Observation of $CP$ violation in $B^{0}\!\to{J\mskip-3mu/\mskip-2muψ}ρ(770)^0$ decays

Using LHCb proton-proton collision data from 2015–2018, this paper reports the first observation of time-dependent $CP$ violation in $B^{0}\!\to{J/\psi}\rho(770)^{0}$ decays, yielding precise $CP$-violation parameters that, when combined with previous measurements under SU(3) flavor symmetry, provide the most stringent constraint to date on the penguin contribution to the $CP$-violating phase in $B^{0}_{s}\!\to{J/\psi}\phi(1020)$ decays.

The Gist

Imagine the universe as a giant, high-speed dance floor where tiny particles called B mesons are the dancers. Usually, these dancers follow a strict set of choreography dictated by the "Standard Model," which is like the rulebook of physics. However, physicists love to look for moments where the dancers break the rules, specifically a rule called CP violation.

Think of CP violation like a mirror test. If you watch a dancer in a mirror, they should look like they are doing the exact opposite moves. But sometimes, the real dancer and their mirror image do slightly different things. Finding these differences is crucial because it helps scientists understand why our universe is made of matter (us) instead of being empty, or why there isn't an equal amount of "anti-matter."

The Big Discovery

This paper from the LHCb collaboration at CERN reports a major breakthrough: they have finally caught a B meson "breaking the rules" in a specific dance move called $B^0 \to J/\psi \rho(770)^0$.

Here is the simple breakdown of what they did and found:

1. The Setup: A High-Speed Camera
The scientists used the Large Hadron Collider (LHC), a massive machine that smashes protons together at nearly the speed of light. They acted like a high-speed camera, recording billions of these collisions over four years (2015–2018). They were looking for a very specific "dance" where a B meson decays into a $J/\psi$ particle (which is like a heavy, stable couple) and a $\rho(770)^0$ particle (which is like a short-lived, energetic pair of pions).

2. The Problem: The "Ghost" Interference
In the past, scientists wanted to measure a specific angle (called $\phi_s$) that tells us how these particles mix and change. However, there was a "ghost" in the machine. In physics, there are two ways a particle can decay:

• The Main Path: The direct, fast way (like taking a highway).
• The Penguin Path: A slower, more complicated loop involving virtual particles (like taking a winding backroad).

The "Penguin" path (named because the Feynman diagram looks a bit like a penguin) messes up the measurement of the main path. It's like trying to measure the speed of a car on a highway, but there's a slow, winding road merging in that makes the speedometer jump around. Scientists needed to know exactly how much the "backroad" was messing up the "highway" measurement.

3. The Solution: The Control Group
To fix this, the scientists needed a "control group." They looked at a different, but very similar, dance: $B^0 \to J/\psi \rho(770)^0$.

• Think of the main dance ($B_s$) as a complex ballet.
• Think of this new dance ($B^0$) as a simpler version of the same ballet.

By measuring how the "Penguin" ghost interfered with the simpler dance, they could mathematically calculate how much it was interfering with the complex ballet. This is like measuring how much wind affects a small toy car to predict how much it will affect a real race car.

4. The Result: A Clear Signal
Using a massive amount of data (6 times more than their previous attempt), they measured the "CP violation parameters" for this new dance.

• They found a value of 0.710 radians for the phase shift (the amount of rule-breaking).
• They found the "mirror symmetry" was broken with high precision.

This is the first time anyone has seen this specific type of time-dependent CP violation in this kind of decay. It's like finally hearing a whisper in a noisy room because you finally built a better microphone.

5. Why It Matters
Because they measured this "Penguin" effect so precisely in the control group, they could now correct the measurements of the main "ballet" dance ($B_s \to J/\psi \phi$).

• Before: The measurement of the main dance was blurry because of the "Penguin" ghost.
• Now: They have subtracted the ghost's effect and found that the "Penguin" shift is tiny: 5.0 ± 4.2 milliradians.

The Bottom Line

This paper doesn't invent a new technology or cure a disease. Instead, it's a massive step in precision physics.

• They proved that a specific type of particle decay breaks the rules of symmetry (CP violation) for the first time.
• They used this new proof to clean up the data on a different, more important particle decay.
• The result is a much sharper, more accurate picture of how the universe works, confirming that our current "rulebook" (the Standard Model) is holding up, but with much tighter margins for error.

In short: They found a new way to measure the "noise" in the universe so they can hear the "signal" much more clearly.

Technical Summary

Technical Summary: Observation of CP Violation in $B^0 \to J/\psi\rho(770)^0$ Decays

Problem and Motivation
Studies of CP violation in neutral $B$ mesons are critical for testing the Standard Model (SM) and probing for new physics. A primary observable is the CP-violating phase $\phi_s$ associated with $B^0_s$–$\bar{B}^0_s$ mixing. In the SM, $\phi_s$ is predicted to be $-37.6^{+0.6}_{-0.5}$ mrad. Current experimental measurements in the "golden" channel $B^0_s \to J/\psi\phi(1020)$ yield an average of $\phi_s = -50 \pm 17$ mrad. However, the experimental uncertainty is now comparable to the theoretical shift, $\Delta\phi_s$, caused by neglected penguin (loop) contributions. These long-distance nonperturbative effects prevent precise theoretical calculations of $\Delta\phi_s$.

