Measurement of B meson production fraction ratios in proton-proton collisions at $\sqrt{s}$ = 13 TeV using open-charm and charmonium decays

This paper presents the first absolute normalization measurements of B meson production fraction ratios ($f_{B^+}/f_{B^0}$, $f_{B^0_s}/f_{B^0}$, and $f_{B^0_s}/f_{B^+}$) as functions of transverse momentum and rapidity in proton-proton collisions at $\sqrt{s} = 13$ TeV, utilizing a high-statistics 2018 CMS dataset with both open-charm and charmonium decay channels to improve branching fraction ratios and confirm isospin invariance.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle smasher. When it smashes protons together, it doesn't just create a random mess; it creates a specific family of heavy particles called B mesons. Think of these B mesons as the "royal family" of the particle world. They are heavy, short-lived, and they come in three main "flavors" or siblings: B+, B0, and B0s.

For a long time, physicists have been trying to answer a simple question: When the LHC smashes protons, how many of each sibling are born? Do they come in equal numbers, or is one flavor more popular than the others?

This paper is like a massive census taken by the CMS experiment (one of the giant detectors at the LHC) to count these particles. Here is the story of how they did it, explained simply.

1. The Challenge: Finding a Needle in a Haystack

Usually, when scientists look for these particles, they have to be very picky. They set up "traps" (triggers) that only catch specific types of events, like a fisherman using a net with holes that only let certain fish through. This is efficient, but it introduces a bias. If your net only catches blue fish, you might wrongly conclude that blue fish are the only ones in the ocean.

To get a true count, the team needed an unbiased sample. They needed to catch everything without prejudice.

The "B Parking" Strategy:
Imagine a busy highway (the LHC) where traffic is so heavy that you can't stop every car to check who is inside. Instead, the CMS team used a clever trick called "B Parking."

• They knew that B mesons are usually born in pairs (twins).
• They set a trap to catch one twin if it had a specific feature (a muon, which is like a heavy electron).
• Once that first twin was caught, they said, "Okay, we have a B meson event! Let's park the data for the other twin, no matter what it looks like."
• This allowed them to collect a massive, unbiased library of 10 billion (10¹⁰) B meson decays, essentially giving them a perfect snapshot of the "family tree" without the filter of their usual nets.

2. The Two Ways to Identify the Siblings

Once they had this massive library, they had to figure out which sibling was which. They used two different "languages" or decay patterns to identify them:

• The "Open-Charms" Language:
  Think of this as looking at the fingerprint of the decay. The B meson breaks apart into a D meson (a lighter cousin) and some other particles. The team looked for specific combinations of pions and kaons (lighter particles).

  • The Analogy: It's like identifying a person by the specific brand of shoes and hat they are wearing. This method is very clean and relies on solid theoretical math to tell the difference between the siblings.

• The "Charmonium" Language:
  This is like looking at a famous celebrity in the crowd. The B meson decays into a J/ψ particle (a very distinct, heavy particle made of a charm quark and its anti-quark) which then instantly splits into two muons.

  • The Analogy: It's like spotting a celebrity (the J/ψ) wearing a bright red coat. It's very easy to spot, but until now, scientists didn't know exactly how many celebrities were there relative to the regular people because they didn't know the "conversion rate" between the two languages.

3. The Big Breakthrough: Connecting the Dots

In the past, scientists could count the "Open-Charms" (the fingerprints) very accurately. They could also count the "Charmonium" (the celebrities) very accurately. But they couldn't easily compare the two because they didn't know the exact conversion rate between them.

This paper's magic trick:
The team combined both methods.

1. They used the "Open-Charms" data (which they trust theoretically) to get the absolute numbers of the siblings.
2. They used the "Charmonium" data (which is very precise but was previously only relative) to see how the numbers changed based on the speed (momentum) of the particles.
3. By matching the two, they created a universal translator. They could now say, "For every 100 B+ mesons, there are exactly X B0s mesons," with a level of precision never seen before.

4. What Did They Find?

The results were fascinating:

• The "Sibling Rivalry" (Isospin):
  Physics has a rule called "Isospin Invariance," which predicts that the B+ and B0 siblings should be born in equal numbers (a 1:1 ratio).

  • The Result: The team checked this carefully. They found the ratio is 0.956, which is incredibly close to 1.
  • The Metaphor: It's like flipping a coin a billion times. You expect 50% heads and 50% tails. They got 47.8% heads and 52.2% tails. That's close enough to say, "Yes, the coin is fair." The universe treats these two siblings equally.

• The "Speed Limit" (Momentum Dependence):
  Previous studies suggested that the ratio of the rare B0s sibling to the common ones changes depending on how fast the particles are moving.

