The universe is built from tiny asymmetries. The way matter slightly outnumbers antimatter in the early cosmos still echoes through the particles we study today. CP violation — a shorthand for violations of charge conjugation (C) and parity (P) symmetry — is one of the few levers physicists have to explain why there is something rather than nothing when the universe began. In the subatomic world, those levers show up as tiny, precise differences in how particles decay compared with their antiparticles. For decades, researchers have chased these faint fingerprints, hoping they might whisper about new physics beyond the well-tested Standard Model or sharpen our view of the existing theory to a razor’s edge.
The LHCb collaboration at CERN has been one of the busiest whisper-trackers in this quest. Using data collected during the Large Hadron Collider’s Run 2, they’ve pushed into sharper territory on a particular family of particles known as B mesons — specifically the B_s meson, which contains a bottom quark and a strange antiquark. In a new analysis, they studied the decay B_s → J/ψ K*(892)0, where the J/ψ becomes a pair of muons and the K*(892)0 decays into a kaon and a pion. The goal wasn’t just to count how often this decay happens; it was to dissect the angular patterns of the decay products, tease apart different quantum waves, and extract CP-violating signatures with unprecedented precision. The paper, produced by the LHCb collaboration at CERN, lists R. Aaij as the first author among hundreds of collaborators who played a role in this measurement. That naming signals the human, ground-level effort behind a result that is fundamentally about how nature treats matter and antimatter in the tiniest of clocks.
Why it matters: CP-violating phases in B_s decays are a clean probe of the CKM mechanism — the part of the Standard Model that ties quark flavors to weak interactions. The phase called φ_s is especially interesting because, in the simplest approximation, it should be a fixed, tiny number set by the underlying quark mixing angles. If new particles or forces exist, they could nudge φ_s away from the Standard Model prediction. But measurements aren’t that straightforward: subleading processes, known as penguin diagrams, can also shift the observed phase. The challenge is to separate a genuine hint of new physics from a robust, theory-laden effect of known physics. This is where precision, data-driven techniques and clever use of related decay channels come in. The Run 2 analysis adds a new layer of precision, tightening the noose on where penguin effects could hide and, in the process, sharpening the test of the Standard Model itself.
In the pages that follow, we’ll travel through the experiment’s approach: how LHCb teases out polarization fractions, CP asymmetries, and their phases from angular distributions, how the data is disentangled from backgrounds, and how these pieces sew together into a narrative about whether nature still obeys the rules we’ve built for it. We’ll also meet the subtle, often overlooked star of the show: the S-wave component of the Kπ system, a spin-zero background that interferes with the main resonance and matters for the precision of the CP measurements. And we’ll end with the broader stakes — what these measurements tell us about penguin pollution and why that matters for chasing new physics at the energy frontier.
The hunt for CP violation in B_s
To understand what LHCb is measuring, imagine a clockwork dance where a B_s meson can decay directly to a final state or do so after a brief interlude of mixing with its antiparticle. The interference between these two paths encodes φ_s, a CP-violating phase tied to the oscillations between B_s and anti-B_s. In the Standard Model, when you look at decays governed by the b → c c̄ s transition — the route that leads to J/ψ and a light strange meson — φ_s is predicted to be a small, negative angle, roughly a few tens of milliradians. It’s not zero, but it’s tiny enough that any sizable deviation could signal new physics entering through quantum loops.
The legacy measurements have already pinned φ_s down with impressive care, but penguin contributions — loop-level processes that subtly skirt the clean path to φ_s — can muddy the interpretation. A data-driven route to tame this confusion is to study related decays that share the same quark-level transitions but involve different final-state companions, such as B_s → J/ψ K*(892)0 and its sibling B^0 → J/ψ K*(892)0. By comparing CP asymmetries in these channels and exploiting SU(3) flavor symmetry, physicists can bound how much penguin contamination could be skewing the φ_s extracted from J/ψ φ decays. The Run 2 analysis adds to this program by extracting polarisation fractions and CP asymmetries directly from the angular patterns of B_s → J/ψ K*(892)0, in multiple mass bins of the Kπ system, and then combining with Run 1. The result is not just a set of numbers; it’s a more precise map of where new physics could still be hiding and where the Standard Model continues to hold its own.
