B-factories yield first evidence for elusive D⁰–D̅⁰ mixing

30 April 2007

It is more than 50 years since researchers first observed particle–antiparticle mixing, with the discovery of a second, longer-lived neutral kaon state. This discovery pre-dated the quark model, but the effect became understood in terms of transitions between the quarks (s and d) in these neutral mesons. Thirty years later, scientists found the phenomenon in neutral Bd mesons (b and d quarks), and then last year the D⁰ and CDF collaborations at Fermilab’s Tevatron reported mixing in neutral Bs mesons (b and s). This left the neutral D meson (c and u quarks) as the only system remaining where mixing was possible, but not yet observed.

Now, experiments at the two B-factories, KEKB at KEK in Japan and PEP-II at SLAC in the US, have filled the gap, with reports of the first evidence for D⁰–D⁰ mixing. On 13 March at the Rencontres de Moriond in La Thuile, Marko Staric presented results for D⁰–D⁰ mixing from the Belle experiment at KEKB. Kevin Flood followed with evidence from the BaBar experiment at the PEP-II storage rings.

As in the kaon and B-meson systems, the D⁰–D⁰ are created in “flavour” eigenstates consisting of a quark and an antiquark, but in each case mixing through weak interactions between the quarks should give rise to two different mass eigenstates that are particle–antiparticle mixtures and have different lifetimes. Mixing should therefore modify the decay times of D mesons by a small but observable amount.

The Belle Collaboration has compared decay times in three decay modes of D mesons: two decays to CP-even eigenstates, K⁺K⁻ and π⁺π⁻, and a “flavour-specific decay” to a mixed CP state, D⁰ → K⁻π⁺. The mass eigenstates are CP eigenstates, assuming no CP violation, one being CP-odd, the other CP-even, so in comparing these decay modes, the team is in effect comparing the lifetimes, τ, of the mass eigenstates, which would be the same in the absence of mixing. They measure the relative lifetime difference, yCP = {τ(K⁻π⁺)/τ(K⁺K⁻)} – 1 to be (1.31 ± 0.32(stat.) ± 0.25(syst.))% (M Starič et al. 2007). This differs from zero by 3.2 σ after including systematic uncertainties, and so represents clear evidence for D⁰ mixing.

The BaBar Collaboration has approached the problem slightly differently by focusing on the decay D⁰ → K⁺π⁻, and analysing the data in terms of the parameters, x’ and y’. (These are rotations through a strong phase of the mixing parameters x = ΔM/Γ and y = ΔΓ/2Γ, which depend on the differences in mass (ΔM) and width (ΔΓ) of the mass eigenstates, where Γ is the average width.) They find y’ = (9.7 ± 4.4(stat.) ± 3.1(syst.)) × 10⁻³, while x’² is consistent with zero – a result that they say is inconsistent with the hypothesis of no mixing at 3.9 σ (Aubert et al. 2007).

Both collaborations have also analysed the data for CP violation associated with D⁰–D⁰ mixing but have found no evidence for this. The new results, meanwhile, can be compared with the Standard Model to search for new physics, as D-meson mixing is particularly sensitive to any contributions from particles or processes that have not so far been observed.