Double Spin Asymmetries Research Articles

Spin asymmetries for C -even quarkonium production as a probe of gluon distributions

Within the framework of transverse momentum dependent factorization in combination with nonrelativistic quantum chromodynamics (QCD), we study charmonium and bottomonium production in hadronic collisions. We focus on quarkonium states with even charge conjugation, for which the color-singlet production mechanism is expected to be also dominant in the small transverse momentum region, qT2≪4Mc,b2. It is shown that the distributions of linearly polarized gluons inside unpolarized, longitudinally, and transversely polarized protons contribute to the cross sections for scalar and pseudoscalar quarkonia in a very distinctive, parity-dependent way, whereas their effects on higher angular momentum states are strongly suppressed. We derive analytical expressions for single and double spin asymmetries, which would allow for the direct extraction of the gluon transverse momentum dependent distributions, mirroring the phenomenological studies of the Drell-Yan processes aimed at the extraction of their quark counterparts. By adopting Gaussian models for the gluon transverse momentum dependent distributions, which fulfill without saturating everywhere their positivity bounds, we provide numerical predictions for the transverse single-spin asymmetries. These observables could be measured at LHCSpin, the fixed target experiment planned at the LHC. Published by the American Physical Society 2024

Extraction of transhelicity worm-gear distributions and opportunities at the Electron-Ion Collider in China

We present a global analysis of the transhelicity worm-gear distribution function, g1T⊥, by fitting the longitudinal-transverse double-spin asymmetry data of the semi-inclusive deep inelastic scattering. The analysis is performed within the framework of transverse momentum dependent factorization and evolution. It is found that the u-quark favors a positive distribution and the d-quark favors a negative distribution, which is consistent with previous model calculations and phenomenological extractions. Based on the fit to existing world data, we also study the impact of the proposed Electron-Ion Collider in China and conclude that it can significantly improve the precision of the worm-gear distribution function and hence enhance our understanding of nucleon spin structures. Published by the American Physical Society 2024

Probing the four-fermion operators via the transverse double spin asymmetry at the Electron-Ion Collider

The chirality-flipping operators of light fermions are currently poorly constrained by experimental analyses due to the lack of interference with standard model (SM) amplitudes in traditional observables. In this work, we propose to investigate the semileptonic scalar and tensor four-fermion operators of electron and quarks through the transverse double spin asymmetry (DSA) at Electron-Ion Collider, where both the electron and proton beams could be highly transversely polarized. Due to the chirality-flipping nature of these operators, we demonstrate that their interference with the SM results in an unsuppressed contribution to the DSA, and could lead to nontrivial azimuthal cos2ϕ and sin2ϕ distributions that are linearly dependent on their Wilson coefficients. This new method has the potential to significantly improve the current constraints on these scalar and tensor four-fermion operators without relying on theoretical assumptions about other types of new physics effects, particularly for the tensor-type operator of the u quark. Additionally, our findings indicate that both the real and imaginary parts of these operators can be simultaneously constrained and offer a new opportunity for probing potential CP-violation effects. However, it is important to note that these results would be sensitive to the quark transversity distributions, which are currently poorly constrained by the experimental data, but could be significantly improved at the upcoming Electron-Ion Collider. Therefore, our work opens up a new avenue to utilize this new spin asymmetry for exploring the new physics effects from the scalar/tensor four-fermion operators. Published by the American Physical Society 2024

Gluon double-spin asymmetry in the longitudinally polarized p + p collisions

We derive the first-ever small-x expression for the inclusive gluon production cross section in the central rapidity region of the longitudinally polarized proton-proton collisions. The cross section depends on the polarizations of both protons, therefore comprising the numerator of the longitudinal double-spin asymmetry ALL for the produced gluons. The cross section is calculated in the shock wave formalism and is expressed in terms of the polarized dipole scattering amplitudes on the projectile and target protons. We show that the small-x evolution corrections are included into our cross section expression if one evolves these polarized dipole amplitudes using the double-logarithmic helicity evolution derived in [1–4]. Our calculation is performed for the gluon sector only, with the quark contribution left for future work. When that work is complete, the resulting formula will be applicable to longitudinally polarized proton-proton and proton-nucleus collisions, as well as to polarized semi-inclusive deep inelastic scattering (SIDIS) on a proton or a nucleus. Our results should allow one to extend the small-x helicity phenomenology analysis of [5] to the jet/hadron production data reported for the longitudinally polarized proton-proton collisions at RHIC and to polarized SIDIS measurements at central rapidities to be performed at the EIC.

