The partial waves of $B_2^{\ast }(5747)$ and their contributions in strong decays

Abstract

By adopting the relativistic Bethe-Salpeter method, the OZI allowed strong decays of the $2^{+}$ state $B_2^{\ast }(5747{)}^0$ are studied, emphasis is paid to the relativistic corrections. We first study the partial waves in the wave functions used, find that there are $P$, $D$ and $F$ partial waves in $B_2^{\ast }(5747{)}^0$ meson, and the ratios $P:D:F=1:0.421:0.051$. We also find $S:P:D=1:0.354:0.046$ for $B^{\ast }$, and $S:P=1:0.343$ for $B$ meson. The large components of the $D$ wave in $B_2^{\ast }(5747{)}^0$ and $P$ wave in $B^{(\ast )}$ means that large relativistic effects existing in these states. Second, we calculate the strong decays, the obtained total decay width $\Gamma (B_2^{\ast }(5747{)}^0)=25.9$ MeV and the branching fraction $\Gamma (B_2^{\ast }(5747{)}^0\to B^{\ast }\pi )$ / $\Gamma (B_2^{\ast }(5747{)}^0\to B\pi )=0.96$ are consistent well with experimental data. Third, we study the contributions of different partial waves in the initial and final wave functions, find that the relativistic effects are about $15\%$ and $11\%$ for $B_2^{\ast }(5747{)}^0\to B\pi$ and $B_2^{\ast }(5747{)}^0\to B^{\ast }\pi$, respectively, which are much smaller than our expected, showing that the relativistic corrections are cancelled to each other in these decays.

arXiv commentVersion published in EPJC

References in corpus (18)

• Excited Heavy-Light Systems and Hadronic Transitions
• Decay Constants of Heavy Vector Mesons in Relativistic Bethe-Salpeter Method
• Strong decays of heavy-light mesons in a chiral quark model
• $B$ and $B_s$ Meson Spectroscopy
• Excited bottom and bottom-strange mesons in the quark model
• Excited Heavy Mesons Beyond Leading Order in the Heavy Quark Expansion
• Higher bottom and bottom-strange mesons
• Annihilation Rate of $2^{++}$ Charmonium and Bottomonium
• Strong decays of the bottom mesons $B_1(5721)$, $B_2(5747)$, $B_{s1}(5830)$, $B_{s2}(5840)$ and $B(5970)$
• Is $D_{sJ}^{+}(2632)$ the first radial excitation of $D_s^{\ast }(2112)$?
• Decay widths of B_1 and B^*_2 up to the order of O(1/m_Q) in HQET
• The mass spectrum and wave functions of the $B_c$ system
• Decays and spectrum of bottom and bottom strange mesons
• Towards establishing an abundant $B$ and $B_s$ spectrum up to the second orbital excitations
• Relativistic effects in the semileptonic $B_c$ decays to charmonium with the Bethe-Salpeter method
• The analysis of the excited bottom and bottom strange states $B_1(5721)$, $B_2^{\ast }(5747)$, $B_{s1}(5830)$, $B_{s2}^{\ast }(5840)$, $B_J(5840)$ and $B_J(5970)$ in B meson family
• Placing the newly observed state $B_J(5840)$ in bottom spectra along with states $B_1(5721)$, $B_2^{\ast }(5747)$, $B_{s1}(5830)$, $B_{2s}^{\ast }(5840)$ and $B_J(5970)$
• Average speed and its powers $v^n$ of a heavy quark in quarkonia