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First Observation of Particle-Antiparticle Oscillation of B_s⁰ Meson

Figure 1 : A diagram of the particle-antiparticle oscillation of Bs0.

Figure 2 : Flavor tagging of Bs0 production.

Figure 3 : Invariant mass distribution reconstructed from Bs0 → Ds+(ϕπ+)π−.

Table 1 : Event numbers of  Bs0 in which the reconstruction succeeded.

Figure 4 : Angular frequency of the particle-antiparticle oscillation of Bs0 .

Figure 5 : Likelihood ratio between the case with an assumption that oscillation occurred and not occurred.

Figure 6 : Time variation of amplitude obtained from the measured particle-antiparticle oscillation frequency.

Neutral B mesons undergo “particle-antiparticle oscillation” due to weak interactions that change the flavor of their constituent quarks. To explain in more detail, the mass eigenstates of the quarks and the eigenstates of the weak interaction Hamiltonian differ, causing oscillation between particles and antiparticles at an angular frequency of Δm = (m(B_H⁰ − m(B_L⁰)). Here, B_H⁰ and B_L⁰ represent the “heavy” and “light” mass eigenstates of the neutral B meson, respectively, and Δm is the mass difference. While particle-antiparticle oscillation of B_d⁰ (consisting of a (db) pair) had been observed previously, the particle-antiparticle oscillation of B_s⁰ (consisting of an (sb) pair) was observed for the first time in the CDF experiment, in which Osaka City University participates, and its angular frequency was measured. Viewing the B_s⁰ particle-antiparticle oscillation microscopically, within the meson, as shown in Figure 1, two W bosons are exchanged between the two quarks, causing the transformation from particle to antiparticle (box diagram).

In practice, to observe the oscillation, a B_s⁰ or its antiparticle B_s⁰ is first produced in a proton-antiproton collision. Since these particles are unstable, they decay after a certain time. By knowing whether it was a B_s⁰ or B_s⁰ at production, the proper time until decay, and whether it was a B_s⁰ or B_s⁰ at decay, we can determine if oscillation occurred and, if so, measure the oscillation frequency. Considering the production of B_s⁰, in proton-antiproton collisions, b (b) quarks are mainly produced in bb pair production, and each b and b quark independently hadronizes and decays. If a b quark combines with an s quark to form a B_s⁰, the s quark is produced in ss pair production, so the remaining s quark usually forms a K⁻, which flies out in the same direction as the B_s⁰. Conversely, if a B_s⁰ is formed, it is accompanied by a K⁺. Therefore, by observing the charge sign of this K^±, we can tag the initial state of the B_s meson (whether it was B_s⁰ or B_s⁰). This method is called “flavor tagging.” Besides the method mentioned above, there is another method for flavor tagging, which involves capturing the semileptonic decay of the opposite side b (b) quark in the initially produced bb pair. The charge of the lepton preserves the charge sign of the b quark before decay, allowing for flavor tagging (Figure 2).

Next, to identify the particle-antiparticle state when the B_s meson decays, we reconstruct the decay products of the B_s meson. The CDF detector is equipped with high-performance tracking detectors, calorimeters, time-of-flight detectors, and muon detectors, enabling the reconstruction of many decay modes from B_s⁰. Figure 3 shows the reconstruction result of one such decay mode, B_s⁰ → D_s⁺(ϕ π⁺)π⁻. Including partially successful reconstructions, 8700 hadronic decays and 61500 semileptonic decays of B_s mesons were obtained, as shown in Table 1. Furthermore, the proper time until B_s meson decay can be calculated from the distance between the point of proton-antiproton collision and the point of reconstructed B_s meson decay, as well as the momentum of the B_s meson.

The data on the number of produced B_s mesons and the proper time until decay obtained in this manner represent the “waveform” of particle-antiparticle oscillation. Thus, by performing a Fourier transform considering decay attenuation on this waveform, if oscillation occurs at a constant angular frequency, a sharp peak should appear at that frequency. Figure 4 shows this, with a peak observed around 17 ps⁻¹. Figure 5, although difficult to explain briefly, indicates the probability of an oscillation-like feature occurring due to “random fluctuations”. Near 17 ps⁻¹, Λ drops to −15, corresponding to a probability of 5.7 × 10⁻⁷ for occurrence due to random fluctuations. From this, the existence of B_s⁰ meson particle-antiparticle oscillation is confirmed, with an angular frequency measured as

Additionally, viewing this oscillation more straightforwardly, Figure 6 shows the amplitude at each time point by dividing the period obtained from the measured oscillation frequency into five. The experimental data neatly align with a cosine waveform, indicating oscillation between particle and antiparticle occurs about 3 trillion times per second.

This result of B_s⁰ particle-antiparticle oscillation yields important information on the transition probability between quark generations, specifically the value of the Cabibbo-Kobayashi-Maskawa matrix elements. Using the measured Δm_s, the following value is obtained:

This value records the highest measurement precision in the world as of September 2006. Another significant point is that the experimental measurement error is an order of magnitude smaller than the error from theoretical calculations. In this measurement, the experiment has surpassed the theory.

• Press release of Fermilab