Flavor Decomposition for the Proton Helicity Parton Distribution Functions
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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Flavor decomposition of the nucleon unpolarized, helicity, and transversity parton distribution functions from lattice QCD simulations
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79 ASTRONOMY AND ASTROPHYSICS↗
Sea Asymmetry from Polarized W Boson Production
We present the results of a global QCD analysis of helicity parton distribution functions (PDFs) that includes the latest polarized W-lepton production data from the STAR collaboration at the Relativistic Heavy-Ion Collider (RHIC). This data allows the first extraction of a nonzero helicity light-quark sea asymmetry within a simultaneous global QCD analysis of unpolarized and helicity PDFs.
Cocuzza, Christopher↗
Proton isovector helicity PDF at NNLO and the twist-3 moment $\tilde{d}$ 2 from lattice QCD at physical quark masses
We present a lattice quantum chromodynamics calculation of the 𝑥-dependent isovector quark helicity parton distribution function (PDF) of the proton in the large momentum effective theory (LaMET) framework. Through operator product expansion (OPE) we also extract the $\tilde{d}$ 2 moment of the twist-3 PDF 𝑔 𝑇 (𝑥) for the first time in the $\overline{MS}$ scheme, which is proportional to the average color Lorentz force experienced by the quark in the proton. This calculation is performed on a lattice of spacing 𝑎 =0.076 fm at physical quark masses. The quasi-PDF matrix elements are measured in proton states boosted to momenta 𝑃 𝑧 ={0,0.25,1.02,1.53} GeV. We first extract the lowest few helicity PDF moments from the renormalization-group (RG) invariant ratios of the matrix elements with OPE. Combined with the matrix elements relevant for 𝑔 𝑇 (𝑥), we obtain $\tilde{d}$$^{u-d}_2$(2 GeV) =0.0024(46) at next-to-leading order in $\overline{MS}$. Then, the helicity quasi-PDF matrix elements are renormalized in the hybrid scheme with linear renormalon resummation and Fourier transformed to the 𝑥-space after an asymptotic extrapolation. The quasi-PDF is perturbatively matched to the $\overline{MS}$ PDF with RG and threshold resummations at next-to-leading power and next-to-next-to-leading logarithmic accuracies. After resummations, we determine the PDF in the region 𝑥 ∈[0.25,0.75]. The end-point regions are then parametrized, combined with the LaMET prediction at moderate 𝑥, and fitted to the short-distance matrix elements in coordinate space.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Directed flow from parton spin-orbit coupling in $pp$ and $pA$ collisions
We point out a novel mechanism to generate cos φ two-particle azimuthal correlation (‘directed flow’) in unpolarized proton-proton and proton-nucleus collisions in the forward rapidity region of the projectile proton. This is a direct consequence of the recently discovered strong spin-orbit coupling in gluons at small-x. The observable simultaneously serves as a unique probe into the double helicity parton distribution functions of the proton.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
First study of polarized proton-proton scattering with small-𝑥 helicity evolution
We perform a phenomenological study of helicity-dependent parton distribution functions (PDFs) using small-𝑥 helicity evolution equations, incorporating for the first time single-inclusive jet production data in polarized proton-proton (𝑝𝑝) scattering at parton momentum fractions 𝑥 <0.1. We also simultaneously include double-longitudinal spin asymmetries in inclusive and semi-inclusive deep-inelastic scattering probing 𝑥 <0.1. Employing the polarized small-𝑥 pure-glue calculation of 𝑝𝑝 → 𝑔𝑋 for the jet production cross section, we modify the large-𝑁 𝑐 &𝑁 𝑓 KPS-CTT evolution equations by setting 𝑁 𝑓 = 0 to replicate the large-𝑁𝑐 (pure-glue) limit, while retaining external quark flavors for the spinor field operators. We find that the 𝑝𝑝 data have a considerable impact on the helicity PDFs at small 𝑥, reducing their uncertainties and leading to a total quark and gluon helicity in the proton for 𝑥 < 0.1 of −0.04 ±0.23. Combining our analysis with a recent JAM helicity PDF analysis of the world polarized data, which includes 𝑥 > 0.1, we find a total quark and gluon helicity contribution for 𝑥 >10 −7 of between 0.02 and 0.51.
