Measurement of the $Υ$(1S), $Υ$(2S), and $Υ$(3S) differential cross sections in pp collisions at $\sqrt{s}$ = 13.6 TeV

The CMS experiment measured the differential production cross sections of the $\Upsilon$(1S), $\Upsilon$(2S), and $\Upsilon$(3S) mesons in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV using 37.4 fb$^{-1}$ of 2022 data, analyzing their decay into muon pairs across specific transverse momentum and rapidity intervals.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle accelerator, essentially a giant racetrack where protons (tiny subatomic particles) are smashed together at nearly the speed of light. When these protons collide, they create a chaotic explosion of energy that briefly forms new, exotic particles before they instantly decay into something else.

This paper is a detailed report card from the CMS experiment, one of the giant detectors sitting on that racetrack. The team is studying a specific family of these exotic particles called bottomonium (specifically the $\Upsilon(1S)$, $\Upsilon(2S)$, and $\Upsilon(3S)$ states).

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

1. The "Heavyweights" of the Particle World

Think of the universe's particles like a family of musical instruments. Some are light and fast (like a flute), while others are heavy and slow (like a tuba).

• Bottomonium is made of a "beauty" quark and its anti-particle. These are the "tubas" of the particle world—heavy and slow to move.
• The paper focuses on three specific notes in this family: the $\Upsilon(1S)$ (the lowest, deepest note), the $\Upsilon(2S)$ (a slightly higher note), and the $\Upsilon(3S)$ (an even higher note).
• Scientists want to know exactly how often these "tubas" are created when protons crash into each other.

2. The Experiment: A High-Speed Photo Shoot

The researchers used data collected in 2022 from collisions where the energy was 13.6 TeV (a massive amount of energy, like a mosquito hitting a windshield but scaled up to the atomic level).

• The Data: They looked at a huge amount of data, equivalent to 37.4 "inverse femtobarns" of collisions. To use an analogy, if a femtobarn is a tiny grain of sand, they analyzed a mountain of them to find these rare particles.
• The Detection: These heavy particles don't stick around; they instantly fall apart into two muons (particles similar to electrons but much heavier). The CMS detector is like a high-speed camera that takes pictures of these two muons flying away. By measuring how fast they fly and where they go, the scientists can reconstruct the "parent" particle that created them.

3. The Measurement: Counting the Notes

The main goal was to measure the production cross-section. In everyday language, this is just a fancy way of asking: "How likely is it that we will create one of these particles?"

They measured this in two ways:

• Speed (Transverse Momentum, $p_T$): How hard was the particle kicked sideways? They looked at particles moving at speeds ranging from 20 to 200 GeV (a very wide range).
• Angle (Rapidity, $y$): Did the particle fly straight out from the collision point, or did it shoot off at an angle? They looked at two specific "zones" of angles.

The Result: They successfully counted how many of these particles were made in each speed and angle category. They found that:

• The heavier the particle (the higher the "note"), the fewer of them are made.
• The faster they are kicked sideways, the fewer of them are made (which makes sense; it's harder to kick a heavy object very fast).
• The results for the two different angle zones were almost identical.

4. Why This Matters: The "Recipe Book"

The paper explains that our current understanding of how these particles are made relies on a theory called NRQCD (Non-Relativistic Quantum Chromodynamics). Think of this theory as a recipe book for making matter.

• The recipe has ingredients called Long-Distance Matrix Elements (LDMEs). These are like "secret spices" in the recipe. We know the recipe exists, but we don't know the exact amount of spice needed because we can't calculate it with math alone.
• To figure out the right amount of "spice," scientists have to look at real-world data (like this paper) and say, "Okay, if we use this much spice, the recipe predicts exactly what we see in the detector."
• The Paper's Contribution: By measuring these particles at a higher energy (13.6 TeV) and higher speeds (up to 200 GeV) than ever before, this paper provides new, stricter constraints for the recipe book. It tells the theorists, "Your current recipe works okay, but if you tweak these specific numbers, it will match our new, high-speed data perfectly."

5. The "Feed-Down" Effect

One interesting detail the paper mentions is "feed-down."

• Imagine you are counting how many $\Upsilon(1S)$ (the lowest note) particles are made.
• However, some of the $\Upsilon(2S)$ and $\Upsilon(3S)$ (the higher notes) are unstable and quickly decay into the $\Upsilon(1S)$.
• So, when the detector sees an $\Upsilon(1S)$, it might have been made directly, or it might have been a "grandchild" of a heavier particle. The paper includes all of these in their count, ensuring the total picture is complete.

Summary

In short, the CMS team took a massive snapshot of proton collisions at record-breaking speeds. They counted how many heavy "beauty" particles were created at different speeds and angles. They found that the current theoretical "recipe books" generally get the trends right, but this new, high-precision data will help scientists fine-tune the recipes to understand the fundamental forces of nature even better.

