The combined measurements of proton's structure functions in deeply inelastic scattering at the HERA collider provide high-precision data capable of constraining parton density functions over a wide range of the kinematic variables. We perform fits to these data using transverse momentum dependent QCD factorization and CCFM evolution. The results of the fits to precision measurements are used to make a determination of the nonperturbative transverse momentum dependent gluon density function, including experimental and theoretical uncertainties. We present an application of this density function to vector boson + jet production processes at the LHC.
It is known the single transverse spin asymmetry in semi-inclusive deep inelastic scattering can be factorized by a twist-3 distribution function $T_F$, which contains a gluon field strength tensor. With transverse gluon included in the power expansion, we find the gluon field strength tensor can be recovered definitely in soft-gluon-pole contribution at leading order of $α_s$ expansion. This conclusion holds in Feynman and light-cone gauges.
We combine soft and collinear matrix elements to define transverse momentum dependent parton distributions (TMDs) for gluons, free from rapidity divergences. We establish a factorization theorem at next-to-leading order for the Higgs boson transverse momentum ($q_T$) spectrum, and use it to derive evolution equations for gluon TMDs. The evolution for all gluon TMDs is driven by a universal kernel, i.e. the same for all polarizations. In the region of intermediate $q_T$ we match the unpolarized, helicity and linearly polarized gluon distributions onto PDFs. We calculate the resummed Higgs trans…
The back-to-back $J/ψ$ and $π$ associated production at $e^+ e^-$ colliders is proposed to detect the gluon transverse momentum dependent(TMD) fragmentation functions. TMD factorization is assumed for this process. With spinless pion, unpolarized and linearly polarized gluon TMD fragmentation functions can be defined. It is found at parton level the hadronic tensor can be described by four structure functions. As a result, there are three independent angular distributions, of which a $\cos{2ϕ}$ azimuthal asymmetry is sensitive to the linearly polarized gluon fragmentation function.
We present preliminary results on the leading-twist transverse-momentum-dependent (TMD) gluon linearity function, which is directly connected to nucleon transverse-spin asymmetries originating from the density of linearly-polarized gluons. The function is calculated in a spectator-model framework for the parent proton and for the $f$-type gauge-link structure. Our work represents a further step toward the definition of a complete set of gluon TMD distributions at twist-2 that can be used to access the gluon dynamics inside nucleons and nuclei at new-generation colliders.
We investigate the gluon transverse momentum dependent correlators as Fourier transform of matrix elements of nonlocal operator combinations. At the operator level these correlators include both field strength operators and gauge links bridging the nonlocality. In contrast to the collinear PDFs, the gauge links are no longer unique for transverse momentum dependent PDFs (TMDs) and also Wilson loops lead to nontrivial effects. We look at gluon TMDs for unpolarized, vector and tensor polarized targets. In particular a single Wilson loop operators become important when one considers the small-x l…
Using the recently obtained Pgq splitting function we extend the low x evolution equation for gluons to account for contributions originating from quark-to-gluon splitting. In order to write down a consistent equation we resum virtual corrections coming from the gluon channel and demonstrate that this implies a suitable regularization of the Pgq singularity, corresponding to a soft emitted quark. We also note that the obtained equation is in a straightforward manner generalized to a nonlinear evolution equation which takes into account effects due to the presence of high gluon densities.
