Research

The research we perform furthers our knowledge of observables sensitive to parton intrinsic transverse motion and correlations, which allow for a 3D imaging of hadrons in momentum space. This includes performing a global analysis of data from various experiments sensitive to the spin of hadrons in order to extract the relevant functions, using an iterative Monte Carlo routine, that encode their internal structure.  These functions are then used to make predictions for upcoming measurements at Brookhaven National Lab's Relativistic Heavy Ion Collider (BNL-RHIC), Jefferson Lab's 12-GeV upgrade (JLab-12), and the future Electron-Ion Collider (EIC). Since a rigorous theoretical formalism is needed in order to interpret such experimental data, our research also attempts to solidify the framework used in spin observables through higher-order calculations within QCD. In addition, our research investigates certain aspects of how the proton spin arises from its constituent partons by analyzing how much of this spin is due to partons that carry only a small fraction of the proton's momentum.  Most of our research falls under the activities of the Jefferson Lab Angular Momentum (JAM) Collaboration.

This is an image of how (unpolarized) up and down quarks move inside a transversely polarized proton, based on an extraction of the so-called Sivers function from Phys. Rev. D 102, 054002 (2020) [arXiv:2002.08384 [hep-ph]] (“Origin of single transverse-spin asymmetries in high-energy collisions”).  The x- and y-components of the transverse momenta of the up and down quarks are shown along with the probability for a quark to carry that momentum (indicated by the different colors, with the scale given by the bar on the right).  The proton has its spin oriented in the y (vertical) direction and is moving out of the screen.  These results show that the quark distribution is distorted, in that down quarks tend to shift off to the left and up quarks to the right.

RECENT HIGHLIGHTS

New framework for the extraction of dihadron fragmentation functions, and the universality of transversity PDFs and tensor charges of the nucleon

An important class of reactions is where two hadrons are detected from a single parton fragmentation, which makes one sensitive to dihadron FFs (DiFFs).  A key feature of any quantum field-theoretic definition of a PDF or FF is that they are number densities in a parton model framework.  This had not been the case for DiFFs for almost 25 years.  In Phys. Rev. Lett. 132, 011902 (2024) [arXiv:2305.11995 [hep-ph]] (“Number density interpretation of dihadron fragmentation functions”) we presented a new quantum field-theoretic definition of fully unintegrated DiFFs as well as a generalized version for n-hadron fragmentation functions. We demonstrated that this definition allows certain sum rules to be satisfied, making it consistent with a number density interpretation. Moreover, we showed how our corresponding so-called extended DiFFs that enter existing phenomenological studies are number densities and also derived their evolution equations. Within this new framework, DiFFs extracted from experimental measurements now have a clear physical meaning.  For example, our extraction of D1(z,Mh) in arXiv:2308.14857 [hep-ph] (“First Simultaneous Global QCD Analysis of Dihadron Fragmentation Functions and Transversity Parton Distribution Functions”) gives a density in the total momentum fraction z and invariant mass Mh of the number of hadron pairs fragmenting from a parton.

This figure shows a 3D plot of the DiFFs D1(z,Mh) for the up, strange, charm, and bottom quarks for the case of fragmentation into a oppositely charged pion pair.

One of the main benefits of observables with dihadron fragmentation is that more azimuthal modulations survive the integration over transverse momentum than in the situation where only a single hadron is detected.  This allows the transversity PDF to be extracted along with DiFFs in a collinear framework.  We performed such a simultaneous QCD global analysis in arXiv:2306.12998 [hep-ph] (“Transversity distributions and tensor charges of the nucleon: extraction from dihadron production and their universal nature”) and arXiv:2308.14857 [hep-ph] (“First Simultaneous Global QCD Analysis of Dihadron Fragmentation Functions and Transversity Parton Distribution Functions”).  We also showed consistency in the tensor charges of the nucleon calculated from these transversity PDFs and those from our TMD/collinear twist-3 analysis as well as computations in lattice QCD. Thus, we demonstrated, for the first time, the universal nature of all available information on the transversity PDFs and tensor charges of the nucleon. 

The tensor charges are especially important to other areas of nuclear physics research.  The ability to measure certain beyond the Standard Model (BSM) couplings in neutron beta decay relies on knowledge of the isovector tensor charge gT, which is given by the up and down quark tensor charges, δu and δd, through gT = δu − δd. The quark tensor charges themselves are ingredients for BSM physics in computing the nucleon electric dipole moment from those of the quarks. Therefore, it is crucial to have precise values for δu, δd, and gT and compatibility between different techniques used for their determination.

