Nucleon Tensor Research Articles

First simultaneous global QCD analysis of dihadron fragmentation functions and transversity parton distribution functions

We perform a comprehensive study within quantum chromodynamics (QCD) of dihadron observables in electron-positron annihilation, semi-inclusive deep-inelastic scattering, and proton-proton collisions, including recent cross section data from Belle and azimuthal asymmetries from STAR. We extract simultaneously for the first time π+π− dihadron fragmentation functions (DiFFs) and the nucleon transversity distributions for up and down quarks as well as antiquarks. For the transversity distributions we impose their small-x asymptotic behavior and the Soffer bound. In addition, we utilize a new definition of DiFFs that has a number density interpretation to then calculate expectation values for the dihadron invariant mass and momentum fraction. Furthermore, we investigate the compatibility of our transversity results with those from single-hadron fragmentation (from a transverse momentum dependent/collinear twist-3 framework) and the nucleon tensor charges computed in lattice QCD. We find a universal nature to all of this available information. Future measurements of dihadron production can significantly further this research, especially, as we show, those that are sensitive to the region of large parton momentum fractions. Published by the American Physical Society 2024

Global Analysis of SSAs and the Impact of the EIC and SoLID on Tensor Charge Extractions

Single transverse-spin asymmetries (SSAs) give great insight into the 3-dimensional structure of hadrons. We report on the first global QCD analysis of SSAs in semi-inclusive deep-inelastic scattering, electron-positron annihilation, Drell-Yan, and single-inclusive proton-proton collisions. One byproduct of the analysis is an extraction of the transversity function, from which the nucleon tensor charges can be computed, and we find, for the first time, agreement with lattice QCD for these quantities. Based on this analysis, we perform an impact study of future data on extractions of the nucleon tensor charges.

Nucleon isovector tensor charge from lattice QCD using chiral fermions

In this work we present the isovector flavor combination for the nucleon tensor charge extracted from lattice QCD simulations using overlap fermions on $N_f=2+1$ domain-wall configurations. The pion mass dependence is studied using six valence quark masses, each reproducing a value for the pion mass in the valence sector between 147 and 330 MeV. We investigate and eliminate systematic uncertainties due to contamination by excited states, by employing several values for the source-sink separation that span from 1 fm to 1.6 fm. We apply a chiral extrapolation in the valence sector using a quadratic and a logarithmic term to fit the pion mass dependence, which describes well the lattice data. The lattice matrix element is renormalized non-perturbatively, and the final result is $g_T=1.096(30)$ in the $\overline{\rm MS}$ scheme at a renormalization scale of 2 GeV.

Dressed quark tensor vertex and nucleon tensor charge

We construct the quark-antiquark scattering kernels of Bethe-Salpeter equation from the quark self-energy directly under two specific forms of quark-gluon vertices. The quark dressed tensor vertex is then calculated within this consistent framework and rainbow-ladder(RL) approximation. After employing a simplified nucleon model, the nucleon tensor charge can be defined with the tensor vertex. We then compute the tensor charge with the bare tensor vertex and the dressed vertices obtained in this framework and in RL approximation. The obtained results are consistent with the lattice QCD calculations. We also find that typically the gluon dressing effects suppress the nucleon tensor charge compared to the bare tensor vertex, by about $23\%$ for RL approximation, and turn to be about $13\%$ in this framework.

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

We report on the first global QCD analysis of the quark transversity distributions in the nucleon from semi-inclusive deep-inelastic scattering (SIDIS), using a new MonteCarlo method based on nested sampling and constraints on the isovector tensor charge g_{T} from lattice QCD. A simultaneous fit to the available SIDIS Collins asymmetry data is compatible with g_{T} values extracted from a comprehensive reanalysis of existing lattice simulations, in contrast to previous analyses, which found significantly smaller g_{T} values. The contributions to the nucleon tensor charge from u and d quarks are found to be δu=0.3(2) and δd=-0.7(2) at a scale Q^{2}=2 GeV^{2}.

