<p>We establish an approach to analyze the free hadron and transition (nonperturbative) regions of near-side energy-energy correlators (EECs) based on dihadron fragmentation functions (DiFFs). We introduce a (nonperturbative) function we call the “EEC DiFF” and explicitly show that expanding it for large relative transverse momentum between the two hadrons gives the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">)</mo></mrow></math> expression for the “EEC jet” function used in the quark-gluon (perturbative) region. This connection indicates that a formal theoretical matching will be able to bridge the free-hadron region, transition, and quark-gluon regions and allow all of them to be analyzed simultaneously. We further derive a result valid for near-side EECs in the free hadron and transition regions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> annihilation in terms of the EEC DiFF. Using a simple model for the function, we perform the first fit within the dihadron framework to experimental data in this regime. We find reasonable agreement with the measurements and reproduce the salient features of near-side EECs in the free hadron and transition regions.</p>

United States

Zhong-Bo Kang

Andreas Metz

Daniel Pitonyak

Congyue Zhang

Dihadron Fragmentation Framework for Near-Side Energy-Energy Correlators

<p>We perform a phenomenological study of helicity-dependent parton distribution functions (PDFs) using small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> helicity evolution equations, incorporating for the first time single-inclusive jet production data in polarized proton-proton (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math>) scattering at parton momentum fractions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi><mo>&lt;</mo><mn>0.1</mn></math>. We also simultaneously include double-longitudinal spin asymmetries in inclusive and semi-inclusive deep-inelastic scattering probing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi><mo>&lt;</mo><mn>0.1</mn></math>. Employing the polarized small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> pure-glue calculation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi><mo stretchy="false">→</mo><mi>g</mi><mi>X</mi></math> for the jet production cross section, we modify the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>&amp;</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub></mrow></math> KPS-CTT evolution equations by setting <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>0</mn></math> to replicate the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> (pure-glue) limit, while retaining external quark flavors for the spinor field operators. We find that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> data have a considerable impact on the helicity PDFs at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>, reducing their uncertainties and leading to a total quark and gluon helicity in the proton for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi><mo>&lt;</mo><mn>0.1</mn></math> of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>0.04</mn><mo>±</mo><mn>0.23</mn></math>. Combining our analysis with a recent JAM helicity PDF analysis of the world polarized data, which includes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi><mo>&gt;</mo><mn>0.1</mn></math>, we find a total quark and gluon helicity contribution for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi><mo>&gt;</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>7</mn></mrow></msup></math> of between 0.02 and 0.51.</p>

Daniel Adamiak

Nicholas Baldonado

Yuri V. Kovchegov

Ming Li

W. Melnitchouk

Nobuo Sato

Matthew D. Sievert

Andrey Tarasov

Thailand

Yossathorn Tawabutr

First study of polarized proton-proton scattering with small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> helicity evolution

