Measurements of the mass difference m(B$^{0}$) − m(B$^{+}$) and the energy dependence of the cross-section ratio $\sigma ({e}^{+}{e}^{-}\to {B}^{0}{\overline{B} }^{0})/\sigma ({e}^{+}{e}^{-}\to {B}^{+}{B}^{-})$ at Belle and Belle II

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Using data samples collected by the Belle and Belle II experiments at the Υ(4S) 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 ${\overline{M} }_{bc}$, which is related to the B momentum, for B$^{0}$ and B$^{+}$ candidates; and to the energy dependence of $\mathcal{R}=\sigma ({e}^{+}{e}^{-}\to {B}^{0}{\overline{B} }^{0}) / \sigma ({e}^{+}{e}^{-}\to {B}^{+}{B}^{-})$, which is measured using changes in the average center-of-mass energy over the data taking periods. The phase-space hypothesis $\mathcal{R}={({p}_{{B}^{0}} /{p}_{{B}^{+}})}^{3}$, 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 $\mathcal{R}$ in a broader energy range than covered by the direct measurement and extract the energy dependence of $\mathcal{R}$ in the range from the $B\overline{B }$ threshold up to 10.59 GeV. We interpret the results using a phenomenological model and constrain the parameters of the $B\overline{B }$ potential in the isovector channel.[graphic not available: see fulltext]

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