Adamiak, Daniel [Michigan State University] (ORCID↗
Lattice QCD Benchmark of Proton Helicity and Flavor-Dependent Unpolarized Transverse Momentum-Dependent Parton Distribution Functions at Physical Quark Masses
We present the first lattice QCD calculations of the isovector helicity transverse momentum-dependent parton distribution function (TMDPDF) and the flavor-dependent unpolarized TMDPDFs for up and down quarks in the proton. Our computations utilize domain-wall fermion discretization with physical quark masses. Employing Coulomb-gauge-fixed quark correlation functions within the large-momentum effective theory framework, we access nonperturbative transverse quark separations 𝑏 𝑇 up to approximately 1 fm, corresponding to transverse momenta as low as 200 MeV. Based on the quasi-TMD factorization theorem, we construct renormalization-group–invariant ratios that are equal to the corresponding light-cone TMDPDF ratios. At moderate 𝑥, our results reveal that the isovector helicity and unpolarized TMDPDFs exhibit nearly identical transverse structure up to a normalization factor, and the unpolarized distributions display only mild flavor dependence. These findings not only support key trends observed in recent global analyses but also provide robust, nonperturbative constraints that can distinguish between different parameterizations. This Letter establishes a first-principles benchmark for TMDPDFs, offering valuable input for ongoing and future experimental efforts to map the proton’s three-dimensional structure.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Evaluation of longitudinal double-spin asymmetry measurements in semi-inclusive deep-inelastic scattering from the proton for the ECCE detector design
The evaluation of the measurement of double-spin asymmetries for charge-separated pions and kaons produced in deep-inelastic scattering from the proton using the ECCE detector design concept is presented, for the combinations of lepton and hadron beam energies of 5 × 41 GeV 2 and 18 × 275 GeV 2 . The study uses unpolarised simulated data that are processed through a full GEANT simulation of the detector. These data are then reweighted at the parton level with DSSV helicity distributions and DSS fragmentation functions, in order to generate the relevant asymmetries, and subsequently analysed. Furthermore, the performed analysis shows that the ECCE detector concept provides the resolution and acceptance, with a broad coverage in kinematic phase space, needed for a robust extraction of asymmetries. This, in turn, allows for a precise extraction of sea-quark helicity distributions.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Gluon helicity in the nucleon from lattice QCD and machine learning
We present the first lattice QCD determination of the light cone gluon helicity correlation parton distribution function (PDF) with numerical evidence toward disfavoring negative gluon polarization in the nucleon. We present a solution for eliminating an inevitable contamination term that dominates the Euclidean correlations and makes determining gluon helicity PDF unfeasible. The proposed synergy between lattice QCD and artificial intelligence offers a superior platform to alleviate the defining challenge of extracting quark and gluon PDFs from the lattice data that are available in a limited domain due to a finite range of accessible hadron momenta. We suggest a systematically improvable method to extract PDFs from the lattice data, independent of inadequate parametrizations. The result of the gluon helicity will improve our understanding of the role of spin in the strong interaction and the nucleon-spin structure.
