⚛️ phenomenology

Evading Sudakov Dilution in Gluon Tomography

This paper proposes using fiducial hadronic recoil combined with a tagged jet to suppress Sudakov broadening and competing azimuthal harmonics from final-state soft radiation, thereby enabling precision gluon transverse-momentum-dependent (TMD) tomography by significantly enhancing the signal of the $h_1^{\perp g}$ distribution while minimizing soft-radiation effects without requiring a veto.

Original authors: Shuo Lin, Jian Zhou

Published 2026-09-03

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Shuo Lin, 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 proton, the building block of ordinary matter, a chaotic sea of particles called gluons zips around at nearly the speed of light. These gluons carry the force that binds the proton together, but they also possess a hidden layer of complexity: they move not just forward and backward, but also side-to-side, and they can be stretched or squeezed in specific directions. Physicists call this side-to-side motion and stretching "transverse momentum" and "linear polarization." Mapping these movements is like creating a three-dimensional portrait of the proton, revealing how the spin of the particles inside is entangled with their orbital motion. This map is crucial for understanding the fundamental structure of matter and the extreme conditions found in the early universe. However, trying to photograph this internal landscape is incredibly difficult because the act of measuring it is clouded by a fog of extra particles that are emitted during the collision, obscuring the true signal the scientists are trying to see.

To clear this fog, researchers Shuo Lin and Jian Zhou have proposed a new method for peering inside the proton that avoids the usual pitfalls of current experiments. In their study, they focus on a specific type of collision where a high-energy electron smashes into a proton, knocking out a pair of quarks that fly out as jets of particles. The goal is to measure the "cos 2ϕ modulation," a specific pattern in the angles of these jets that reveals the linear polarization of the gluons. The problem is that two types of unwanted radiation usually drown out this signal. First, particles emitted before the collision cause a "broadening" effect that smears the data. Second, particles emitted after the collision create a competing pattern that looks exactly like the signal the scientists want to find, making it impossible to tell the difference. Traditional methods try to solve this by ignoring any extra particles, but this throws away too much data and reduces the precision of the measurement.

The authors' solution is to change how they define the "recoil," or the pushback felt by the system. Instead of looking only at the two main jets, they propose measuring the total pushback of every single hadron—a type of particle made of quarks—that appears within a specific, wide window of space and time around the collision. They call this the "fiducial hadronic recoil." By summing up the momentum of all these particles within a defined region, they use the law of conservation of momentum to their advantage. If a particle is emitted inside this window, its push is automatically canceled out by the other particles in the sum, meaning it does not distort the measurement. Only particles that fly outside this window contribute to the noise. This clever setup means that by simply widening the window, the researchers can reduce the blurring effect of the initial radiation without having to discard any events.

Furthermore, this method naturally suppresses the confusing background from particles emitted after the collision. The researchers found that the influence of these late-emitting particles drops off rapidly as they move further away from the main jets in terms of speed and direction. By choosing a wide enough window, the unwanted background signal becomes negligible, leaving the true signal from the gluons standing out clearly. In their simulations, which serve as a benchmark for future experiments at the proposed Electron-Ion Collider, they tested a window width corresponding to a rapidity interval of 3. Under these conditions, the contribution from the linearly polarized gluons became 4.6 times stronger relative to the background noise compared to the standard method of measuring just the two jets. At the same time, the confusing background from the final-state radiation was reduced by a factor of 4.0.

The results show that this approach does not require complex new equipment or the rejection of valuable data. Instead, it relies on a smarter way of grouping the data that is already there. By including all the hadronic activity within a specific zone and letting the physics of momentum conservation do the work of filtering out the noise, the researchers have created a path to a much clearer view of the proton's interior. This technique promises to transform the field of gluon tomography, allowing scientists to finally measure the elusive linear polarization of gluons with high precision. It opens a new avenue for understanding how the spin and motion of the smallest particles in the universe are linked, turning a previously obscured view into a sharp, detailed image of the proton's inner life.

Technical Summary: Evading Sudakov Dilution in Gluon Tomography

Problem Statement
Mapping the transverse motion and linear polarization of gluons inside the proton is a central objective of nucleon tomography, specifically through the measurement of the gluon transverse-momentum-dependent (TMD) distribution $h^{\perp g}_1$ . While this distribution correlates gluon transverse momentum with linear polarization and probes saturation dynamics and spin–orbit entanglement, it remains unmeasured. The primary obstacle is the presence of two distinct radiative effects in processes involving colored final states:

Sudakov Broadening: Initial-state radiation (ISR) drives a broadening of the transverse momentum spectrum, shifting events toward larger imbalances and weakening sensitivity to TMDs in the small-recoil region.
Competing Azimuthal Harmonics: Final-state soft gluons generate additional azimuthal modulations, including a competing $\cos 2\phi$ term that obscures the signal from $h^{\perp g}_1$ .

