We extend the formalism relating electromagnetic form factors to transverse quark charge densities in the light-front frame to the case of a spin-3/2 baryon and calculate these transverse densities for the $Δ(1232)$ isobar using lattice QCD. The transverse charge densities for a transversely polarized spin-3/2 particle are characterized by monopole, dipole, quadrupole, and octupole patterns representing the structure beyond that of a pure point-like spin-3/2 particle. We present lattice QCD results for the $Δ$-isobar electromagnetic form factors for pion masses down to approximatively 350 MeV for three cases: quenched QCD, two-degenerate flavors of dynamical Wilson quarks, and three flavors of quarks using a mixed action that combines domain wall valence quarks and dynamical staggered sea quarks. We extract transverse quark charge densities from these lattice results and find that the $Δ$ is prolately deformed, as indicated by the fact that the quadrupole moment $G_{E2}(0$) is larger than the value -3 characterizing a point particle and the fact that the transverse charge density in a $Δ^+$ of maximal transverse spin projection is elongated along the axis of the spin.
Transverse spin structure of the nucleon from lattice QCD simulations
本文首次在格点量子色动力学中计算了核子中夸克横自旋密度的最低两阶矩。它们编码了夸克自旋和轨道角动量之间的相关性。我们的动力学模拟是基于两种风格的三叶草改进的威尔逊费米子和威尔逊胶子。我们发现某些夸克螺旋度翻转广义部分子分布的显着贡献，导致强烈扭曲的核子中的横向极化夸克的密度。特别地，基于我们的结果和Burkardt [Phys. Rev. D 72（2005）094020]的最新论证，我们预测了描述横夸克自旋和夸克内禀横动量关联的Boer-Mulders函数$h_1^\perp$对于上夸克和下夸克都是大的且为负的。
We discuss in detail a method to study transverse momentum dependent parton distribution functions (TMDs) using lattice QCD. To develop the formalism and to obtain first numerical results, we directly implement a bi-local quark-quark operator connected by a straight Wilson line, allowing us to study T-even, "process-independent" TMDs. Beyond results for x-integrated TMDs and quark densities, we present a study of correlations in x and transverse momentum. Our calculations are based on domain wall valence quark propagators by the LHP collaboration calculated on top of gauge configurations provi…
A better understanding of transverse momentum (k_T-) dependent quark distributions in a hadron is needed to interpret several experimentally observed large angular asymmetries and to clarify the fundamental role of gauge links in non-abelian gauge theories. Based on manifestly non-local gauge invariant quark operators we introduce process-independent k_T-distributions and study their properties in lattice QCD. We find that the longitudinal and transverse momentum dependence approximately factorizes, in contrast to the behavior of generalized parton distributions. The resulting quark k_T-probab…
We present a study of longitudinal momentum densities ($p^+ \rm densities$) in the transverse impact parameter space for $u$ and $d$ quarks in both unpolarized and transversely polarized nucleons by taking a two dimensional Fourier transform of the gravitational form factors with respect to the momentum transfer in the transverse direction. The gravitational form factors are obtained by the second moments of GPDs. Here we consider the GPDs of two different soft-wall models in AdS/QCD correspondence.
In this work, we perform a lattice QCD study of the intrinsic, rapidity-independent soft function within the framework of large momentum effective theory. The computation is carried out using a gauge ensemble of $N_f=2+1+1$ clover-improved twisted mass fermion. After applying an appropriate renormalization procedure and the removal of significant higher-twist contamination, we obtain the intrinsic soft function that is comparable to the one-loop perturbative result at large external momentum. The determination of the nonperturbative soft function from first principles is crucial to sharpen our…
We investigate the transverse charge densities of the deuteron in a soft-wall AdS/QCD model by considering both the unpolarized and the transversely polarized cases. The deuteron form factors are derived from the soft-wall AdS/QCD model and it is shown that the calculated results agree with the phenomenological parametrization and experimental data. The transverse charge densities of the deuteron are also derived from the soft-wall AdS/QCD model, and we notice slight deviations from those of the phenomenological parametrization.
We review the current status of collinear and Transverse Momentum Dependent densities based on the Parton Branching method. We investigate the performance of the PB-TMD evolution as well as PB-TMD parton shower with different configurations of the hard process in the four- and five-flavour schemes.
We propose a consistent treatment of divergences emerging in the computation of transverse-momentum-dependent parton densities in leading $α_s$-order of QCD perturbation theory.
