More details on Bs mixing

I can give a few more details on the new measurement by the CDF collaboration of the oscillation frequency of Bs mesons, made public yesterday at a seminar by Ivan Furic.

Bs mesons are formed by a bottom and a anti-strange quark. They can transmute into their antiparticle via second-order weak interactions, and since in particle physics whatever is not forbidden is compulsory, oscillations happen between the two states, at a frequency that is an extremely precise probe of the interaction responsible for the transmutation.

CDF has very recently "opened the box" and analyzed the full dataset collected since 2001 – one inverse femtobarn of proton-antiproton collisions at 1.96 TeV of center-of-mass energy delivered by the Fermilab collider. They did so only after performing endless checks that the analysis procedure, the fitting methods, and the tagging algorithms that allow the determination of the flavor of the meson at production and decay were completely finalized and understood, by applying them to several control datasets and Monte Carlo simulations.

Bs mesons are collected at CDF thanks to a novel device installed for Run II, the Silicon Vertex Tracker (SVT). It consists of a set of custom-built hardware boards that process the huge flux of data coming from the hit information in the five layers of silicon detectors in the core of CDF, to measure charged tracks online.

The SVT is capable of measuring track impact parameter, transverse momentum, and azimuthal angle with a precision close to that attainable offline in 10 microseconds – thus allowing the second-level trigger system of CDF to select with high efficiency the decay of particles of long lifetime such as Bs mesons – these produce in fact tracks with significant impact parameter with respect to the beamline.

Thanks to the SVT large samples of Bs decays have been collected. These are divided in two, depending on the characteristics of the decay: semileptonic and fully hadronic. Semileptonic Bs decays yield an electron or a muon and a Ds meson (which is then reconstructed with its decay into charged hadrons). Fully reconstructed hadronic decays instead yield only charged particles and provide very clean signals.

In order to measure the oscillation frequency of Bs mesons one needs to be able to do two very important things. The first is to determine ("tag") the flavor of the meson at production and decay: this allows to determine whether the meson has oscillated to its antiparticle or not. The second is to measure very accurately the decay length of the meson, thus reconstructing the proper time passed from production to decay.

The flavor tagging can be done in several ways – and CDF pursues all of them for maximum precision. Opposite-side-tagging relies on the fact that b quarks are produced in quark-antiquark pairs, and therefore the flavor of one Bs meson at production is the opposite of that of the recoiling B meson. Same-side tagging relies on finding accompanying charged hadrons produced during fragmentation of the original b quark which made the Bs meson. These measurements are statistical in nature, and are thoroughly checked with Monte Carlo simulations.

The determination of proper time is done by reconstructing the decay vertex of the Bs meson, with a kinematical fitting of the tracks produced in the decay. CDF has shown to be able to measure with great precision the lifetime of B mesons, and its determination of the oscillation frequency of Bd mesons is in very close agreement to the world average (driven by BaBar and Belle determinations).

Finally, a combined likelihood is performed to find the probability that the data is consistent with a given oscillation frequency. 

Putting everything together, one obtains a plot called an "amplitude scan", where on the y axis a line is drawn at A=1, and an intersection is sought with the most probable amplitude born by the data, plotted as a function of the mass difference between Bs and anti-Bs mesons (which is inversely proportional to the oscillation frequency, and is measured in inverse picoseconds).

Shown below is the plot by CDF. You can see that the experimental determinations (the black points) are well consistent with A=1 at 17.33 inverse picoseconds. The final measurement reads Delta(Ms) = 17.33 +0.42 -0.21 (stat.) +- 0.07 (syst) ps-1. From that determination, a very precise value of the ratio between the two elements of the Cabibbo-Kobajashi-Maskawa mixing matrix Vtd and Vts can be obtained: CDF finds |Vtd|/|Vts| = 0.209 +0.005 -0.008.