Recent developments in nucleon spin structure with focus on h_{1L}^{\perp} and pretzelosity h_{1T}^\perp
H. Avakian, A. V. Efremov, P. Schweitzer, A. Metz, T. Teckentrup
备注：
12 pages, 12 figure, presented at Advanced Studies Institute -- Symmetries And Spin" (SPIN-Praha-2008), Prague, July 20-26, 2008, to be published Eur.Phys.J, ST, style files included. Dedicated to 65 anniversary of Professor Klaus Goeke
The leading twist transverse momentum dependent parton distribution functions h_{1L}^{\perp} and h_{1T}^\perp, which is sometimes called "pretzelosity," are studied. For h_{1L}^{\perp} we consider a "Wandzura-Wilczek-type" approximation, which follows from QCD equations of motion upon the neglect of pure twist-3 terms and allows to express it in terms of transversity. On the basis of available data from HERMES we test the practical usefulness of this approximation and discuss how it can be further tested by future CLAS and COMPASS data. We review the theoretical properties of retzelosity and observe an interesting relation valid in a large class of relativistic models: The difference between helicity and transversity distributions, which is often said to be a 'measure of relativistic effects' in the nucleon, is nothing but the transverse moment of pretzelosity. We discuss preliminary deuteron target data from COMPASS on the single spin asymmetry (SSA) in semi-inclusive deep inelastic scattering (SIDIS) related to pretzelosity, and make predictions for future experiments at JLab, COMPASS and HERMES.
The pretzelosity distribution function $h_{1T}^\perp$ is studied in a covariant the quark-parton model which describes the structure of the nucleon in terms of 3D quark intrinsic motion. This relativistic model framework supports the relation between helicity, transversity and pretzelosity observed in other relativistic models {\sl without} assuming SU(6) spin-flavor symmetry. Numerical results and predictions for SIDIS experiments are presented.
The leading twist transverse momentum dependent parton distribution function h_1T^perp, which is sometimes called ``pretzelosity,'' is studied. We review the theoretical properties of this function, and present bag model predictions. We observe an interesting relation valid in a large class of relativistic models: The difference between helicity and transversity distributions, which is often said to be a 'measure of relativistic effects' in nucleon, is nothing but the pretzelosity distribution. Pretzelosity is chirally odd and can be accessed in combination with the Collins effect in semi-incl…
We attempt an extraction of the pretzelosity distribution ($h^{\perp}_{1T}$) from preliminary COMPASS, HERMES, and JLAB experimental data on $\sin(3ϕ_h - ϕ_S)$ asymmetry on proton, and effective deuteron and neutron targets. The resulting distributions, albeit with big errors, for the first time show tendency for up-quark pretzelosity to be positive and down-quark pretzelosity to be negative. A model relation of pretzelosity distribution and orbital angular momentum of quarks is used to estimate contributions of up and down quarks.
We calculate the pretzelosity distribution ($h_{1T}^{\perp}$), which is one of the eight leading twist transverse momentum dependent parton distributions (TMDs), in the light-cone formalism. We find that this quantity has a simple relation with the quark orbital angular momentum distribution, thus it may provide a new possibility to access the quark orbital angular momentum inside the nucleon. The pretzelosity distribution can manifest itself through the $\sin(3ϕ_h-ϕ_S)$ asymmetry in semi-inclusive deep inelastic scattering process. We calculate the $\sin(3ϕ_h-ϕ_S)$ asymmetry at HERMES, COMPAS…
We show that the polarized proton-antiproton Drell-Yan process is ideal to probe the pretzelosity distribution ($h_{1T}^\perp$), which is one of the new transverse-momentum-dependent parton distributions of the nucleon. We present predictions of the $\cos(2ϕ+ ϕ_a - ϕ_b)$ asymmetry in the transversely polarized proton-antiproton Drell-Yan process at PAX kinematics and find that the results are significantly larger compared with those of the $\sin(3ϕ_h - ϕ_S)$ asymmetry in the semi-inclusive deep inelastic scattering process at HERMES, COMPASS, and JLab kinematics. We conclude that the $\cos(2ϕ+…
We present a phenomenological analysis of the $q_{\mathrm{T}}$-weighted transverse spin dependent azimuthal asymmetry recently measured by the COMPASS Collaboration in polarized pion-proton Drell-Yan process. In the kinematical regimes explored by experiments, we consider the leading-twist contributions from the Boer-Mulders distribution functions $h_{1}^{\perp}(x,k_{\mathrm{T}}^{2})$ of both the pion and the proton, the transversity distribution $h_{1}(x,k_{\mathrm{T}}^{2})$ and the pretzelosity distribution $h_{1\mathrm{T}}^{\perp}(x,k_{\mathrm{T}}^{2})$ of the proton, with the unpolarized t…
We study the connection between the quark orbital angular momentum and the pretzelosity transverse-momentum dependent parton distribution function. We discuss the origin of this relation in quark models, identifying as key ingredient for its validity the assumption of spherical symmetry for the nucleon in its rest frame. Finally we show that the individual quark contributions to the orbital angular momentum obtained from this relation can not be interpreted as the intrinsic contributions, but include the contribution from the transverse centre of momentum which cancels out only in the total or…
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.
