A. W. Thomas
We derive the consequences of the Myhrer-Thomas explanation of the proton spin problem for the distribution of orbital angular momentum on the valence and sea quarks. After QCD evolution these results are found to be in very good agreement with both recent lattice QCD calculations and the experimental constraints from Hermes and JLab.
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We argue that there are two mechanisms responsable for the growth of high energy cross-sections - σ_{tot} and σ_{el}, say - in pp collisions. One is by the increase of matter \emph{density}, resulting in the black disk saturation. The other is by exclusively radial expansion affecting the periphery of the overlap area. Within this simple model we can reproduce all available data in pp from ISR to LHC. In order to achieve a fast growth in the very high energy cosmic ray energies, we propose a fast black disk saturation followed by the dominance of geometric scaling (GS).
Effect of the quark intrinsic motion on the proton spin structure functions is demonstrated. It is shown, that the covariant version of the quark-parton model taking into account the orbital motion gives the consistent picture of the proton spin structure, which is based on the valence quarks. This picture is supported by the recent data, which indicate, that the spin contributions from the sea quarks and gluons are compatible with zero.
The Wigner distributions for u and d quarks in a proton are calculated using the light front wave functions (LFWFs) of the scalar quark-diquark model for nucleon constructed from the soft-wall AdS/QCD correspondence. We present a detail study of the quark orbital angular momentum(OAM) and its correlation with quark spin and proton spin. The quark density distributions, considering the different polarizations of quarks and proton, in transverse momentum plane as well as in transverse impact parameter plane are presented for both u and d quarks.
The orbital angular momentum ($L_q$) of the proton is studied by employing the extended constituent quark model. Contributions from different flavors, namely, up, down, strange, and charm quarks in the proton are investigated. Probabilities of the intrinsic $q\bar{q}$ pairs are calculated using a $^{3}P_{0}$ transition operator to fit the sea flavor asymmetry $I_a=\bar{d}-\bar{u}=0.118\pm0.012$ of the proton. Our numerical results lead to $L_q=0.158 \pm 0.014$, in agreement with $4/3I_a=0.157 \pm 0.016$, and consistent with findings based on various other approaches.
Covariant version of the quark-parton model is studied. Dependence of the structure functions on the 3D quark intrinsic motion is discussed. The important role of the quark orbital momentum, which is a particular case of intrinsic motion, appears as a direct consequence of the covariant description. Effect of orbital motion is substantial especially for polarized structure functions. At the same time, the procedure for obtaining the quark momentum distribution from the structure functions is suggested.
Since the announcement of the proton spin crisis by the European Muon Collaboration there has been considerable progress in unravelling the distribution of spin and orbital angular momentum within the proton. We review the current status of the problem, showing that not only have strong upper limits have been placed on the amount of polarized glue in the proton but that the experimental determination of the spin content has become much more precise. It is now clear that the origin of the discrepancy between experiment and the naive expectation of the fraction of spin carried by the quarks and …
We study the covariant version of the quark-parton model, in which the general rules of the angular momentum composition are accurately taken into account. We demonstrate how these rules affect the relativistic interplay between the quark spins and orbital angular momenta, which collectively contribute to the proton spin. The spin structure functions $g_{1}$ and $g_{2}$ corresponding to the many-quark state $J=1/2$ are studied and it is shown they satisfy constraints and relations well compatible with the available experimental data including proton spin content $ΔΣ\lesssim1/3$. The suggested …
We examine the single-spin asymmetry (SSA) caused by the five-quark components of the proton for semi-inclusive electroproduction of charged pions in deep-inelastic scattering on a transversely polarized hydrogen target. The large SSA is considered to have close relation with quark orbital motion in the proton and suggests that the quark orbital angular momentum is nonzero. For the five-quark $qqqq\bar{q}$ components of the proton, the lowest configurations with $qqqq$ system orbitally excited and the $\bar{q}$ in the ground state would give spin-orbit correlations naturally for the quarks in …
