Nikolaos Kidonakis
I present approximate next-to-next-to-leading-order (NNLO) top-quark transverse momentum, pT, distributions in t-channel single-top production. These distributions are derived from next-to-next-to-leading-logarithm (NNLL) soft-gluon resummation. Theoretical results for the single top as well as the single antitop pT distributions are shown for LHC and Tevatron energies.
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The interaction dependent part of the $x^2$-moment of the twist-3 polarized parton distribution $g_2(x)$ is related to the transverse force acting on the active quark in deep-inelastic scattering off a transversely polarized nucleon immediately after it has absorbed the virtual photon. Similarly, the $x^2$-moment of the chirally odd twist-3 unpolarized parton distribution $e(x)$ can be related to the transverse force experienced by a transversely polarized quark ejected from a transversely polarized nucleon.
The azimuthal dependence of hadrons produced in lepton scattering off a polarized hadron probes the quark transverse-spin distributions. In the calculation of the asymmetries, transverse momenta of quarks in the distribution and fragmentation functions must be incorporated. In addition to the $\sin (ϕ+ ϕ_S)$ asymmetry for transversely polarized hadrons, known as the Collins effect, we find $\sin 2ϕ$ asymmetries for both transversely and longitudinally polarized hadrons.
Generalized Parton Distributions (GPDs) provide information on the distribution of quarks in impact paarmeter space. For transversely polarized nucleons, these impact parameter distributions are transversely distorted and this deviation from axial symmetry leads on average to a net transverse force from the spectators on the active quark in a DIS experiment. %The strength of that force can be related to twist-3 PDFs. This force when acting along the whole trajectory of the active quark leads to a transverse single-spin asymmetries. For a longitudinally polarized nucleon target, the transverse …
We derive a nonperturbative transverse momentum distribution for partons using a potential model to describe the quark-quark interaction inside the proton. We use this distribution to calculate the diferential cross-section of $π^0$-production for intermediate values of transverse momentum in $p-p$ collisions at high energies. Assuming a variable string tension constant for the quark-quark potential we obtain a very good description of the experimental data at different energies. The corresponding values of the mean transverse momentum of the partons are essentially lower than those obtained u…
We calculate the q q correlation function associated to transverse target lepton-nucleon inclusive deep-inelastic scattering by direct evaluation of the corresponding matrix element. We use the electromagnetic impact parameter potential for a transversely polarized nucleon to define the q q correlation function for each avor in terms of the field components of that avor. The results are compared with the two existing models for the q q correlator. Using the calculated q q correlation function, we estimated the transverse target SSA in IDIS process.
Accounting for transverse momenta of the quarks, a longitudinal quark spin asymmetry exists in a transversely polarized nucleon target. The relevant leading quark distribution $g_{1T}(x,k_T^2)$ can be measured in the semi-inclusive deep-inelastic scattering. The average $k_T^2$ weighted distribution function $g^{(1)}_{1T}$ can be obtained directly from the inclusive measurement of $g_2$.
Quarkonium production in hadron collisions at low transverse momentum $q_\perp \ll M$ with $M$ as the quarkonium mass can be used for probing transverse momentum dependent (TMD) gluon distributions. For this purpose, one needs to establish the TMD factorization for the process. We examine the factorization at the one-loop level for the production of $η_c$ or $η_b$. The perturbative coefficient in the factorization is determined at one-loop accuracy. Comparing the factorization derived at tree level and that beyond the tree level, a soft factor is, in general, needed to completely cancel soft d…
In the symmetric string fragmentation recipe adopted by PYTHIA for jet simulations, the transverse momenta of successive quarks are uncorrelated. This is a simplification but has no theoretical reason. Transverse momentum correlations are naturally expected, for instance, in a covariant multiperipheral model of quark hadronization. We propose a simple recipe of string fragmentation which lead to such correlations. The definition of the jet axis and its relation with the primordial transverse momentum of the quark is also discussed.
