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We present a precise calculation of the dilepton invariant-mass spectrum and the decay rate for $B^\pm \to \pi^\pm \ell^+ \ell^-$ ($\ell^\pm = e^\pm, \mu^\pm $) in the Standard Model (SM) based on the effective Hamiltonian approach for the $b \to d \ell^+ \ell^-$ transitions.
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It is expected to be somewhere within the signal called as the B J ∗ ( 5732 ) B_{J}^{*}(5732) resonance Beringer et al. 2012 with the mass m B J ∗ ( 5732 ) = ( 5698 ± 8 ) m_{B_{J}^{*}(5732)}=(5698\pm 8) MeV and width Γ B J ∗ ( 5732 ) = ( 128 ± 18 ) \Gamma_{B_{J}^{*}(5732)}=(128\pm 18) MeV which can be interpreted as stemming from several narrow and broad resonances. Approximately the same mass difference m B s ∗ ∗ − m B s = ( 385 ± 16 ± 5 ± 25 ) m_{B_{s}^{**}}-m_{B_{s}}=(385\pm 16\pm 5\pm 25) MeV in the B s B_{s} -meson sector was obtained by the HPQCD Collaboration Gregory et al. 2011
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