Using the full CDF Run II data sample, we report evidence for a new resonance, which we refer to as $B(5970)$, found simultaneously in the $B^0pi^+$ and $B^+pi^-$ mass distributions with a significance of 4.4 standard deviations. We further report the first study of resonances consistent with orbitally excited $B^{+}$ mesons and an updated measurement of the properties of orbitally excited $B^0$ and $B_s^0$ mesons. We measure the masses and widths of all states, as well as the relative production rates of $B_1$, $B_2^*$, and $B(5970)$ states and the branching fraction of the $B_{s2}^{*0}$ state to either $B^{*+} K^-$ and $B^{+} K^-$. Furthermore, we measure the production rates of the orbitally excited $B^{0,+}$ states relative to the $B^{0,+}$ ground state. The masses of the new $B(5970)$ resonances are $5978pm5(textrm{stat})pm12(textrm{syst}) textrm{ MeV/c}^{2}$ for the neutral state and $5961pm5(textrm{stat})pm12(textrm{syst}) textrm{ MeV/c}^{2}$ for the charged state, assuming that the resonance decays into $Bpi$ final states. The properties of the orbitally excited and the new $B(5970)^{0,+}$ states are compatible with isospin symmetry.
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