We derive new Lorentz Invariance and Equation of Motion Relations between twist-three Generalized Parton Distributions (GPDs) and moments in the parton transverse momentum, $k_T$, of twist-two Generalized Transverse Momentum-Dependent Distributions (GTMDs), as a function of the parton longitudinal momentum fraction $x$. Although GTMDs in principle define the observables for partonic orbital motion, experiments that can unambiguously detect them appear remote at present. The relations presented here provide a solution to this impasse in that, e.g., the orbital angular momentum density is connec…
We study the three-quark light-cone amplitudes of the proton including quarks' transverse momenta. We classify these amplitudes using a newly-developed method in which light-cone wave functions are constructed from a class of light-cone matrix elements. We derive the constraints on the amplitudes from parity and time-reversal symmetries. We use the amplitudes to calculate the physical observables which vanish when the quark orbital angular momentum is absent. These include transverse-momentum dependent parton distributions $Δq_T(x, k_\perp)$, $q_T(x, k_\perp)$, $δq(x, k_\perp)$, and $δq_L(x,k_…
On the Interplay of Nuclear and Higher-Twist Corrections in Nuclear Structure Functions
该研究通过纳入氘、³H和³He核数据的全局QCD分析，联合确定部分子分布、高扭度项与核子离壳修正，发现单一同位旋标量离壳函数可解释核截面比，并给出相关夸克分布与未来宇称破坏DIS的EMC效应预测。
The complementarity of polarized DIS experiments and polarized Proton-Proton experiments is illustrated for two examples. It is shown how the twist-3 part of the second moment of $g_2(x,Q^2)$ and the single-spin photon asymmetry are connected and it is discussed how the polarized gluon distribution can be obtained from the measurement of direct gamma asymmetries.
A striking prediction of several extensions of the constituent quark model, including the unquenched quark model, the pion cloud model and the chiral quark model, is a proportionality relationship between the quark sea asymmetry and the orbital angular momentum of the proton. We investigate to which extent a relationship of this kind is corroborated by the experiment, through a systematic comparison between expectations based on models and predictions obtained from a global analysis of hard-scattering data in perturbative Quantum Chromodynamics. We find that the data allows the angular momentu…
We argue that the process of the proton diffraction into three jets in proton-nucleus scattering at LHC will allow to investigate the light-cone wave function of protons, generalized gluon densities in nuclei at small x, as well as the interplay of the color transparency and opacity phenomena.
Given a Wigner distribution simultaneously characterizing quark transverse positions and momenta in a proton, one can directly evaluate their cross-product, i.e., quark orbital angular momentum. The aforementioned distribution can be obtained by generalizing the proton matrix elements of quark bilocal operators which define transverse momentum-dependent parton distributions (TMDs); the transverse momentum information is supplemented with transverse position information by introducing an additional nonzero momentum transfer. A gauge connection between the quarks must be specified in the quark b…
We study the orbital angular momentum contribution to the spin structure of the proton. It is well known that the quark and gluon spin contributions do not add up to the proton spin. We motivate the connection between the Generalized Transverse Momentum Distribution (GTMD) $F_{14}$, and orbital angular momentum by exploring the underlying quark proton helicity amplitude structure. The twist three Generalized Parton Distribution (GPD) $\tilde{E}_{2T}$, was shown to connect to OAM. We study these functions using a diquark model calculation. The GTMD $F_{14}$ is unique in that it can describe bot…
The proton spin puzzle has challenged our understanding of QCD for the last 20 years. We survey new developments in theory and experiment. The proton spin puzzle seems to be telling us about the interplay of valence quarks with chiral dynamics and the complex vacuum structure of QCD.
We calculate the leading-twist helicity-dependent generalized parton distributions (GPDs) of the proton at finite skewness in the Nambu--Jona-Lasinio (NJL) model of quantum chromodynamics (QCD). From these (and previously calculated helicity-independent GPDs) we obtain the spin decomposition of the proton, including predictions for quark intrinsic spin and orbital angular momentum. The inclusion of multiple species of diquarks is found to have a significant effect on the flavor decomposition, and resolving the internal structure of these dynamical diquark correlations proves essential for the …
The proton spin puzzle has challenged our understanding of QCD for the last 20 years. New measurements of polarized glue, valence and sea quark polarization, including strange quark polarization, are available. What is new and exciting in the data, and what might this tell us about the structure of the proton ? The proton spin puzzle seems to be telling us about the interplay of valence quarks with the complex vacuum structure of QCD.
