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<p>Using data samples collected by the Belle and Belle II experiments at the Υ(4<i>S</i>) resonance with integrated luminosities of 571 fb<sup><i>−</i>1</sup> and 365 fb<sup><i>−</i>1</sup>, respectively, we measure the pseudoscalar <i>B</i>-meson mass difference to be <i>m</i>(<i>B</i><sup>0</sup>) − <i>m</i>(<i>B</i><sup>+</sup>) = (0<i>.</i>495 ± 0<i>.</i>024 ± 0<i>.</i>005) MeV/<i>c</i><sup>2</sup>. The results are based on a simultaneous fit to the variable <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\overline{M} }_{bc}\)</EquationSource> </InlineEquation>, which is related to the <i>B</i> momentum, for <i>B</i><sup>0</sup> and <i>B</i><sup>+</sup> candidates; and to the energy dependence of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal{R}=\sigma ({e}^{+}{e}^{-}\to {B}^{0}{\overline{B} }^{0}) / \sigma ({e}^{+}{e}^{-}\to {B}^{+}{B}^{-})\)</EquationSource> </InlineEquation>, which is measured using changes in the average center-of-mass energy over the data taking periods. The phase-space hypothesis <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal{R}={({p}_{{B}^{0}} /{p}_{{B}^{+}})}^{3}\)</EquationSource> </InlineEquation>, 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 <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathcal{R}\)</EquationSource> </InlineEquation> in a broader energy range than covered by the direct measurement and extract the energy dependence of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathcal{R}\)</EquationSource> </InlineEquation> in the range from the <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(B\overline{B }\)</EquationSource> </InlineEquation> threshold up to 10.59 GeV. We interpret the results using a phenomenological model and constrain the parameters of the <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(B\overline{B }\)</EquationSource> </InlineEquation> potential in the isovector channel.</p>

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Measurements of the mass difference m(B0) − 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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    2026年5月15日

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  • M. Abumusabh,
  • I. Adachi,
  • L. Aggarwal,
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  • H. Aihara,
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  • T. Iijima,
  • N. Ipsita,
  • A. Ishikawa,
  • R. Itoh,
  • M. Iwasaki,
  • D. Jacobi,
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  • D. E. Jaffe,
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  • Q. P. Ji,
  • S. Jia,
  • Y. Jin,
  • A. Johnson,
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  • K. H. Kang,
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  • G. Karyan,
  • F. Keil,
  • C. Kiesling,
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  • M. Maggiora,
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  • R. Maiti,
  • G. Mancinelli,
  • R. Manfredi,
  • E. Manoni,
  • M. Mantovano,
  • D. Marcantonio,
  • M. Marfoli,
  • C. Marinas,
  • C. Martellini,
  • A. Martens,
  • T. Martinov,
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  • H. Murakami,
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  • Z. Natkaniec,
  • A. Natochii,
  • M. Nayak,
  • M. Neu,
  • S. Nishida,
  • R. Nomaru,
  • S. Ogawa,
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  • F. Otani,
  • G. Pakhlova,
  • A. Panta,
  • S. Pardi,
  • K. Parham,
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  • A. Passeri,
  • S. Patra,
  • S. Paul,
  • T. K. Pedlar,
  • R. Pestotnik,
  • M. Piccolo,
  • L. E. Piilonen,
  • P. L. M. Podesta-Lerma,
  • T. Podobnik,
  • C. Praz,
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  • S. Saha,
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  • L. Salutari,
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  • V. Savinov,
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  • C. Schmitt,
  • S. Schneider,
  • G. Schnell,
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  • K. Schoenning,
  • C. Schwanda,
  • Y. Seino,
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  • G. Sharma,
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  • B. Shwartz,
  • A. Sibidanov,
  • F. Simon,
  • J. Skorupa,
  • R. J. Sobie,
  • M. Sobotzik,
  • A. Soffer,
  • A. Sokolov,
  • E. Solovieva,
  • S. Spataro,
  • K. Špenko,
  • B. Spruck,
  • M. Starič,
  • P. Stavroulakis,
  • R. Stroili,
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  • U. Tamponi,
  • S. S. Tang,
  • K. Tanida,
  • F. Tenchini,
  • F. Testa,
  • A. Thaller,
  • T. Tien Manh,
  • O. Tittel,
  • R. Tiwary,
  • E. Torassa,
  • K. Trabelsi,
  • F. F. Trantou,
  • I. Ueda,
  • K. Unger,
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  • K. Uno,
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  • P. Urquijo,
  • Y. Ushiroda,
  • S. E. Vahsen,
  • R. van Tonder,
  • K. E. Varvell,
  • M. Veronesi,
  • V. S. Vismaya,
  • L. Vitale,
  • V. Vobbilisetti,
  • R. Volpe,
  • M. Wakai,
  • S. Wallner,
  • M.-Z. Wang,
  • A. Warburton,
  • M. Watanabe,
  • S. Watanuki,
  • C. Wessel,
  • E. Won,
  • X. P. Xu,
  • B. D. Yabsley,
  • W. Yan,
  • W. Yan,
  • J. Yelton,
  • K. Yi,
  • J. H. Yin,
  • K. Yoshihara,
  • J. Yuan,
  • L. Zani,
  • F. Zeng,
  • M. Zeyrek,
  • B. Zhang,
  • V. Zhilich,
  • J. S. Zhou,
  • Q. D. Zhou,
  • L. Zhu,
  • R. Žlebčík

摘要

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(B0) − m(B+) = (0.495 ± 0.024 ± 0.005) MeV/c2. The results are based on a simultaneous fit to the variable \({\overline{M} }_{bc}\) , which is related to the B momentum, for B0 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.