We present a study of flavor structures of transverse charge and anomalous magnetization densities for both unpolarized and transversely polarized nucleons. We consider two different models for the electromagnetic form factors in holographic QCD. The flavor form factors are obtained by decomposing the Dirac and Pauli form factors for nucleons using the charge and isospin symmetry. The results are compared with two standard phenomenological parametrizations.
We investigated the transverse charge densities in the nucleon in nuclear matter within the framework of the in-medium modified Skyrme model. The medium modification of the nucleon electromagnetic form factors are first discussed. The results show that the form factors in nuclear matter fall off faster than those in free space, as the momentum transfer increases. As a result, the charge radii of the nucleon become larger, as the nuclear matter density increases. The transverse charge densities in the nucleon indicate that the size of the nucleon tends to bulge out in nuclear matter. This salie…
We investigate the transverse charge density in the longitudinally as well as transversely polarized deuteron using the recent empirical description of the deuteron electromagnetic form factors in the framework of holographic QCD. The predictions of the holographic QCD are compared with the results of a standard phenomenological parameterization. In addition, we evaluate GPDs and the gravitational form factors for the deuteron. The longitudinal momentum densities are also investigated in the transverse plane.
This talk provides a short overview of the phenomenology of transverse momentum depedent distribution and fragmention functions, focussing on the most recent phenomenological developments in the study of their scale evolution and energy depedence.
The current status of the theoretical understanding of the transverse-momentum dependent parton densities (TMDs) is discussed. Special attention is payed to the difference between the operator definitions of TMDs proposed so far, the treatment of specific divergences, the geometry of the gauge links, and the role of the soft factors.
The transverse symmetry transformations associated with the normal symmetry transformations in gauge theories are introduced, which at first are used to reproduce the transverse Ward-Takahashi identities in the Abelian theory QED. Then the transverse symmetry transformations associated with the BRST symmetry and chiral transformations in the non-Abelian theory QCD are used to derive the transverse Slavnov-Taylor identities for the vector and axial-vector quark-gluon vertices, respectively. Based on the set of normal and transverse Slavnov-Taylor identities, an expression of the quark-gluon ver…
We investigate the medium modification of the generalized vector form factors of the nucleon, which include the electromagnetic and energy-momentum tensor form factors, based on an in-medium modified $π$-$ρ$-$ω$ soliton model. We find that the vector form factors of the nucleon in nuclear matter fall off faster than those in free space, which implies that the charge radii of the nucleon become larger in nuclear medium than in free space. We also compute the corresponding transverse charge densities of the nucleon in nuclear matter, which clearly reveal the increasing of the nucleon size in nuc…
We extend the density-of-states approach to gauge systems (LLR method) to QCD at finite temperature and density with heavy quarks. The approach features an exponential error suppression and yields the Polyakov loop probability distribution function over a range of more than hundred orders of magnitude. SU(2) gauge theory is considered in the confinement and the high-temperature phase, and at finite densities of heavy quarks. In the latter case, a smooth rise of the density with the chemical potential is observed, and no critical phenomenon associated with deconfinement due to finite densities …
We have investigated the transverse charge density for longitudinal and transversely polarized $ρ$ meson in light-front quark model (LFQM). Charge densities are obtained from the elastic form factors of the $ρ$ meson calculated in LFQM including the zero-mode contributions. We have computed the different helicity matrix elements of the $ρ$ meson. In addition to this, we have also presented the results for the generalized parton distributions (GPDs) and impact-parameter dependent parton distribution functions (ipdpdfs) of the $ρ$ meson.
We investigate the transverse quark spin densities of the nucleon with the lowest moment within the framework of the SU(3) chiral quark-soliton model, emphasizing the strange quark spin density. Based on previous results of the vector and tensor form factors, we are able to determine the impact-parameter dependent probability densities of transversely polarized quarks in an unpolarized nucleon as well as those of unpolarized quarks in a transversely polarized nucleon. We find that the present numerical results for the transverse spin densities of the up and down quarks are in good agreement wi…
We discuss different operator definitions of the transverse-momentum dependent (TMD) parton densities from the point of view of their renormalization-group (RG) properties and UV evolution. We also consider the structure of the gauge links (Wilson lines) in these operator definitions and examine the role of the soft factor in the factorization formula within the TMD approach to semi-inclusive processes.