We calculate in this paper the perturbative gluon transverse momentum dependent parton distribution functions (TMDPDFs) and fragmentation functions (TMDFFs) using the exponential regulator for rapidity divergences. We obtain results for both unpolarized and linearly polarized distributions through next-to-next-to leading order in strong coupling constant, and through ${\cal O}(ε^2)$ in dimensional regulator (finding discrepancy for the linearly polarized gluon TMDPDFs with a previous result in the literature). We find a nontrivial momentum conservation sum rule for the linearly polarized compo…
We introduce the spin-operator representation for the gluon as well as quark distribution functions as nucleon matrix element of the gauge-invariant bilocal light-cone operators in QCD. To identify the relevant spin operators for quarks and gluons in a unified manner, we rely on the transformation properties of the quark and gluon fields in the coordinate space under the action of the generator of the Lorentz group. In particular, this approach allows us to define the transverse-spin gluon distribution function $G_T(x)$, which is the genuine counterpart of the transverse-spin quark distributio…
We present a model calculation of transverse-momentum-dependent distributions (TMDs) of gluons in the nucleon. The model is based on the assumption that a nucleon can emit a gluon, and what remains after the emission is treated as a single spectator particle. This spectator particle is considered to be on-shell, but its mass is allowed to take a continuous range of values, described by a spectral function. The nucleon-gluon-spectator coupling is described by an effective vertex containing two form factors. We fix the model parameters to obtain the best agreement with collinear gluon distributi…
We present exploratory studies of the proton content via unpolarized and polarized transverse-momentum-dependent gluon distributions in the proton at leading twist. We make use of an enhanced spectator-model approach to encode in our densities both small- and moderate-$x$ effects. These studies are relevant to the investigation of the inner structure of hadrons via tomographic analyses at new-generation colliding machines.
We report progresses on leading-twist transverse-momentum-dependent (TMD) gluon distributions, calculated in a spectator-model framework for the parent nucleon. We encode in our formalism a fit-based parameterization for the spectator-mass density, suited to describe the gluon content of the proton in a wide range of $x$. We present preliminary results on the $f$-type Sivers function, a key ingredient to access relevant spin-asymmetries emerging when the nucleon is transversely polarized. These studies are helpful to shed light on the gluon dynamics inside nucleons and nuclei, which is one of …
Transverse-momentum-dependent (TMD) gluon distributions have different operator definitions, depending on the process under consideration. We study that aspect of TMD factorization in the small-x limit, for the various unpolarized TMD gluon distributions encountered in the literature. To do this, we consider di-jet production in hadronic collisions, since this process allows to be exhaustive with respect to the possible operator definitions, and is suitable to be investigated at small x. Indeed, for forward and nearly back-to-back jets, one can apply both the TMD factorization and Color Glass …
Linearly polarized gluons inside an unpolarized proton contribute to the transverse momentum distributions of (pseudo)scalar particles produced in hadronic collisions, such as Higgs bosons and quarkonia with even charge conjugation ($η_c$, $η_b$, $χ_{c0}$, $χ_{b0}$). Moreover, they can produce azimuthal asymmetries in the associated production of a photon and a $J/ψ$ or a $Υ$ particle, in a kinematic configuration in which they are almost back to back. These observables, which can be measured in the running experiments at the LHC, could lead to a first extraction of both the polarized and the …
We perform explorative analyses of the 3D gluon content of the proton via a study of (un)polarized twist-2 gluon TMDs, calculated in a spectator model for the parent nucleon. Our approach encodes a flexible parametrization for the spectator-mass density, suited to describe both moderate and small-$x$ effects. All these prospective developments are relevant in the investigation of the gluon dynamics inside nucleons and nuclei, which constitutes one of the major goals of new-generation colliding machines, as the EIC, the HL-LHC and NICA.
The Gluon Sivers Distribution in D production at RHIC
RHIC D介子产生中的单横自旋不对称性可以提供胶子Sivers分布函数的一个干净的度量。在中等快度下，D的产生主要由基本的gg -> c c-bar通道控制，在那里不可能有任何横向自旋转移。因此，在极化质子-质子相互作用中所观察到的D's的任何横向单自旋不对称性只能源于胶子分布函数中的Sivers效应。由PHENIX或STAR实验测量的相当大的横向单自旋不对称性将给出关于胶子西弗斯分布函数大小的直接信息。
We study the role of the non-perturbative input to the transverse momentum dependent (TMD) gluon density in hard processes at the LHC. We derive the input TMD gluon distribution at low scale mu0^2 ~ 1 GeV^2 from the fit of the inclusive hadron spectra measured at low transverse momenta in pp collisions at the LHC and demonstrate that the best description of these spectra for larger hadron transverse momenta can be achieved by matching the derived TMD gluon distribution with the exact solution of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation obtained at low x and small gluon transverse mome…
Probing quark transverse momentum distributions in the Color Glass Condensate: quark-gluon dijets in Deep Inelastic Scattering at next-to-eikonal accuracy