A new picture is given of generalized parton distributions probed in experiments in which the probe scale $Q^{2}$ and the momentum transfer $\DD^{2}$ are well separated. Application of this picture to the $Q^{2}$ dependence of the form factors $F_{1}, F_{2}$ shows that gauge invariant quark orbital angular momentum can be measured and indeed {\it localized} in the transverse profile of the proton. A previous prediction that $\sqrt{Q^{2}}F_{2}(Q^{2})/F_{1}(Q^{2}) \sim const. $ is generalized to GPD language. This prediction appears to have been confirmed by recent CEBAF data.
Transverse Orbital Angular Momentum in the Proton
本文利用QCD运动方程与Lorentz不变性关系，提出质子夸克横向角动量的自旋—轨道分解新途径，并将轨道分量表示为$F_{12}$的$k_T$矩或$H_{2T}$、$\widetilde{E}_{2T}$。
We have recently examined the static properties of the baryon octet (magnetic moments and axial vector coupling constants) in a generalized quark model in which the angular momentum of a polarized nucleon is partly spin $\langle S_z \rangle$ and partly orbital $\langle L_z \rangle$. The orbital momentum was represented by the rotation of a flux-tube connecting the three constituent quarks. The best fit is obtained with $\langle S_z \rangle = 0.08\pm 0.15$, $\langle L_z \rangle = 0.42\pm 0.14$. We now consider the consequences of this idea for the $q^2$-dependence of the magnetic and axial vect…
A delicate interplay between the anomalous magnetic moments of the proton and neutron makes, in magnetic fields $B\ge 2\times 10^{14}$ T, the neutron stable and for fields $B\ge 5\times 10^{14}$ T the proton becomes unstable to a decay into a neutron via $β$ emission. Limits on the field strengths for which these arguments hold are presented and are related to questions of vacuum stability in the presence of such fields. Possible astrophysical consequences are discussed.
The orbital angular momenta $L^u$ and $L^d$ of up and down quarks in the proton are estimated as functions of the energy scale as model-independently as possible, on the basis of Ji's angular momentum sum rule. This analysis indicates that $L^u - L^d$ is large and negative even at low energy scale of nonperturbative QCD, in contrast to Thomas' similar analysis based on the refined cloudy bag model. We pursuit the origin of this apparent discrepancy and suggest that it may have a connection with the fundamental question of how to define quark orbital angular momenta in QCD.
The impact of different assumptions about high energy behavior of the total cross section of proton-proton interactions on the ratio of the real to imaginary part of the forward elastic scattering amplitude is analyzed. It is shown how experimental data about this ratio at LHC energies can help in the proper choice of the asymptotic dependence of the total cross section.
Probing quark orbital angular momentum at EIC and EicC
本研究提出通过电子-质子碰撞中的独占π⁰产生及sin 2φ方位角关联探测夸克轨道角动量，为EIC和EicC实验提供数值估计，推动首次实验验证Jaffe-Manohar自旋求和规则。
The deuteron coalescence parameter $B_2$ in proton+proton and nucleus+nucleus collisions in the energy range of $\sqrt{s_{NN}}=$ 900 - 7000 GeV for proton+proton and $\sqrt{s_{NN}}=$ 2 - 2760 GeV for nucleus+nucleus collisions is analyzed with the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) transport model, supplemented by an event-by-event phase space coalescence model for deuteron and anti-deuteron production. The results are compared to data by the E866, E877, PHENIX, STAR and ALICE experiments. The $B_2$ values are calculated from the final spectra of protons and deuterons. At low…
We propose a novel observable for the experimental detection of the gluon orbital angular momentum (OAM) that constitutes the proton spin sum rule. We consider longitudinal double spin asymmetry in exclusive dijet production in electron-proton scattering and demonstrate that the $\cos ϕ$ azimuthal angle correlation between the scattered electron and proton is a sensitive probe of the gluon OAM at small-$x$ and its interplay with the gluon helicity. We also present a numerical estimate of the cross section for the kinematics of the Electron-Ion Collider.
We analyze the proton electromagnetic form factor ratio $R(Q^{2})=QF_2(Q^{2})/F_1(Q^{2})$ as a function of momentum transfer $Q^{2}$ within perturbative QCD. We find that the prediction for $R(Q^{2})$ at large momentum transfer $Q$ depends on the exclusive quark wave functions, which are unknown. For a wide range of wave functions we find that $ QF_2/F_1 \sim\ const$ at large momentum transfer, in agreement with recent JLAB data.
