First evidence for mixing-induced $CP$ violation in B$^0_\mathrm{s}$ $\to$ J/$\psi\,\phi$(1020) decays in pp collisions at $\sqrt{s} =$ 13 TeV

Using a novel machine-learning-based flavor-tagging algorithm on CMS data from 13 TeV proton-proton collisions, researchers achieved the first evidence for mixing-induced CP violation in B$^0_\mathrm{s}$ $\to$ J/$\psi\,\phi$ decays by measuring a weak phase $\phi_\mathrm{s}$ that deviates from zero by 3.2 standard deviations.

The Gist

The Big Picture: Catching a Ghost in the Machine

Imagine you are watching a magic show. A magician (nature) takes a particle called a $B^0_s$ meson and turns it into a specific set of other particles: a $J/\psi$ and a $\phi$.

In the world of particle physics, there is a fundamental rule called CP symmetry. Think of this as a perfect mirror. If you take a particle, flip it in a mirror (changing it to its "antiparticle" version), and run the movie backward, the laws of physics should look exactly the same. The universe should treat the particle and its mirror-image twin with total fairness.

However, the Standard Model (our current best rulebook for how the universe works) predicts that sometimes, the universe is a bit unfair. It treats the particle and its twin slightly differently. This unfairness is called CP Violation.

This paper is about the CMS experiment at CERN (the Large Hadron Collider) catching the universe "cheating" on this rule. They found the first solid evidence that the $B^0_s$ meson and its twin don't just sit still; they mix, swap identities, and decay at slightly different rates, proving that nature has a slight preference for one over the other.

The Cast of Characters

1. The $B^0_s$ Meson: The main actor. It's a heavy, unstable particle that doesn't last long.
2. The "Mixing" (The Identity Swap): Before the $B^0_s$ dies, it has a habit of turning into its own antiparticle and then back again. It's like a chameleon that keeps switching its skin color rapidly before it finally settles down and disappears.
3. The "Weak Phase" ($\phi_s$): This is the paper's main character. Think of this as the angle of the cheat. If the universe were perfectly fair, this angle would be zero. If it's unfair, the angle is non-zero. The paper measures this angle to see exactly how unfair nature is being.
4. The "Flavor Taggers" (The Detectives): To know if the universe is cheating, you need to know what the particle was before it started mixing. Did it start as a "particle" or an "antiparticle"?
   • The paper introduces a new, super-smart detective team (a machine-learning algorithm).
   • These detectives look at the debris left behind by the collision. Some look at particles flying in the opposite direction (Opposite-Side), while others look at particles flying alongside the main actor (Same-Side).
   • By combining these clues, the team can guess the particle's original identity with much higher accuracy than before.

The Experiment: A High-Speed Photo Shoot

The scientists used the CMS detector, a giant camera at CERN, to take pictures of proton collisions.

• The Data: They looked at 96.5 "inverse femtobarns" of data (a fancy way of saying a massive amount of collision data collected in 2017 and 2018).
• The Target: They specifically hunted for $B^0_s$ mesons that decayed into a $J/\psi$ (which turns into two muons) and a $\phi$ (which turns into two kaons). It's like looking for a specific, rare combination of Lego bricks that only appear when a specific toy breaks apart.
• The Result: They found about 27,500 of these specific, "tagged" events. This is a huge number for this type of rare measurement, giving them a very clear picture.

The Discovery: The 3.2 Standard Deviation "Wink"

After analyzing the angles and timing of how these particles decayed, the scientists measured the "Weak Phase" ($\phi_s$).

• The Prediction: The Standard Model predicted a very small, specific angle (around -37 milliradians).
• The Measurement: The CMS team measured the angle to be -75 milliradians.
• The Significance: The difference between zero (perfect fairness) and their measurement is 3.2 standard deviations.

What does "3.2 standard deviations" mean?
Imagine you flip a coin 1,000 times. If it's a fair coin, you expect 500 heads. If you get 550 heads, that's suspicious. If you get 600, that's very suspicious.
In physics, a "standard deviation" is a measure of how surprised we should be.

• 1 sigma: "Maybe just luck."
• 3 sigma: "This is a strong hint. We should pay attention." (This is what the paper claims: First Evidence).
• 5 sigma: "This is a discovery. We are 99.9999% sure."

The paper states they have reached the 3-sigma level. They haven't "discovered" new physics yet (which requires 5 sigma), but they have found the first strong evidence that mixing-induced CP violation exists in this specific decay. It's the universe giving a clear "wink" that it is not perfectly symmetrical.

The Verdict

The paper concludes that:

1. The Cheat is Real: The $B^0_s$ meson does indeed mix and decay in a way that violates CP symmetry.
2. The Numbers Match: The amount of "unfairness" they measured (-75 mrad) is consistent with what the Standard Model predicts when you combine it with previous data from 8 TeV collisions.
3. No New Physics (Yet): Because their result matches the Standard Model's prediction, they haven't found a "new particle" or a "new force" yet. They just confirmed that the existing rulebook is correct in this specific, difficult-to-measure area.

Summary Analogy

Imagine a race between two runners, Particle and Antiparticle.

• Old Theory: They run at the exact same speed.
• The Paper's Finding: The scientists used a new, high-tech camera (the machine-learning tagger) to watch them. They saw that Particle runs slightly faster than Antiparticle in this specific race.
• The Conclusion: They are 99.9% sure the speed difference is real (3.2 sigma). However, the speed difference is exactly what the rulebook (Standard Model) said it would be. So, while they proved the runners are different, they haven't found a secret shortcut or a new track (New Physics) yet. They just confirmed the map was right all along.