To constrain these penguin effects, the LHCb collaboration utilizes SU(3) flavor symmetry to relate the penguin contributions in $B^0_s \to J/\psi\phi(1020)$ ($b \to c\bar{c}s$) to those in $B^0 \to J/\psi\rho(770)^0$ ($b \to c\bar{c}d$). The latter channel serves as a control mode with enhanced sensitivity to hadronic penguin parameters. Previous measurements using Run 1 data (2011–2012) yielded a $\Delta\phi_s$ constraint of $0.9 \pm 9.8$ mrad, which was insufficient to significantly limit penguin contamination. This paper presents an updated analysis using Run 2 data to improve precision and, for the first time, observe time-dependent CP violation in this specific decay mode.

Methodology
The analysis utilizes proton-proton collision data collected by the LHCb detector at a center-of-mass energy of $\sqrt{s} = 13$ TeV during 2015–2018, corresponding to an integrated luminosity of $6$ fb$^{-1}$. The study focuses on the decay chain $B^0 \to J/\psi(\to \mu^+\mu^-)\rho(770)^0(\to \pi^+\pi^-)$.

• Reconstruction and Selection: Candidates are reconstructed within the invariant mass range $[5250, 5500]$ MeV/$c^2$. A boosted decision tree classifier suppresses combinatorial background. Peaking backgrounds from misidentified kaons and protons are removed via particle identification, and $B^0 \to J/\psi K_S^0$ decays are vetoed.
• Yield Extraction: An unbinned maximum-likelihood fit to the $m(J/\psi\pi^+\pi^-)$ distribution separates the signal from combinatorial background (modeled by a fifth-order polynomial) and partially reconstructed backgrounds (e.g., $B^0_s \to J/\psi \eta' \rho^0 \gamma$). The signal yield is approximately 51,000 events. Residual backgrounds are subtracted statistically using negative-weight events.
• Amplitude Analysis: A weighted multidimensional maximum-likelihood fit is performed on the background-subtracted distributions of decay time, the $\pi^+\pi^-$ invariant mass ($m_{\pi\pi}$), and angular variables ($\cos\theta_\pi, \cos\theta_\mu, \chi$). The fit is performed simultaneously across six subsamples defined by data-taking period and trigger category.
• Efficiency and Tagging: The analysis accounts for non-uniform detection efficiencies in decay time and angular variables. Decay-time efficiency is determined using the control channel $B^0 \to J/\psi K^{*0}$. Flavor tagging is performed using opposite-side and same-side algorithms, with a combined effective tagging power of 4.5%. Untagged candidates (12% of the signal) are excluded from the CP fit.
• Resonance Modeling: The $m_{\pi\pi}$ spectrum is modeled using six resonances: $\rho(770)^0$, $\rho(1450)^0$, $\rho(1700)^0$, $f_0(500)$, $f_2(1270)$, and $\omega(782)$. The $\rho(770)^0$ component is assigned independent CP-violation parameters ($2\beta_{c\bar{c}d}^{\text{eff}}$ and $|\lambda|$), while other resonances share a common set.
• Dilution Reduction: To mitigate the dilution of the CP asymmetry caused by phase-space integration, a transformed decay time variable $t'$ is used, aligning oscillation phases across different regions of the Dalitz plot.

Key Results
The time-dependent CP-violation parameters for the $B^0 \to J/\psi\rho(770)^0$ process are measured as:

• $2\beta_{c\bar{c}d}^{\text{eff}} = 0.710 \pm 0.084 \text{ (stat)} \pm 0.028 \text{ (syst)}$ rad
• $|\lambda| = 1.019 \pm 0.034 \text{ (stat)} \pm 0.009 \text{ (syst)}$

The statistical significance of a non-zero value for $2\beta_{c\bar{c}d}^{\text{eff}}$ is approximately 10 standard deviations, establishing the first observation of time-dependent CP violation in $B$ meson decays to charmonium final states mediated by a $b \to c\bar{c}d$ transition. The results show no evidence for polarization-dependent effects, as parameters measured separately for different transversity amplitudes are mutually consistent.

Combining these Run 2 results with the previous Run 1 measurement yields:

• $2\beta_{c\bar{c}d}^{\text{eff}} = 0.718 \pm 0.081$ rad
• $|\lambda| = 1.030 \pm 0.031$

Using these combined parameters and assuming approximate SU(3) flavor symmetry, the penguin shift to the $B^0_s \to J/\psi\phi(1020)$ phase is constrained to:

• $\Delta\phi_s = 5.0 \pm 4.2$ mrad

A study of SU(3) flavor symmetry breaking, scanning the amplitude magnitude ratio and phase difference between the $b \to c\bar{c}d$ and $b \to c\bar{c}s$ transitions, indicates that symmetry breaking uncertainties could increase the error on $\Delta\phi_s$ to at most 6.4 mrad.

Significance
This work constitutes the first observation of time-dependent CP violation in $B^0 \to J/\psi\rho(770)^0$ decays. The precision of the measurement is approximately twice that of the previous LHCb result. By providing the most stringent constraint to date on the penguin contribution ($\Delta\phi_s$) to the $B^0_s \to J/\psi\phi(1020)$ CP-violating phase, these results are essential for precision tests of the Standard Model. The measured parameters serve as critical inputs for global analyses aiming to simultaneously determine the phases $2\beta$ and $\phi_s$ in the presence of penguin pollution.