Transverse single-spin asymmetries in the semi-inclusive deep-inelastic production of isolated photons ( <math altimg='si27.svg'><mi>&#947;</mi></math>SIDIS), <math altimg='si18.svg'><msubsup><mi>A</mi><mrow><mi>U</mi><mi>T</mi></mrow><mrow><mi>&#947;</mi><mrow><mrow><mi mathvariant='normal'>S</mi></mrow><mi>I</mi><mi>D</mi><mi>I</mi><mi>S</mi></mrow></mrow></msubsup></math>, provide an unprecedented opportunity to extract the quark-gluon-quark correlators <math altimg='si1.svg'><mrow><msub><mi>F</mi><mrow><mi>F</mi><mi>T</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>x</mi><mo>&#8242;</mo></msup><mo>)</mo></mrow></mrow></math> and <math altimg='si5.svg'><mrow><msub><mi>G</mi><mrow><mi>F</mi><mi>T</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>x</mi><mo>&#8242;</mo></msup><mo>)</mo></mrow></mrow></math> point-by-point in their full support <math altimg='si28.svg'><mrow><mi>x</mi><mo>,</mo><msup><mi>x</mi><mo>&#8242;</mo></msup></mrow></math>. We utilize realistic models for these functions, based on input from the Sivers transverse momentum dependent parton distribution function and imposing constraints from the <math altimg='si29.svg'><msub><mi>d</mi><mn>2</mn></msub></math> matrix element calculated in lattice QCD, in order to provide numerical estimates for <math altimg='si18.svg'><msubsup><mi>A</mi><mrow><mi>U</mi><mi>T</mi></mrow><mrow><mi>&#947;</mi><mrow><mrow><mi mathvariant='normal'>S</mi></mrow><mi>I</mi><mi>D</mi><mi>I</mi><mi>S</mi></mrow></mrow></msubsup></math> at the Electron-Ion Collider (EIC). We thoroughly explore the EIC phase space in order to isolate in which regions the asymmetry can be sizable, finding it can be as much as <math altimg='si30.svg'><mrow><mn>10</mn><mspace width='0.16em' /><mo>%</mo></mrow></math> or larger for certain kinematics. Given that <math altimg='si1.svg'><mrow><msub><mi>F</mi><mrow><mi>F</mi><mi>T</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>x</mi><mo>&#8242;</mo></msup><mo>)</mo></mrow></mrow></math> and <math altimg='si5.svg'><mrow><msub><mi>G</mi><mrow><mi>F</mi><mi>T</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>x</mi><mo>&#8242;</mo></msup><mo>)</mo></mrow></mrow></math> are basically unknown, <math altimg='si18.svg'><msubsup><mi>A</mi><mrow><mi>U</mi><mi>T</mi></mrow><mrow><mi>&#947;</mi><mrow><mrow><mi mathvariant='normal'>S</mi></mrow><mi>I</mi><mi>D</mi><mi>I</mi><mi>S</mi></mrow></mrow></msubsup></math> will be an important future measurement to learn about multi-parton correlations in the nucleon.

Michael Harris

Jacob Marsh

Alexei Prokudin

Jack Putnam

Germany

Daniel Rein

Marc Schlegel

Transverse single-spin asymmetries in <math altimg='si27.svg'><mi>&#947;</mi></math>SIDIS as a direct probe of quark-gluon-quark longitudinal momentum structure

We revisit the analysis of transverse single-spin asymmetries <math><msub><mrow><mi>A</mi></mrow><mrow><mi>N</mi></mrow></msub></math> in lepton-nucleon scattering where only a single pion is detected in the final state, <math><mi>ℓ</mi><mspace width="0.2em"></mspace><msup><mrow><mi>N</mi></mrow><mrow><mo>↑</mo></mrow></msup><mo>→</mo><mi>h</mi><mspace width="0.2em"></mspace><mi>X</mi></math>. This observable is the Electron-Ion Collider (EIC) analogue to <math><msub><mrow><mi>A</mi></mrow><mrow><mi>N</mi></mrow></msub></math> in proton-proton collisions, <math><msup><mrow><mi>p</mi></mrow><mrow><mo>↑</mo></mrow></msup><mi>p</mi><mo>→</mo><mi>h</mi><mspace width="0.2em"></mspace><mi>X</mi></math>, that has been studied intensely for decades, especially at the Relativistic Heavy Ion Collider (RHIC). We incorporate new theoretical developments in the collinear twist-3 framework and utilize recent extractions of (Sivers-like and Collins-like) quark-gluon-quark correlators in the numerical computations. We compare our calculations to HERMES measurements as well as make predictions for Jefferson Lab, COMPASS, and EIC kinematics. We further explore the role of next-to-leading order (NLO) corrections to the (twist-2) unpolarized cross section (denominator of <math><msub><mrow><mi>A</mi></mrow><mrow><mi>N</mi></mrow></msub></math>) and consider what can be deduced empirically about the potential numerical significance of the full NLO calculation of <math><msub><mrow><mi>A</mi></mrow><mrow><mi>N</mi></mrow></msub></math> in this process. We consider sources of theoretical uncertainty in our predictions, which present potential opportunities then for future measurements to improve our understanding of <math><msub><mrow><mi>A</mi></mrow><mrow><mi>N</mi></mrow></msub></math> and multi-parton correlations in hadrons.

