Hadronic decays of B→a1(1260)b1(1235) in the perturbative QCD approach

Abstract

We calculate the branching ratios and polarization fractions of the $B\ensuremath{\rightarrow}{a}_{1}{b}_{1}$ decays in the perturbative QCD(pQCD) approach at leading order, where ${a}_{1}({b}_{1})$ stands for the axial-vector ${a}_{1}(1260)[{b}_{1}(1235)]$ state. By combining the phenomenological analyses with the perturbative calculations, we find the following results: (a) the large decay rates around ${10}^{\ensuremath{-}5}$ to ${10}^{\ensuremath{-}6}$ of the $B\ensuremath{\rightarrow}{a}_{1}{b}_{1}$ decays dominated by the longitudinal polarization(except for the ${B}^{+}\ensuremath{\rightarrow}{b}_{1}^{+}{a}_{1}^{0}$ mode) are predicted and basically consistent with those in the QCD factorization(QCDF) within errors, which are expected to be tested by the Large Hadron Collider and Belle-II experiments. The large ${B}^{0}\ensuremath{\rightarrow}{a}_{1}^{0}{b}_{1}^{0}$ branching ratio could provide hints to help explore the mechanism of the color-suppressed decays. (b) the rather different QCD behaviors between the ${a}_{1}$ and ${b}_{1}$ mesons result in the destructive(constructive) contributions in the nonfactorizable spectator diagrams with ${a}_{1}({b}_{1})$ emission. Therefore, an interesting pattern of the branching ratios appears for the color-suppressed ${B}^{0}\ensuremath{\rightarrow}{a}_{1}^{0}{a}_{1}^{0},{a}_{1}^{0}{b}_{1}^{0}$, and ${b}_{1}^{0}{b}_{1}^{0}$ modes in the pQCD approach, $\mathrm{BR}({B}^{0}\ensuremath{\rightarrow}{b}_{1}^{0}{b}_{1}^{0})>\mathrm{BR}({B}^{0}\ensuremath{\rightarrow}{a}_{1}^{0}{b}_{1}^{0})\ensuremath{\gtrsim}\phantom{\rule{0ex}{0ex}}\mathrm{BR}({B}^{0}\ensuremath{\rightarrow}{a}_{1}^{0}{a}_{1}^{0})$, which is different from $\mathrm{BR}({B}^{0}\ensuremath{\rightarrow}{b}_{1}^{0}{b}_{1}^{0})\ensuremath{\sim}\mathrm{BR}({B}^{0}\ensuremath{\rightarrow}{a}_{1}^{0}{b}_{1}^{0})\ensuremath{\gtrsim}\mathrm{BR}({B}^{0}\ensuremath{\rightarrow}{a}_{1}^{0}{a}_{1}^{0})$ in the QCDF and would be verified at future experiments. (c) the large naive factorization breaking effects are observed in these $B\ensuremath{\rightarrow}{a}_{1}{b}_{1}$ decays. Specifically, the large nonfactorizable spectator(weak annihilation) amplitudes contribute to the ${B}^{0}\ensuremath{\rightarrow}{b}_{1}^{+}{a}_{1}^{\ensuremath{-}}({B}^{+}\ensuremath{\rightarrow}{a}_{1}^{+}{b}_{1}^{0}\phantom{\rule[-0.0ex]{1em}{0.0ex}}\text{and}\phantom{\rule[-0.0ex]{1em}{0.0ex}}{B}^{+}\ensuremath{\rightarrow}{b}_{1}^{+}{a}_{1}^{0})$ mode(s), which demand confirmations via the precise measurements. Furthermore, the different phenomenologies shown among $B\ensuremath{\rightarrow}{a}_{1}{b}_{1}$, $B\ensuremath{\rightarrow}{a}_{1}{a}_{1}$, and $B\ensuremath{\rightarrow}{b}_{1}{b}_{1}$ decays are also expected to be tested stringently, which could shed light on the typical QCD dynamics involved in these modes, even further distinguish those two popular pQCD and QCDF approaches.