  • The Result: They confirmed that at lower speeds, the ratio changes, but once the particles get fast enough (above a certain speed), the ratio flattens out and stays constant. It's like a car accelerating: it speeds up quickly at first, but eventually, it hits a cruising speed and stays there.

5. Why Does This Matter?

You might ask, "Who cares about counting B mesons?"

• The Cosmic Scale: These measurements are crucial for understanding the Standard Model of physics. If the ratios were different than expected, it would mean there is "New Physics" hiding in the shadows—perhaps a new force or a new particle we don't know about yet.
• The Precision Tool: By pinning down these ratios so accurately, scientists can now measure other rare events (like the decay of a B0s into two muons) with much higher precision. It's like calibrating a scale so perfectly that you can now weigh a feather with a microscope.

Summary

In short, the CMS team used a clever "parking" strategy to collect a massive, unbiased sample of B mesons. They used two different identification methods to cross-check their work, effectively creating a new, ultra-precise ruler for the particle world. They confirmed that the universe treats the B+ and B0 siblings equally and mapped out exactly how the rare B0s sibling behaves at different speeds. This work removes a major source of uncertainty for future physics discoveries, acting as a solid foundation for the next generation of experiments.

Technical Summary

1. Problem Statement

The production fractions of $b$-hadrons ($f_u, f_d, f_s$), representing the probabilities that a $b$-quark fragments into a $B^+$, $B^0$, or $B^0_s$ meson, are critical inputs for precision measurements in flavor physics.

• Normalization Dependency: Measurements of rare $B^0_s$ decay branching fractions (e.g., $B^0_s \to \mu^+\mu^-$) often rely on normalizing yields to $B^+$ or $B^0$ decays. This requires precise knowledge of the production fraction ratios (PFRs), specifically $f_s/f_u$ and $f_s/f_d$.
• Kinematic Dependence: Previous studies (LHCb, CMS) indicated that these ratios depend on the transverse momentum ($p_T$) of the $B$ meson, particularly at low $p_T$. However, absolute normalization for charmonium-based measurements has been elusive, often relying on theoretical inputs or relative shapes.
• Isospin Invariance: A fundamental assumption in many analyses is that $f_d = f_u$ (isospin invariance). While valid in $e^+e^-$ collisions at the $Z$ pole, this assumption is less certain in hadronic collisions and requires direct experimental verification without theoretical bias.
• Theoretical Uncertainties: Extracting $f_s/f_d$ from open-charm decays is complicated by non-factorizable contributions in certain decay channels, requiring a strategy to minimize theoretical uncertainties.

2. Methodology

The analysis utilizes a unique dataset recorded by the CMS experiment during the 2018 LHC run at $\sqrt{s} = 13$ TeV.

Data Sample

• Source: A special "B parking" dataset collected with high-rate single-muon triggers.
• Luminosity: $41.6 \pm 1.0 \text{ fb}^{-1}$.
• Sample Size: Approximately $10^{10}$ unbiased $b$-hadron decays.
• Trigger Strategy: The "B parking" strategy uses a high-$p_T$ muon from one $b$-hadron (tag-side) to trigger the event, allowing the other $b$-hadron (probe-side) to decay arbitrarily. This provides an unbiased sample of $B$ meson decays, crucial for measuring production fractions without trigger bias.

Decay Channels

The analysis measures PFRs using two distinct decay topologies:

1. Open-Charm Decays (Probe-side):
   • $B^+ \to \pi^+ D^0 (K^-\pi^+)$
   • $B^0 \to \pi^+ D^- (K^-\pi^+\pi^-)$
   • $B^0_s \to \pi^+ D_s^- (\pi^- \phi(K^+K^-))$
   • Significance: These channels allow for absolute normalization using precision theoretical calculations of branching fraction ratios (QCD factorization).
2. Charmonium Decays:
   • $B^+ \to J/\psi(\mu^+\mu^-) K^+$
   • $B^0 \to J/\psi(\mu^+\mu^-) K^{*0}(K^+\pi^-)$
   • $B^0_s \to J/\psi(\mu^+\mu^-) \phi(K^+K^-)$
   • Significance: These are measured in both "tag-side" (triggered by the $J/\psi$ muon) and "probe-side" categories to study kinematic dependencies and cross-check results.