The 2+1 dimensional (2 space dimensions and 1 time dimension) Transverse Lattice is constructed using the Color Dielectric formalism. The dynamics of the Color Dielectric link fields are not known from first principles, so an ansatz for the effective action is made, which is truncated at fourth order in the fields. Since the Transverse Lattice is a Light-Front field theory, it lacks manifest rotational invariance. This lack of manifest rotational invariance is exploited to determine the couplings in the effective action by calculating the Quark/Anti-quark Potential, an observable that is very …
We study the semi-classical interpretation of the $x^3$ and $x^4$ moments of twist-3 parton distribution functions (PDFs). While no semi-classical interpretation for the higher moments of $g_T(x)$ and $e(x)$ was find, the $x^3$ moment of the chirally odd spin-dependent twist-3 PDF $h_L^3(x)$ can be related to the longitudinal gradient of the transverse force on transversely polarized quarks in longitudinally polarized nucleons in a DIS experiment. We discuss how this result relates to the torque acting on a quark in the same experiment. This has further implications for comparisons between tha…
We study the spin-dependent quark distributions at large transverse momentum. We derive their transverse momentum behaviors in the collinear factorization approach in this region. We further calculate the angular distribution of the Drell-Yan lepton pair production with polarized beams and present the results in terms of the collinear twist-three quark-gluon correlation functions. In the intermediate transverse momentum region, we find that the two pproaches: the collinear factorization and the transverse momentum dependent factorization approaches are consistent in the description of the lept…
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…
Quarkonium production at low transverse momentum in hadron collisions can be used to extract Transverse-Momentum-Dependent(TMD) gluon distribution functions, if TMD factorization holds there. We show that TMD factorization for the case of P-wave quarkonium with $J^{PC}=0^{++}, 2^{++}$ holds at one-loop level, but is violated beyond one-loop level. TMD factorization for other P-wave quarkonium is also violated already at one-loop.
We calculate the electroweak and finite width corrections to the decay of an unpolarized top quark into a bottom quark and a $ W $-gauge boson where the helicities of the $ W $ are specified as longitudinal, transverse-plus and transverse-minus. Together with the $ O(α_s) $ corrections these corrections may become relevant for the determination of the mass of the top quark through angular decay measurements.
We present a calculation of the perturbative quark-to-quark transverse parton distribution function at next-to-next-to-leading order based on a gauge invariant operator definition. We demonstrate for the first time that such a definition works beyond the first non-trivial order. We extract from our calculation the coefficient functions relevant for a next-to-next-to-next-to-leading logarithmic $Q_T$ resummation in a large class of processes at hadron colliders.
I present NNLO approximate calculations, based on NNLL resummation, for top quark differential transverse momentum and rapidity distributions. In particular recent results are presented for top-pair production and single-top production processes and compared to the latest experimental data from the LHC.
We study the transverse momentum distribution for a $pair$ of heavy quarks produced in hadron-hadron interactions. Predictions for the large transverse momentum region are based on exact order $α_s^3$ QCD perturbation theory. For the small transverse momentum region, we use techniques for all orders resummation of leading logarithmic contributions associated with initial state soft gluon radiation. The combination provides the transverse momentum distribution of heavy quark pairs for all transverse momenta. Explicit results are presented for $b\bar b$ pair production at the Fermilab Tevatron c…
Transverse polarization of $Λ^0$ hyperons in inclusive photoproduction at x_F>0 is tackled within the framework of the quark recombination model, which has been successfully applied to the polarization of different hyperons in a variety of unpolarized hadron-hadron reactions. The results are compared with recent experimental data of HERMES.
We present a detailed analysis of the Bc form factors in the BSW framework, by investigating the effects of the flavor dependence on the average transverse quark momentum inside a meson. Branching ratios of two body decays of Bc meson to pseudoscalar and vector mesons are predicted.
We present the results of an O(alpha_s) calculation of the transverse polarization of top quarks produced in e+e- annihilation. In a first step we determine the transverse polarization of the top with regard to the hadron plane spanned by the (q,bar q,g) system. We then rotate the transverse components of the polarization to the lepton plane spanned by the (q,e+,e-) system. After azimuthal averaging we determine the three remaining inclusive transversely polarized structure functions. Together with the one-loop and Born term contributions they determine the sin(theta) and sin(2*theta) beam-qua…
We calculate transverse momentum dependent quark splitting kernels $P_{gq}$ and $P_{qq}$ within $k_T$-factorization, completing earlier results which concentrated on gluon splitting functions $P_{gg}$ and $P_{qg}$. The complete set of splitting kernels is an essential requirement for the formulation of a complete set of evolution equations for transverse momentum dependent parton distribution functions and the development of corresponding parton shower algorithms.