Nucleon elastic and transition form factors at high momentum transfer -t are treated in terms of generalized parton distributions in a two-body framework. In this framework the high -t dependence of the form factors give information about the high k_perp, or short distance b_perp correlations of nucleon model wave functions. Applications are made to elastic and resonance nucleon form factors, and real Compton Scattering.
We study contributions from color-octet quarkonium formation mechanisms to $p_\perp$-integrated $ψ'$ production cross sections in pion-nucleon reactions. The observed polarization of the $ψ'$ is not reproduced by the lowest-order leading-twist color-singlet and color-octet mechanisms. This suggests that there are important quarkonium production mechanisms beyond leading twist.
The single pion production (SPP) in the charged-current neutrino (antineutrino) scattering off the polarized nucleon is discussed. The spin asymmetry is predicted within two approaches. The spin polarizations of the target nucleon that are longitudinal and perpendicular to the neutrino momentum are considered. It is shown, in several examples, that information about the SPP dynamics coming from the spin asymmetry is complementary to information obtained from measurements of spin averaged cross section. Indeed, the spin asymmetry is sensitive to the nonresonance background description of the SP…
Using a three stage model of hadron formation we calculate the change of the transverse momentum distribution of hadrons produced in semi-inclusive deep inelastic scattering (SIDIS) on nuclei. In the first stage after its interaction with the virtual photon, the struck quark propagates quasi free in the nuclear environment undergoing multiple collisions with nucleons. During this stage it can acquire transverse momentum. In the second stage a prehadron is formed which has a very small elastic cross section with the nucleons. In the third stage the prehadron turns into a hadron. For HERMES ener…
We study the Wigner distributions of quarks and gluons in light-front dressed quark model using the overlap of light front wave functions (LFWFs). We take the target to be a dressed quark, this is a composite spin $-1/2$ state of quark dressed with a gluon. This state allows us to calculate the quark and gluon Wigner distributions analytically in terms of LFWFs using Hamiltonian perturbation theory. We analyze numerically the Wigner distributions of quark and gluon and report their nature in the contour plots. We use an improved numerical technique to remove the cutoff dependence of the Fourie…
We study the beam single-spin asymmetries $A_{LU}^{\sinϕ_h}$ for charged hadrons produced in semi-inclusive deep inelastic scattering process, by considering the $e H_1^\perp$ term and the $g^\perp D_1$ term simultaneously. Besides the asymmetries for charged pions, for the first time we present the analysis on the asymmetries in the production of charged kaons, protons and antiprotons by longitudinally polarized leptons scattered off unpolarized proton and deuteron targets. In our calculation we use two sets of transverse momentum dependent distributions $g^\perp(x,\bm k_T^2)$ and $e(x,\bm k_…
We present the results of T-even TMDs in a light front quark-diquark model of nucleons with the wave functions constructed from the soft-wall AdS/QCD prediction. The relations amongst TMDs are discussed. The $p_\perp$ dependence of the TMDs are compared with the $t$-dependence of the GPDs. AdS/QCD wave function provides an explanation behind the approximate $x$ and $p_\perp$ factorization observed in lattice TMD calculations.
We investigate the Generalized Parton Distributions (GPDs) in impact parameter space using the explicit light front wave functions (LFWFs) for the two-particle Fock state of the electron in QED. The Fourier transform (FT) of the GPDs gives the distribution of quarks in the transverse plane for zero longitudinal momentum transfer ($ξ=0$). We study the relationship of the spin flip GPD $E(x,0,-\vecΔ_\perp^2)$ with the distortion of unpolarized quark distribution in the transverse plane when the target nucleon is transversely polarized and also determine the sign of distortion from the sign of an…
We report the first calculation of the simplest but most fundamental transverse momentum dependent (TMD) distribution of quarks in the nucleon, i.e. the time-reversal-even unpolarized TMD quark and antiquark distribution with isoscalar combination, within the framework of the chiral quark soliton model. The nonperturbative account of the deformed Dirac-sea quarks within the theoretical scheme enables us to make a reliable predictions not only for the quark distribution but also for the antiquark distribution. We found that the predicted average transverse momentum square $<k_\perp^2>$ of quark…
The flavor dependence of the naive time reversal odd (``T-odd'') parton distributions for $u$- and $d$-quarks are explored in the spectator model. The flavor dependence of $h_{1}^{\perp}$ is of significance for the analysis of the azimuthal $\cos(2ϕ)$ asymmetries in unpolarized SIDIS and DY-processes, as well as for the overall physical understanding of the distribution of transversely polarized quarks in unpolarized nucleons. As a by-product of the formalism, we calculate the chiral-odd but ``T-even'' function $h_{1L}^{\perp}$ which enables us to present a prediction for the single spin asymm…
Fudan University（复旦大学）；Shandong University（山东大学）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（上海理论核物理联合研究中心（NSFC与复旦大学））；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）
The Sivers function, an asymmetric transverse-momentum distribution of the quarks in a transversely polarized nucleon, is calculated in the MIT bag model. The bag quark wave functions contain both $S$-wave and $P$-wave components, and their interference leads to nonvanishing Sivers function in the presence of the final state interactions. We approximate these interactions through one-gluon exchange. An estimate of another transverse momentum dependent distribution $h_1^\perp$ is also performed in the same model.
