Role of $f_0(980)$ and $a_0(980)$ in the $B^{-}\to {\pi }^{-}{K}^{+}{K}^{-}$ and $B^{-}\to {\pi }^{-}{K}^0{\bar{K}}^0$ reactions

Abstract

In this work we study the role of the $f_0(980)$ and $a_0(980)$ resonances in the low $K^{+}{K}^{-}$ and $K^0{\bar{K}}^0$ invariant-mass region of the $B^{-}\to {\pi }^{-}{K}^{+}{K}^{-}$ and $B^{-}\to {\pi }^{-}{K}^0{\bar{K}}^0$ reactions. The amplitudes are calculated by using the chiral unitary $\mathrm{SU}(3)$ formalism, in which these two resonances are dynamically generated from the unitary pseudocalar-pseudoscalar coupled-channel approach. The amplitudes are then used as input in the evaluation of the mass distributions with respect to the $K^{+}{K}^{-}$ and $K^0{\bar{K}}^0$ invariant-masses, where the contributions coming from the $I=0$ and $I=1$ components are explicitly assessed. Furthermore, the contribution of the $K^{\ast }(892{)}^0{K}^{-}$ production and its influence on the ${\pi }^{-}{K}^{+}$ and $K^{+}{K}^{-}$ systems are also evaluated, showing that there is no significant strength for small $K^{+}{K}^{-}$ invariant mass. Lastly, the final distributions of $M_{\mathrm{inv}}^2(K^{\pm }{K}^{\mp })$ for the $B^{\mp }\to {\pi }^{\mp }{K}^{\pm }{K}^{\mp }$ reactions are estimated and compared with the LHCb data. Our results indicate that the $I=0$ component tied to the $f_0(980)$ excitation generates the dominant contribution in the range of low $K^{+}{K}^{-}$ invariant-mass.

11 pages, 10 figures

References in corpus (10)

• Vector meson-vector meson interaction in a hidden gauge unitary approach
• $B^0$ and $B_s^0$ decays into $J/\psi$ $f_0(980)$ and $J/\psi$ $f_0(500)$ and the nature of the scalar resonances
• Measurements of $CP$ violation in the three-body phase space of charmless $B^{\pm }$ decays
• Charmless Three-body Decays of B Mesons
• The low lying scalar resonances in the $D^0$ decays into $K_s^0$ and $f_0(500)$, $f_0(980)$, $a_0(980)$
• Direct CP Violation in Charmless Three-body Decays of $B$ Mesons
• Branching Fractions and CP Violation in $B^{-}\to K^{+}{K}^{-}{\pi }^{-}$ and $B^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-}$ Decays
• Will the subprocesses $\rho (770,1450{)}^0\to K^{+}{K}^{-}$ contribute large branching fractions for $B^{\pm }\to {\pi }^{\pm }{K}^{+}{K}^{-}$ decays?
• Contributions for the kaon pair from $\rho (770)$, $\omega (782)$ and their excited states in the $B\to K\bar{K}h$ decays
• Angular analysis of the low $K^{+}{K}^{-}$ invariant mass enhancement in $B^{+}\to K^{+}{K}^{-}{\pi }^{+}$ decays

Cited by in corpus (2)

• A note on the tensor and vector exchange contributions to $K\bar{K}\to K\bar{K},D\bar{D}\to D\bar{D}$ and ${\pi }^{+}{\pi }^{-}\to {\pi }^{+}{\pi }^{-}$ reactions
• The virtual contributions from $K^{\ast }$ in the $B\to K^{\ast }\pi h$ and $B\to K\rho h$ decays