We consider the leading order result for polarized leptoproduction, putting emphasis on transverse momentum dependent effects appearing in azimuthal asymmetries. Measurements of weighted cross sections enable extraction of the distribution of transversely polarized quarks. We focus on the distribution in a longitudinally polarized hadron and estimate the expected asymmetries in leptoproduction.
We consider the O(alpha_s) radiative corrections to the decay of an unpolarized top quark into a bottom quark and a W-gauge boson where the helicities of the W are specified as longitudinal, transverse-plus and transverse-minus. The O(alpha_s) radiative corrections lower the normalized longitudinal rate Gamma_L/Gamma by 1.06% and increase the the normalized transverse-minus rate Gamma_-/Gamma by 2.17%. We find that the normalized transverse-plus rate Gamma_+/Gamma, which vanishes at the Born term level for m_b->0, receives radiative correction contributions at the sub-percent level. We discuss…
We analyze the Sivers asymmetry in light-cone gauge. The average transverse momentum of the quark distribution is related to the correlation between the quark distribution and the transverse component of the gauge field at $x^-\pm \infty$. We then use finiteness conditions for the light-cone Hamiltonian to relate the transverse gauge field at $x^-=\pm \infty$ to the color density integrated over $x^-$. This result allows us to relate the average transverse momentum of the active quark to color charge correlations in the transverse plane.
It is shown that the azimuthal dependence of the distribution of hadrons in a quark jet is a probe of the transverse spin of the quark initiating the jet. This results in a new spin-dependent fragmentation function that acts at the twist-2 level. One example of a process where it contributes is semi-inclusive deeply inelastic scattering with a transversely polarized nucleon target but with an {\em unpolarized} electron beam. This process is treated in detail. Another process is the cross section for singly polarized hadron-hadron scattering when two high $p_{\perp}$ hadrons are measured in the…
We present all the leading twist T-even TMDs in the light-front quark diquark model(LFQDM) and study the relations among them. The model contains both the scalar and vector diquarks with the light front wave functions modeled from the soft-wall AdS/QCD prediction. The $x-p^2_\perp$ factorization used in phenomenological extraction for TMDs is observed in this model. We present the results for the quark densities and the transverse shape of proton. The shape of the transversely polarized proton is shown to be non-spherical for nonzero transverse momentum. The scale evolution of both integrated …
Probing quark transverse momentum distributions in the Color Glass Condensate: quark-gluon dijets in Deep Inelastic Scattering at next-to-eikonal accuracy
本研究采用色玻璃凝聚方法，在次程函近似下研究高能深度非弹性散射中的夸克-胶子双喷注产生，推导截面因子化表达式，提出背景抑制方案，为电子离子对撞机探测夸克横动量依赖分布提供新方法。
Heavy quark transverse momentum dependent fragmentation
本研究计算重夸克单圈TMDFF，分析$q_\perp \ll m$与$q_\perp \gg m$两种质量极限，并应用于重夸克喷注碎裂及$e^+e^-$碰撞中重强子的横动量分布。
We discuss and compare different approaches to include gluon transverse momenta for heavy quark-antiquark pair production. The correlations in azimuthal angle and in heavy quark, heavy antiquark transverse momenta are studied in detail. The results are illustrated with the help of different unintegrated gluon distribution functons (UGDF) from the literature. We compare results obtained with on-shell and off-shell matrix elements and kinematics and quantify where these effects are negligible and where they are essential. We concentrate on the region of asymmetric transverse momenta of charm qua…
We discuss the general formalism for the calculation in light-cone quark models of the fully unintegrated, off-diagonal quark-quark correlator of the nucleon. The corresponding distributions in impact parameter space are the Wigner or phase-space distributions. The results obtained in two different light-cone quark models in the case of unpolarized quarks in an unpolarized proton are very similar and present a non-trivial shape which can be understood as due to the orbital motion of the quarks.