The study’s data-set is the Run 2 13 TeV pp collision sample collected by LHCb, totaling about 6 fb−1. The team didn’t just count events; they reconstructed the full kinematics of each decay, imposed a multivariate filter to suppress background, and then performed a simultaneous fit to the mass distribution across several Kπ mass bins. The goal was to isolate the B_s and B^0 signals and to produce clean angular distributions that could be translated into physics parameters. The collaboration’s use of a two-component model for the signal shapes, including a robust description of the tails left by final-state radiation, demonstrates how experimentalists turn real-world detector effects into a faithful portrait of the underlying physics.
Angles, waves, and the dance of particles
Central to this analysis is an angular formalism that translates the way decay products emerge into a set of transversity amplitudes. The B_s → J/ψ K*(892)0 decay has a P-wave component (the K*(892)0 is a vector meson) and an S-wave component (a spin-zero Kπ combination). Each component contributes a distinct pattern to the angular distributions of the muons from J/ψ and the kaon-pion pair from K*(892)0. In the language of the analysis, the amplitudes A0, A∥, A⊥ describe the longitudinal, parallel, and perpendicular polarizations of the J/ψ, while AS captures the S-wave piece. The amplitudes carry both magnitudes and phases, written as complex numbers |Ak| eiδk. The CP-conjugate decay flips some signs in the interference terms, giving researchers a handle on CP violation through ACPk, the direct CP asymmetries of each polarization component.
The angular rate can be expanded into a set of ten terms, each built from products of the amplitudes and specific angular functions. In practice, this means the data tell you how often you see particular angular configurations of the decay products, and from that you infer how much of the decay proceeds through each polarization state and how the phases between states differ between B_s and its antiparticle. The analysis uses an eight-category fit that splits the data into four Kπ mass bins and two kaon-charge states (which tag whether you’re looking at B_s or its antiparticle). This simultaneous fit yields the P-wave polarisation fractions f0 and f∥, the corresponding CP asymmetries ACP0 and ACP∥, and the phase differences δ∥−δ0 and δ⊥−δ0, all averaged over the Kπ mass range, along with the S-wave fraction FS and its phase δS. The results are then complemented by an updated measurement of the B_s → J/ψ K*(892)0 branching fraction relative to B^0 → J/ψ K*(892)0.
One technical triumph here is the careful handling of the angular acceptance — how the detector and selection criteria distort the true decay-angle distributions. The LHCb team calculates per-subsample normalisation weights that encode the angular acceptance from simulated data, then folds them into the likelihood that extracts the physics parameters. They also account for correlations between the mass fit used to separate signal from background and the angular observables, verifying that any residual links don’t bias the extraction. It’s a reminder of how precision flavor physics is as much about understanding your instrument as about understanding the particles themselves.
So what did they find? The Run 2 results for the P-wave polarisation fractions are f0 = 0.534 with a small statistical and a slightly smaller systematic uncertainty, and f∥ = 0.211 with similar precision. The direct CP asymmetries in the P-wave components come out consistent with zero within uncertainties: ACP0 ≈ 0.01–0.02, ACP∥ ≈ −0.05 to 0.06, ACP⊥ ≈ 0.06 to 0.07, depending on the exact treatment of systematics and whether you quote Run 2 alone or include the Run 1 combination. In plain language: there is no strong sign yet of CP violation in these specific angular channels beyond what the Standard Model expects, and the uncertainties have been driven down enough that the room for large, unexpected effects has narrowed. The S-wave sector — the sometimes-mischievous cousin to the P-wave — is messier by construction, but the analysis teases out its fraction FS and phase δS across several Kπ mass bins, providing a more complete picture of how these different partial waves interfere.
Beyond the angular narrative, the analysis delivers a refined branching-fraction ratio: B(B_s → J/ψ K*(892)0) relative to B(B^0 → J/ψ K*(892)0) is about 3 percent, with uncertainties that reflect both statistical limitations and the need to understand how the angular distribution influences the detection efficiency. When combined with Run 1 data, the collaboration offers the most precise picture to date, including an updated absolute branching fraction for B_s → J/ψ K*(892)0 anchored to external inputs from Belle and other experiments. The numbers matter because they feed into the global puzzle: how penguin contributions shift φ_s in the contexts where the underlying quark transitions are cleanest to measure.