We study the single-spin asymmetries of pions produced in semi-inclusive deep-inelastic scattering on the longitudinally polarized nucleon targets. We particularly consider the effects of the twist-3 transverse-momentum dependent distribution functions $f_L^\perp$ and $h_L$ to the asymmetry. We calculate the asymmetric moment $A_{UL}^{\sinϕ_h}$ for $π^+$, $π^-$ and $π^0$ produced off the proton target at HERMES and compare the results with the HERMES data. We also present the prediction of the same asymmetries for different pions at the kinematics of CLAS 5.5 GeV on a proton target, as well as…
We present the first calculation in lattice QCD of the lowest two moments of transverse spin densities of quarks in the nucleon. They encode correlations between quark spin and orbital angular momentum. Our dynamical simulations are based on two flavors of clover-improved Wilson fermions and Wilson gluons. We find significant contributions from certain quark helicity flip generalized parton distributions, leading to strongly distorted densities of transversely polarized quarks in the nucleon. In particular, based on our results and recent arguments by Burkardt [Phys. Rev. D 72 (2005) 094020], …
We investigate the $\sin (ϕ_Λ-ϕ_S)$ single-spin asymmetry in the transversely polarized $Λ$ production in semi-inclusive deeply inelastic scattering process within the framework of the transverse momentum dependent~(TMD) factorization. The asymmetry is contributed by the convolution of the polarizing TMD fragmentation function $D_{1T}^\perp$ of the $Λ$ hyperon and the unpolarized TMD distribution function $f_1$ of the target nucleon. We apply two sets of $D_{1T}^{\perp,Λ^\uparrow/q}$, the spectator diquark model result and available parametrization, to numerically estimate the $\sin (ϕ_Λ-ϕ_S)$…
The naive time reversal odd (``T-odd'') parton distribution $h_{1}^{\perp}$, the so-called Boer-Mulders function, for both up ($u$) and down ($d$) quarks is considered in the diquark spectator model. While the results of different articles in the literature suggest that the signs of the Boer-Mulders function in semi-inclusive DIS for both flavors $u$ and $d$ are the same and negative, a previous calculation in the diquark-spectator model found that $h_{1}^{\perp(u)}$ and $h_{1}^{\perp(d)}$ have different signs. The flavor dependence is of significance for the analysis of the azimuthal $\cos(2ϕ…
We present predictions of the unweighted and weighted double spin asymmetries related to the transversal helicity distribution $g_{1T}$ and the longitudinal transversity distribution $h_{1L}^\perp$, two of eight leading-twist transverse momentum dependent parton distributions (TMDs) or three-dimensional parton distribution functions (3dPDFs), in the polarized proton-antiproton Drell-Yan process at typical kinematics on the Facility for Antiproton and Ion Research (FAIR). We conclude that FAIR is ideal to access the new 3dPDFs towards a detailed picture of the nucleon structure.
