Please also see "Can We Unlock the Secrets Hidden Deep Within the Nucleus of an Atom?" This is an article and animation about Dr. Pitonyak's research produced by Futurum Careers, a free online resource and magazine aimed at encouraging 14-19-year-olds worldwide to pursue careers in science, technology, engineering, mathematics and medicine (STEM), and social sciences, humanities and the arts for people and the economy (SHAPE).  A brief synopsis was also written for an Open-Access Government article.

The nucleus of an atom is made up of protons and neutrons, which are a part of a broader category of particles called hadrons.  However, these hadrons are not a fundamental form of matter since they are composed of other particles, namely, quarks and gluons (collectively called partons).  The partons form a dynamical system inside of hadrons that is governed by the strong nuclear force, with quantum chromodynamics (QCD) being the theory of those interactions.  A goal of nuclear physics research is to understand this internal structure through these partons, the elementary pieces of visible matter.  In particular, the analysis of high-energy collisions sensitive to an intrinsic property, called spin, of hadrons and/or partons is especially useful.  These observables allow us to explore the 3-dimensional (3D) motion of partons inside of hadrons and how the proton's spin arises from its constituent partons.  Our research attempts to give us better insight into these aspects of hadronic structure as well as support the science of the future Electron-Ion Collider to be built in the United States at Brookhaven National Lab.

This image shows the constituents of an atom as one zooms in to smaller and smaller distances, eventually becoming sensitive to quarks (and gluons) inside of protons and neutrons.  One can only probe these partons through very high-energy collisions.

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.


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 arXiv:2302.01192 [hep-ph] 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 5σ 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.

This figure shows the worm-gear function g1T for up and down quarks.

First anlysis of polarized DIS data using 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 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.

This figure shows (left) the extracted g1 structure function with its relative uncertainty for our analysis (JAMsmallx) compared to another fit (DSSV), which demonstrates the much more precise determination of g1 at small x we achieve both from current data and that from the future EIC, (top right) using EIC pseudo-data to extract the helicity parton distribution functions (PDFs) for the up, down, and strange quarks, and (bottom right) the sum of the helicity PDFs that can be used to calculate the quark contribution to the proton's spin.