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Collins effect in pion-in-jet production in polarized $pp$ and $ep$ collisions

This paper employs a hybrid transverse momentum dependent approach to confirm the universality of the Collins function by successfully describing STAR proton-proton collision data and subsequently provides leading-order predictions for Electron-Ion Collider kinematics, demonstrating that quasireal photon exchange effects, while sizable, do not hinder the clear extraction of the transversity distribution and its sea-quark component in lepton-proton collisions.

Original authors: Carlo Flore, Umberto D'Alesio, Marco Zaccheddu

Published 2026-07-09

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CC BY 4.0

Original authors: Carlo Flore, Umberto D'Alesio, Marco Zaccheddu

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

Imagine you are trying to understand the inner workings of a complex machine, like a car engine, but you can only see the smoke coming out of the exhaust. You can't open the hood, so you have to guess how the pistons are moving based on the direction and spin of that smoke.

This paper is about doing exactly that, but with the smallest building blocks of the universe: protons (the heavy particles in the center of atoms). Scientists want to map out the "3D structure" of these protons to understand how their internal parts (quarks) spin and move.

Here is a simple breakdown of what the authors, Carlo Flore and his team, did and found:

1. The "Spin" Mystery

Inside a proton, there are tiny particles called quarks. Some of these quarks are spinning sideways (transversely polarized). The scientists are trying to figure out how this sideways spin affects the particles that fly out when protons smash into each other.

They are looking for a specific "signature" called the Collins effect. Think of it like a spinning top. If you throw a spinning top, it doesn't just fly straight; it tends to wobble or curve in a specific direction depending on which way it was spinning. The Collins effect is that "wobble" in the subatomic world.

2. The Two Experiments: The "Smash" and the "Hit"

The team studied this effect in two different ways, like using two different cameras to film the same event:

The "Smash" (Proton-Proton Collisions): They looked at data from smashing two protons together (like at the STAR experiment). They found that their mathematical model, which was built using data from other types of collisions, predicted the results perfectly.
- The Takeaway: This confirms that the "Collins wobble" is a universal rule. It works the same way whether you are looking at protons smashing into protons or electrons hitting protons. It's like finding that the same law of physics applies whether you are in New York or Tokyo.
The "Hit" (Electron-Proton Collisions): This is the new part of their study. They looked at what happens when a fast electron hits a proton. This is cleaner and simpler than smashing two protons because there is less "noise" (fewer extra particles getting in the way).
- The Analogy: Imagine trying to hear a whisper in a crowded room (proton-proton) versus hearing it in a quiet library (electron-proton). The library setting lets you hear the whisper (the specific spin signal) much more clearly.

3. The "Photon" Twist

In the electron-proton experiments, the scientists had to account for something tricky. Sometimes, the electron acts like a flashlight, shooting out a beam of light (a "quasireal photon") that hits the proton.

They calculated how much this "flashlight" effect changes the results.
The Result: It does add some extra activity (about 50% to 100% more "noise" in the data), but it doesn't ruin the experiment. The main signal (the quarks doing the spinning) is still the loudest voice in the room.

4. Why This Matters

The authors predict that if we build a future machine called the Electron-Ion Collider (EIC), we will be able to see things we've never seen before.

The "Sea" of Particles: Inside a proton, there are "valence" quarks (the main ones) and a "sea" of temporary quarks that pop in and out. We know a lot about the main ones, but the "sea" is a mystery.
Because the electron-proton collision is so clean, this new method allows scientists to finally get a good look at the "sea" quarks and how they spin.

Summary

The paper says:

We have a good map of how protons spin based on past data.
We checked this map against proton-smashing data, and it fits perfectly.
We used this map to predict what will happen in future electron-proton collisions.
Even with some extra "noise" from light beams, the electron-proton method is a much clearer way to see the hidden spinning parts of the proton, especially the mysterious "sea" particles.

In short, they are refining their tools to take a sharper, clearer picture of the hidden spin inside the atom's core.

Technical Summary: Collins Effect in Pion-in-Jet Production in Polarized $pp$ and $ep$ Collisions

Problem and Motivation
The primary objective of this work is to investigate the Collins azimuthal asymmetry in the production of pions within jets. This observable serves as a critical testing ground for Transverse Momentum Dependent (TMD) factorization and the universality of the Collins fragmentation function ( $H_1^{\perp}$ ). While the Collins function, which correlates the transverse polarization of a quark with the transverse momentum of the produced hadron, has been successfully extracted from Semi-Inclusive Deep Inelastic Scattering (SIDIS) and $e^+e^-$ annihilation data, its universality across different processes requires independent verification. Specifically, the authors aim to extend the analysis from proton-proton ($pp$) collisions to lepton-proton ( $\ell p$ ) collisions, such as those anticipated at the Electron-Ion Collider (EIC). The $\ell p$ channel offers a complementary environment where the absence of initial-state gluon contributions in the leading-order (LO) asymmetry numerator could provide a cleaner access to the transversity distribution ( $h_1^q$ ), particularly its sea-quark component.

