Observation of $Υ$(1S) + Z associated production and measurement of the effective double-parton scattering cross section in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}$ = 13 TeV collected by the CMS detector, this study reports the first observation of associated $\Upsilon$(1S) and Z boson production and measures the effective double-parton scattering cross section, including its dependence on transverse momentum.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle smasher. Every second, it fires two beams of protons (tiny particles that make up atoms) at each other at nearly the speed of light. When they collide, they create a chaotic explosion of new particles.

For decades, physicists have been trying to understand exactly how these collisions happen. Usually, they assume that when two protons crash, it's a "one-on-one" fight: one piece of the first proton hits one piece of the second proton, and that's it. This is called Single-Parton Scattering (SPS).

However, this paper suggests that sometimes, it's more like a double-header game. In a single collision, two separate pairs of pieces might interact at the exact same time. This is called Double-Parton Scattering (DPS).

The Big Discovery: Catching a Rare "Double-Date"

The CMS team (a massive group of scientists) looked at 138 billion collisions (a huge amount of data) to find a very specific, rare event. They were looking for a collision that produced two heavy, distinct things at the same time:

1. A Z boson: A heavy particle that acts like a messenger of the weak nuclear force.
2. An $\Upsilon$(1S) meson: A heavy particle made of a bottom quark and its anti-particle (think of it as a very heavy, short-lived atom).

Finding these two heavy particles together is like finding a specific pair of twins in a crowd of billions. The team successfully identified 34.6 events (with a statistical certainty of over 5 standard deviations, meaning it's almost certainly a real discovery and not a fluke).

How They Did It: The "Four-Muon" Clue

Both the Z boson and the $\Upsilon$(1S) meson are unstable; they fall apart almost instantly. However, they both have a habit of decaying into pairs of muons (heavy cousins of electrons).

• The Z boson splits into 2 muons.
• The $\Upsilon$(1S) splits into 2 muons.
• Total: 4 muons flying out of the collision.

The scientists acted like detectives at a crime scene. They looked for these four muons and checked if they all came from the exact same spot (a common vertex).

• The "One-on-One" Theory (SPS): If it was a standard collision, all four muons would naturally come from the same single crash point.
• The "Double-Date" Theory (DPS): If it was a double collision, the Z boson might come from one crash, and the $\Upsilon$ from a completely separate crash happening right next to it. In this case, the muons would come from two different spots.

By analyzing the angles and distances between the muons, the team could separate the "One-on-One" events from the "Double-Date" events.

The Results: Measuring the "Effective Cross Section"

The paper calculates a number called $\sigma_{eff}$ (sigma-eff). Think of this as a measure of how crowded the proton is.

• The Analogy: Imagine a proton is a busy dance floor.
  • If the dancers (partons) are spread out evenly, it's easy to find two separate pairs to dance at the same time.
  • If the dancers are clumped together in a tight group, it's harder for two separate pairs to interact without bumping into each other.

The team measured this "crowdedness" to be 13.0 mb (millibarns). This number tells us how likely it is for two separate interactions to happen in a single proton crash.

A New Level of Detail

What makes this paper special is that they didn't just give one average number. They measured this "crowdedness" in different bins based on how fast the particles were moving (their momentum).

• They found that as the $\Upsilon$(1S) meson moves faster, the effective cross-section changes.
• This suggests that the "dance floor" isn't uniform; the arrangement of dancers changes depending on how hard you hit them.

Summary

In simple terms, this paper is the first time scientists have successfully observed a Z boson and an $\Upsilon$(1S) meson being created together in a proton collision. By studying this rare event, they confirmed that "double collisions" (where two pairs of particles interact at once) are happening more often than previously thought in this specific scenario. They used this to map out the internal structure of the proton, revealing how its tiny components are arranged in space.

Key Takeaway: Protons aren't just simple billiard balls; they are complex clouds where multiple interactions can happen simultaneously, and this paper provides a new, detailed map of how those interactions occur.

Technical Summary

Technical Summary: Observation of $\Upsilon(1S) + Z$ Associated Production and Measurement of the Effective Double-Parton Scattering Cross Section

Problem and Motivation
The production mechanism of heavy quarkonia in hadron collisions remains an area where theoretical understanding is incomplete, particularly regarding the non-perturbative hadronization of heavy quark-antiquark pairs. This complexity increases significantly when quarkonia are produced in association with electroweak bosons, such as the $Z$ boson. In these processes, the final state can arise from two distinct mechanisms: Single-Parton Scattering (SPS), where a single pair of partons interacts, or Double-Parton Scattering (DPS), where two independent pairs of partons interact within the same proton-proton collision.

The contribution of the DPS process is quantified by the effective DPS cross section, $\sigma_{\text{eff}}$, which is related to the transverse spatial distribution of partons within the nucleon. While previous experimental measurements have provided integrated values of $\sigma_{\text{eff}}$ for various processes, there is a lack of data regarding the dependence of $\sigma_{\text{eff}}$ on kinematic variables, such as transverse momentum ($p_T$). Furthermore, theoretical models struggle to fully capture the interplay between SPS and DPS in associated production channels. This study addresses these gaps by investigating the associated production of a $\Upsilon(1S)$ meson and a $Z$ boson in proton-proton collisions at $\sqrt{s} = 13$ TeV.