Penguins, puzzles, and the precision frontier
Penguin diagrams are the roguish performers in a crowded math club. They represent loop processes in which a bottom quark can transform into a charm quark by flirting with quantum fluctuations. In CP-violation measurements, these loops can introduce small, hard-to-calculate phase shifts, which complicate the extraction of the fundamental φ_s from decays like B_s → J/ψ φ. The beauty of the LHCb approach, as laid out in this paper, is to use data-driven strategies to corral these penguin effects instead of trying to compute them from first principles in the nonperturbative world of strong interactions. One widely discussed strategy is to exploit SU(3) flavor symmetry, comparing b → c c̄ s transitions in B_s decays to CKM-suppressed analogues like B_s → J/ψ K*(892)0 and B^0 → J/ψ ρ^0. By measuring CP asymmetries in these related decays, researchers can set bounds on the shifts that penguin processes could induce in φ_s. In other words, they’re using the family of related decays as a compass to navigate the penguin fog.
The Run 2 angular analysis contributes directly to this plan. By extracting CP asymmetries for the P-wave components and mapping how they vary with the Kπ mass (and therefore with the interference pattern between P- and S-waves), the team tightens the constraints on how penguin topologies might bias φ_s in the B_s → J/ψ φ channel. When these new Run 2 results are combined with Run 1 data, the overall precision improves further, delivering the most precise observables to date for these angular parameters and boosting confidence in the robustness of CKM-based tests of the Standard Model. The paper also provides a careful accounting of systematic uncertainties: how mass-fit choices, angular-acceptance corrections, potential D-wave contributions, and external asymmetries propagate into the final numbers. The end product is not just a catalog of numbers but a clarified landscape in which any future deviation from the Standard Model would be meaningful and interpretable.
So how does this influence the broader physics program? The key message is one of tightening constraints. If penguin contributions can mimic a wrong φ_s by a few tens of milliradians, then every improvement in the angular observables and branching fractions that pins down those penguin effects reduces the risk of misinterpreting a Standard Model-internal effect as a signal of new physics. At the same time, the results keep alive the possibility that new particles or interactions could whisper through tiny shifts in CP-violating phases. The Run 2 measurements don’t reveal a smoking gun for new physics, but they sharpen the map that theorists and experimentalists use to search for it. And this is precisely the kind of precision frontier where collaborations like LHCb deserve the spotlight: years of meticulous detector work, data processing, and cross-checks converge into numbers that both validate the Standard Model’s elegance and illuminate where it might bend.
The study is also a reminder of the collaborative scale of modern physics. It sits at CERN, powered by the LHCb detector, and draws on a global network of universities and institutes that build the detector, develop the analysis tools, calibrate the particle ID, and interpret the results. The paper explicitly credits the LHCb collaboration as the authoring body and names a long chain of contributing institutes, with the first author listed as R. Aaij. The practical upshot is a result that is as much about a community of scientists refining a shared language to talk about the subatomic world as it is about any single new number. The people behind the science — traveling from Monash in Australia to universities across Europe, the United States, and beyond — embody a culture of collaboration that makes these minute measurements possible.
Looking ahead, the path is clear. As the LHC continues to deliver more data and detector upgrades push sensitivities even further, CP-violation measurements in B_s and related systems will become even more precise. The same data-driven strategies that tame penguin pollution now can be extended to other decay channels and to time-dependent analyses that reveal not only the magnitude of CP violation but its evolution over time. In that sense, these latest Run 2 results are both a finale of a chapter — the most precise angular analyses in this specific decay to date — and a prologue to a longer story about how small asymmetries, measured with surgical care, can illuminate the deepest questions about why anything exists at all.
In the end, the LHCb study is more than a catalog of fractions and phases. It’s a demonstration of science at a scale where patience pays off: the patient accumulation of data, the disciplined separation of signal from noise, and the careful accounting for every possible bias. It’s a reminder that in particle physics, as in life, the smallest differences can matter most — and that chasing those differences with clarity and humility is the surest way to advance our understanding of the cosmos.
