Collinear Parton Distribution Research Articles

Forward hadron productions in proton-proton collisions in small-xformalism

Employing the so-called hybrid formalism, we calculate the cross section of inclusive hadron production in proton-proton collisions at forward rapidity in small-$x$ formalism at one-loop order. For the case of hadron production at forward rapidity, we can uses collinear parton distributions for projectile proton and $k_\perp$ dependent gluon distribution for target proton. We show that collinear divergences associated with initial and final state parton radiations are renormalized into parton distributions and fragmentation functions in terms of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equation, respectively. Furthermore, rapidity divergence can be absorbed into the wave function of target proton which gives rise to the well-known Balitsky-Fadin-Kuraev-Lipatov equation. These divergences are completely separated from the short distance partonic hard parts, which is now finite at the next-to-leading order accuracy. The result presented in this paper can be reckoned as a baseline calculation without any non-linear QCD effects in small-$x$ formalism. As a consistency check, we compare our results with the previous calculation for non-linear proton-nucleus collisions in the small-$x$ formalism and find complete agreement in the dilute and large $N_c$ limit. In phenomenology, the direct comparison of the above two separate calculations can reveal the role and strength of the non-linear dynamics in high energy QCD, and thus help us reliably study the onset of gluon saturation when genuine non-linear interactions become important.

Higher-twist contributions to the transverse momentum broadening in semi-inclusive deep inelastic scattering off large nuclei

Multiple scattering leads to transverse momentum broadening of the struck quark in semi-inclusive deeply inelastic scatterings (SIDIS). Nuclear broadening of the transverse momentum squared at the leading twist is determined by the twist-four collinear quark-gluon correlation function of the target nucleus that is in turn related to the jet transport parameter inside the nuclear medium. The twist-six contributions to the transverse momentum broadening are calculated as power corrections $\sim 1/Q^2$. Such power corrections are found to have no extra nuclear enhancement beyond the twist-four matrix elements and are determined by the nuclear modification of collinear parton distribution and correlation functions. They become important for an accurate extraction of the jet transport parameter inside large nuclei and its scale evolution at intermediate values of the hard scale $Q^2$.

Color Entanglement in Hadronic Processes for Transverse Momentum Dependent Parton Distribution Functions

In the description of protons, we go beyond the ordinary collinear parton distribution functions (PDFs), by including transverse momentum dependent PDFs (TMDs). As such, we become sensitive to polarization modes of the partons and protons that one cannot probe without accounting for transverse momenta of partons, in particular when looking at azimuthal asymmetries. Hadronic processes require the inclusion of gluon contributions forming the gauge links, which are path-ordered exponentials tracing the color flow. In processes with two hadrons in the initial state, such as Drell-Yan (DY), the gauge links from different parts of the process get entangled. We show that in color disentangling this gauge link structure, one becomes sensitive to this color flow. After disentanglement, particular combinations of TMDs will require a different numerical color factor than one naively might have expected. Such color factors will even play a role for azimuthal asymmetries in the simplest hadronic processes such as DY.

TMDlib and TMDplotter: library and plotting tools for transverse-momentum-dependent parton distributions.

Transverse-momentum-dependent distributions (TMDs) are extensions of collinear parton distributions and are important in high-energy physics from both theoretical and phenomenological points of view. In this manual we introduce the library {TMDlib }, a tool to collect transverse-momentum-dependent parton distribution functions (TMD PDFs) and fragmentation functions (TMD FFs) together with an online plotting tool, TMDplotter. We provide a description of the program components and of the different physical frameworks the user can access via the available parameterisations.

Non-perturbative QCD effects in q T spectra of Drell-Yan and Z-boson production

The factorization theorems for transverse momentum distributions of dilepton/boson production, recently formulated by Collins and Echevarria-Idilbi-Scimemi in terms of well-defined transverse momentum dependent distributions (TMDs), allows for a systematic and quantitative analysis of non-perturbative QCD effects of the cross sections involving these quantities. In this paper we perform a global fit using all current available data for Drell-Yan and Z-boson production at hadron colliders within this framework. The perturbative calculable pieces of our estimates are included using a complete resummation at next-to-next-to-leading-logarithmic accuracy. Performing the matching of transverse momentum distributions onto the standard collinear parton distribution functions and recalling that the corresponding matching coefficient can be partially exponentiated, we find that this exponentiated part is spin-independent and resummable. We argue that the inclusion of higher order perturbative pieces is necessary when data from lower energy scales are analyzed. We consider non-perturbative corrections both to the intrinsic nucleon structure and to the evolution kernel and find that the non-perturbative part of the TMDs could be parametrized in terms of a minimal set of parameters (namely 2-3). When all corrections are included the global fit so performed gives a χ 2 /d.o.f. ≲ 1 and a very precise prediction for vector boson production at the Large Hadron Collider (LHC).