The gluon collision process that creates a heavy-quark-antiquark pair with small relative momentum and large transverse momentum predicts at leading-order in the QCD coupling constant that the transverse polarization of the pair should increase with its transverse momentum. Measurements at the Fermilab Tevatron of the polarization of charmonium and bottomonium states with respect to a particular spin-quantization axis are inconsistent with this prediction. However the predicted rate of approach to complete transverse polarization depends on the choice of spin-quantization axis. We introduce ax…
We find that a simple extension of the coalescence model is sufficient to incorporate the perfect quark number scaling behavior of the elliptic flow in transverse kinetic energy, recently discovered by the PHENIX Collaboration. The flavor dependence of the elliptic flow can be consistently described in the low and intermediate $p_T$ if the transverse kinetic energy is conserved in the $2\to1$ or $3\to1$ parton coalescence process at the hadronization. Thus suggesting the quark coalescence as a possible hadronization mechanism at low $p_T$ as well.
The role of transverse momentum of quarks in semi-inclusive leptoproduction will be discussed. It involves generalized distribution and fragmentation functions which depend on both the longitudinal lightcone momentum fraction of the quarks and on the transverse momentum. Constraints on these functions and relations between them arise as a consequence of the QCD equation of motion for the quark fields, Lorentz invariance and of C, P, and T invariance of the strong interactions. Experimentally one has access to the functions for instance in measurements of azimuthal asymmetries in hard processes…
Impact parameter dependent parton distributions are transversely distorted when one considers transversely polarized nucleons and/or quarks. This provides a physical mechanism for the T-odd Sivers effect in semi-inclusive deep-inelastic scattering. The transverse distortion can also be related to Ji's sum rule for the angular momentum carried by the quarks. The distortion of chirally odd impact parameter dependent parton distributions is related to chirally odd GPDs. This result is used to provide a decomposition of the quark angular momentum w.r.t. quarks of definite transversity. Chirally od…
The leading twist transverse momentum dependent parton distributions (TMDs) are studied in a light-cone description of the nucleon where the Fock expansion is truncated to consider only valence quarks. General analytic expressions are derived in terms of the six amplitudes needed to describe the three-quark sector of the nucleon light-cone wave function. Numerical calculations for the T-even TMDs are presented in a light-cone constituent quark model, and the role of the so-called pretzelosity is investigated to produce a nonspherical shape of the nucleon.
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.
Differential distributions for heavy quark production depend on the heavy quark mass and other momentum scales, which can yield additional large logarithms and inhibit accurate predictions. Logarithms involving the heavy quark mass can be summed in heavy quark parton distribution functions in the ACOT factorization scheme. A second class of logarithms involving the heavy-quark transverse momentum can be summed using an extension of Collins-Soper-Sterman (CSS) formalism. We perform a systematic summation of logarithms of both types, thereby obtaining an accurate description of heavy-quark diffe…
We derive the transverse momentum dependent (TMD) factorization for heavy quark pair production in deep inelastic scattering, where the total transverse momentum is much smaller than the invariant mass of the pair. The factorization is demonstrated at one-loop order, in both Ji-Ma-Yuan and Collins-11 schemes for the TMD definitions, and the hard factors are calculated accordingly. Our result provides a solid theoretical foundation for the phenomenological investigations of the gluon TMDs in this process, and can be extended to other similar hard processes, including dijet (di-hadron) productio…
In this talk we consider the O(alpha_s) radiative corrections to the decay of an unpolarized top quark into a bottom quark and a W gauge boson where the helicities of the W are specified as transverse-plus, transverse-minus and longitudinal. The O(alpha_s) radiative corrections lower the normalized longitudinal rate Gamma_L/Gamma by 0.8%. We find that the normalized transverse-plus rate Gamma_+/Gamma, which vanishes at the Born term level for m_b->0, receives radiative correction contributions at the sub-percent level. Our results are discussed in the light of recent measurements of the helici…
Longitudinal and transverse parton distributions for pion and nucleon are calculated from hadron vertexes obtained by a study of form factors within relativistic quark models. The relevance of the one-gluon-exchange dominance at short range for the behavior of the form factors at large momentum transfer and of the parton distributions at the end points is stressed.
