⚛️ phenomenology

Nucleon Tomography with 0-jettiness

This paper proposes a novel strategy using 0-jettiness to suppress initial-state radiation in transverse-momentum-dependent observables, demonstrating that this approach significantly enhances transverse single spin asymmetry signals in $W^\pm$ and $Z^0$ boson production at RHIC and the Electron-Ion Collider to facilitate a more definitive test of the Sivers function sign change.

Original authors: Shen Fang, Shuo Lin, Ding Yu Shao, Jian Zhou

Published 2026-09-01

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CC BY 4.0

Original authors: Shen Fang, Shuo Lin, Ding Yu Shao, Jian Zhou

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Inside every atom, protons and neutrons—collectively called nucleons—are not solid, featureless spheres. Instead, they are bustling cities of smaller particles known as quarks and gluons, constantly moving and interacting. For decades, physicists have sought to map the three-dimensional structure of these nucleons, understanding not just how these particles are arranged, but how they move and spin. This internal motion is crucial because it holds the key to understanding the fundamental forces that bind matter together. A major tool for this exploration is the study of transverse-momentum-dependent distributions, which act like a high-resolution camera capturing the sideways movement of particles inside a proton. However, taking a clear picture has always been difficult. When scientists collide protons at high speeds to study them, the resulting explosion is often clouded by a haze of extra particles radiating outward from the initial crash. This "initial-state radiation" acts like static on a radio signal, obscuring the subtle, intrinsic details of the nucleon's structure that researchers are trying to measure.

A team of physicists has now proposed a new strategy to cut through this static and reveal the nucleon's hidden geometry. By applying a specific filter to their data, they found a way to suppress the distracting background noise, significantly sharpening the signal of the nucleon's internal spin. This approach, tested through theoretical calculations for future experiments at particle accelerators, promises to transform how scientists observe the spin of protons and neutrons. The researchers demonstrated that by carefully selecting which collision events to keep and which to discard, they could enhance the visibility of a specific quantum effect by more than double, making it possible to test long-standing predictions about how matter behaves at the smallest scales.

The core of this new method involves a technique called "zero-jettiness." In the chaotic environment of a particle collider, when two protons smash together to create a heavy particle like a W or Z boson, they often emit extra sprays of energy. The researchers realized that by imposing a strict rule to veto, or reject, any event where extra energy is emitted in the central region of the collision, they could isolate the cleanest possible interactions. Imagine trying to hear a whisper in a crowded room; if you could somehow silence everyone except the person speaking, the message would become instantly clear. In this case, the "whisper" is the subtle spin-dependent motion of quarks, and the "crowd" is the unwanted radiation. By filtering out the central radiation, the team effectively silenced the noise, allowing the intrinsic signal to stand out with much greater clarity.

The team applied this filtering strategy to the study of transverse single spin asymmetries. This is a specific measurement that looks at how the direction of a proton's spin influences the direction in which particles fly after a collision. If the proton spins one way, the debris might prefer to fly to the left; if it spins the other way, it might fly to the right. This asymmetry is a direct window into the Sivers function, a theoretical description of how a quark's sideways motion is linked to the proton's spin. For years, physicists have predicted that this relationship should flip its sign depending on whether the quark is inside a proton or a neutron, but proving this has been incredibly difficult because the signal is often washed out by the very radiation the new method suppresses.

Using their new framework, the researchers calculated what would happen if they applied this zero-jettiness filter to collisions at the Relativistic Heavy Ion Collider (RHIC) in New York. They focused on the production of W minus bosons, a type of heavy particle created in these collisions. Their calculations showed that by tightening the filter to reject even small amounts of central radiation, the asymmetry signal would grow dramatically. Specifically, at a transverse momentum of 5 GeV, the size of the asymmetry signal increased by 115 percent. This is a massive gain, effectively doubling the strength of the effect they are trying to measure.

Crucially, the team also accounted for the statistical cost of this filtering. Since rejecting events means having fewer data points to work with, there is a natural trade-off: a stronger signal but fewer samples. However, their analysis revealed that the boost in signal strength far outweighs the loss of data. Even with fewer collisions to analyze, the clarity of the remaining data is so much better that the overall ability to detect the effect improves significantly. The statistical uncertainty, which represents the margin of error in the measurement, increased by only about 80 percent, while the signal itself jumped by 115 percent. This net gain means that experiments could definitively test the predicted sign change of the Sivers function, a result that has remained elusive due to the blurring effects of radiation in previous studies.

The implications of this work extend beyond the current experiments at RHIC. The researchers also explored how this method would perform at the future Electron-Ion Collider, a planned facility designed to probe the structure of matter with unprecedented precision. Their simulations showed that the same filtering technique would enhance the measurement of spin asymmetries in the production of pions, a type of subatomic particle, by a similar margin. The error bands for the filtered data and the unfiltered data would not overlap, indicating a clear, measurable improvement in sensitivity. This suggests that the technique is not just a theoretical curiosity but a practical tool that can be deployed across a wide range of experiments to map the three-dimensional structure of nucleons with greater accuracy than ever before.

By systematically isolating the non-perturbative, or intrinsic, structure of the nucleon from the messy perturbative radiation that usually accompanies it, this new approach offers a fresh path forward. It addresses a persistent difficulty in high-energy physics: separating the fundamental properties of matter from the complex interactions that occur during high-speed collisions. The ability to tune the energy scale of the filter gives researchers a new lever to control how they view the subatomic world. This work paves the way for a new era of precision, where the spin structure of the nucleon can be mapped with a level of detail that was previously impossible, bringing scientists closer to a complete understanding of the building blocks of our universe.