Gluon TMDs from J/ψ production in longitudinally polarized deeply inelastic scattering

We investigate the feasibility of exploring the gluon transverse-momentum-dependent distribution functions (TMDs) inside a longitudinally polarized nucleon. We utilize quarkonium production via the color-octet mechanism combined with TMD formalism in semi-inclusive deeply inelastic scattering (SIDIS) at low transverse momentum as a tool to access polarized gluon TMDs. The corresponding cross-section of the process is expressed in terms of gluon TMDs and non-relativistic QCD matrix elements. We provide the expressions for the sin⁡2ϕ azimuthal asymmetries of J/ψ production in SIDIS with an unpolarized beam colliding on longitudinally polarized nucleon. The asymmetry receives a contribution from the time-reversal-odd gluon TMD h1L⊥g(x,pT2). The maximum possible asymmetry deduced from the positivity bound is sizable and could be measured. We also estimate the double longitudinal spin asymmetry ALL of J/ψ production using a spectator model result for g1Lg(x,pT2).

Exploring the spin structure of the nucleon at STAR

Understanding the internal spin structure of the nucleon remains a challenge in strong interaction physics. The unique capability of RHIC opened new avenues in studying the internal structure of the proton with unprecedented depth and precision. Significant progress has been made in the last few years through various measurements at STAR. The longitudinal spin measurements have contributed significantly to our understanding of the quark and gluon helicity distributions inside the proton. The longitudinal double-spin asymmetry, ALL, from STAR inclusive jet and dijet measurements provides the first evidence of a positive gluon polarization with partonic momentum fraction x > 0.05. The reconstruction of W±/Z in longitudinally polarized proton-proton collisions indicates that there is a flavor separation of the light sea quark helicity distributions. In transversely polarized proton collisions, W±/Z-bosons provide the first constraint on the sea-quark Sivers function and contributes to the tests of the predicted sign change. The tilt of the dijet opening angle provides a direct access to the first Mellin momentum of the Sivers function and avoids the spin-correlated fragmentation contributions. The novel measurements of the azimuthal distributions of identified hadrons in jets and spin-dependent dihadron correlations directly probe the collinear quark transversity in the proton, with the former coupled to the transverse momentum dependent (TMD) Collins fragmentation function and the latter to the dihadron interference fragmentation function. These measurements shed lights on Sivers function, quark transversity and spin-dependent fragmentation functions in both collinear and TMD formalism. In this proceeding, recent jet results on both the longitudinal and transverse spin structure of the proton from STAR are presented.

Small x physics beyond eikonal approximation: an effective Hamiltonian approach

Understanding the spin structure of hadrons in the small x regime is an important direction to unravel the spin puzzle in hadronic physics. To include spin degrees of freedom in the small x regime requires going beyond the usual eikonal approximation in high energy QCD. We developed an effective Hamiltonian approach to study spin related observables in the small x regime using the shockwave formalism. The small-x effective Hamiltonian incorporates both quark and gluon propagators in the background fields and the background field induced interaction vertices up to next-to-eikonal order. A novel feature of sub-eikonal interactions is the background gluon field induced gluon radiation inside the shockwave. Its relation to chromo-electrically polarized Wilson line correlator is established both in small x helicity evolution and in longitudinal double-spin asymmetry for gluon production.

Accessing gluon polarization with high- PT hadrons in SIDIS

A recent global QCD analysis of jet production and other polarized scattering data has found the presence of negative solutions for the gluon helicity distribution in the proton, $\Delta g$, along with the traditional $\Delta g > 0$ solutions. We consider polarized semi-inclusive deep-inelastic scattering for hadrons produced with large transverse momentum as a means of constraining the dependence of $\Delta g$ on the parton momentum fraction, $x$. Focusing on the double longitudinal spin asymmetry, we identify the kinematics relevant for future experiments at Jefferson Lab and the Electron-Ion Collider which are particularly sensitive to the polarized gluon channel and could discriminate between the different $\Delta g$ behaviors.

Numerical study of the twist-3 asymmetry ALT in single-inclusive electron-nucleon and proton-proton collisions

We provide the first rigorous numerical analysis of the longitudinal-transverse double-spin asymmetry ${A}_{LT}$ 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 ${A}_{LT}$ 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 ${A}_{LT}$ 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.