Lebanon

Sophia Fitzgibbons

Michel Malda

Penn Smith

Updated numerical study of transverse single-spin asymmetries in single-inclusive pion production from lepton-nucleon collisions

We analyze the world polarized deep-inelastic scattering (DIS) and semi-inclusive DIS (SIDIS) data at low values of <math><mi>x</mi><mo>&lt;</mo><mn>0.1</mn></math>, using small-<math><mi>x</mi></math> evolution equations for the flavor singlet and nonsinglet helicity parton distribution functions (hPDFs), which resum all powers of both <math><msub><mi>α</mi><mi>s</mi></msub><msup><mi>ln</mi><mn>2</mn></msup><mo>(</mo><mn>1</mn><mo>/</mo><mi>x</mi><mo>)</mo></math> and <math><msub><mi>α</mi><mi>s</mi></msub><mi>ln</mi><mo>(</mo><mn>1</mn><mo>/</mo><mi>x</mi><mo>)</mo><mi>ln</mi><mo>(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>/</mo><msubsup><mi>Q</mi><mn>0</mn><mn>2</mn></msubsup><mo>)</mo></math>, with <math><msub><mi>α</mi><mi>s</mi></msub></math> being the strong coupling constant. The hPDFs for quarks, antiquarks, and gluons are extracted and evolved to lower values of <math><mi>x</mi></math> to make predictions for the future Electron-Ion Collider (EIC). We improve on our earlier work by employing the more realistic large-<math><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>&amp;</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub></mrow></math> limit of the revised small-<math><mi>x</mi></math> helicity evolution, and by incorporating running coupling corrections along with SIDIS data into the fit. We find an anticorrelation between the signs of the gluon and <math><mi>C</mi></math>-even quark hPDFs, as well as the <math><msub><mi>g</mi><mn>1</mn></msub></math> structure function. While the existing low-<math><mi>x</mi></math> polarized DIS and SIDIS data are 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 <math><msub><mi>g</mi><mn>1</mn></msub></math> structure function for <math><mi>x</mi></math> values beyond those probed at the EIC. Using the obtained hPDFs, we discuss the contributions to the proton spin from quark and gluon spins at small <math><mi>x</mi></math>.

Finland

Global analysis of polarized DIS and SIDIS data with improved small-<math><mi>x</mi></math> helicity evolution

We provide the first rigorous numerical analysis of the longitudinal-transverse double-spin asymmetry <math><msub><mi>A</mi><mrow><mi>L</mi><mi>T</mi></mrow></msub></math> in electron-nucleon and proton-proton collisions for the case where only a single pion, jet, or photon is detected in the final state. Given recent extractions of certain, previously unknown, nonperturbative functions, we are able to compute contributions from all terms relevant for <math><msub><mi>A</mi><mrow><mi>L</mi><mi>T</mi></mrow></msub></math> and make realistic predictions for the observable at Jefferson Lab (JLab) 12 GeV, COMPASS, the future Electron-Ion Collider, and the Relativistic Heavy Ion Collider. We also compare our results to a JLab 6 GeV measurement, which are the only data available for this type of reaction. The twist-3 nature of <math><msub><mi>A</mi><mrow><mi>L</mi><mi>T</mi></mrow></msub></math> makes it a potentially fruitful avenue to probe quark-gluon-quark correlations in hadrons as well as provide insights into dynamical quark mass generation in QCD.