Parton distributions in impact parameter space, which are obtained by Fourier transforming GPDs, exhibit a significant deviation from axial symmetry when the target and/or quark are transversely polarized. Connections between this deformation and transverse single-spin asymmetries as well as with quark-gluon correlations are discussed. The sign of transverse deformation of impact parameter dependent parton distributions in a transversely polarized target can be related to the sign of the contribution from that quark flavor to the nucleon anomalous magnetic moment. Therefore, the signs of the S…
We review the present state of knowledge regarding the transverse polarisation (or transversity) distributions of quarks. After some generalities on transverse polarisation, we formally define the transversity distributions within the framework of a classification of all leading-twist distribution functions. We describe the QCD evolution of transversity at leading and next-to-leading order. A comprehensive treatment of non-perturbative calculations of transversity distributions (within the framework of quark models, lattice QCD and QCD sum rules) is presented. The phenomenology of transversity…
We investigate the prospects to observe effects of transverse polarization of top quarks in $pp,p\bar{p}\to t\bar{t}X$. QCD absorptive parts generate a polarization of top quarks and antiquarks transverse to the production plane in the partonic processes $q\bar{q}\to t\bar{t}$ and $gg\to t\bar{t}$, which reaches values of a few percent. These perturbative QCD effects are decreased at the hadronic level. A measurement through momentum correlations among the $t$ and $\bar{t}$ decay products will be difficult both at an upgraded Tevatron and at the LHC.
The nuclear suppression of heavy quarkonium production at low transverse momentum in pA collisions in high energy scatterings is investigated in the small-x factorization formalism. A universal suppression is found in the large Nc limit between the two formalisms to describe the heavy quarkonium production: the non-relativistic QCD (NRQCD) and the color-evaporation model (CEM). This provides an important probe to the saturation momentum at small-x in big nucleus. We also comment on the phenomenological applications of our results.
Recent results on transverse mass spectra of $J/ψ$ and $ψ^{\prime}$ mesons in central Pb+Pb collisions at 158 A$\cdot$GeV are considered. It is shown that those results support a hypothesis of statistical production of charmonia at hadronization and suggest the early thermal freeze--out of $J/ψ$ and $ψ^{\prime}$ mesons. Based on this approach the collective transverse velocity of hadronizing quark gluon plasma is estimated to be $<v^H_T> \approx 0.2$. Predictions for transverse mass spectra of hidden and open charm mesons at SPS and RHIC are discussed.
Recent theoretical studies have provided new insight into the intrinsic transverse momentum distributions of valence and sea quarks in the nucleon at a low scale. The valence quark transverse momentum distributions (q - qbar) are governed by the nucleon's inverse hadronic size R^{-1} ~ 0.2 GeV and drop steeply at large p_T. The sea quark distributions (qbar) are in large part generated by non-perturbative chiral-symmetry-breaking interactions and extend up to the scale rho^{-1} ~ 0.6 GeV. These findings have many implications for modeling the initial conditions of perturbative QCD evolution of…
We calculate the light cone wave functions for the QCD Fock components in a transverse virtual photon necessary for applications at next-to-leading order in the QCD coupling, including quark masses. We present a detailed calculation of both the one loop wave function for the quark-antiquark Fock component and the tree level wave function for the quark-antiquark-gluon Fock component. The quark masses are renormalized in the pole mass scheme, satisfying constraints from the requirement of Lorentz invariance. In particular the quark Pauli form factor at NLO is recovered from the on-shell limit of…
The transverse polarization of $Λ^0$ hyperons produced in the inclusive $ep$ reaction at the 27.6 GeV beam energy is assumed to appear mostly via scattering of the strange quark in a color field. Results of application of such an idea to the preliminary data of HERMES are presented. Contributions of $Σ^0$, $Ξ$, and $Σ^*$ resonances to the polarization are taken into account.
The conventional NLO parton model is enough for the description of total cross sections and one-particle distributions. In the case of two-particle correlations, the collinear approximation has failed, and it is necessary to account for the transverse momenta of initial partons. The different possibilities to do this are discussed.
We study the transverse momenta and (pseudo)rapidity spectrum of the top quark and their decay products, the tt-system, and the total number of jets in proton-proton (pp) collisions at 13 TeV by using the Tsallis-Pareto-type function and the three-source Landau hydrodynamic model, respectively. The related parameters, such as the effective temperature of the interacting system (T), the non-extensivity of the process (n) and the width ($σ$) of (pseudo)rapidity distribution are extracted.