Tensor force effect on the evolution of single-particle energies in some isotopic chains in the relativistic Hartree–Fock approximation

Within a nonlinear relativistic Hartree–Fock approximation combined with the BCS method, we study the effect of the nucleon–nucleon tensor force of the π-exchange potential on the spin- and pseudospin–orbit doublets along the Ca and Sn isotopic chains.We show how the self-consistent tensor force effect modifies the splitting of both kinds of doublets in an interdependent form, leading, quite generally, to opposite effects in the accomplishment of the spin and pseudospin symmetries (the one is restored, the other one deteriorates and vice versa). The ordering of the single-particle energy levels is crucial to this respect.Also, we observe a mutual dependence on the evolution of the shell closure gap Z = 50 and the energy band outside the core, along the Sn chain, as due to the tensor force. In fact, when the shell gap is quenched the outside energy band is enlarged, and vice versa. A reduction of the strength of the pion tensor force with respect to its experimental value from the nucleon–nucleon scattering is needed to get results closer to the experiment. Pairing correlations act to some extent in the opposite direction of the tensor term of the one-pion-exchange force.

The Tensor and the Scalar Charges of the Nucleon from Hadron Phenomenology

We discuss the impact of the determination of the nucleon tensor charge on searches for physics Beyond the Standard Model. We also comment on the future extraction of the subleading-twist PDF e(x) from Jefferson Lab soon-to-be-released Beam Spin Asymmetry data as well as from the expected data of CLAS12 and SoLID, as the latter is related to the scalar charge. These analyses are possible through the phenomenology of Dihadron Fragmentation Functions related processes, which we report on here as well.

Collinear parton distributions and the structure of the nucleon sea in a light-front meson-cloud model

The unpolarized, helicity and transversity parton distribution functions of the nucleon are studied within a convolution model where the bare nucleon is dressed by its virtual meson cloud. Using light-front time-ordered perturbation theory, the Fock states of the physical nucleon are expanded in a series involving a bare nucleon and two-particle, meson-baryon, states. The bare baryons and mesons are described with light-front wave functions (LFWFs) for the corresponding valence-parton components. Using a representation in terms of overlap of LFWFs, the role of the non-perturbative antiquark degrees of freedom and the valence quark contribution at the input scale of the model is discussed for the leading-twist collinear parton distributions. After introducing perturbative QCD effects through evolution to experimental scales, the results are compared with available data and phenomenological extractions. Predictions for the nucleon tensor charge are also presented, finding a very good agreement with recent phenomenological extractions.

Unveiling the nucleon tensor charge at Jefferson Lab: A study of the SoLID case

Future experiments at the Jefferson Lab 12 GeV upgrade, in particular, the Solenoidal Large Intensity Device (SoLID), aim at a very precise data set in the region where the partonic structure of the nucleon is dominated by the valence quarks. One of the main goals is to constrain the quark transversity distributions. We apply recent theoretical advances of the global QCD extraction of the transversity distributions to study the impact of future experimental data from the SoLID experiments. Especially, we develop a simple strategy based on the Hessian matrix analysis that allows one to estimate the uncertainties of the transversity quark distributions and their tensor charges extracted from SoLID data simulation. We find that the SoLID measurements with the proton and the effective neutron targets can improve the precision of the u- and d-quark transversity distributions up to one order of magnitude in the range 0.05 < x < 0.6.

Nucleon tensor form factors in a relativistic confined quark model

We present results for the isotriplet and isosinglet tensor form factors of the nucleon in the relativistic confined quark model. The model allows us to calculate not only their normalizations at ${Q}^{2}=0$ and the related tensor charges, but also the full ${Q}^{2}$-dependence. Our results are compared to existing data and predictions of other theoretical approaches. We stress the importance of these form factors for the phenomenology of physics beyond the Standard Model.

Phenomenology of Dihadron Fragmentation Function.