Using the model of Nambu and Jona-Lasinio to provide a microscopic description of both the structure of the nucleon and of the quark to hadron elementary fragmentation functions, we investigate the transverse momentum dependence of the unpolarized quark distributions in the nucleon and of the quark to pion and kaon fragmentation functions. The transverse momentum dependence of the fragmentation functions is determined within a Monte Carlo framework, with the notable result that the average $P_\perp^2$ of the produced kaons is significantly larger than that of the pions. We also find that $<P_\…
At leading twist the transverse-momentum dependent parton distributions of the pion consist of two functions, the unpolarized $f_{1,π}(x,\boldsymbol k^{\, 2}_\perp)$ and the Boer-Mulders function $h_{1,π}^{\perp}(x,\boldsymbol k^{\, 2}_\perp)$. We study both functions within a light-front constituent model of the pion, comparing the results with different pion models and the corresponding nucleon distributions from a light-front constituent model. After evolution from the model scale to the relevant experimental scales, the results for the collinear pion valence parton distribution function $f…
Accessing nucleon transversity with one-point energy correlators
Fudan University（复旦大学）；University of California, Los Angeles（加州大学洛杉矶分校）；Mani L. Bhaumik Institute for Theoretical Physics, University of California, Los Angeles（加州大学洛杉矶分校马尼·L·巴乌米克理论物理研究所）；Center for Frontiers in Nuclear Science, Stony Brook University（纽约州立大学石溪分校核科学前沿中心）；Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Fudan University（复旦大学核物理与离子束应用教育部重点实验室）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（国家自然科学基金委与复旦大学上海理论核物理研究中心）；Center for High Energy Physics, Peking University（北京大学高能物理中心）
Hadron production at low transverse momenta in semi-inclusive deep inelastic scattering can be described by transverse momentum dependent (TMD) factorization. This formalism has also been widely used to study the Drell-Yan process and back-to-back hadron pair production in $e^+e^-$ collisions. These processes are the main ones for extractions of TMD parton distribution functions and TMD fragmentation functions, which encode important information about nucleon structure and hadronization. One of the most widely used TMD factorization formalism in phenomenology formulates TMD observables in coor…
We propose a new method to determine at what transverse momenta particle production in high-energy pp collisions is governed by hard parton-parton processes. Using information on the transverse spatial distribution of partons obtained from hard exclusive processes in ep/gamma p scattering, we evaluate the impact parameter distribution of pp collisions with a hard parton-parton process as a function of p_T of the produced parton (jet). We find that the average pp impact parameters in such events depend very weakly on p_T in the range 2 < p_T < few 100 GeV, while they are much smaller than those…
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…
The spin dependent deuteron structure functions are investigated in the relativistic model of deuteron. It is shown that the deuteron structure function $g_{2}(X)$ can be considered properly only in the infinite momentum frame where the virtual photon has pure transverse components ($q_{0}=-q_{3}\rightarrow 0$ at $ P\rightarrow \infty $), whereas in the conventional Breit frame the impulse approximation for $g_{2}(X)$ may be violated due to $q\bar{q}$ pair creation by the virtual photon. It is shown that due to relativistic effects the deuteron structure function $g_{2}(X)$ has a nontrivial co…
The diffractive t-slope, B_V, of elastic charmonia (V=J/psi, psi') photo- and leptoproductions off a nucleon is studied at low |t| (< 1 GeV^2) in the leading logarithmic approximation of perturbative QCD, with a special emphasis on the space-time evolution of the c\bar{c}-dipole. We obey a framework based on QCD factorization, which describes a certain Fermi motion effect due to the $c(\bar{c})$-quarks in the proper manner and includes appropriately kinematical corrections of the momentum transfer Delta_perp in the t-channel. Assuming the universal two-gluon form factor of the nucleon, we show…
We study the cross section for vector boson ($W^{\pm}/Z^0/γ^*$) production in polarized nucleon-nucleon collisions for low transverse momentum of the observed vector boson. For the case where one measures the transverse momentum and azimuthal angle of the vector bosons, we present the cross sections and the associated spin asymmetries in terms of transverse momentum dependent parton distribution functions (TMDs) at tree level within the TMD factorization formalism. To assess the feasibility of experimental measurements, we estimate the spin asymmetries for $W^{\pm}/Z^0$ boson production in pol…
We have examined the spin structure of the proton in the region of the nucleon resonances (1.085 GeV < W < 1.910 GeV) at an average four momentum transfer of Q^2 = 1.3 GeV^2. Using the Jefferson Lab polarized electron beam, a spectrometer, and a polarized solid target, we measured the asymmetries A_parallel and A_perp to high precision, and extracted the asymmetries A_1 and A_2, and the spin structure functions g_1 and g_2. We found a notably non-zero A_perp, significant contributions from higher-twist effects, and only weak support for polarized quark--hadron duality.
The first measurement of transverse-spin-dependent azimuthal asymmetries in the pion-induced Drell-Yan (DY) process is reported. We use the CERN SPS 190 GeV/$c$, $π^{-}$ beam and a transversely polarized ammonia target. Three azimuthal asymmetries giving access to different transverse-momentum-dependent (TMD) parton distribution functions (PDFs) are extracted using dimuon events with invariant mass between 4.3 GeV/$c^2$ and 8.5 GeV/$c^2$. The observed sign of the Sivers asymmetry is found to be consistent with the fundamental prediction of Quantum Chromodynamics (QCD) that the Sivers TMD PDFs …