Lattice QCD↗
Non-singlet quark helicity $\mathrm{PDF}$s of the nucleon from pseudo-distributions
The non-singlet helicity quark parton distribution functions (PDFs) of the nucleon are determined from lattice QCD, by jointly leveraging pseudo-distributions and the distillation spatial smearing paradigm. A Lorentz decomposition of appropriately isolated space-like matrix elements reveals pseudo-distributions that contain information on the leading-twist helicity PDFs, as well as an invariant amplitude that induces an additional z 2 contamination of the leading-twist signal. An analysis of the short-distance behavior of the space-like matrix elements using matching coefficients computed to next-to-leading order (NLO) exposes the desired PDF up to this additional z 2 contamination. Due to the non-conservation of the axial current, we elect to isolate the helicity PDFs normalized by the nucleon axial charge at the same scale μ 2 . The leading-twist helicity PDFs as well as several sources of systematic error, including higher-twist effects, discretization errors, and the aforementioned z 2 contaminating amplitude are jointly determined by characterizing the computed pseudo-distribution in a basis of Jacobi polynomials. The Akaike Information Criterion is exploited to effectively average over distinct model parameterizations and cuts on the pseudo-distribution. Encouraging agreement is observed with recent global analyses of each non-singlet quark helicity PDF, notably a rather small non-singlet anti-quark helicity PDF for all quark momentum fractions.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Helicity at small x: oscillations generated by bringing back the quarks
We construct a numerical solution of the recently-derived large-N c &N f small-x helicity evolution equations with the aim to establish the small-x asymptotics of the quark helicity distribution beyond the large-N c limit explored previously in the same framework. (Here N c and N f are the numbers of quark colors and flavors.) While the large-N c helicity evolution involves gluons only, the large-N c &N f evolution includes contributions from quarks as well. We find that adding quarks to the evolution makes quark helicity distribution oscillate as a function of x. Our numerical results in the large-N c &N f limit lead to the x-dependence of the flavor-singlet quark helicity distribution which is well-approximated by $$ {\left.\Delta \Sigma \left(x,{Q}^2\right)\right|}_{\mathrm{large}\hbox{-} {N}_c\&{N}_f}\sim {\left(\frac{1}{x}\right)}^{\alpha_h^q}\cos \left[{\omega}_q\ln \left(\frac{1}{x}\right)+{\varphi}_q\right]. $$. The power $α^{q}_{h}$ exhibits a weak N f -dependence, and, for all Nf values considered, remains very close to $α^{q}_{h}$(N f =0)=$\left(4/\sqrt{3}\right)\sqrt{\alpha_s{N}_c/\left(2\pi \right)}$ obtained earlier in the large-N c limit. The novel oscillation frequency ω q and phase shift φ q depend more strongly on the number of flavors N f (with ω q = 0 in the pure-glue large-N c limit). The typical period of oscillations for ΔΣ is rather long, spanning many units of rapidity. We speculate whether the oscillations we find are related to the sign variation with x seen in the strange quark helicity distribution extracted from the data.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Proton Spin Structure from Simultaneous Monte Carlo Global QCD Analysis
Despite the great effort and achievements made towards understanding proton spin structure in the past few decades, a complete picture is still elusive. Parton distribution functions (PDFs), which in quantum chromodynamics (QCD) encode the momentum and helicity distributions of quarks and gluons inside a proton, provide the means by which to quantify the proton structure information. Being inherently nonperturbative, PDFs have to be extracted from unpolarized and polarized lepton-hadron and hadron-hadron scattering data. In particular, experiments that measure unpolarized and polarized jet observables can provide insight into the momentum and helicity distributions of gluons, which have generally been more difficult to determine reliably than those of quarks. In the past, extraction of the spin-averaged and spin-dependent (or helicity) PDFs has been performed in separate analyses. In this thesis, we perform the first simultaneous extraction of both types of quantities from deep-inelastic scattering (DIS), Drell-Yan and single jet observables, within the Monte Carlo global QCD analysis framework developed by the Jefferson Lab Angular Momentum (JAM) Collaboration. The results from this work indicate that the gluon helicity distributions depend rather strongly on the theory assumptions on which the global analysis is based, which calls for the need of measurements with higher precision. As an application of the new simultaneous JAM analysis, we perform an impact study for future Electron-Ion Collider (EIC) data with parity-conserving and parity-violating polarization asymmetries on quark and gluon helicity distributions in the proton. The extrapolation of structure functions from the current data is studied for the first time in the context of the impact study. Theory assumptions, such as SU(2) and SU(3) flavor symmetries, are also studied to give a more thorough understanding of the impact of EIC pseudodata on proton spin structure.