Technical Summary: Nucleon Tomography with 0-jettiness

Problem Statement
Probing the intrinsic three-dimensional (3D) structure of the nucleon, specifically the transverse-momentum-dependent (TMD) parton distributions, is a central objective of modern hadron physics. A significant obstacle in extracting these non-perturbative structures is the contamination from initial-state radiation (ISR). The recoil effects of ISR introduce perturbative contributions that obscure the non-perturbative dynamics, complicating the disentanglement of TMDs. This issue is particularly acute in electroweak Drell-Yan processes (such as $W^\pm$ and $Z^0$ production), where the hard scale $Q$ is fixed by the gauge boson mass, unlike in semi-inclusive deep inelastic scattering (SIDIS) where $Q$ can be tuned. Consequently, existing measurements of transverse single spin asymmetries (SSAs) at high energies are strongly diluted by TMD evolution effects, limiting the precision of tests for fundamental QCD predictions, such as the sign change of the Sivers function.

Methodology
The authors propose a novel strategy to isolate intrinsic non-perturbative TMD dynamics by employing 0-jettiness ( $\tau$ ) as a veto to suppress central ISR. The 0-jettiness observable is defined as a global event shape that sums the transverse momenta of all final-state particles (excluding the gauge boson) weighted by their rapidity distance from the boson:
$\tau \equiv \frac{2}{Q^2} \sum_i \min\{p_a \cdot l_i, p_b \cdot l_i\} = \sum_i \frac{|\vec{l}_{\perp,i}|}{Q} e^{-|y_i - y|}$
Imposing a veto $\tau < \tau_0$ effectively suppresses central gluon radiation while allowing collinear radiation along the beam directions, thereby constraining ISR effects.

To theoretically describe this process, the authors develop a joint resummation framework that systematically resums large logarithms associated with both the veto scale ( $\ln(1/\tau_0)$ ) and the gauge boson's transverse momentum ( $\ln(Q^2/q_\perp^2)$ ). This approach extends beyond standard TMD resummation by unifying Soft-Collinear Effective Theory (SCET) regimes (SCET $_{\text{I}}$ , SCET $_{\text{II}}$ , and SCET $_{+}$ ) to cover a comprehensive kinematic region. The authors derive a modified perturbative Sudakov factor, $S_P(b)$ , which incorporates the phase space restrictions imposed by the 0-jettiness veto. This derivation is performed independently using both perturbative QCD phase space analysis and the SCET formalism, achieving Next-to-Leading Logarithmic (NLL) accuracy.

Key Contributions

Theoretical Formalism: The paper presents the first extension of joint resummation to polarization-dependent observables in Drell-Yan-like processes. It provides a transparent derivation of the Sudakov factor under a 0-jettiness veto, unifying various SCET regimes to handle the interplay between the veto scale and transverse momentum.
Phenomenological Application: The formalism is applied to transverse single spin asymmetries (SSAs) in $W^\pm$ and $Z^0$ boson production at the Relativistic Heavy Ion Collider (RHIC). The authors demonstrate how the veto enhances the signal generated by the Qiu-Sterman mechanism (the twist-3 quark-gluon correlation function) relative to the unpolarized cross-section.
Extension to EIC: The framework is applied to SIDIS processes at the proposed Electron-Ion Collider (EIC), specifically analyzing SSAs for $\pi^+$ and $\pi^-$ production.

Results

Enhancement of Asymmetry: Numerical results for $W^-$ production at RHIC ( $\sqrt{s} = 500$ GeV) show that imposing a central 0-jettiness veto significantly increases the magnitude of the SSA. For instance, at a transverse momentum $q_\perp = 5$ GeV, the asymmetry is enhanced by approximately 115% when $\tau_0 = 0.015$ compared to the inclusive case ( $\tau_0 = 1$ ).
Net Sensitivity Gain: Crucially, the authors calculate the statistical uncertainty associated with the veto. They find that while the veto reduces the event rate (increasing statistical uncertainty), the enhancement in the asymmetry signal is substantial enough to yield a net gain in experimental sensitivity. In the $q_\perp \approx 5$ GeV bin, the asymmetry increases by ~115% while the statistical uncertainty increases by only ~80%.
EIC Applicability: For SIDIS at the EIC ( $\sqrt{s} = 100$ GeV), the application of a 1-jettiness veto ( $\tau_0 = 0.04$ ) demonstrates a clear enhancement of asymmetries at moderate $q_\perp$ . The projected statistical error bands for the vetoed and inclusive cases show no overlap for $q_\perp \gtrsim 1$ GeV, confirming a measurable improvement in sensitivity.

Significance and Claims
The paper claims that this approach offers a systematic strategy to isolate the nucleon's intrinsic non-perturbative 3D structure by suppressing perturbative contamination. By providing a tunable energy scale ( $\tau_0$ ) in processes where the hard scale is fixed, the method offers new flexibility in controlling TMD evolution effects.

The authors assert that this technique facilitates a more definitive test of the predicted sign change of the Sivers function, a fundamental prediction of QCD factorization theorems that has been difficult to verify due to evolution dilution. The work is presented as a broad strategy applicable to a wide range of TMD observables at RHIC, the LHC, and the future EIC, paving the way for a new era of precision in mapping the nucleon's 3D structure. The authors remain modest regarding the theoretical precision, noting that their calculation is at NLL accuracy and that extending the formalism to Next-to-Next-to-Leading Logarithmic (NNLL) accuracy for polarized TMDs under a 0-jettiness veto remains an open task.

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