Conventional measurements using dijet imbalance suffer because radiation outside the reconstructed jets is omitted from the recoil sum, appearing directly as transverse-momentum imbalance. Previous proposals to suppress these effects, such as 0-jettiness requirements or rapidity-restricted vetoes, often reduce experimental acceptance by vetoing soft radiation.

Methodology
The authors propose a novel strategy utilizing fiducial hadronic recoil to simultaneously suppress both Sudakov broadening and final-state soft-gluon contamination without vetoing radiation. The methodology involves:

Definition of Recoil: The hadronic recoil ( $\vec{l}$ ) is defined as the vector sum of all hadronic transverse momenta within a specific rapidity interval ( $\Delta\eta$ ). A single tagged jet fixes the azimuthal reference axis.
Momentum Conservation Mechanism: By including all hadrons within the fiducial interval in the recoil sum, momentum conservation ensures that emissions inside the interval contribute neither to recoil broadening nor to azimuthal harmonics. Only radiation outside the interval affects the measured recoil.
Kinematic Selection: Events are restricted to a two-parton hard topology where both hard outgoing partons lie inside the fiducial interval. This is verified via lepton–jet kinematics without requiring a second jet tag.
Theoretical Formalism: The calculation is performed in impact-parameter ( $b$ ) space to resum logarithmically enhanced recoil broadening. The measurement function assigns a weight of unity to emissions inside the interval and $e^{i\vec{b}\cdot\vec{k}}$ to those outside. This leads to a Sudakov factor where the out-of-interval phase space is exponentially suppressed as $\Delta\eta$ increases. The final-state soft-gluon contribution to the $\cos 2\phi$ harmonic is calculated at one-emission accuracy, showing an exponential suppression ( $e^{-2|\eta|}$ ) relative to the interval width.

Key Results
The authors benchmark this method using Deep Inelastic Scattering (DIS) kinematics ( $Q=10$ GeV, $P_T=15$ GeV, $\sqrt{s_{\gamma p}}=100$ GeV) at a future Electron-Ion Collider (EIC), comparing the fiducial recoil against the conventional $R=0.4$ dijet imbalance:

Enhancement of Signal: For a rapidity interval of $\Delta\eta = 3$ and a recoil magnitude of $l_T = 2$ GeV, the contribution of the linearly polarized gluon ( $h^{\perp g}_1$ ) to the $\cos 2\phi$ moment is enhanced by a factor of 4.6 relative to the dijet imbalance.
Suppression of Background: The competing final-state soft-gluon term is suppressed by a factor of 4.0 under the same conditions.
Spectral Behavior: As the interval width ( $\Delta\eta$ ) increases, the Sudakov broadening weakens, shifting the recoil spectrum toward smaller $l_T$ values and increasing the low-recoil yield. The azimuthally averaged channel also exhibits an enhanced yield at low recoil.
Polarization Dependence: For transverse photons, the polarized-gluon term becomes negative while the soft-gluon term remains positive. At $\Delta\eta = 3$ , the polarized-gluon contribution dominates for both longitudinal and transverse photons, making the modulation a clean probe of $h^{\perp g}_1$ without a soft-radiation veto. The difference between longitudinal and transverse moments ( $\langle \cos 2\phi \rangle_L - \langle \cos 2\phi \rangle_T$ ) isolates the $h^{\perp g}_1$ contribution, yielding a value 4.6 times larger than the dijet case.

Significance and Claims
The paper claims that fiducial hadronic recoil establishes a general strategy for precision gluon-TMD tomography. Its significance lies in:

Simultaneous Mitigation: It addresses both Sudakov broadening and final-state soft-gluon contamination simultaneously without the need for soft-radiation vetoes, thereby preserving event statistics.
Cleaner Probes: By widening the rapidity interval, the method exponentially suppresses the harmonic weight of soft emissions far from the outgoing partons, allowing the linearly polarized gluon signal to dominate.
Experimental Feasibility: The method requires only a single tagged jet to define the axis and lepton–jet kinematics to verify the topology, avoiding the need for precise reconstruction of a second jet.
Extensibility: Because the momentum-conservation cancellation is spin-independent, the technique can be extended to other leading-twist gluon TMDs through appropriate beam and target polarizations.

The authors conclude that this approach opens a new avenue for precision nucleon tomography, significantly improving sensitivity to nonperturbative gluon motion and spin–momentum correlations.

Technical Summary: Evading Sudakov Dilution in Gluon Tomography

More like this