Zhou, Yiyu↗
Gluon helicity from global analysis of experimental data and lattice QCD Ioffe time distributions
We perform a new global analysis of spin-dependent parton distribution functions with the inclusion of Ioffe time pseudodistributions computed in lattice QCD (LQCD), which are directly sensitive to the gluon helicity distribution, Δ g . These lattice data have an analogous relationship to parton distributions as do experimental cross sections, and can be readily included in global analyses. We focus in particular on the constraining capability of current LQCD data on the sign of Δ g at intermediate parton momentum fractions x , which was recently brought into question by analysis of data in the absence of parton positivity constraints. We find that present LQCD data cannot discriminate between positive and negative Δ g solutions, although significant changes in the solutions for both the gluon and quark sectors are observed. Published by the American Physical Society 2024
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Rapidity-dependent spin decomposition of the nucleon
We revisit the two-dimensional Fourier transform of generalized parton distributions (GPDs) at nonzero skewness. At 𝜂 = 0 it reduces to the standard impact-parameter density, while at 𝜂 ≠ 0 it is an off-forward amplitude that we interpret as a genuine parton–nucleon correlation. Its overall strength (the transverse-plane integral of the density) is fixed by the GPD at the kinematic point 𝑡 =−𝑐 𝜂 =−4𝜂 2 𝑚$^{2}_{𝑁}$/(1 − 𝜂 2 ) and decreases monotonically with the rapidity gap Δ𝑦 = ln[(1+𝜂)/(1−𝜂)] = 2 artanh(𝜂). This rapidity dependence implies rapidity-modified Ji identities that connect helicity, orbital, and total angular momenta of the correlation in closed form. To quantify these effects, we construct leading-twist quark and gluon GPDs in a string-based conformal framework: conformal moments are parametrized by linear open- and closed-string Regge trajectories with slopes constrained by parton distribution functions (PDFs), hadron/glueball spectroscopy, and form-factor data, and GPDs are reconstructed over the full (𝑥,𝜂,𝑡) domain by Mellin-Barnes inversion with next-to-leading order evolution. We find qualitative agreement (and fair quantitative agreement within quoted uncertainties) for several moments and selected nonsinglet 𝑥-space channels at 𝜇 = 2 GeV when compared with lattice QCD, while we also identify channels with visible tension and discuss likely sources (PDF priors and 𝑡-slope systematics).
Gauge-gravity dualities↗
Quark and gluon helicity evolution at small x: revised and updated
We revisit the problem of small Bjorken-x evolution of the gluon and flavor-singlet quark helicity distributions in the shock wave (s-channel) formalism. Earlier works on the subject in the same framework resulted in an evolution equation for the gluon field-strength F 12 and quark “axial current” $\overline{\psi}\gamma$ + γ 5 ψ operators (sandwiched between the appropriate light-cone Wilson lines) in the double-logarithmic approximation (summing powers of α s ln 2 (1/x) with α s the strong coupling constant). In this work, we observe that an important mixing of the above operators with another gluon operator, ${}_D{}^{\leftarrow i} {}_D{}^{i}$, also sandwiched between the light-cone Wilson lines (with the repeated transverse index i = 1, 2 summed over), was missing in the previous works. This operator has the physical meaning of the sub-eikonal (covariant) phase: its contribution to helicity evolution is shown to be proportional to another sub-eikonal operator, ${}_D{}^{i} {}_D{}^{\leftarrow i}$, which is related to the Jaffe-Manohar polarized gluon distribution. In this work we include this new operator into small-x helicity evolution, and construct novel evolution equations mixing all three operators (${}_D{}^{i} {}_D{}^{\leftarrow i}$, F 12 , and $\overline{\psi}\gamma$ + γ 5 ψ), generalizing the results of . We also construct closed double-logarithmic evolution equations in the large-N c and large-N c &N f limits, with N c and N f the numbers of quark colors and flavors, respectively. Solving the large-N c equations numerically we obtain the following small-x asymptotics of the quark and gluon helicity distributions ΔΣ and ΔG, along with the g 1 structure function, $$ \Delta \Sigma \left(x,{Q}^2\right)\sim \Delta G\left(x,{Q}^2\right)\sim {g}_1\left(x,{Q}^2\right)\sim {\left(\frac{1}{x}\right)}^{3.66\sqrt{\frac{\alpha_s{N}_c}{2\pi }}} $$ in complete agreement with the earlier work by Bartels, Ermolaev and Ryskin.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Physical implications of the extrapolation and statistical bootstrap of nucleon structure function ratios F 2 n F 2 p for mirror nuclei He 3 and H 3