This figure shows (left) the up and down quark transversity PDFs from our results (JAMDiFF) both without (red) and with (blue) lattice QCD data included in the fit as well as (right) the δu, δd tensor charges.  They are compared to those from JAM3D*, Radici-Bacchetta (2018), and lattice QCD (PNDME and ETMC). 

Global analysis of polarized DIS & SIDIS data with small-x helicity evolution

The proton's spin of 1/2 dynamically arises from its constituent quarks and gluons.  How much each of the spin and orbital angular momenta of the quarks and gluons contributes to this 1/2 remains one of the outstanding puzzles in hadron structure physics.  At very high energy, partons carry a very small fraction x of the proton's momentum.  These "small-x partons" are able to contribute to the proton spin, yet the exact amount they give has not been precisely determined due to the lack of measurements in that region.  In Phys. Rev. D 104, L031501 (2021) [arXiv:2102.06159 [hep-ph]] (“First analysis of world polarized DIS data with small-x helicity evolution”) we used the Kovchegov-Pitonyak-Sievert (KPS) small-x helicity evolution equations to extract the g1 structure function from the world polarized DIS data and made a genuine prediction for its behavior at smaller x with well-controlled uncertainties.  We also studied the impact of the future EIC on the analysis.  Since even with the EIC, the x coverage is limited to around 0.00001, our formalism is mandatory to accurately determine the full contribution to the proton's spin from small-x partons.

In Phys. Rev. D 108, 114007 (2023) [arXiv:2308.07461 [hep-ph]] (“Global analysis of polarized DIS & SIDIS data with improved small-x helicity evolution”) we analyzed the world polarized deep-inelastic scattering (DIS) and semi-inclusive DIS (SIDIS) data at low values of x < 0.1, using small-x evolution equations for the flavor singlet and nonsinglet helicity parton distribution functions (hPDFs). The hPDFs for quarks, antiquarks, and gluons were extracted and evolved to lower values of x to make predictions for the future Electron-Ion Collider (EIC). We improved on our earlier work by employing the more realistic large-Nc & Nf limit of the revised small-x helicity evolution (KPS-CTT), and incorporating running coupling corrections along with SIDIS data into the fit.  While the existing low-x polarized DIS and SIDIS data were insufficient to constrain the initial conditions for the polarized dipole amplitudes in the helicity evolution equations, future EIC data will allow more precise predictions for hPDFs and the g1 structure function for x values beyond those probed at the EIC. 

This figure shows (top panel) the quark and gluon helicity PDFs vs. x < 0.1, (bottom left) the quark flavor singlet helicity distribution, and (bottom right) the g1 structure function along with EIC impact studies, all extracted using small-x helicity evolution.

Tomography of pions and protons via TMDs

Decades of high-energy experiments have provided data allowing for the high resolution of the longitudinal structure of protons, and to a lesser extent also of pions. The information on the transverse structure of hadrons is comparatively less well known. In particular, achieving a 3-dimensional mapping of internal hadron structure requires sensitivity to both collinear and transverse parton degrees of freedom, which can be encoded in transverse momentum dependent distributions (TMDs).  In Phys. Rev. D 108, L091504 (2023) [arXiv:2302.01192 [hep-ph]] (“Tomography of pions and protons via transverse momentum dependent distributions”) we performed the first simultaneous extraction of parton collinear and transverse degrees of freedom from low-energy fixed-target Drell-Yan data in order to compare the TMDs of the pion and proton. We demonstrated that the transverse separation of the quark field bT encoded in TMDs of the pion is more than 4σ smaller than that of the proton. Additionally, we found the transverse separation of the quark field decreases as its longitudinal momentum fraction decreases, possibly indicating the onset of a quark-antiquark condensate. In studying the nuclear modification of TMDs, we discovered clear evidence for a transverse EMC effect. 

This figure shows (left) the TMDs for the pion and proton as a function of bT for various x values, (right top) the average bT for the u quark in the proton and in the pion for two Q values as a function of x, and (right bottom) the ratio of the average bT of the u quark in a proton bound in a tungsten nucleus to that of a free proton.  

