Using U-spin to squeeze CP violation

The LHCb collaboration has undertaken a new study of B → DD decays using data from LHC Run 2. In the case of B⁰ → D⁺D^– decays, the analysis excludes CP-symmetry at a confidence level greater than six standard deviations – a first in the analysis of a single decay mode.

The study of differences between matter and antimatter (CP violation) is a core aspect of the physics programme at LHCb. Measurements of CP violation in decays of neutral B⁰ mesons play a crucial role in the search for physics beyond the Standard Model thanks to the ability of the B⁰ meson to oscillate into its antiparticle, the B⁰ meson. Given increases in experimental precision, improved control over the magnitude of hadronic effects becomes important, which is a major challenge in most decay modes. In this measurement, a neutral B meson decays to two charm D mesons – an interesting topology that offers a method to control these high-order hadronic contributions from the Standard Model via the concept of U-spin symmetry.

In the new analysis, B⁰ → D⁺D^– and B_s⁰ → D_s⁺D_s^– are studied simultaneously. U-spin symmetry exchanges the spectator down quarks in the first decay with strange quarks to form the second decay. A joint analysis therefore strongly constrains uncertainties related to hadronic matrix elements by relating CP-violation and branching-fraction measurements in the two decay channels.

In both decays, the same final state is accessible to both matter and antimatter states of the B⁰ or B_s⁰ meson, enabling interference between two decay paths: the direct decay of the meson to the final state; and a decay after the meson has oscillated into its antiparticle counterpart. The time-dependent decay rate of each flavour (matter or antimatter) of the meson depends on CP-violating effects and is parameterised in terms dependent on the fundamental properties of the B mesons and the fundamental CP-violating weak phases β and β_s, in the case of B⁰ and B_s⁰ decays, respectively. The tree-level and exchange Feynman diagrams participating to this decay process, which in turn depend on specific values of the terms in the Cabibbo–Kobayashi–Maskawa quark-mixing matrix, determine the expected value of the β_(s) phases. This matrix encodes our best understanding of the CP-violating effects within the Standard Model, and testing its expected properties is a crucial means to fully exploit closure tests of this theoretical framework.

The study of differences between matter and antimatter is a core aspect of the physics programme at LHCb

The analysis uses flavour tagging to identify the matter or antimatter flavour of the neutral B meson at its production and thus allows the determination of the decay path – a key task in time- dependent measurements of CP violation. The flavour-tagging algorithms exploit the fact that b and b quarks are almost exclusively produced in pairs in pp collisions. When the b quark forms a B meson (and similarly for its antimatter equivalent), additional particles are produced in the fragmentation process of the pp collision. From the charges and species of these particles, the flavour of the signal B meson at production can be inferred. This information is combined with the reconstructed position of the decay vertex of the meson, allowing the flavour-tagged decay-time distribution of each analysed flavour to be measured.

Figure 1 shows the asymmetry between the decay-time distributions of the B⁰ and the B⁰ mesons for the B⁰ → D⁺D^–decay mode. Alongside the B_s⁰ → D_s⁺D_s^– data, these results represent the most precise single measurements of the CP-violation parameters in their respective channels. Results from the two decay modes are used in combination with other B → DD measurements to precisely determine Standard Model parameters.