We present a calculation of the Mellin moments of the nucleon transverse quark spin densities extracted from the unpolarized and transversity generalized form factors. We use three $N_F=2+1+1$ ensembles of twisted mass fermions with quark masses tuned to their physical values and lattice spacings $a\sim 0.08$~fm, $a\sim 0.07$~fm and $a\sim 0.06$~fm and extrapolate the form factors to the continuum limit. Besides isovector densities we also include results for the tensor charge for each quark flavor using the ensemble with $a\sim 0.08$~fm for which we include the disconnected contributions.
We reconsider the evolution equations for transverse momentum dependent distributions recently proposed by us and recast them in a form which allows the comparison with results recently appeared in the literature. We show under which conditions the obtained results might be consistent with each other.
We present a study of the flavor form factors in the framework of a hard-wall AdS/QCD model and compare with the available experimental data. We obtain the flavor form factors by decomposing the Dirac and Pauli form factors for the nucleons using the charge and isospin symmetry. Further, we present a detailed study of the flavor structures of the charge and anomalous magnetization densities in the transverse plane. Both the unpolarized and the transversely polarized nucleons are considered here. We compare the AdS/QCD results with two standard phenomenological parametrizations.
We explore the structure of the spin-1/2 flavor-octet baryons (hyperons) through their electromagnetic transverse densities. The transverse densities describe the distribution of charge and magnetization at fixed light-front time and enable a spatial representation of the baryons as relativistic systems. At peripheral distances b~1/M_pi the transverse densities are computed using a new method that combines chiral effective field theory and dispersion analysis. The peripheral isovector densities arise from two-pion exchange, which includes the rho-meson resonance through elastic unitarity. The …
We investigate the nucleon to $Δ$ transition form factors in a soft-wall AdS/QCD model and a light-front quark-diquark model inspired by AdS/QCD. From the transition form factors we evaluate the transition charge densities which influences the nucleon to $Δ$ excitation. Here we consider both the unpolarized and the transversely polarized cases. The AdS/QCD predictions are compared with available experimental data and with the results of the global parameterization, MAID2007.
We present a study of the generalized parton distributions for the quarks in a proton in both momentum and position spaces using the light-front wave functions of a quark-diquark model for the nucleon predicted by the soft-wall model of AdS/QCD. The results are compared with the soft-wall AdS/QCD model of proton GPDs for zero skewness. We also calculate the GPDs for nonzero skewness. We observe that the GPDs have a diffraction pattern in longitudinal position space, as seen before in other models. Then we present a comparitive study of the nucleon charge and anomalous magnetization densities i…
We use the Bessel-inspired behavior of parton densities at small Bjorken $x$ values, obtained in the case of the flat initial conditions for DGLAP evolution equations in the double scaling QCD approximation (DAS), to evaluate the transverse momentum dependent (TMD, or unintegrated) quark and gluon distribution functions in a proton. The calculations are performed analytically using the Kimber-Martin-Ryskin (KMR) prescription with different implementation of kinematical constraint, reflecting the angular and strong ordering conditions. The relations between the differential and integral formula…
Different approaches to define transverse-momentum dependent parton distribution functions are considered from the point of view of their renormalization-group properties. The associated one-loop anomalous dimensions of these quantities are presented and compared to each other. We give arguments in favor of the "pure light-like" definition, and the use of the light-cone gauge.
The baryon electromagnetic form factors are expressed in terms of two-dimensional densities describing the distribution of charge and magnetization in transverse space at fixed light-front time. We calculate the transverse densities of the spin-1/2 flavor-octet baryons at peripheral distances b = O(M_π^{-1}) using methods of relativistic chiral effective field theory (χEFT) and dispersion analysis. The densities are represented as dispersive integrals over the imaginary parts of the form factors in the timelike region (spectral functions). The isovector spectral functions on the two-pion cut t…
The nucleon's electromagnetic form factors are expressed in terms of the transverse densities of charge and magnetization at fixed light-front time. At peripheral transverse distances $b = O(M_π^{-1})$ the densities are governed by chiral dynamics and can be calculated model-independently using chiral effective field theory (EFT). We represent the leading-order chiral EFT results for the peripheral transverse densities as overlap integrals of chiral light-front wave functions, describing the transition of the initial nucleon to soft pion-nucleon intermediate states and back. The new representa…
Double Transverse-Spin Asymmetries for Drell-Yan Process in pp and p\bar{p} Collisions: Role of Nonleading QCD Corrections at Small Transverse Momentum