Brandon Bauer

Cody Shay

Numerical study of the twist-3 asymmetry <math><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>L</mi><mi>T</mi></mrow></msub></mrow></math> in single-inclusive electron-nucleon and proton-proton collisions

We present an update to the QCD global analysis of single transverse-spin asymmetries presented in [J. Cammarota et al. (Jefferson Lab Angular Momentum Collaboration), Phys. Rev. D 102, 054002 (2020).] (JAM3D-20). JAM3D-20 simultaneously included transverse momentum dependent and collinear twist-3 observables, both of which are sensitive to quark-gluon-quark correlations in hadrons. In this study we extract for the first time the twist-3 chiral odd fragmentation function <math><mover><mi>H</mi><mo>˜</mo></mover></math> by incorporating the <math><mrow><mi>sin</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></math> modulation data from semi-inclusive deep-inelastic scattering along with its contribution to the single transverse-spin asymmetry in pion production from proton-proton collisions. We also explore the impact of lattice QCD tensor charge calculations and the Soffer bound on our global analysis. We find that both constraints can be accommodated within our results, with <math><mover><mi>H</mi><mo>˜</mo></mover></math> playing a key role in maintaining agreement with the data from proton-proton collisions.

Leonard Gamberg

Joshua A. Miller

Updated QCD global analysis of single transverse-spin asymmetries: Extracting <math><mrow><mover><mrow><mi>H</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow></math>, and the role of the Soffer bound and lattice QCD

The worm-gear transverse momentum dependent (TMD) function <math><msub><mi>g</mi><mrow><mn>1</mn><mi>T</mi></mrow></msub></math> is one of the eight leading-twist TMDs and has the probabilistic interpretation of finding a longitudinally polarized quark inside a transversely polarized hadron. In this work, we present the first simultaneous extraction of <math><msub><mi>g</mi><mrow><mn>1</mn><mi>T</mi></mrow></msub></math> from all the available experimental measurements. The study involves the analysis of COMPASS, HERMES, and Jefferson Lab data on semi-inclusive deep-inelastic scattering using Monte Carlo techniques. We also compare <math><msub><mi>g</mi><mrow><mn>1</mn><mi>T</mi></mrow></msub></math> obtained from this experimental data with different theoretical approaches, such as the large-<math><msub><mi>N</mi><mi>c</mi></msub></math> approximation, the Wandzura-Wilczek-type approximation, and lattice QCD.

Shohini Bhattacharya

Gregory Penn

First global QCD analysis of the TMD <math><msub><mi>g</mi><mrow><mn>1</mn><mi>T</mi></mrow></msub></math> from semi-inclusive DIS data

In this letter we study the impact of the Electron-Ion Collider (EIC) on the phenomenological extraction of the tensor charge from a QCD global analysis of single transverse-spin asymmetries (SSAs). We generate EIC pseudo-data for the Collins effect in semi-inclusive deep-inelastic scattering for proton and <math><mmultiscripts><mrow><mi>H</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts><mi>e</mi></math> beams across multiple center-of-mass energies. We find a significant reduction in the uncertainties for the up, down, and isovector tensor charges that will make their extraction from EIC data on SSAs as precise as current lattice QCD calculations. We also analyze the constraints placed by future data from the proposed SoLID experiment at Jefferson Lab, discuss its important complementary role to the EIC, and present the combined impact from both facilities.

Ralf Seidl

Electron-ion collider impact study on the tensor charge of the nucleon

We present a Monte Carlo based analysis of the combined world data on polarized lepton-nucleon deep-inelastic scattering at small Bjorken <math><mi>x</mi></math> within the polarized quark dipole formalism. We show for the first time that double-spin asymmetries at <math><mi>x</mi><mo>&lt;</mo><mn>0.1</mn></math> can be successfully described using only small-<math><mi>x</mi></math> evolution derived from first-principles QCD, allowing predictions to be made for the <math><msub><mi>g</mi><mn>1</mn></msub></math> structure function at much smaller <math><mi>x</mi></math>. Anticipating future data from the Electron-Ion Collider, we assess the impact of electromagnetic and parity-violating polarization asymmetries on <math><msub><mi>g</mi><mn>1</mn></msub></math> and demonstrate an extraction of the individual flavor helicity parton distribution functions at small <math><mi>x</mi></math>.

First analysis of world polarized DIS data with small-<math><mi>x</mi></math> helicity evolution