We generalize the Bartels-Ermolaev-Ryskin approach for the $g_1$ structure function at small-$x$ to determine the small-$x$ asymptotic behavior of the orbital angular momentum distributions in QCD. We present an exact analytical solution of the evolution equation in the double logarithmic approximation and discuss its implications for the proton spin problem.
I calculate the quark contributions to the axial and tensor charges and the spin structure of the proton. The result indicates that the valence current quark spins carry 1/3 of the proton spin, the total contribution of quark spins to the proton spin satisfies $ΔΣ= 1/3 + ΔΣ_{sea} \le 1/3$, and the quarks (their spin plus orbital contributions) contribute about one half of the proton spin at scale of 1 $GeV$. The valence current quark contributions to the proton tensor charge are also obtained.
We present a systematic study of the proton spin structure in terms of measurable parton distributions. For a transversely-polarizedproton, we derive a polarization sum rule from the leading generalized parton distributions appearing in hard exclusive processes. For a longitudinally-polarized proton, we obtain a helicity decomposition from well-known quark and gluon helicity distributions and orbital angular-momentum contributions. The latter is shown to be related to measurable subleading generalized parton distributions and quantum-phase space Wigner distributions.
Electron-Ion Collision Environment: Distribution of Quark Spin and Orbital Angular Momentum
研究利用NJL模型确定夸克质量，在光前着装夸克模型中计算GTMDs，并引入eP和eA碰撞间的GTMD比率，旨在通过未来电子-离子对撞机测量质子和原子核内夸克自旋与轨道角动量分布，间接测量非微扰QCD的多体核密度效应。
Quark orbital angular momentum in the proton from a twist-3 generalized parton distribution
本文基于Lattice QCD计算twist-3广义部分子分布$\widetilde{E}_{2T}$的第二个Mellin矩，评估了质子中的夸克轨道角动量，验证了该方法与既有替代方法结果的一致性。
Nucleon form factors play an especially important role in studying the dynamics of nucleons and explicit structure of the wave functions at arbitrary nucleon velocity. The purpose of the paper is to explain theoretically all four nucleon form factors measured experimentally in the cross section measurements (by the Rosenbluth method), yielding almost equal normalized form factors $G^p_E,G^p_M,G^n_M$, as well as in the polarization transfer experiments, where a strongly decreasing proton electric form factor has been discovered. It is shown, using relativistic hyperspherical formalism, that the…
The spin structure of the proton is investigated in the framework of an extended quark potential model which in addition to the conventional $3q$--structure also takes into account $(3q)(q\bar q)$--admixtures in the proton wave function. For reasons of parity such admixtures contain an odd orbital angular momentum thus allowing the proton spin to be shared among quark spins and orbital angular momenta. We show that only certain admixtures are suited for a significant reduction of the quark spin content of the proton as suggested by the EMC--result. Within a Hamiltonian model quark spin contrib…
We calculate the quark orbital angular momentum of the nucleon from the quark energy-momentum tensor form factors on the lattice. The disconnected insertion is estimated stochastically which employs the $Z_2$ noise with an unbiased subtraction. This reduced the error by a factor of 4 with negligible overhead. The total quark contribution to the proton spin is found to be $0.30 \pm 0.07$. From this and the quark spin content we deduce the quark orbital angular momentum to be $0.17 \pm 0.06$ which is $\sim 34$% of the proton spin. We further predict that the gluon angular momentum to be $0.20 \p…
We provide a theoretical basis for understanding the spin structure of the proton in terms of the spin and orbital angular momenta of free quarks and gluons in Feynman's parton picture. We show that each term in the Jaffe-Manohar spin sum rule can be related to the matrix element of a gauge-invariant, but frame-dependent operator through a matching formula in large-momentum effective field theory. We present all the matching conditions for the spin content at one-loop order in perturbation theory, which provide a basis to calculate parton orbital angular momentum in lattice QCD at leading loga…
Quark orbital angular momentum (OAM) in the proton can be calculated directly given a Wigner function encoding the simultaneous distribution of quark transverse positions and momenta. This distribution can be accessed via proton matrix elements of a quark bilocal operator (the separation in which is Fourier conjugate to the quark momentum) featuring a momentum transfer (which is Fourier conjugate to the quark position). To generate the weighting by quark transverse position needed to calculate OAM, a derivative with respect to momentum transfer is consequently required. This derivative is eval…