Analysis Strategy

• Event Selection:
  • Open-charm: Uses a Boosted Decision Tree (BDT) to separate signal from combinatorial background. Requires reconstruction of secondary vertices (SV) and tertiary vertices (TV) for the $D$ meson.
  • Charmonium: Uses a cut-based analysis due to higher signal purity. Requires opposite-sign muon pairs consistent with $J/\psi$ mass.
• Signal Extraction: Binned maximum likelihood fits to the $B$ candidate invariant mass spectrum. Signal shapes are modeled using Double-Gaussian (open-charm) or Johnson functions (charmonium). Backgrounds include Cabibbo-suppressed decays, partially reconstructed decays, and combinatorial backgrounds.
• Efficiency Correction: Ratios of efficiency-corrected yields ($N_{corr}$) are used to cancel systematic uncertainties. Simulated samples are reweighted to match data distributions in $p_T$ and rapidity ($y$).
• Absolute Normalization: The paper derives absolute normalization factors ($c_{sd}, c_{su}$) by combining the open-charm PFRs (which have absolute theoretical normalization) with the charmonium relative ratios. This allows the charmonium results to be converted to absolute PFRs for the first time.

3. Key Contributions

1. First Absolute Normalization for Charmonium PFRs: By combining open-charm and charmonium results, the authors determine absolute normalization factors ($c_{sd} = 1.64 \pm 0.14$, $c_{su} = 2.02 \pm 0.18$). This converts relative charmonium measurements into absolute production fractions, removing reliance on external theoretical inputs for the charmonium channel.
2. Direct Test of Isospin Invariance: The measurement of $f_d/f_u$ is performed directly in both open-charm and charmonium channels without assuming $f_d = f_u$.
3. Improved Branching Fraction Ratios: The analysis provides new, high-precision measurements of ratios of branching fractions between charmonium and open-charm decays (e.g., $\mathcal{B}(B^0_s \to J/\psi\phi)/\mathcal{B}(B^0_s \to \pi^+ D_s^-)$), improving upon world averages by $\approx 40\%$ for $B^0_s$ decays.
4. Extended Kinematic Range: The measurement covers $8 < p_T < 60$ GeV and $|y| < 2.25$, extending previous CMS measurements and providing data on the high-$p_T$ plateau.

4. Results

• Production Fraction Ratios ($f_s/f_u$ and $f_s/f_d$):

  • Measured as functions of $p_T$ and $|y|$ in the open-charm channel.
  • Kinematic Dependence: No significant linear dependence on $p_T$ or $|y|$ was found within the statistical precision of this specific dataset (though low-$p_T$ trends are known from other analyses).
  • Averages:
    • $\langle f_s/f_d \rangle = 0.219 \pm 0.008 (\text{stat}) \pm 0.014 (\text{syst})$
    • $\langle f_s/f_u \rangle = 0.218 \pm 0.008 (\text{stat}) \pm 0.015 (\text{syst})$
  • High-$p_T$ ($p_T > 18$ GeV):
    • $f_s/f_d = 0.215 \pm 0.010 (\text{stat}) \pm 0.014 (\text{syst})$
    • $f_s/f_u = 0.218 \pm 0.009 (\text{stat}) \pm 0.016 (\text{syst})$
  • These values are consistent with LHCb and LEP measurements.

• Isospin Invariance ($f_d/f_u$):

  • Combined result from open-charm and charmonium channels:
    • $f_d/f_u = 0.956 \pm 0.043$
  • Conclusion: The result is consistent with unity ($1.0$) within $5\%$ precision, supporting the hypothesis of isospin invariance in $b$-hadron production in $pp$ collisions.

• Branching Fraction Ratios:

  • $\mathcal{B}(B^+ \to J/\psi K^+)/\mathcal{B}(B^+ \to \pi^+ D^0) = 0.213 \pm 0.007$
  • $\mathcal{B}(B^0_s \to J/\psi \phi)/\mathcal{B}(B^0_s \to \pi^+ D_s^-) = 0.358 \pm 0.019$
  • $\mathcal{B}(B^0 \to J/\psi K^{*0})/\mathcal{B}(B^0 \to \pi^+ D^-) = 0.479 \pm 0.022$

5. Significance

• Precision Flavor Physics: The derived absolute normalization for charmonium channels significantly reduces systematic uncertainties in future measurements of rare $B^0_s$ decays, such as $B^0_s \to \mu^+\mu^-$, where the production fraction ratio is a dominant systematic uncertainty.
• Validation of Theory: The results validate the use of QCD factorization predictions for open-charm decays as a robust method for absolute normalization.
• Isospin Symmetry: The confirmation of $f_d \approx f_u$ in $pp$ collisions strengthens the theoretical foundation for many B-physics analyses that assume isospin symmetry.
• Methodological Advancement: The "B parking" technique demonstrated here proves capable of collecting massive, unbiased samples of heavy-flavor decays, opening new avenues for precision measurements that were previously limited by trigger biases.

In summary, this paper provides a comprehensive, model-independent measurement of $b$-hadron production fractions, establishing a new standard for absolute normalization in charmonium analyses and confirming isospin invariance in high-energy proton-proton collisions.