Methodology
The analysis utilizes proton-proton collision data collected by the CMS detector at the CERN LHC during the 2016–2018 run periods, corresponding to an integrated luminosity of $138 \text{ fb}^{-1}$.

• Event Selection: Both the $Z$ boson and the $\Upsilon(nS)$ mesons ($n=1, 2, 3$) are reconstructed via their decays into opposite-sign muon pairs ($\mu^+\mu^-$). The signal channel requires four muons in the final state.

  • $\Upsilon$ Candidates: Muons must satisfy soft identification criteria, $p_T > 3$ GeV, $|\eta| < 2.4$, and an invariant mass between 8.5 and 11 GeV.
  • $Z$ Candidates: Muons must satisfy tight identification criteria, with leading and subleading $p_T$ thresholds of 30 and 15 GeV respectively, $|\eta| < 2.4$, and an invariant mass between 66 and 116 GeV.
  • Vertexing: A crucial requirement is that all four muons must originate from a common vertex with a fit probability $>1\%$. This suppresses background from pileup interactions where the $\Upsilon$ and $Z$ originate from independent collisions.
  • Isolation: Muons are required to be isolated from hadronic activity, with specific isolation ratios ($I$) applied based on whether they belong to the $\Upsilon$ or $Z$ candidate.

• Normalization: To reduce systematic uncertainties, the signal cross section is normalized to the fiducial cross section of $Z \to 4\mu$ production. This normalization channel uses similar selection criteria but does not require a common vertex for all four muons, as the background from independent vertices in this mass window is negligible.

• Statistical Analysis:

  • Signal Extraction: An extended unbinned maximum likelihood fit is performed in two dimensions (invariant masses of the $\Upsilon$ and $Z$ candidates). Signal shapes are modeled using Voigtian and Gaussian functions, while backgrounds are described by exponential functions.
  • SPS vs. DPS Separation: The $sPlot$ technique is used to extract weights for the signal events. These weights are applied to the distributions of the rapidity difference ($\Delta y$) and azimuthal angle difference ($\Delta \phi$) between the $\Upsilon(1S)$ and $Z$ candidates. A 2D template fit using kernel density estimation (derived from simulation) separates the SPS and DPS contributions.

Key Contributions and Results

1. Observation of $Z + \Upsilon(1S)$: The analysis observes $34.6 \pm 9.0$ events of $Z + \Upsilon(1S)$ production. The statistical significance of this signal, relative to the background-only hypothesis, is 5.3 standard deviations, constituting the first observation of this associated production channel. Signals for $Z + \Upsilon(2S)$ and $Z + \Upsilon(3S)$ were found to have significances below 3 standard deviations.
2. Fiducial Cross Section Ratio: The ratio of the fiducial cross sections is measured as:
   $$R_{Z+\Upsilon(1S)} = \frac{\sigma(pp \to Z + \Upsilon(1S)) \mathcal{B}(Z \to \mu^+\mu^-) \mathcal{B}(\Upsilon(1S) \to \mu^+\mu^-)}{\sigma(pp \to Z) \mathcal{B}(Z \to 4\mu)} = (21.1 \pm 5.5 \text{ (stat)} \pm 0.6 \text{ (syst)}) \times 10^{-3}$$
3. DPS Fraction and $\sigma_{\text{eff}}$: The fit to the $\Delta y$ and $\Delta \phi$ distributions yields a DPS fraction of $f_{\text{DPS}} = 0.95 \pm 0.25$. Consequently, the DPS yield is determined to be $32.9 \pm 8.7$ events. Using this yield and the measured ratio, the effective double-parton scattering cross section is extracted:
   $$\sigma_{\text{eff}} = 13.0^{+7.7}_{-3.4} \text{ mb}$$
   This value is consistent with previous measurements of $\sigma_{\text{eff}}$ from double-quarkonium and other multi-jet processes.
4. Differential Measurement: For the first time, $\sigma_{\text{eff}}$ is measured in bins of the transverse momentum ($p_T$) of the $\Upsilon(1S)$ meson and the $Z$ boson. The results show no significant deviation from the inclusive value within the large statistical uncertainties, though the trend suggests a potential decrease in $\sigma_{\text{eff}}$ with increasing $\Upsilon(1S)$ $p_T$, consistent with expectations that higher-$p_T$ quarkonia originate from partons closer to the proton core.

Significance
The paper reports the first observation of associated $\Upsilon(1S) + Z$ production in proton-proton collisions. By successfully separating the SPS and DPS components, the study provides a measurement of $\sigma_{\text{eff}}$ in a new kinematic regime involving a heavy quarkonium state and an electroweak boson. The primary significance lies in the first-ever differential measurement of $\sigma_{\text{eff}}$ as a function of $p_T$ for these specific particles. These binned measurements offer new constraints for theoretical models of double-parton distribution functions and the transverse structure of the proton, addressing the limitation of previous studies that only provided integrated measurements over the full phase space. The result is consistent with the geometric interpretation of $\sigma_{\text{eff}}$ and supports the validity of using this parameter to quantify DPS contributions in complex final states.