Measurements of transverse-momentum dependent effects in semi-inclusive DIS at COMPASS

This paper presents recent and upcoming results from the COMPASS experiment on transverse-momentum dependent effects in semi-inclusive deep inelastic scattering, highlighting improved constraints on quark transversity from a polarized deuteron target and the prospective first extraction of the Boer-Mulders function from unpolarized hydrogen data.

The Gist

Imagine the nucleus of an atom not as a solid marble, but as a bustling, chaotic city filled with tiny citizens called quarks. For a long time, scientists thought these citizens just moved in straight lines. But the COMPASS experiment at CERN is like a high-speed camera that has finally caught them doing something much more interesting: they are spinning, wobbling, and moving sideways in complex patterns.

This paper is a progress report from Jan Matousek (speaking for the COMPASS team) about what they've learned by shooting a beam of "muons" (heavy, unstable cousins of electrons) at these atomic nuclei. Here is the story of their findings, broken down into simple concepts.

1. The Experiment: A Cosmic Pinball Machine

Think of the COMPASS experiment as a giant, ultra-precise pinball machine.

• The Ball: A beam of muons.
• The Bumpers: The target nuclei (either liquid hydrogen or a special polarized deuteron).
• The Goal: When the muon hits a quark inside the nucleus, it knocks a new particle (a hadron) out. By watching exactly where and how fast this new particle flies out, scientists can reverse-engineer the secrets of the quark it came from.

The team has been running this machine for 20 years. They are now in the "analysis phase," meaning they are taking the mountains of data they collected and trying to decode the patterns.

2. The Mystery of the "Sideways" Spin

The main focus of this paper is Transverse Momentum.

• The Old View: Imagine a spinning top. We knew how fast it spins (helicity).
• The New View: COMPASS is asking: "Is the top also wobbling sideways?"

They are looking for two specific types of "wobble":

1. The Boer-Mulders Effect: Even if the nucleus itself isn't spinning sideways, the quarks inside might be. It's like a crowd of people standing still, but everyone is secretly leaning to the left. The paper suggests that new data from 2016–2017 might finally allow them to "see" this leaning for the first time.
2. The Sivers Effect: This is about the connection between the nucleus's spin and the quark's movement. If the nucleus is spinning like a top, does it push the quarks to one side? This is like a spinning carousel pushing the horses outward.

3. The "Deuteron" Breakthrough

One of the most exciting parts of the paper involves a specific target: Deuterium (a heavy form of hydrogen).

• The Challenge: Measuring the "sideways spin" (transversity) of the down-quark was like trying to hear a whisper in a noisy room. Previous data was too fuzzy, with huge margins of error.
• The Solution: In 2022, they used a transversely polarized deuteron target. Think of this as tuning the radio to a specific frequency where the "down-quark" signal is loud and clear.
• The Result: This new data has cut the uncertainty (the "noise") by a factor of 2.5. It's like going from a blurry, pixelated photo to a high-definition image. We now know much more about how down-quarks behave inside a proton.

4. Cleaning Up the Mess (Radiative Corrections)

The paper also talks about a technical headache: Radiative Corrections.

• The Analogy: Imagine trying to measure the speed of a car, but a strong wind (radiation) is blowing the car off course and distorting your speedometer.
• The Fix: The team has developed new methods to mathematically "cancel out" the wind. They found that without this correction, their measurements of how particles fly out were significantly distorted. By fixing this, their new results are much more trustworthy.

5. What's Next?

The paper concludes that the team is currently finalizing the analysis of two major datasets:

1. Liquid Hydrogen (2016–2017): With the new "wind correction" and background removal, they expect to extract the "Boer-Mulders" function (the secret leaning of quarks) for the first time.
2. Polarized Deuteron (2022): This unique data is already refining our map of the down-quark's behavior.

In Summary:
The COMPASS collaboration is using a massive particle accelerator to map the hidden, sideways movements of quarks inside atoms. By using better targets and cleaning up their data with advanced math, they are turning a blurry, confusing picture of the subatomic world into a sharp, detailed map. They aren't just seeing that quarks move; they are finally starting to understand how they spin and wobble in three dimensions.

Technical Summary

Technical Summary: Measurements of Transverse-Momentum Dependent Effects in Semi-Inclusive DIS at COMPASS

Problem and Context
The COMPASS experiment at CERN aims to investigate the internal structure of the nucleon, specifically focusing on hadron production in deep inelastic scattering (DIS). The primary physics goal is to interpret these interactions within the transverse-momentum-dependent (TMD) factorisation framework. This approach allows for the extraction of TMD parton distribution functions (PDFs) and TMD fragmentation functions (FFs), which describe the correlations between the polarization and transverse momentum of quarks within the nucleon.