Technical Summary

Technical Summary: Measurement of the $\Upsilon(1S)$, $\Upsilon(2S)$, and $\Upsilon(3S)$ Differential Cross Sections in $pp$ Collisions at $\sqrt{s} = 13.6$ TeV

Problem and Context
The production of heavy quarkonium states, specifically bottomonium ($\Upsilon(nS)$), serves as a critical probe for understanding hadron formation within the framework of Quantum Chromodynamics (QCD). The prevailing theoretical description, Non-Relativistic QCD (NRQCD), posits that quarkonium production involves a factorization of short-distance effects (calculable via perturbative QCD) and long-distance effects (parameterized by Long-Distance Matrix Elements, or LDMEs). While the short-distance coefficients are computed up to next-to-leading order (NLO), the LDMEs must be extracted from global fits to experimental data. A significant challenge in this field is the dependence of extracted LDMEs on the specific datasets used, kinematic thresholds, and the inclusion of polarization measurements. Previous measurements by the CMS Collaboration at $\sqrt{s} = 13$ TeV established a baseline, but extending the kinematic reach to higher transverse momenta ($p_T$) and utilizing the higher collision energy of 13.6 TeV is necessary to provide tighter constraints on these phenomenological parameters.

Methodology
This analysis utilizes a proton-proton collision dataset collected by the CMS experiment in 2022 at a center-of-mass energy of $\sqrt{s} = 13.6$ TeV, corresponding to an integrated luminosity of $37.4 \text{ fb}^{-1}$. The measurement focuses on the dimuon decay channels ($\Upsilon(nS) \to \mu^+\mu^-$) for the ground state $\Upsilon(1S)$ and excited states $\Upsilon(2S)$ and $\Upsilon(3S)$.

• Event Selection: Events are selected via a two-tiered trigger system. The Level-1 (L1) trigger requires at least two opposite-sign muons with $p_T > 4.5$ GeV and a dimuon mass $m_{\mu\mu} > 7$ GeV. The High-Level Trigger (HLT) further refines this to $8.5 < m_{\mu\mu} < 11.5$ GeV, $p_T > 9.9$ GeV, and $|y| < 1.4$. Offline selection requires muons with $p_T > 10$ GeV and $|\eta| < 1.4$, with a dimuon vertex fit probability $> 1\%$.
• Yield Extraction: Signal yields, $N(p_T, |y|)$, are extracted in two-dimensional bins of transverse momentum ($20 \le p_T \le 200$ GeV) and rapidity ($|y| < 0.6$ and $0.6 < |y| < 1.2$). This is achieved through an extended maximum likelihood fit to the dimuon invariant mass spectrum. The signal model comprises three resonances, each described by a sum of two Crystal Ball functions, while the background is modeled by a second-order polynomial. Shape parameters for the resonances are constrained using world-average mass values and scaling relations derived from simulation.
• Efficiency and Acceptance: The differential cross sections are calculated using the formula:
  $$\mathcal{B} \frac{d^2\sigma}{dy dp_T} = \frac{N(p_T, |y|)}{\mathcal{L} \Delta y \Delta p_T} \frac{1}{\epsilon(p_T, |y|)} \frac{1}{A(p_T, |y|)}$$
  where $\mathcal{L}$ is the integrated luminosity. The acceptance $A(p_T, |y|)$ is determined via Monte Carlo simulation (PYTHIA 8.306 with CP5 tune and NNPDF3.1 NNLO PDFs), assuming unpolarized production. The detection efficiency $\epsilon(p_T, |y|)$ is measured using the tag-and-probe method on data, accounting for trigger, reconstruction, and identification efficiencies, as well as a correction for muon-pair trigger inefficiencies when tracks are close in phase space.
• Systematic Uncertainties: Major sources include the luminosity measurement (1.4%), signal yield extraction (varying fit models for signal and background), acceptance modeling (reweighting simulated distributions), and efficiency uncertainties (propagated from tag-and-probe and muon-pair trigger emulation studies).

Key Contributions and Results
The paper reports the first measurement of $\Upsilon(1S)$, $\Upsilon(2S)$, and $\Upsilon(3S)$ differential cross sections at $\sqrt{s} = 13.6$ TeV.

• Kinematic Reach: The analysis extends the $p_T$ coverage from the previous CMS 13 TeV result (which stopped at 100 GeV) up to 200 GeV.
• Cross Sections: The measured cross sections, times the dimuon branching fractions, are provided for the unpolarized scenario. The results include feed-down contributions from heavier bottomonium states.
• Ratios: The ratios of excited states to the ground state ($\Upsilon(2S)/\Upsilon(1S)$ and $\Upsilon(3S)/\Upsilon(1S)$) are presented. These ratios appear to reach a plateau for $p_T \gtrsim 55$ GeV.
• Comparison with Theory: The measured cross sections are compared to NRQCD predictions that include feed-down from S- and P-wave bottomonia. The predictions describe the general trends of the data reasonably well.
• Energy Scaling: Ratios of the $\Upsilon(1S)$ cross sections between the 13.6 TeV measurement and previous measurements at 7 and 13 TeV are provided, showing consistency within uncertainties.

Significance
The authors state that these results constitute an important input for global fits of quarkonium cross sections and polarizations. By providing precise differential measurements over a broad $p_T$ range at a new collision energy, the data helps constrain the Long-Distance Matrix Elements (LDMEs) that determine inclusive quarkonium production within the NRQCD framework. The paper emphasizes that while the specific comparison to NRQCD curves is illustrative, the new measurements provide necessary constraints for improved phenomenological analyses. The results are made available in the HEPData record to facilitate further theoretical developments.