In the heavy-quark limit, the valence Fock-state components in the B mesons are described by a set of two light-cone wavefunctions. We show that these two wavefunctions obey simple coupled differential equations, which are based on the equations of motion in the Heavy Quark Effective Theory (HQET), and the analytic solutions for them are obtained. The results generalize the recently obtained longitudinal-momentum distribution in the Wandzura-Wilczek approximation by including the transverse momenta. We find that the transverse momentum distribution depends on the longitudinal momentum of the c…
We investigate the flavour decomposition of the electromagnetic form factors of the nucleon, based on the chiral quark-soliton model ($χ$QSM) with symmetry-conserving quantisation. We consider the rotational $1/N_c$ and linear strange-quark mass ($m_s$) corrections. We discuss the results of the flavour-decomposed electromagnetic form factors in comparison with the recent experimental data. In order to see the effects of the strange quark, we compare the SU(3) results with those of SU(2). We finally discuss the transverse charge densities for both unpolarised and polarised nucleons. The transv…
We formulate the single transverse spin asymmetry in heavy quarkonium production in lepton-nucleon and nucleon-nucleon collisions in the non-relativistic limit. We find that the asymmetry is very sensitive to the production mechanism. The final state interactions with the heavy quark and antiquark cancel out among themselves when the pair are produced in a color-single configuration, or cancel out with the initial state interaction in pp scattering when they are in color-octet. As a consequence, the asymmetry is nonzero in ep collisions only in the color-octet model, whereas in pp collisions o…
We calculate the non-zero Boer-Mulders functions of sea quarks inside the proton in a meson-baryon fluctuation model. The results show that the transverse spin effects of sea quarks in an unpolarized nucleon are sizable. Using the obtained antiquark Boer-Mulders functions, we estimate the $\cos 2 ϕ$ asymmetries in the unpolarized $pp$ and $p D$ Drell-Yan processes at FNAL E866/NuSea experiments. The prediction for the $\cos 2 ϕ$ asymmetries in the unpolarized $pp$ Drell-Yan process at the BNL Relativistic Heavy Ion Collider (RHIC) is also given.
We investigate the transverse momentum dependent (TMD) quark and gluon distribution functions in the modified chiral quark model ($χQM$). Calculations of the TMD quark and gluon densities, using the modified $χQM$ are done for the first time in this article. For this propose we first formulate the TMD interactions that occur in the $χQM$ at low $Q^2$ scale ($Q^2=0.35~ GeV^2$) and then obtain the TMD parton distributions inside the proton, considering the interactions. To this end, we need to compute the TMD bare quark distributions. These TMD bare densities are calculated, using the solution o…
Transverse parton momentum dependent distribution functions (TMDs) of the nucleon are studied in a covariant model, which describes the intrinsic motion of partons in terms of a covariant momentum distribution. The consistency of the approach is demonstrated, and model relations among TMDs are studied. As a byproduct it is shown how the approach allows to formulate the non-relativistic limit.
We present a next-to-leading order calculation of H+jet in gluon fusion including the effect of a finite top quark mass $m_t$ at large transverse momenta. Using the recently published two-loop amplitudes in the high energy expansion and our previous setup that includes finite $m_t$ effects in a low energy expansion, we are able to obtain $m_t$-finite results for transverse momenta below 225 GeV and above 500 GeV with negligible remaining top quark mass uncertainty. The only remaining region that has to rely on the common leading order rescaling approach is the threshold region $\sqrt{\hat s}\s…
We investigate the transverse momentum resummation for top quark pair production at hadron colliders using the soft-collinear effective theory and the heavy-quark effective theory. We derive the factorization formula for $t\bar{t}$ production at small pair transverse momentum, and show in detail the procedure for calculating the key ingredient of the factorization formula: the next-to-leading order soft functions. We compare our numerical results with experimental data and find that they are consistent within theoretical and experimental uncertainties. To verify the correctness of our resummat…
The large-$x$ behavior of the transverse-momentum dependent quark distributions is analyzed in the factorization-inspired perturbative QCD framework, particularly for the naive time-reversal-odd quark Sivers function which is responsible for the single transverse-spin asymmetries in various semi-inclusive hard processes. By examining the dominant hard gluon exchange Feynman diagrams, and using the resulting power counting rule, we find that the Sivers function has power behavior $(1-x)^4$ at $x \to 1$, which is one power of $(1-x)$ suppressed relative to the unpolarized quark distribution. The…
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…
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