A significant challenge in this field involves disentangling various contributions to azimuthal asymmetries in the cross-section. Specifically, understanding the interplay between kinematic effects (such as the Cahn effect), higher-twist contributions, and genuine TMD effects (like the Boer–Mulders and Sivers functions) has been difficult. Furthermore, experimental data requires rigorous correction for backgrounds, such as the decay of diffractively produced vector mesons ($\rho, \phi$), and QED radiative effects, which distort hadron variables ($z, P_T, \phi_h$) and dilute asymmetries.

Methodology
The paper summarizes recent results and analysis progress based on data collected by the COMPASS Collaboration between 2002 and 2022. The analysis focuses on semi-inclusive DIS (SIDIS) events ($\mu N \to \mu' h X$) using two specific target configurations:

1. Liquid Hydrogen Target (2016–2017): Data collected to study unpolarized targets and extract information on unpolarized quark distributions and the Boer–Mulders function.
2. Transversely Polarized Deuteron Target (2022): Data collected using a $^6$LiD target to probe the transversity of the $d$-quark and the Sivers function.

The differential cross-section is analyzed in terms of standard variables ($x, y, Q^2$), the energy fraction $z$, transverse momentum $P_T$, and azimuthal angles ($\phi_h, \phi_S$). The analysis extracts the amplitudes of azimuthal modulations (asymmetries) described in the cross-section formula.

Key methodological advancements highlighted include:

• Radiative Corrections: Implementation of corrections using the Djangoh Monte Carlo generator to address QED radiative effects, which significantly impact hadron variables and asymmetry amplitudes.
• Background Subtraction: Correction for the contamination of the DIS hadron sample by diffractively produced vector mesons (e.g., $\rho \to \pi^+\pi^-$), which exhibit large azimuthal modulations.
• Global Fits: Utilization of the new data to perform point-by-point extractions of TMD PDFs, comparing results with previous global fits that relied on older datasets.

Key Contributions and Results

• Unpolarized Target Results (Liquid Hydrogen):

  • Preliminary results for the target-polarization-independent asymmetries $A_{UU}^{\cos \phi_h}$, $A_{UU}^{\cos 2\phi_h}$, and $A_{LU}^{\sin \phi_h}$ have been presented. These measurements are corrected for diffractive vector meson backgrounds and QED radiative effects.
  • The radiative corrections are shown to be sizeable, altering the amplitude values significantly compared to uncorrected data.
  • The analysis aims to disentangle the contributions of the Boer–Mulders function ($h_1^\perp$) and the Cahn effect (kinematic contribution from non-zero $\langle k_T \rangle$) to the $A_{UU}^{\cos 2\phi_h}$ and $A_{UU}^{\cos \phi_h}$ asymmetries.
  • The $PT$-dependent multiplicity of hadrons is being finalized to improve global extractions of the unpolarized TMD PDF $f_1$ and FF $D_1$.

• Transversely Polarized Target Results (Deuteron):

  • The 2022 dataset, comprising a large sample of DIS events on a transversely polarized deuteron target, has reduced the statistical uncertainties on the Sivers ($A_{UT}^{\sin(\phi_h - \phi_S)}$) and Collins ($A_{UT}^{\sin(\phi_h + \phi_S)}$) asymmetries by up to a factor of three compared to previous measurements.
  • Preliminary extractions of the $d$-quark transversity and the first moment of the Sivers function demonstrate that the new data significantly reduces uncertainties, particularly at large Bjorken-$x$.
  • The results show that the $d$-quark transversity uncertainty is reduced by a factor of 2.5 at large $x$ in global fits incorporating the new data.

Significance and Claims
The paper claims that the COMPASS experiment provides a cornerstone for the study of hadron production in DIS. The significance of the work lies in two main areas:

1. Advancement in Analysis Techniques: The 2016–2017 liquid hydrogen data, when combined with improved analysis methods (background subtraction and radiative corrections), offers the potential to extract the transverse polarization of quarks within an unpolarized nucleon (the Boer–Mulders function) for the first time with high precision.
2. Unique Polarized Data: The 2022 transversely polarized deuteron data is described as "unique." It provides the most precise constraints to date on the $d$-quark transversity, a crucial component of the nucleon spin structure that was previously poorly constrained in global fits.

The authors conclude that these datasets are currently in the analysis phase and are expected to yield further interesting results, including asymmetries for identified hadrons and hadron pairs, which will serve as benchmarks for lattice QCD calculations and phenomenological models.