Azimuthal Asymmetries in Unpolarised Semi-Inclusive DIS at COMPASS

Using 2016–2017 COMPASS data from muon scattering on a liquid hydrogen target, this study extracts amplitudes of azimuthal modulations in unpolarised semi-inclusive deep inelastic scattering, employing a new background subtraction method for diffractive vector mesons to present results that qualitatively agree with earlier findings on isoscalar targets.

The Gist

Imagine the inside of a proton (a tiny building block of matter) not as a solid marble, but as a bustling, chaotic dance floor filled with smaller particles called quarks. Usually, scientists study these quarks by looking at how they move straight ahead. But in this paper, the researchers at the COMPASS experiment decided to look at something more subtle: how these quarks wobble side-to-side as they spin.

Here is a simple breakdown of what they did and what they found, using everyday analogies.

The Experiment: A High-Speed Pinball Game

Think of the experiment as a high-speed game of pinball.

• The Ball: A beam of muons (heavy cousins of electrons) traveling at nearly the speed of light.
• The Target: A tank of liquid hydrogen, which is essentially a collection of protons.
• The Collision: The muons smash into the protons. When they hit, they knock a quark loose, and that quark eventually turns into a new particle (a hadron) that flies out.

The scientists wanted to know: When these new particles fly out, do they fly straight, or do they curve?

The "Wobble" (Azimuthal Asymmetries)

If you throw a ball straight at a wall, it bounces back straight. But if the ball is spinning or wobbling, it might bounce off at a weird angle.

In this experiment, the researchers measured the angle at which the new particles flew out. They looked for three specific types of "wobbles" (mathematical patterns called modulations):

1. The "Cahn Effect" (The Side-to-Side Wobble): This is like a quark that is naturally jittery. Even if the beam is perfectly straight, the quark's own internal jitter makes the resulting particle curve slightly left or right. The paper calls this a $\cos \phi_h$ pattern.
2. The "Boer-Mulders" Effect (The Double Wobble): This is a more complex twist, like a figure-eight pattern. It suggests that the quarks inside the proton have a specific kind of internal spin alignment that makes them curve in a double-loop pattern. This is the $\cos 2\phi_h$ pattern.
3. The "Beam-Spin" Effect (The Spin-Induced Curve): Since the muon beam was spinning (polarized), it acted like a spinning top hitting the target. This spin transferred a twist to the particles flying out, creating a $\sin \phi_h$ pattern.

The "Ghost" Problem

There was a tricky problem. Some of the particles they saw weren't actually from the main collision. They were "ghosts" coming from the decay of short-lived particles called vector mesons (like a $\rho$ meson splitting into two pions).

Imagine trying to count how many people are dancing at a club, but suddenly a group of people walks in, does a quick spin, and leaves. If you don't account for them, your count of "dancers" is wrong.

• The COMPASS team developed a new method to identify these "ghost" particles and subtract them from their data, ensuring they were only measuring the true quark wobbles.

What They Found

After cleaning up the data, they looked at the results for protons (hydrogen targets):

• The Side-to-Side Wobble ($\cos \phi_h$): They found this wobble was definitely real and not zero. Interestingly, the wobble looked different for positively charged particles ($h^+$) compared to negatively charged ones ($h^-$). This suggests that the "jitteriness" of the quarks depends on their "flavor" (type).
• The Double Wobble ($\cos 2\phi_h$): For positive particles, this wobble was basically zero. For negative particles, it was positive.
• The Spin Curve ($\sin \phi_h$): This effect was positive for both types of particles.

A Surprising Twist

The researchers noticed something that didn't quite fit their expectations. They expected the "jitteriness" (the Cahn effect) to get smaller as the collision energy increased (because high energy usually smooths things out). Instead, they found the wobble actually got bigger as the energy went up.

They admit this is counter-intuitive. It's like expecting a spinning top to wobble less as you spin it faster, but instead, it starts wobbling more. They note that this might be because the variables they are measuring are tightly linked in their specific setup, but it remains a puzzle to solve.

The Bottom Line

This paper is a "preliminary report" (a first look at new data). The main takeaway is that the COMPASS team successfully measured these subtle wobbles in protons using a new method to remove background noise. Their results generally match what they found earlier with a different type of target (an "isoscalar" target), giving them confidence that their new measurements are correct.

They haven't solved the mystery of why the wobble gets bigger with energy yet, but they have provided a clearer, cleaner map of how quarks move inside a proton.

Technical Summary

Technical Summary: Azimuthal Asymmetries in Unpolarised Semi-Inclusive DIS at COMPASS

Problem Statement
In the framework of Quantum Chromodynamics (QCD), the internal structure of the nucleon, particularly regarding transverse momentum, is described by Transverse Momentum Dependent Parton Distribution Functions (TMD PDFs). In Semi-Inclusive Deep Inelastic Scattering (SIDIS), the non-zero transverse momentum of partons induces azimuthal dependence in the cross-section. For an unpolarised nucleon, three specific azimuthal modulations arise, carrying information about TMD PDFs and fragmentation functions (FFs):

1. A $\cos \phi_h$ modulation (the Cahn effect), related to unpolarised TMDs ($f_1, D_1$).
2. A $\cos 2\phi_h$ modulation, related to the Boer–Mulders TMD PDF ($h^\perp_1$) and the Collins FF ($H^\perp_1$).
3. A $\sin \phi_h$ modulation (beam-spin asymmetry), related to twist-three functions ($e, g^\perp$).

