Theta and Tau, two generations later

This kitten, seen in the mirror, is just a little different, due to the dark spot on her nose. She is almost, but not exactly, “CP-even.” If the reflection is replaced with the reflection of the same kitten but composed of antimatter, she would be CP-even.

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How can the Bs0 (pronounced “bee sub ess”) or indeed any particle have different lifetimes when decaying into different particles? Getting the right answer to this question started quite some time ago.

About 60 years ago, physicists were pondering the “Theta-Tau puzzle.” They knew of two particles, which they called Theta and Tau (those names have since been retired or recycled), which had the same mass and spin. On those grounds, they should obviously have been the same particle. However, Theta decayed into two pions, and Tau decayed into three pions, which made it seem as though two particles just happened to have the same mass and spin. That seemed like too big a coincidence to be true.

We now have a solution to the Theta-Tau puzzle. The Thetas and Taus, now called kaons, are created as combinations of strange and light quarks. But those kaons are the superposition of two possibilities, which we call “CP-odd” or “CP-even,” and these specific states are appropriate to describe the decays of the kaon. The component that is CP-odd decays into three pions, whereas the CP-even component decays into two pions. The CP-even decays are fairly quick, in contrast to the CP-odd decays. It turns out that the masses of the CP-odd and CP-even cases are just a tiny bit different, too.

From top left to bottom right:
Michel Hernandez-Villanueva and Eduard De La Cruz-Burelo (CINVESTAV, Mexico) Marj Corcoran (Rice University), Jesus Orduna (Brown University) and Brad Abbott (U Oklahoma) are the primary analysts for this measurement.

Quarks, like people, have generations. The light quarks are what we call the first generation, and strange quarks are in the second generation. Particles in the first generation were discovered first! The last generation of quarks, the bottom and top quarks, were the last to be discovered. With people we say, “The apple doesn’t fall far from the tree,” and the same is true for quarks; the properties of quarks in one generation are similar to those of quarks in the other generations.

Now substitute the light quark of a kaon with a bottom quark, replacing a first-generation quark with a third-generation quark. This combination of a strange and a bottom quark is the Bs0, and it too can appear as either a CP-odd or a CP-even state. Will the CP-odd case also decay more slowly than the CP-even case? It seems so.

Recently, DZero measured the lifetime of Bs0 decay into a J/ψ meson and an f0 meson. This is a CP-odd combination, akin to the three-pion decay of the kaon. We found that the lifetime is (1.70 ±0.15) picoseconds, in good agreement with the world average of 1.71 ± 0.04 picoseconds. The average lifetime of all Bs0 decays, both the CP-odd and CP-even cases, is 1.510 ±0.005 picoseconds; that makes the CP-even lifetime about 1.36 picoseconds.

Two generations later, the puzzle still has the same solution. The CP-odd “Theta” has both a different decay and a different lifetime than the CP-even “Tau” even though it has (almost) the same mass.

View the INSPIRE record for this result.