Due to proton spin crisis it is necessary to understand the gauge invariant definition of the spin and orbital angular momentum of the quark and gluon from first principle. In this paper we derive the gauge invariant Noether's theorem by using combined Lorentz transformation plus local gauge transformation. We find that the notion of the gauge invariant definition of the spin (or orbital) angular momentum of the electromagnetic field does not exist in Dirac-Maxwell theory although the notion of the gauge invariant definition of the spin (or orbital) angular momentum of the electron exists. We …
We calculate the form factor of the quark energy momentum tensor and thereby extract the quark orbital angular momentum of the nucleon. The calculation is done on a quenched $16^3 \times 24$ lattice at $β= 6.0$ and with Wilson fermions at $κ$ = 0.148, 0.152, 0.154 and 0.155. We calculate the disconnected insertion stochastically which employs the $Z_2$ noise with an unbiased subtraction. This proves to be an efficient method of reduce the error from the noise. We find that the total quark contribution to the proton spin is $0.29 \pm 0.07$. From this we deduce that the quark orbital angular mom…
We discuss the effects of the electromagnetic interaction in high-energy proton collisions with nuclei of large Z at strong coupling $λ=g^2N_c$. Using the holographic dual limit of large $N_c>λ\gg 1$, we describe the Reggeon exchange as a twisted surface and show that it gets essentially modified by the electromagnetic interaction.
Elastic Dijet Production in Electron Scattering on a Longitudinally Polarized Proton at Small $x$: A Portal to Orbital Angular Momentum Distributions
本文在小$x$光锥算符形式体系中计算电子-纵向极化质子弹性双喷注产生的DSA与SSA，表明DSA可稳健探测夸克和胶子OAM分布，而SSA提取尚不可行。
We discuss the potential impacts on the CMSSM of future LHC runs and possible electron-positron and higher-energy proton-proton colliders, considering searches for supersymmetry via MET events, precision electroweak physics, Higgs measurements and dark matter searches. We validate and present estimates of the physics reach for exclusion or discovery of supersymmetry via MET searches at the LHC, which should cover the low-mass regions of the CMSSM parameter space favoured in a recent global analysis. As we illustrate with a low-mass benchmark point, a discovery would make possible accurate LHC …
Exploring Short-Range Correlations in Symmetric Nuclei: Insights into Contacts and Entanglement Entropy
本文研究对称核中核子短程关联的轨道纠缠熵与Tan接触之间的关系，发现质子-质子对与中子-质子对的纠缠熵比值近似为2.0，并提出该标度关系对所有对称核普遍成立的可能解释。
Applying the connection between the parton Wigner distribution and orbital angular momentum (OAM), we investigate the probe of the gluon OAM in hard scattering processes at the planned electron-ion collider. We show that the single longitudinal target-spin asymmetry in the hard diffractive dijet production is very sensitive to the gluon OAM distribution. The associated spin asymmetry leads to a characteristic azimuthal angular correlation of $\sin(ϕ_q -ϕ_Δ)$, where $ϕ_Δ$ and $ϕ_q$ are the azimuthal angles of the proton momentum transfer and the relative transverse momentum between the quark-an…
A Lattice QCD approach to quark orbital angular momentum in the proton based on generalized transverse momentum-dependent parton distributions (GTMDs) is enhanced methodologically by incorporating a direct derivative technique. This improvement removes a significant numerical bias that had been seen to afflict results of a previous study. In particular, the value obtained for Ji quark orbital angular momentum is reconciled with the one obtained independently via Ji's sum rule, validating the GMTD approach. Since GTMDs simultaneously contain information about the quark impact parameter and tran…
We derive a new twist-3 partonic sum rule for the transverse spin of the proton, which involves the well-know quark spin structure function $g_T(x)=g_1(x)+g_2(x)$, the less-studied but known transverse gluon polarization density $ΔG_T(x)$, and quark and gluon canonical orbital angular momentum densities associated with transverse polarization. This is the counter part of the sum rule for the longitudinal spin of the proton derived by Jaffe and Manohar previously. We relate the partonic canonical orbital angular momentum densities to a new class of twist-3 generalized parton distribution functi…
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