Methodology
The authors employ a hybrid TMD approach characterized by a collinear configuration for the initial state and a TMD treatment for the fragmentation sector. The calculation is performed at Leading Order (LO) in the partonic cross-section, with the hard scale set to the jet transverse momentum ( $\mu = p_{jT}$ ).

Inputs: The analysis utilizes transversity ( $h_1^q$ ) and Collins ( $H_1^{\perp q}$ ) fragmentation functions extracted from global fits of SIDIS and $e^+e^-$ data (specifically Ref. [6]). For collinear inputs, the MSHT20nlo proton Parton Distribution Functions (PDFs) and DEHSS pion Fragmentation Functions (FFs) are used. The transversity function is evolved using a modified version of HOPPET.
$pp$ Collisions: The study first revisits the $p^\uparrow p \to \text{jet } \pi X$ process. The asymmetry is calculated as a convolution of the collinear transversity, the polarized partonic cross-section, and the Collins TMD FF.
$\ell p$ Collisions: For the $\ell p^\uparrow \to \text{jet } \pi X$ process (where the final-state lepton is unobserved), the authors include contributions beyond the standard LO ( $O(\alpha^2)$ ). Specifically, they incorporate the quasireal photon exchange via the Weizsäcker-Williams (WW) approximation at $O(\alpha^2 \alpha_s)$ . In this approximation, the lepton acts as a source of real photons. The unpolarized cross-section includes channels such as $q\gamma \to qg$ , $q\gamma \to gq$ , and $g\gamma \to q\bar{q}$ . Crucially, the numerator of the Collins asymmetry receives contributions only from the $q\gamma \to qg$ scattering channel, as other spin transfers vanish and gluon transversity is zero for a spin-1/2 target.

Key Results

Validation in $pp$ Collisions:
The authors present postdictions for the Collins asymmetry in $pp$ collisions at center-of-mass energies of $\sqrt{s} = 200$ and $510$ GeV. The results show good agreement with STAR experimental data across the entire $z$ (momentum fraction) range. This agreement supports the universality of the Collins function when moving from SIDIS/ $e^+e^-$ to $pp$ processes and validates the TMD factorization framework for hadron-in-jet production. The study notes that the small- $z$ region, not covered by the extraction data, is highlighted but the overall description remains robust.
Predictions for $\ell p$ Collisions (EIC Kinematics):
Predictions are provided for EIC kinematics at $\sqrt{s} = 45, 105,$ and $141$ GeV.
- Cross-Section Enhancement: The inclusion of the Weizsäcker-Williams (WW) photon exchange significantly enhances the unpolarized cross-section, increasing the total rate by a factor of approximately 1.5 to 2 compared to the pure LO result, particularly in the backward rapidity region.
- Channel Dominance: Despite the sizable WW contribution, quark-initiated channels remain dominant, accounting for 80–90% of the total cross-section. Gluon-induced channels play a marginal role in the denominator of the asymmetry.
- Asymmetry Magnitude: The Collins asymmetry is predicted to be sizable, reaching values of 8–10% depending on kinematics.
  - For $\pi^-$ , the asymmetry is relatively flat at approximately 2–3%.
  - For $\pi^+$ , the asymmetry increases with $z$ , reaching up to 8% in the forward region. This behavior is attributed to the dominance of the up-quark transversity (which is large) combined with the favored Collins FF, whereas $\pi^-$ production involves suppressed factors.
- Kinematic Dependence: The asymmetry decreases when including the WW contribution, especially at forward rapidity. At large negative pseudorapidities and higher energies (probing small- $x \sim 10^{-2}$ ), the asymmetries are strongly suppressed due to the valence-like parametrization of transversity. This suppression highlights the sensitivity of this kinematic region to the poorly constrained sea-quark component of transversity.

Significance and Claims
The paper claims that the study provides a consistent description of existing STAR data, thereby reinforcing the universality of the Collins function. More importantly, the extension to $\ell p$ collisions demonstrates that the Electron-Ion Collider offers a unique environment for studying transversity. Unlike $pp$ collisions, where gluon contributions can complicate the extraction, the $\ell p$ process allows for a "cleaner access" to the transversity distribution because the numerator of the asymmetry is driven almost exclusively by quark channels, and the gluon contribution to the denominator remains subleading even after including WW corrections.

The authors conclude that pion-in-jet production at the EIC will enable a more precise determination of the transversity distribution, including its sea-quark component, and will serve as a further test of TMD factorization and Collins function universality. The work is modest in its scope, noting that future refinements will require more sophisticated parameterizations, full TMD evolution, and a more accurate treatment of jet fragmentation beyond LO accuracy.

1. The "Spin" Mystery

2. The Two Experiments: The "Smash" and the "Hit"

3. The "Photon" Twist

4. Why This Matters

Summary

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