Di-hadron SIDIS measurements at CLAS

Semi-inclusive deep-inelastic scattering (SIDIS) is an essential tool to probe nucleon internal structure. Through single hadron SIDIS processes, indeed, it is possible to access the TMDs, containing information on both the longitudinal and transverse motion of the partons. In recent years, moreover, an increasing attention has been devoted to dihadron SIDIS. It constitutes the golden channel to access the higher-twist collinear Parton Distribution Functions e(x )a ndhL(x), so far only marginally known, whose extraction will complete the collinear description of the nucleon at the twist-3 level. The CLAS detector in the Hall-B at JLab, thanks to its large acceptance, is particularly suited for such measurements. Analyses aiming at the extraction of dihadron SIDIS Beam and Target- Spin Asymmetries are presently in progress. In these proceedings, preliminary results for the Beam-Spin Asymmetry are reported, together with a summary of the dihadron SIDIS experimental program at JLab.

Analyticity and sum rules for photon GPDs

The photon is explored as an object to test the applications of QCD to the perturbatively calculable collinear parton distributions. We investigate analytic properties of DVCS amplitudes and related sum rules of generalized parton distributions of the photon using as an input their earlier calculations in the leading order. The relation of these GPDs to the quintessential functions in the framework of the dual parametrization approach is also found.

Inclusive jet production at the tevatron collider in the Regge limit of quantum chromodynamics

We consider the inclusive hadroproduction of jets, prompt photons, and b-quark jets in the quasimulti-Regge kinematics approach based on the hypothesis of gluon and quark reggeization in t-channel exchanges at high energies. The data taken by CDF and D0 collaborations at the Fermilab Tevatron collider are well described in the region of \(x_T = 2p_T /\sqrt s \lesssim 0.1\) without the introduction of any free parameters. In numeric calculations we use the Kimber-Martin-Ryskin prescription for unintegrated gluon and quark distribution functions with Martin-Roberts-Stirling-Thorne collinear parton distribution functions taken as input.

LOOP SPACE AND EVOLUTION OF THE LIGHT-LIKE WILSON POLYGONS

We address a connection between the energy evolution of the polygonal light-like Wilson exponentials and the geometry of the loop space with the gauge invariant Wilson loops of a variety of shapes being the fundamental degrees of freedom. The renormalization properties and the differential area evolution of these Wilson polygons are studied by making use of the universal Schwinger quantum dynamical approach. We discuss the appropriateness of the dynamical differential equations in the loop space to the study of the energy evolution of the collinear and transverse-momentum dependent parton distribution functions.

Inclusivebandbb¯production with quasi-multi-Regge kinematics at the Tevatron

We consider $b$-jet hadroproduction in the quasi-multi-Regge-kinematics approach based on the hypothesis of gluon and quark Reggeization in $t$-channel exchanges at high energies. The preliminary data on inclusive $b$-jet and $b\overline{b}$-dijet production taken by the CDF Collaboration at the Fermilab Tevatron are well described without adjusting parameters. We find the main contribution to inclusive $b$-jet production to be the scattering of a Reggeized gluon and a Reggeized $b$ quark to a $b$ quark, which is described by the effective Reggeon-Reggeon-quark vertex. The main contribution to $b\overline{b}$-pair production arises from the scattering of two Reggeized gluons to a $b\overline{b}$ pair, which is described by the effective Reggeon-Reggeon-quark-quark vertex. Our analysis is based on the Kimber-Martin-Ryskin prescription for unintegrated gluon and quark distribution functions using as input the Martin-Roberts-Stirling-Thorne collinear parton distribution functions of the proton.