First Monte Carlo Global Analysis of Nucleon Transversity with Lattice QCD Constraints

New Data-Driven Constraints on the Sign of Gluon Polarization in the Proton

Recently, the possible existence of negative gluon helicity Δg has been observed to be compatible with existing empirical constraints, including from jet production in polarized proton-proton collisions at the Relativistic Heavy Ion Collider, and lattice QCD data on polarized gluon Ioffe time distributions. We perform a new global analysis of polarized parton distributions in the proton with new constraints from the high-x region of deep-inelastic scattering (DIS). A dramatic reduction in the quality of the fit for the negative Δg replicas compared to those with positive Δg suggests that the negative Δg solution cannot simultaneously account for high-x polarized DIS data along with lattice and polarized jet data.

Transversity Distributions and Tensor Charges of the Nucleon: Extraction from Dihadron Production and Their Universal Nature

We perform the first global quantum chromodynamics (QCD) analysis of dihadron production for a comprehensive set of data in electron-positron annihilation, semi-inclusive deep-inelastic scattering, and proton-proton collisions, from which we extract simultaneously the transversity distributions of the nucleon and π^{+}π^{-} dihadron fragmentation functions. We incorporate in our fits known theoretical constraints on transversity, namely, its small-x asymptotic behavior and the Soffer bound. We furthermore show that lattice-QCD results for the tensor charges can be successfully included in the analysis. This resolves the previously reported incompatibility between the tensor charges extracted from dihadron production data and lattice QCD. We also find agreement with results for the transversity and tensor charges obtained from measurements on single-hadron production. Overall, our work demonstrates for the first time the universal nature of all available information for the transversity distributions and the tensor charges of the nucleon.

Nucleon Transversity Distribution in the Continuum and Physical Mass Limit from Lattice QCD

We report a state-of-the-art lattice QCD calculation of the isovector quark transversity distribution of the proton in the continuum and physical mass limit using large-momentum effective theory. The calculation is done at four lattice spacings a={0.098,0.085,0.064,0.049}  fm and various pion masses ranging between 220 and 350 MeV, with proton momenta up to 2.8 GeV. The result is nonperturbatively renormalized in the hybrid scheme with self-renormalization, which treats the infrared physics at large correlation distance properly, and extrapolated to the continuum, physical mass, and infinite momentum limit. We also compare with recent global analyses for the nucleon isovector quark transversity distribution.

Global QCD Analysis of Pion Parton Distributions with Threshold Resummation

We perform the first global QCD analysis of pion valence, sea quark, and gluon distributions within a Bayesian Monte Carlo framework with threshold resummation on Drell-Yan cross sections at next-to-leading log accuracy. Exploring various treatments of resummation, we find that the large-x asymptotics of the valence quark distribution ∼(1-x)^{β_{v}} can differ significantly, with β_{v} ranging from ≈1 to >2.5 at the input scale. Regardless of the specific implementation, however, the resummation induced redistribution of the momentum between valence quarks and gluons boosts the total momentum carried by gluons to ≈40%, increasing the gluon contribution to the pion mass to ≈40  MeV.

Lattice QCD Constraints on the Parton Distribution Functions of ^{3}He

The fraction of the longitudinal momentum of ^{3}He that is carried by the isovector combination of u and d quarks is determined using lattice QCD for the first time. The ratio of this combination to that in the constituent nucleons is found to be consistent with unity at the few-percent level from calculations with quark masses corresponding to m_{π}∼800  MeV. With a naive extrapolation to the physical quark masses, this constraint is consistent with, and more precise than, determinations from global nuclear parton distribution function fits through the nnnpdf framework. It is thus concretely demonstrated that lattice QCD calculations of light nuclei have imminent potential to enable more precise determinations of the u and d parton distributions in light nuclei and to reveal the QCD origins of the EMC effect.

