{"id":555,"date":"2006-09-25T17:55:56","date_gmt":"2006-09-25T08:55:56","guid":{"rendered":"http:\/\/hepsv.sci.osaka-cu.ac.jp\/?p=555"},"modified":"2024-07-02T01:16:58","modified_gmt":"2024-07-01T16:16:58","slug":"bs0_oscillation","status":"publish","type":"post","link":"https:\/\/hepsv.sci.osaka-cu.ac.jp\/en\/ocuhep-news\/bs0_oscillation\/","title":{"rendered":"First Observation of Particle-Antiparticle Oscillation of Bs<\/sub><\/i>0<\/sup><\/span> Meson"},"content":{"rendered":"

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\"asymmetry\"<\/a>

Figure 6 : Time variation of amplitude obtained from the measured particle-antiparticle oscillation frequency.<\/p><\/div><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Neutral B<\/i><\/span> 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 \u0394m<\/em> = (m<\/em>(BH<\/sub><\/i>0<\/sup> \u2212 m<\/em>(BL<\/sub><\/i>0<\/sup>))<\/span>. Here, BH<\/sub><\/i>0<\/sup> and BL<\/sub><\/i>0<\/sup><\/span> represent the “heavy” and “light” mass eigenstates of the neutral B<\/i><\/span> meson, respectively, and \u0394m<\/span><\/em> is the mass difference. While particle-antiparticle oscillation of Bd<\/sub><\/i>0<\/sup><\/span> (consisting of a (db<\/i><\/span>) pair) had been observed previously, the particle-antiparticle oscillation of Bs<\/sub><\/i>0<\/sup><\/span> (consisting of an (sb<\/i><\/span>) 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 Bs<\/sub><\/i>0<\/sup><\/span> particle-antiparticle oscillation microscopically, within the meson, as shown in Figure 1, two W<\/i><\/span> bosons are exchanged between the two quarks, causing the transformation from particle to antiparticle (box diagram).<\/p>\n

In practice, to observe the oscillation, a Bs<\/sub><\/i>0<\/sup><\/span> or its antiparticle B<\/i><\/span>s<\/sub><\/i>0<\/sup><\/span> 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 Bs<\/sub><\/i>0<\/sup><\/span> or B<\/i><\/span>s<\/sub><\/i>0<\/sup><\/span> at production, the proper time until decay, and whether it was a Bs<\/sub><\/i>0<\/sup><\/span> or B<\/i><\/span>s<\/sub><\/i>0<\/sup><\/span> at decay, we can determine if oscillation occurred and, if so, measure the oscillation frequency. Considering the production of Bs<\/sub><\/i>0<\/sup><\/span>, in proton-antiproton collisions, b<\/i><\/span> (b<\/i><\/span><\/span>) quarks are mainly produced in bb<\/span><\/i><\/span> pair production, and each b<\/i><\/span> and b<\/i><\/span><\/span> quark independently hadronizes and decays. If a b<\/i><\/span> quark combines with an s<\/i><\/span> quark to form a B<\/i>s<\/sub><\/i>0<\/sup><\/span>, the s<\/i><\/span> quark is produced in ss<\/span><\/i><\/span> pair production, so the remaining s<\/i><\/span> quark usually forms a K<\/i>\u2212<\/sup><\/span>, which flies out in the same direction as the B<\/i>s<\/sub><\/i>0<\/sup><\/span>. Conversely, if a B<\/i><\/span>s<\/sub><\/i>0<\/sup><\/span> is formed, it is accompanied by a K<\/i>+<\/sup><\/span>. Therefore, by observing the charge sign of this K<\/i>\u00b1<\/sup><\/span>, we can tag the initial state of the Bs<\/sub><\/i><\/span> meson (whether it was Bs<\/sub><\/i>0<\/sup><\/span> or B<\/i><\/span>s<\/sub><\/i>0<\/sup><\/span>). 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<\/i> (b<\/i><\/span>)<\/span> quark in the initially produced bb<\/span><\/i><\/span> pair. The charge of the lepton preserves the charge sign of the b<\/i><\/span> quark before decay, allowing for flavor tagging (Figure 2).<\/p>\n

Next, to identify the particle-antiparticle state when the Bs<\/sub><\/i><\/span> meson decays, we reconstruct the decay products of the Bs<\/sub><\/i><\/span> 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 Bs<\/sub><\/i>0<\/sup><\/span>. Figure 3 shows the reconstruction result of one such decay mode, B<\/span><\/span><\/i>s<\/sub><\/i>0<\/sup>\u00a0\u2192\u00a0Ds<\/sub><\/i>+<\/sup><\/span>(\u03d5<\/i>\u2009\u03c0<\/em>+<\/sup>)\u03c0<\/em>\u2212<\/sup><\/span>. Including partially successful reconstructions, 8700 hadronic decays and 61500 semileptonic decays of Bs<\/sub><\/i><\/span> mesons were obtained, as shown in Table 1. Furthermore, the proper time until Bs<\/sub><\/i><\/span> meson decay can be calculated from the distance between the point of proton-antiproton collision and the point of reconstructed Bs<\/sub><\/i><\/span> meson decay, as well as the momentum of the Bs<\/sub><\/i><\/span> meson.<\/p>\n

The data on the number of produced Bs<\/sub><\/i><\/span> 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\u22121<\/sup>. Figure 5, although difficult to explain briefly, indicates the probability of an oscillation-like feature occurring due to “random fluctuations”. Near 17 ps\u22121<\/sup>, \u039b drops to \u221215, corresponding to a probability of 5.7 \u00d7 10\u22127<\/sup> for occurrence due to random fluctuations. From this, the existence of Bs<\/sub><\/i>0<\/sup><\/span> meson particle-antiparticle oscillation is confirmed, with an angular frequency measured as<\/p>\n\n\n\n
\u0394m<\/em>s<\/i><\/sub><\/td>\n=<\/td>\n17.77<\/td>\n\u00b1<\/td>\n0.10(stat.)<\/td>\n\u00b1<\/td>\n0.07(sys.)<\/td>\nps\u22121<\/sup>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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.<\/p>\n

This result of Bs<\/sub><\/i>0<\/sup><\/span> 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 \u0394m<\/em>s<\/i><\/sub><\/span>, the following value is obtained:<\/p>\n\n\n\n\n
|Vtd<\/sub>\/Vts<\/sub><\/i>|<\/td>\n=<\/td>\n0.2060<\/td>\n\u00b1<\/td>\n0.0007(exp)<\/td>\n+0.0081<\/td>\n(theory) .<\/td>\n<\/tr>\n
\u22120.0060<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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.<\/p>\n