high transverse momentum, which is surprising but may be mathematically reasonable, since the perturbative approximation to the cross section may break down under those kinematic conditions. However, it may be possible to make meaningful predictions for the nuclear modification ratio R pA despite the negative cross section. Moving beyond next-to-leading order, it may be possible to cure the negativity of the inclusive hadron cross section by altering the formulas used. I'll show two possible methods of doing so: first, a straightforward resummation of selected higher-order terms corresponding to gluon loop diagrams is able to mitigate the negativity, though it requires some alterations of unclear theoretical origin. A more promising alternative seems to be use of exact kinematic definitions, incorporating terms which disappear in the infinite-energy limit; this constrains the kinematics to eliminate the region of phase space which most strongly contributes to the negativity. In this way, the calculation can be adapted to produce reasonable results at high transverse momentum.

Low-x physics is reviewed, with particular emphasis on searches for deviations from Gribov-Lipatov-Altarelli-Parisi (GLAP) evolution of the parton densities. Although there are several intriguing indications, both in HERA and in Tevatron data, as yet there is no unambiguous evidence for other than standard next-to-leading-order GLAP evolution. The framework of dipole models and saturation of parton densities is examined and confronted with the data. Although such models give a good qualitative description of the data, so do other, more conventional, explanations.

A bstract We calculate the one-loop corrections to single inclusive hadron production in Deep Inelastic Scattering (DIS) at small x in the forward rapidity region using the Color Glass Condensate formalism. We show that the divergent parts of the next to leading order (NLO) corrections either cancel among each other or lead to x (rapidity) evolution of the leading order (LO) dipole cross section according to the JIMWLK evolution equation and DGLAP evolution of the parton-hadron fragmentation function. The remaining finite parts constitute the NLO ( α s ) corrections to the LO single inclusive hadron production cross section in DIS at small x .

A bstract The standard formulation of the high-energy evolution in perturbative QCD, based on the Balitsky-Kovchegov equation, is known to suffer from severe instabilities associated with radiative corrections enhanced by double transverse logarithms, which occur in all orders starting with the next-to-leading one. Over the last years, several methods have been devised to resum such corrections by enforcing the time-ordering of the successive gluon emissions. We observe that the instability problem is not fully cured by these methods: various prescriptions for performing the resummation lead to very different physical results and thus lack of predictive power. We argue that this problem can be avoided by using the rapidity of the dense target (which corresponds to Bjorken x ) instead of that of the dilute projectile as an evolution time. This automatically ensures the proper time-ordering and also allows for a direct physical interpretation of the results. We explicitly perform this change of variables at NLO. We observe the emergence of a new class of double logarithmic corrections, potentially leading to instabilities, which are however less severe, since disfavoured by the typical BK evolution for “dilute-dense” scattering. We propose several prescriptions for resumming these new double-logarithms to all orders and find only little scheme dependence: different prescriptions lead to results which are consistent to each other to the accuracy of interest. We restore full NLO accuracy by completing one of the resummed equations (non-local in rapidity) with the remaining NLO corrections.

A bstract We study parton-branching solutions of QCD evolution equations and present a method to construct both collinear and transverse momentum dependent (TMD) parton densities from this approach. We work with next-to-leading-order (NLO) accuracy in the strong coupling. Using the unitarity picture in terms of resolvable and non-resolvable branchings, we analyze the role of the soft-gluon resolution scale in the evolution equations. For longitudinal momentum distributions, we find agreement of our numerical calculations with existing evolution programs at the level of better than 1% over a range of five orders of magnitude both in evolution scale and in longitudinal momentum fraction. We make predictions for the evolution of transverse momentum distributions. We perform fits to the high-precision deep inelastic scattering (DIS) structure function measurements, and we present a set of NLO TMD distributions based on the parton branching approach.

A bstract We perform global fit to the quark Sivers function within the transverse momentum dependent (TMD) factorization formalism in QCD. We simultaneously fit Sivers asymmetry data from Semi-Inclusive Deep Inelastic Scattering (SIDIS) at COMPASS, HERMES, and JLab, from Drell-Yan lepton pair production at COMPASS, and from W/Z boson at RHIC. This extraction is performed at next-to-leading order (NLO) and next-to-next-to leading logarithmic (NNLL) accuracy. We find excellent agreement between our extracted asymmetry and the experimental data for SIDIS and Drell-Yan lepton pair production, while tension arises when trying to describe the spin asymmetries of W/Z bosons at RHIC. We carefully assess the situation, and we study in details the impact of the RHIC data and their implications through different ways of performing the fit. In addition, we find that the quality of the description of W/Z vector boson asymmetry data could be strongly sensitive to the DGLAP evolution of Qiu-Sterman function, besides the usual TMD evolution. We present discussion on this and the implications for measurements of the transverse-spin asymmetries at the future Electron Ion Collider.