Angular Dependence of the Polarization Transfer to the Proton in the evec {p} to evec {p} Process

The dependence of the longitudinal polarization transfer to the proton in the evec {p} to evec {p} process on the proton scattering angle has been numerically analyzed for the case where the initial (at rest) proton is partially polarized along the direction of motion of the detected recoil proton. The analysis is based on the results of JLab polarization experiments on measuring the ratio of the Sachs form factors in the vec {e}p to evec {p} process using the Kelly (2004) and Qattan (2015) parameterizations for their ratio, in the kinematics of the SANE Collaboration experiment (2020) on measuring the double spin asymmetry in the vec {e}vec {p} to ep process. It is shown that the violation of the scaling of the Sachs form factors leads to a significant increase in the magnitude of the polarization transfer to the proton in comparison with the case of dipole dependence.

Azimuthal single- and double-spin asymmetries in semi-inclusive deep-inelastic lepton scattering by transversely polarized protons

A comprehensive set of azimuthal single-spin and double-spin asymmetries in semi-inclusive leptoproduction of pions, charged kaons, protons, and antiprotons from transversely polarized protons is presented. These asymmetries include the previously published HERMES results on Collins and Sivers asymmetries, the analysis of which has been extended to include protons and antiprotons and also to an extraction in a three-dimensional kinematic binning and enlarged phase space. They are complemented by corresponding results for the remaining single-spin and double-spin asymmetries for transverse target-polarization orientation.

Longitudinal double-spin asymmetry for inclusive jet and dijet production in polarized proton collisions at s=510 GeV

We report measurements of the longitudinal double-spin asymmetry, ALL, for inclusive jet and dijet production in polarized proton-proton collisions at midrapidity and center-of-mass energy s=510 GeV, using the high luminosity data sample collected by the STAR experiment in 2013. These measurements complement and improve the precision of previous STAR measurements at the same center-of-mass energy that probe the polarized gluon distribution function at partonic momentum fraction 0.015≲x≲0.25. The dijet asymmetries are separated into four jet-pair topologies, which provide further constraints on the x dependence of the polarized gluon distribution function. These measurements are in agreement with previous STAR measurements and with predictions from current next-to-leading-order global analyses. They provide more precise data at low dijet invariant mass that will better constrain the shape of the polarized gluon distribution function of the proton.Received 21 October 2021Accepted 4 April 2022DOI:https://doi.org/10.1103/PhysRevD.105.092011Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuark & gluon jetsPhysical SystemsGluonsPropertiesSpinTechniquesHadron collidersParticles & FieldsNuclear Physics

Signature of the Gluon Orbital Angular Momentum.

We propose a novel observable for the experimental detection of the gluon orbital angular momentum (OAM) that constitutes the proton spin sum rule. We consider longitudinal double spin asymmetry in exclusive dijet production in electron-proton scattering and demonstrate that the cosϕ azimuthal angle correlation between the scattered electron and proton is a sensitive probe of the gluon OAM at small x and its interplay with the gluon helicity. We also present a numerical estimate of the cross section for the kinematics of the Electron-Ion Collider.

Reliability Analysis of the Results of the Known Experiments on Measuring of the Sachs Form Factor Ratio Using the Rosenbluth Technique. Polarization of the Final Proton in the $$e\vec {p} \to e\vec {p}$$ Elastic Process

A criterion for assessing the reliability of measurements of the Sachs form factor ratio using the Rosenbluth technique is proposed and applied to an analysis of three known experiments (Andivahis1994, Walker1994, Qattan2005) and a recent experiment on the CEBAF accelerator upgraded to 12 GeV at JLab (arXiv:2103.01842 [nucl-ex]). Based on the results of the JLab polarization experiments on measuring the ratio $\mu_p G_E/G_M$ in the $\vec e p \to e \vec p$ process, in the kinematics of the SANE Collaboration experiment (2020) on the measurement of double spin asymmetry in the $\vec e \vec p \to e p$ process numerical calculations are performed for the $Q^2$ dependence of polarization transferred to the proton in the $e \vec p \to e \vec p$ process when the initial proton at rest is partially polarized along the direction of motion of the detected recoil proton.

Twist-3 double-spin asymmetries in Drell-Yan processes

We study double spin asymmetries in Drell-Yan processes in which one initial hadron is transversely polarized and another one is longitudinally polarized. The complete part of the hadronic tensor relevant to asymmetries is derived. This part consists of twist-2 and twist-3 parton distributions and is gauge invariant. We construct some observables which can be used to extract these parton distributions from experimental measurements.