While previous COMPASS measurements using an isoscalar ($^6$LiD) target provided data on these asymmetries, a new analysis was required using a liquid hydrogen (proton) target to explore flavor dependence and refine understanding of the nucleon structure. A significant challenge in this analysis is the contamination from hadrons originating from the decay of exclusively produced vector mesons (e.g., $\rho^0 \to \pi^+\pi^-$, $\phi \to K^+K^-$), which exhibit large azimuthal modulations and must be subtracted to isolate the true SIDIS signal.

Methodology
The analysis utilizes data collected by the COMPASS experiment at CERN during 2016 and 2017. The experiment employed a longitudinally polarized 160 GeV/c muon beam ($\mu^+$ and $\mu^-$) scattering off a liquid hydrogen target. The beam polarization was approximately $\lambda_{\mu^-} \approx 0.8$ and $\lambda_{\mu^+} \approx -0.8$.

• Event Selection: SIDIS events were selected based on kinematic cuts: $Q^2 > 1 \text{ (GeV/c)}^2$, $W > 5 \text{ GeV/c}^2$, $x < 0.13$, $0.2 < y < 0.9$, and a virtual photon polar angle $\theta_{\gamma^*} < 60 \text{ mrad}$. Only hadrons with $z > 0.1$ and $P_T > 0.1 \text{ GeV/c}$ were considered to ensure good resolution in the azimuthal angle $\phi_h$.
• Background Subtraction: A critical methodological advancement in this work is a new procedure to subtract background from diffractively produced vector mesons. These mesons decay into hadron pairs that populate the low $Q^2$ and low $P_T$ regions but extend across the full $z$ range.
  • Events with a final state containing only $\mu' h^+ h^-$ and a combined $z_{h^+} + z_{h^-} > 0.95$ were explicitly rejected.
  • The remaining contamination from partially reconstructed pairs was estimated using the HEPGEN Monte Carlo (MC) generator, normalized to data via the missing energy distribution of reconstructed pairs, and subtracted bin-by-bin in $\phi_h$.
• Analysis Approach: The azimuthal modulation amplitudes were extracted by fitting the $\phi_h$ distributions. The analysis was performed in two ways:
  1. 1D approach: Integrating over two variables ($x, z, P_T$) to study the remaining variable.
  2. 3D approach: Binning simultaneously in $x, z,$ and $P_T$.
  • The 1D results were further subdivided into four $Q^2$ ranges.
  • Data from $\mu^+$ and $\mu^-$ beams were found compatible and merged.
• Corrections: Acceptance corrections were determined using the LEPTO MC. No QED radiative corrections were applied at the time of this presentation, though work using the DJANGO MC is ongoing. Systematic uncertainties were estimated to be comparable in magnitude to statistical uncertainties.

Key Contributions

1. New Background Subtraction Technique: The paper introduces and applies a refined method to isolate the SIDIS signal by combining explicit event rejection with MC-driven subtraction of the non-visible vector meson decay component.
2. Proton Target Data: This work presents the first extraction of these azimuthal asymmetries using a liquid hydrogen target within the COMPASS collaboration, complementing previous isoscalar target results.
3. $Q^2$ Dependence Analysis: The analysis explicitly investigates the dependence of the asymmetries on $Q^2$, a dimension not fully explored in previous isoscalar target analyses.

Results

• $\cos \phi_h$ Amplitude ($A_{UU}^{\cos \phi_h}$):
  • The amplitudes are clearly non-zero and show a difference between positive ($h^+$) and negative ($h^-$) hadrons, suggesting a potential flavor dependence of the intrinsic transverse momentum $\langle k_T^2 \rangle$.
  • Contrary to the expectation that the Cahn effect (suppressed by $1/Q$) would dominate, the amplitudes were observed to increase with $Q^2$. This trend was consistent across six different $x$ ranges.
  • The difference between $h^+$ and $h^-$ is more pronounced than in previous isoscalar target results.
• $\cos 2\phi_h$ Amplitude ($A_{UU}^{\cos 2\phi_h}$):
  • Amplitudes for $h^+$ are generally compatible with zero.
  • Amplitudes for $h^-$ are positive.
  • No visible dependence on $Q^2$ was observed.
• $\sin \phi_h$ Amplitude ($A_{LU}^{\sin \phi_h}$):
  • The beam-spin asymmetry results are positive and compatible for both $h^+$ and $h^-$.

Significance and Claims
The authors state that the results presented "qualitatively agree with earlier COMPASS results obtained with an isoscalar target." The primary significance lies in the confirmation of these asymmetries on a proton target and the observation of the $Q^2$ dependence in the $\cos \phi_h$ amplitude. The paper notes that the observed increase of the amplitude with $Q^2$ is "counter-intuitive" given the theoretical expectation for the Cahn effect, but clarifies that a direct comparison with isoscalar target data regarding this specific $Q^2$ dependence is currently not possible because the previous analysis did not extract this dependence. The work serves as a qualitative validation of the TMD framework on the proton and highlights the necessity of rigorous background subtraction for precise measurements.