Measurements of the mass difference m(B0) − m(B+) and the energy dependence of the cross-section ratio σ (e⁺e⁻→ B⁰B̄ ⁰)/σ (e⁺e⁻→ B⁺B⁻) at Belle and Belle II

A bstract Using data samples collected by the Belle and Belle II experiments at the Υ(4 S ) resonance with integrated luminosities of 571 fb − 1 and 365 fb − 1 , respectively, we measure the pseudoscalar B -meson mass difference to be m ( B 0 ) − m ( B + ) = (0 . 495 ± 0 . 024 ± 0 . 005) MeV/ c 2 . The results are based on a simultaneous fit to the variable M̄ bc , which is related to the B momentum, for B 0 and B + candidates; and to the energy dependence of R=σ (e⁺e⁻→ B⁰B̄ ⁰) / σ (e⁺e⁻→ B⁺B⁻) , which is measured using changes in the average center-of-mass energy over the data taking periods. The phase-space hypothesis R=(p_B⁰ /p_B⁺)³ , upon which previous measurements rely, is strongly disfavored by our fit; the measured mass-difference value for the phase-space hypothesis also differs significantly from our measurement. We constrain R in a broader energy range than covered by the direct measurement and extract the energy dependence of R in the range from the BB ̄ threshold up to 10.59 GeV. We interpret the results using a phenomenological model and constrain the parameters of the BB ̄ potential in the isovector channel.