We report on the phenomenological results obtained through Dihadron Fragmentation Functions related processes. In 2015, an update on the fitting techniques for the Dihadron Fragmentation Functions has led to an improved extraction of the transversity PDF and, as a consequence, the nucleon tensor charge. We discuss the impact of the determination of the latter on search for physics Beyond the Standard Model, focusing on the error treatment. We also comment on the future of the extraction of the subleading-twist PDF e(x) from JLab soon-to-be-released Beam Spin Asymmetry data.

Erratum: Nucleon and pion structure with lattice QCD simulations at physical value of the pion mass [Phys. Rev. D92, 114513 (2015)

We present results on the nucleon scalar, axial and tensor charges as well as on the momentum fraction, and the helicity and transversity moments. The pion momentum fraction is also presented. The computation of these key observables is carried out using lattice QCD simulations at a physical value of the pion mass. The evaluation is based on gauge configurations generated with two degenerate sea quarks of twisted mass fermions with a clover term. We investigate excited states contributions with the nucleon quantum numbers by analyzing three sink-source time separations. We find that, for the scalar charge, excited states contribute significantly and to a less degree to the nucleon momentum fraction and helicity moment. Our analysis yields a value for the nucleon axial charge agrees with the experimental value and we predict a value of 1.027(62) in the $\overline{\text{MS}}$ scheme at 2 GeV for the isovector nucleon tensor charge directly at the physical point. The pion momentum fraction is found to be $\langle x\rangle_{u-d}^{\pi^\pm}=0.214(15)(^{+12}_{-9})$ in the $\overline{\rm MS}$ at 2 GeV.

Nucleon and pion structure with lattice QCD simulations at physical value of the pion mass

We present results on the nucleon scalar, axial, and tensor charges as well as on the momentum fraction, and the helicity and transversity moments. The pion momentum fraction is also presented. The computation of these key observables is carried out using lattice QCD simulations at a physical value of the pion mass. The evaluation is based on gauge configurations generated with two degenerate sea quarks of twisted mass fermions with a clover term. We investigate excited states contributions with the nucleon quantum numbers by analyzing three sink-source time separations. We find that, for the scalar charge, excited states contribute significantly and to a less degree to the nucleon momentum fraction and helicity moment. Our result for the nucleon axial charge agrees with the experimental value. Furthermore, we predict a value of 1.027(62) in the $\overline{\mathrm{MS}}$ scheme at 2 GeV for the isovector nucleon tensor charge directly at the physical point. The pion momentum fraction is found to be $⟨x{⟩}_{u\ensuremath{-}d}^{{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}}=0.214(15){(}_{\ensuremath{-}9}^{+12})$ in the $\overline{\mathrm{MS}}$ at 2 GeV.

Isovector and isoscalar tensor charges of the nucleon from lattice QCD

We present results for the iso-vector and flavor diagonal tensor charges $g^{u-d}_T$, $g^{u}_T$, $g^{d}_T$, and $g^{s}_T$ needed to probe novel tensor interactions at the TeV scale in neutron and nuclear $\beta$-decays and the contribution of the quark electric dipole moment (EDM) to the neutron EDM. The lattice QCD calculations were done using nine ensembles of gauge configurations generated by the MILC collaboration using the HISQ action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings $a \approx 0.06, 0.09$ and $0.12 $ fm and three quark masses corresponding to the pion masses $M_\pi \approx 130, 220$ and $310 $ MeV. Using estimates from these ensembles, we quantify all systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, volume and light quark masses for the connected contributions. The final estimates of the connected nucleon (proton) tensor charge for the iso-vector combination is $g_T^{u-d} = 1.020(76) $ in the $\bar{\text{MS}}$ scheme at $2$ GeV. The additional disconnected quark loop contributions needed for the flavor-diagonal matrix elements are calculated using a stochastic estimator employing the truncated solver method with the all-mode-averaging technique. We find that the size of the disconnected contribution is smaller than the statistical error in the connected contribution. This allows us to bound the disconnected contribution and include it as an additional uncertainty in the flavor-diagonal charges. After a continuum extrapolation, we find $g_T^{u} = 0.774(66) $, $g_T^{d} = -0.233(28) $ and $g_T^{u+d} = 0.541(67) $. The strangeness tensor charge, that can make a significant contribution to the neutron EDM due to the large ratio $m_s/m_{u,d}$, is $g_T^{s}=0.008(9)$ in the continuum limit.