Numerical analysis of longitudinal-transverse double-spin asymmetries

High-energy collisions where one particle is longitudinally polarized (spin in the same direction as its momentum) and the other is transversely polarized (spin perpendicular to its momentum) give rise to asymmetries that probe a rich structure of multi-parton correlations in hadrons.  In Phys. Rev. D 107, 014013 (2023) [arXiv:2210.14334 [hep-ph]] (“Numerical study of the twist-3 asymmetry ALT in single-inclusive electron-nucleon and proton-proton collisions”) we provided the first rigorous numerical analysis of the longitudinal-transverse double-spin asymmetry ALT in electron-nucleon and proton-proton collisions for the case where only a single pion, jet, or photon is detected in the final state. We were able to compute contributions from all terms relevant for ALT and make realistic predictions for the observable at Jefferson Lab (JLab) 12 GeV, COMPASS, the future Electron-Ion Collider (EIC), and the Relativistic Heavy Ion Collider. We also compared our results to a JLab 6 GeV measurement, which are the only data available for this type of reaction, and found good agreement.  The lower-energy electron-nucleon collisions at JLab, COMPASS, and the future EIC provide the best avenue to using ALT to access quark-gluon-quark correlations in hadrons as well as gain insight into dynamical quark mass generation.

This figure shows (left) a comparison of our theoretical results for ALT (as a function of the transverse momentum PT of the produced particle) to the JLab 6 GeV experimental data for various model scenarios, and (right) predictions for the ALT asymmetry at a future EIC in a lower-energy configuration.  

Global analyses of single transverse-spin asymmetries

Single transverse-spin asymmetries (SSAs) are observables that involve a hadron with a transverse polarization (spin perpendicular to its momentum) with the other particles in the reaction unpolarized.  Due to parton/hadron spin-orbit correlations, as well as dynamical quark-gluon interactions, particles are produced in certain preferred directions (i.e., asymmetrically) in such collisions.  We pioneered the global analysis of SSAs in Phys. Rev. D 102, 054002 (2020) [arXiv:2002.08384 [hep-ph]] (“Origin of single transverse-spin asymmetries in high-energy collisions”) by including data from semi-inclusive deep-inelastic scattering (SIDIS), electron-positron annihilation, Drell-Yan weak gauge boson or lepton-pair production, and single-inclusive proton-proton collisions.  Impact studies for the future Electron-Ion Collider at Brookhaven National Lab and SoLID experiment at Jefferson Lab were performed in Phys. Lett. B 816, 136255 (2021) [arXiv:2101.06200 [hep-ph]] (“Electron-Ion Collider impact study on the tensor charge of the nucleon”).  An update to this analysis in Phys. Rev. D 106, 034014 (2022) [arXiv:2205.00999 [hep-ph]] (“Updated QCD global analysis of single transverse-spin asymmetries: Extracting H~, and the role of the Soffer bound and lattice QCD”) included new SIDIS data as well as constraints from lattice QCD and the Soffer bound on the transversity parton distribution function.  The results of this collective work was the subject of a U.S. Department of Energy Science Highlight.

This figure shows (left) the functions extracted (up and down quark transversity and Sivers, favored and unfavored Collins and H~) that the encode information on the internal structure of hadrons, (top right) the tensor charges of the nucleon computed from the transversity function h1(x), and (bottom right) the impact of the future EIC and SoLID measurements on those values.

Interactive tool for categorizing kinematic regions of semi-incluisve deep-inelastic scattering

Semi-inclusive deep-inelastic scattering, where a high-energy electron collides with a nucleon and the scattered electron and one of the remnant hadrons are detected, is a powerful reaction that allows us to probe the internal structure of matter.  Each collision has different kinematics for the particles involved, which requires different theoretical formalisms to describe the reaction.  The classification of the different kinematic regions is important for correctly extracting information on the 3D structure of hadrons.  In JHEP 2204, 084 (2022) [arXiv:2201.12197 [hep-ph]] (“New tool for kinematic regime estimation in semi-inclusive deep-inelastic scattering”) we developed an interactive tool that allows one to determine the "affinity" of any kinematic bin to be in a certain region. 

This figure shows the "affinity" for different EIC kinematic bins to be in the "TMD region" where one can extract information on the 3D structure of hadrons.  The darker the color, the higher the affinity to the TMD region.

First extraction of the TMD worm-gear function g1T

The "worm-gear" function g1T describes the distribution of longitudinally polarized quarks inside a transversely polarized nucleon.  This is one of the least know TMD functions, yet nevertheless is an important piece to understanding the complete 3D structure of nucleons as well as giving insight into novel quark-gluon-quark correlations inside of them.  In Phys. Rev. D 105, 034007 (2022) [arXiv:2110.10253 [hep-ph]] (“First global QCD analysis of the TMD g1T from semi-inclusive DIS data”) we performed the first extraction of g1T from the world SIDIS data.  We also found good agreement with lattice QCD for the so-called worm-gear shift <kx>TL.

This figure shows the up and down quark worm-gear function g1T as well as the worm-gear shift <kx>TL.