A nuclear physics example of statistical bootstrap is used on the MARATHON nucleon structure function ratio data in the quark momentum fraction regions x B → 0 and x B → 1. The extrapolated F 2 ratio as quark momentum fraction x B → 1 is $\frac{F^n_2}{F^p_2}$ → 0.4 ± 0.05 and this value is compared to theoretical predictions. The extrapolated ratio when x B → 0 favors the simple model of isospin symmetry with the complete dominance of sea quarks at low momentum fraction. At high- x B , the proton quark distribution function ratio d/u is derived from the F 2 ratio and found to be d/u → 1/6. Our extrapolated values for both the $\frac{F^n_2}{F^p_2}$ ratio and the d/u parton distribution function ratio are within uncertainties of perturbative QCD values from quark counting, helicity conservation arguments, and a Dyson-Schwinger equation with a contact interaction model. In addition, it is possible to match the statistical bootstrap value to theoretical predictions by allowing two compatible models to act simultaneously in the nucleon wave function. Finally, one such example is nucleon wave functions composed of a linear combination of a quark-diquark state and a three-valence quark correlated state with coefficients that combine to give the extrapolated F 2 ratio at x B = 1.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Small-𝑥 asymptotics of the leading-twist flavor-singlet quark TMDs
In this paper, we investigate the small-𝑥 behavior of the flavor-singlet, leading-twist quark transverse-momentum-dependent parton distribution functions (TMDs) using the light-cone operator treatment. This formalism allows us to express TMD operators at small 𝑥 in terms of polarized dipole amplitudes, enabling a systematic approach to their small-𝑥 evolution. We derive the evolution equations for these TMDs and solve them within the large-𝑁 𝑐 approximation under the linearized, double-logarithmic approximation, where 𝑁 𝑐 represents the number of quark colors. Expanding on previous work on unpolarized and helicity TMDs, we present the small-𝑥 asymptotics for a comprehensive set of TMDs, including the Sivers function, helicity worm-gear, transversity, pretzelosity, Boer-Mulders, and transversity worm-gear distributions. Our results provide a complete picture of the small-𝑥 asymptotic behavior for all leading-twist flavor-singlet quark TMDs. We also discuss the implications of our findings for phenomenological applications and outline potential avenues for further research, particularly in understanding nonlinear effects and extending beyond the double-logarithmic approximation and large-𝑁 𝑐 approximations.
Adamiak, Daniel [Thomas Jefferson National Acceler↗
Measurement of the polarizations of prompt and non-prompt J/ψ and ψ ( 2S ) mesons produced in pp collisions at s = 13 TeV
The polarizations of prompt and non-prompt Image 2 and ψ ( 2S ) mesons are measured in proton-proton collisions at s = 13 TeV, using data samples collected by the CMS experiment in 2017 and 2018, corresponding to a total integrated luminosity of 103.3 fb − 1 . Based on the analysis of the dimuon decay angular distributions in the helicity frame, the polar anisotropy, λ ϑ , is measured as a function of the transverse momentum, p T , of the charmonium states, in the 25–120 and 20–100 GeV ranges for the Image 2 and ψ ( 2S ) , respectively. The non-prompt polarizations agree with predictions based on the hypothesis that, for p T ≳ 25 GeV , the non-prompt Image 2 and ψ ( 2S ) are predominantly produced in two-body B meson decays. The prompt results clearly exclude strong transverse polarizations, even for p T exceeding 30 times the Image 2 mass, where λ ϑ tends to an asymptotic value around 0.3. Taken together with previous measurements, by CMS and LHCb at s = 7 TeV, the prompt polarizations show a significant variation with p T , at low p T .
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