The x-dependence of hadronic parton distributions: A review on the progress of lattice QCD

In this article, we review recent lattice calculations on the x-dependence of parton distributions, with the latter providing information on hadron structure. These calculations are based on matrix elements of boosted hadrons coupled to non-local operators and can be related to the standard, light-cone distribution functions via an appropriate factorization formalism. There is significant progress in several directions, including calculations of flavor-singlet parton distribution functions (PDFs), first calculations of generalized parton distributions (GPDs), as well as the implementation of some of the approaches for the transverse-momentum-dependent PDFs (TMD PDFs). This new direction of lattice calculations is particularly interesting for phenomenological fits on experimental data sets, as the lattice results can help improve the constraints on the distribution functions.

Nucleon Matrix Elements of the Antisymmetric Quark Tensor

If physics beyond the standard model enters well above the electroweak scale, its low-energy effects are described by standard model effective field theory. Already, at dimension 6, many operators involve the antisymmetric quark tensor q[over ¯]σ^{μν}q, whose matrix elements are difficult to constrain from experiment, Ward identities, or low-energy theorems, in contrast to the corresponding vector and axial-vector or even scalar and pseudoscalar currents. However, with normalizations determined from lattice QCD, analyticity and unitarity often allow one to predict the momentum dependence in a large kinematic range. Starting from recent results in the meson sector, we extend this method to the nucleon case and, in combination with pole dominance, provide a comprehensive assessment of the current status of the nucleon form factors of the quark tensor.

Parton Distribution Functions and Lattice QCD

Recently, there have been rapid developments in lattice-QCD calculations of proton structure, especially in the parton distribution functions (PDFs). We overcame a longstanding obstacle and for the first time in lattice-QCD are able to directly calculate the Bjorken-x dependence of the quark, helicity and transversity distributions. The PDFs are obtained using the large-momentum effective field theory (LaMET) framework where the full Bjorken-x dependence of finite-momentum PDFs, called “quasi-PDFs”, can be calculated on the lattice. The quasi-PDF nucleon matrix elements are renormalized non-perturbatively in RI/MOM-scheme. Following a nonperturbative renormalization of the parton quasi-distribution in a regularization-independent momentum-subtraction scheme, we establish its matching to the $ \overline {{\rm{MS}}} $ PDF and calculate the non-singlet matching coefficient at next-to-leading order in perturbation theory. In this proceeding, I will show the progress that has been made in recent years, highlighting the latest state-of-the art PDF calculations at the physical pion mass. Future impacts on the large-x global PDF fits are also discussed.

First Monte Carlo Global QCD Analysis of Pion Parton Distributions

We perform the first global QCD analysis of parton distribution functions (PDFs) in the pion, combining πA Drell-Yan data with leading neutron electroproduction from HERA within a Monte Carlo approach based on nested sampling. Inclusion of the HERA data allows the pion PDFs to be determined down to much lower values of x, with relatively weak model dependence from uncertainties in the chiral splitting function. The combined analysis reveals that gluons carry a significantly higher pion momentum fraction, ∼30%, than that inferred from Drell-Yan data alone, with sea quarks carrying a somewhat smaller fraction, ∼15%, at the input scale. Within the same effective theory framework, the chiral splitting function and pion PDFs can be used to describe the d[over ¯]-u[over ¯] asymmetry in the proton.

Light-Cone Parton Distribution Functions from Lattice QCD

We extract parton distribution functions (PDFs) of the nucleon from lattice QCD using an ensemble of gauge field configurations simulated with light quark masses fixed to their physical values. Theoretical and algorithmic improvements that allow such a calculation include momentum smearing to reach large nucleon boosts with reduced statistical errors, nonperturbative renormalization, target mass corrections, and a novel modified matching of lattice QCD results to connect to what is extracted from experimental measurements. We give results on the unpolarized and helicity PDFs in the modified minimal subtraction scheme at a scale of 2 GeV and reproduce the main features of the experimentally determined quantities, showing an overlap for a range of Bjorken-x values. This first direct nonperturbative evaluation opens a most promising path to compute PDFs in an ab initio way on the lattice and provides a framework for investigating also a wider class of similar quantities, which require the evaluation of hadronic matrix elements of nonlocal operators.