Technical Summary

Technical Summary: First Evidence for Mixing-Induced CP Violation in $B^0_s \to J/\psi \phi(1020)$ Decays

Problem and Motivation
The decays of $B^0_s$ mesons serve as a critical probe for testing the Standard Model (SM) predictions regarding CP violation (CPV) in the quark sector and searching for new physics. In the SM, the weak phase $\phi_s$, which arises from CPV in the interference between decays with and without $B^0_s$ mixing, is predicted to be approximately $-37 \pm 1$ mrad. This precise prediction makes $\phi_s$ a sensitive observable for detecting contributions from new particles to the $B^0_s$ mixing process. While previous experiments have measured $\phi_s$ via $b \to c\bar{c}s$ transitions, no evident deviation from SM-based predictions had been established. This study aims to refine the measurement of $\phi_s$ and other parameters of the $B^0_s$–$\bar{B}^0_s$ system using a significantly larger dataset and improved analysis techniques.

Methodology
The analysis utilizes proton-proton collision data collected by the CMS experiment at a center-of-mass energy of $\sqrt{s} = 13$ TeV during 2017–2018, corresponding to an integrated luminosity of 96.5 fb$^{-1}$. The study focuses on the decay channel $B^0_s \to J/\psi \phi(1020) \to \mu^+\mu^- K^+K^-$.

• Event Selection and Triggers: Two independent trigger strategies were employed: a "muon-tagging" (MT) trigger requiring a $J/\psi \to \mu^+\mu^-$ candidate plus an additional muon, and a "standard" (ST) trigger requiring a displaced $J/\psi \to \mu^+\mu^-$ candidate in conjunction with a $\phi(1020) \to K^+K^-$ vertex. Events were selected with strict kinematic and vertex quality requirements, resulting in a sample of approximately 67,908 (MT) and 555,213 (ST) candidates.
• Flavor Tagging: A novel, machine-learning-based flavor-tagging framework was developed, combining four distinct algorithms: opposite-side (OS) muon, OS electron, OS jet, and same-side (SS) tagging. The OS taggers infer the flavor of the signal $b$-quark using the decay products of the other $b$-quark in the event, while the SS tagger exploits charge correlations between the signal $b$-quark and nearby fragmentation particles. Deep neural networks (DNNs) were utilized to estimate the mistag probability ($\omega_{\text{tag}}$) on an event-by-event basis. The combined tagging power achieved was $P_{\text{tag}} \approx 5.6\%$, yielding an effective number of tagged signal candidates of $27,500 \pm 100$.
• Amplitude Analysis: A time- and flavor-dependent angular analysis was performed in the transversity basis. The analysis measured the decay angles ($\theta_T, \psi_T, \phi_T$) and the proper decay time ($ct$) of the reconstructed $B^0_s$ meson. The decay rate model included parameters for the weak phase $\phi_s$, decay width difference $\Delta\Gamma_s$, average decay width $\Gamma_s$, mass difference $\Delta m_s$, direct CPV observable $|\lambda|$, transversity amplitudes ($A_0, A_\parallel, A_\perp$), and strong phases. An additional S-wave term was included to account for non-resonant $K^+K^-$ contributions and $B^0_s \to J/\psi f_0(980)$ decays.
• Statistical Treatment: The parameters of interest were extracted using a simultaneous unbinned multidimensional extended maximum likelihood fit to the data, incorporating seven observables: invariant mass ($m_{\mu\mu KK}$), proper decay time ($ct$), its uncertainty ($\sigma_{ct}$), and the three decay angles, along with the tagging inference ($\omega_{\text{tag}}$). Systematic uncertainties were evaluated through extensive studies on simulated samples, bootstrap methods, and alternative model assumptions.

Key Contributions

• Novel Flavor-Tagging Algorithm: The introduction of a combined OS and SS tagging framework using deep neural networks represents a significant advancement in flavor-tagging efficiency and purity for this specific decay channel.
• Improved Analysis Procedure: The analysis features a comprehensively reworked procedure compared to previous CMS results, including improved trigger paths and a more robust handling of background components (specifically $B^0 \to J/\psi K^{*0}$ and combinatorial backgrounds).
• Largest Effective Sample: This measurement utilizes the largest effective number of tagged signal candidates ever used for a single measurement of $\phi_s$.

Results
The analysis measured the weak phase to be:
$$\phi_s = -73 \pm 22 \text{ (stat)} \pm 10 \text{ (syst) mrad}$$
This value is consistent with Standard Model predictions. The measured value of $|\lambda|$ is consistent with unity, indicating no direct CP violation. All other measured physics parameters ($\Delta\Gamma_s, \Gamma_s, \Delta m_s$, amplitudes, and phases) were found to agree with SM predictions and previous world-average values.

When combined with the previous CMS result obtained at $\sqrt{s} = 8$ TeV using the BLUE method, the combined weak phase is:
$$\phi_s = -75 \pm 23 \text{ mrad}$$
This combined result differs from zero by 3.2 standard deviations.

Significance
The paper claims that the 3.2 standard deviation deviation of the combined $\phi_s$ value from zero constitutes the first evidence for mixing-induced CP violation in $B^0_s \to J/\psi \phi(1020)$ decays. While the result is consistent with the Standard Model, the precision achieved allows for stringent tests of the CKM mechanism and sets constraints on potential new physics contributions to $B^0_s$ mixing. The measurement supersedes previous CMS results and is comparable in precision to the world's most precise single measurements.