Nucleon tensor charge from Collins azimuthal asymmetry measurements

We investigate the nucleon tensor charge from current experiments by a combined analysis of the Collins asymmetries in two hadron production in $e^+e^-$ annihilations and semi-inclusive hadron production in deep inelastic scattering processes. The transverse momentum dependent evolution is taken into account, for the first time, in the global fit of the Collins fragmentation functions and the quark transversity distributions at the approximate next-to-leading logarithmic order. We obtain the nucleon tensor charge contribution from up and down quarks as $\delta u=+0.30^{+0.12}_{-0.08}$ and $\delta d=-0.20_{-0.11}^{+0.28}$ at 90\% confidence level for momentum fraction $0.0065 \le x_B \le 0.35$ and $Q^2=$ 10 GeV$^2$.

Nucleon tensor charges and electric dipole moments

A symmetry-preserving Dyson-Schwinger equation treatment of a vector-vector contact interaction is used to compute dressed-quark-core contributions to the nucleon $\sigma$-term and tensor charges. The latter enable one to directly determine the effect of dressed-quark electric dipole moments (EDMs) on neutron and proton EDMs. The presence of strong scalar and axial-vector diquark correlations within ground-state baryons is a prediction of this approach. These correlations are active participants in all scattering events and thereby modify the contribution of the singly-represented valence-quark relative to that of the doubly-represented quark. Regarding the proton $\sigma$-term and that part of the proton mass which owes to explicit chiral symmetry breaking, with a realistic $d$-$u$ mass splitting the singly-represented $d$-quark contributes 37% more than the doubly-represented $u$-quark; and in connection with the proton's tensor charges, $\delta_T u$, $\delta_T d$, the ratio $\delta_T d/\delta_T u$ is 18% larger than anticipated from simple quark models. Of particular note, the size of $\delta_T u$ is a sensitive measure of the strength of dynamical chiral symmetry breaking; and $\delta_T d$ measures the amount of axial-vector diquark correlation within the proton, vanishing if such correlations are absent.

RECENT PROGRESS ON NUCLEON STRUCTURE WITH LATTICE QCD

I review recent progress made in the calculation of nucleon structure in lattice QCD. Due to space limitations, I will focus on a few specific topics: systematic control of lattice-QCD matrix elements, probing TeV-physics with the aid of nucleon tensor and scalar charges, and Bjorken-x dependence of nucleon parton distribution functions.

Nucleon tensor form factors induced by isovector and isoscalar currents in QCD

Using the most general form of the nucleon interpolating current, we calculate the tensor form factors of the nucleon within light cone QCD sum rules. A comparison of our results on tensor form factors with those of the chiral--soliton model and lattice QCD is given.

An x-space analysis of evolution equations: Soffer's inequality and the non-forward evolution

We analize the use of algorithms based in x-space for the solution of renormalization group equations of DGLAP-type and test their consistency by studying bounds among partons distributions - in our specific case Soffer's inequality and the perturbative behaviour of the nucleon tensor charge - to next-to-leading order in QCD . A discussion of the perturbative resummation implicit in these expansions using Mellin moments is included. We also comment on the (kinetic) proof of positivity of the evolution of $h_1$, using a kinetic analogy and illustrate the extension of the algorithm to the evolution of generalized parton distributions. We prove positivity of the non-forward evolution in a special case and illustrate a Fokker-Planck approximation to it.

FLAVOR-SPIN SYMMETRY AND THE TENSOR CHARGE

Exploiting an approximate phenomenological symmetry of the JPC = 1+- light axial vector mesons and using pole dominance, we calculate the flavor contributions to the nucleon tensor charge. The result depends on the decay constants of the axial vector mesons and their couplings to the nucleons.