Probing gluon helicity with heavy flavor at the Electron-Ion Collider

We propose a new measurement of the heavy flavor hadron double spin asymmetry in deep-inelastic scattering at a future Electron-Ion Collider (EIC) to constrain the polarized gluon distribution function inside the proton. Statistical projection on $D^0$ meson double spin asymmetry is calculated with an EIC central detector using an all-silicon tracker and vertexing subsystem. A first impact study was done by interpreting pseudo-data at next-to-leading order in QCD. The sensitivity of the experimental observable in constraining gluon helicity distribution in a wide range of parton momentum fraction $x$ has been investigated considering different beam energy configurations. This measurement complements the inclusive spin-dependent structure function measurement and provides an opportunity to constrain the gluon helicity distribution in the moderate $x$ region.

Revisiting quark and gluon polarization in the proton at the EIC

We present a comprehensive impact study of future Electron-Ion Collider (EIC) data for parity-conserving and parity-violating polarization asymmetries on quark and gluon helicity distributions in the proton. The study, which is based on the JAM Monte Carlo global QCD analysis framework, explores the role of the extrapolation uncertainty and SU(3) flavor symmetry constraints in the simulated double-spin asymmetry, $A_{LL}$, at small parton momentum fractions $x$ and its effect on the extracted parton polarizations. We find that different assumptions about $A_{LL}$ extrapolations and SU(3) symmetry can have significant consequences for the integrated quark and gluon polarizations, for polarized proton, deuteron and $^3$He beams. For the parity-violating asymmetry, $A_{UL}$, we study the potential impact on the polarized strange quark distribution with different extrapolations of $A_{UL}$, finding the constraining power to be ultimately limited by the EIC machine luminosity.

First analysis of world polarized DIS data with small- x helicity evolution

We present a Monte Carlo based analysis of the combined world data on polarized lepton-nucleon deep-inelastic scattering at small Bjorken $x$ within the polarized quark dipole formalism. We show for the first time that double-spin asymmetries at $x<0.1$ can be successfully described using only small-$x$ evolution derived from first-principles QCD, allowing predictions to be made for the $g_1$ structure function at much smaller $x$. Anticipating future data from the Electron-Ion Collider, we assess the impact of electromagnetic and parity-violating polarization asymmetries on $g_1$ and demonstrate an extraction of the individual flavor helicity PDFs at small $x$.

Differential heavy quark distributions and correlations in longitudinally polarized deep-inelastic scattering

We present a first calculation of the heavy flavor contribution to the longitudinally polarized deep-inelastic scattering structure function $g_1^{Q}$, differential in the transverse momentum or the rapidity of the observed heavy quark $Q$ or antiquark $\overline Q$. All results are obtained at next-to-leading order accuracy in QCD within the framework of a newly developed parton-level Monte Carlo generator that also allows one to study observables associated with the produced heavy quark pair such as its invariant mass distribution or its correlation in azimuthal angle. First phenomenological studies are carried out for various heavy quark distributions in a kinematic regime relevant for a future Electron-Ion Collider with a particular emphasis on the expected size of the corresponding double-spin asymmetries and their sensitivity to the still poorly constrained helicity gluon distribution. Theoretical uncertainties associated with the choice of the factorization scale are discussed for selected observables.

Longitudinal double-spin asymmetry for inclusive jet and dijet production in polarized proton collisions at s=200 GeV

We report high-precision measurements of the longitudinal double-spin asymmetry, ALL, for midrapidity inclusive jet and dijet production in polarized pp collisions at a center-of-mass energy of s=200 GeV. The new inclusive jet data are sensitive to the gluon helicity distribution, Δg(x,Q2), for gluon momentum fractions in the range from x≃0.05 to x≃0.5, while the new dijet data provide further constraints on the x dependence of Δg(x,Q2). The results are in good agreement with previous measurements at s=200 GeV and with recent theoretical evaluations of prior world data. Our new results have better precision and thus strengthen the evidence that Δg(x,Q2) is positive for x>0.05.Received 9 March 2021Accepted 28 April 2021DOI:https://doi.org/10.1103/PhysRevD.103.L091103Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasHadron-hadron interactionsPerturbative QCDQuark & gluon jetsPhysical SystemsGluonsProtonsPropertiesPolarizationSpinTechniquesElectromagnetic calorimetersHadron collidersTime-projection chambersNuclear PhysicsParticles & Fields