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• W4224304406 abstract "We discuss the amplitude of the $Bto l^+l^-l'nu'$ decays and the differential decay rate $d^2Gamma/dq^2dq'^2$, $q$ the momentum of the $l^+l^-$ pair emitted from the electromagnetic vertex and $q'$ the momentum of the $l'nu'$ pair emitted from the weak vertex. For the relevant form factors, we construct dispersion representations in $q^2$ which consistently take into account the Ward identity constraints at $q^2=0$ and the contributions of light vector resonances. This allows a reliable description of the form factors in the range $0 < q^2 le 1$ GeV$^2$ that saturates around 99% of the decay rate. The differential decay rate behaves at small $q^2$ as $dGamma(Bto l^+l^-l' nu')/dq^2propto 1/q^2$ in the limit $m'_l=0$, but contains also more singlular contribution of order ${m'^2_l}/q^4$, which we take into account. For the case $m_l'le m_l$, the latter may be neglected and one obtains a mild logarithmic dependence of $Gamma(Bto l^{+}l^{-}l'nu')$ on $m_l$. For the case $m_lll m'_l$, however, the ${m'^2_l}/q^4$ terms dominate the decay rate leading to $Gamma(Bto l^{+}l^{-}l'nu')sim m'^2_l/m^2_l$. We find the following features of the four-lepton $B$-decays: (i) The decay rates $Gammaleft(Bto mu^+mu^-(mu nu_mu,enu_e)right)$ are fully dominated by the region of light vector resonances $q^2simeq M_rho^2, M_omega^2$; (ii) The decay rate $Gamma(Bto e^{+}e^{-}e nu_e)$ receives comparable contributions from the region near $q^2sim 4m_e^2$ and from the resonance region; (iii) One finds a strong enhancement of the decay rate $Gamma(Bto e^+e^- mu nu_mu)sim m_mu^2/m_e^2$ which is dominated by the region $q^2sim 4m_e^2$ due to the terms $O(m_mu^2/q^4)$ in the differential distribution." @default.
• W4224304406 created "2022-04-26" @default.
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• W4224304406 date "2022-01-26" @default.
• W4224304406 modified "2023-09-26" @default.
• W4224304406 title "Theoretical analysis of the leptonic decays <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:mi>B</mml:mi><mml:mo stretchy=false>→</mml:mo><mml:mo>ℓ</mml:mo><mml:mo>ℓ</mml:mo><mml:msup><mml:mrow><mml:mo>ℓ</mml:mo></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:msub><mml:mrow><mml:mover accent=true><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy=false>¯</mml:mo></mml:mrow></mml:mover></mml:mrow><mml:mrow><mml:msup…" @default.
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• W4224304406 doi "https://doi.org/10.1103/physrevd.105.014028" @default.
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