Anatomy of $B\to K{\eta }^{(\prime )}$ decays in different mixing schemes and effects of next-to-leading order contributions in the perturbative QCD approach

Abstract

In this paper we perform a comprehensive study of the four $B \to K \etap$ decays in the pQCD factorization approach. We calculate the CP-averaged branching ratios and CP-violating asymmetries of $B \to K\etap$ decays in the ordinary $\eta$-$\etar$, the $\eta$-$\etar$-$G$, and the $\eta$-$\etar$-$G$-${\eta }_c$ mixing schemes. Besides the full LO contributions, all currently known NLO contributions to $B \to K \etap$ decays in the pQCD approach are taken into account. From our calculations and phenomenological analysis, we find the following. (a) The NLO contributions in general can provide significant enhancements to the LO pQCD predictions for the decay rates of the two $B \to K \etar$ decays, around $70$ in magnitude, but result in relatively small changes to $Br(B\to K\eta )$. (b) Although the NLO pQCD predictions in all three considered mixing schemes agree well with the data within one standard deviation, those pQCD predictions in the $\eta$-$\etar$-$G$ mixing scheme provide the best interpretation for the measured pattern of $Br(B \to K \etap)$: $Br(B^0\to K^0\eta )\approx 1.13\times 10^{-6}$, $Br(B^0 \to K^0 \etar) \approx 66.5 \times 10^{-6}$, $Br(B^{\pm }\to K^{\pm }\eta )\approx 2.36\times 10^{-6}$, and $Br(B^\pm \to K^\pm \etar) \approx 67.3 \times 10^{-6}$, which agree perfectly with the measured values. (c) The NLO pQCD predictions for the CP-violating asymmetries for the four considered decays are also in good consistent with the data. (d) The newly known NLO contribution to the relevant form factors $\calm_{FF}$ can produce about a 20% enhancement to the branching ratios $Br(B \to K \etar)$, which plays an important role in closing the gap between the pQCD predictions and the relevant data. (e) The general expectations about the relative strength of the LO and NLO contributions from different sources are examined and confirmed by explicit numerical calculations.

42 pages, 5 ps figures

References in corpus (8)

• Charmless non-leptonic B_s decays to PP, PV and VV final states in the pQCD approach
• Measurement of the pseudoscalar mixing angle and ${\eta }^{\prime }$ gluonium content with KLOE detector
• Pseudoscalar glueball mass from $\eta$-${\eta }^{\prime }$-$G$ mixing
• Branching ratios and CP asymmetries of $B\to K{\eta }^{(\prime )}$ decays in the pQCD approach
• Gluonic contribution to $B\to {\eta }^{(\prime )}$ form factors
• Branching Ratio and CP Asymmetry of $B^0\to {\eta }^{(\prime )}{\eta }^{(\prime )}$ Decays in the Perturbative QCD Approach
• Branching Ratio and CP Asymmetry of $B_s\to \rho (\omega )K$ Decays in the Perturbative QCD Approach
• $B^0\to \omega {\eta }^{(\prime )}$ and $\varphi {\eta }^{(\prime )}$ decays in the perturbative QCD approach

Cited by in corpus (27)

• Quasi-two-body decays $B_{(s)}\to P\rho \to P\pi \pi$ in perturbative QCD approach
• Semileptonic decays $B\to D^{(\ast )}l\nu$ in the perturbative QCD factorization approach
• Anatomy of $B_s\to VV$ decays and effects of next-to-leading order contributions in the perturbative QCD factorization approach
• Quasi-two-body decays $B_{(s)}\to P{\rho }^{\prime }(1450),P{\rho }^{\prime \prime }(1700)\to P\pi \pi$ in the perturbative QCD approach
• The $S$-wave resonance contributions to the three-body decays $B_{(s)}^0\to {\eta }_c{f}_0(X)\to {\eta }_c{\pi }^{+}{\pi }^{-}$ in perturbative QCD approach
• Hochschild homology, trace map and $\zeta$-cycles
• Charmless two-body $B$ meson decays in perturbative QCD factorization approach
• $B\to \pi \pi$ decays and effects of the next-to-leading order contributions
• The NLO twist-3 contribution to the pion electromagnetic form factors in $k_T$ factorization
• Anatomy of $B_s\to PV$ decays and effects of next-to-leading order contributions in the perturbative QCD factorization approach
• ${\bar{B}}_s^0\to K\pi ,KK$ decays and effects of the next-to-leading order contribution
• Understanding the cross section of $e^{+}{e}^{-}\to \eta J/\psi$ process via nonrelativistic QCD
• Revisiting $K\pi$ puzzle in the pQCD factorization approach
• Study of ${\bar{B}}_s\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$ decays in the PQCD factorization approach with the lattice QCD input
• The PQCD approach towards to next-to-leading order: a short review
• The NLO contributions to the scalar pion form factors and the $\mathcal{O}({\alpha }_s^2)$ annihilation corrections to the $B\to \pi \pi$ decays
• ${\bar{B}}_s^0\to ({\pi }^0{\eta }^{(\ast )},{\eta }^{(\ast )}{\eta }^{(\ast )})$ decays and the effects of next-to-leading order contributions in the perturbative QCD approach
• Direct $CP$ violation for ${\bar{B}}_s^0\to \varphi {\pi }^{+}{\pi }^{-}$ in Perturbative QCD
• Study of $B^{-}\to \Lambda \bar{p}{\eta }^{{(}^{\prime })}$ and ${\bar{B}}_s^0\to \Lambda \bar{\Lambda }{\eta }^{{(}^{\prime })}$ decays
• $B_{(s)}\to {\eta }_c(P,V)$ decays and effects of the next-to-leading order contributions in the perturbative QCD approach
• Anatomy of $B_s\to PP$ decays and effects of the next-to-leading order contributions in the perturbative QCD approach
• Charmless hadronic $B\to (f_1(1285),f_1(1420))P$ decays in the perturbative QCD approach
• Mixing effects of $\eta -{\eta }^{\prime }$ in ${\Lambda }_b\to \Lambda {\eta }^{{(}^{\prime })}$ decays
• Revisiting the $B^0\to {\pi }^0{\pi }^0$ decays in the perturbative QCD approach
• $B \to K \etap$ decays in the SM with fourth generation fermions
• The semileptonic decays of $B/B_s$ meson in the perturbative QCD approach: A short review
• An analysis of B meson decays to two light pseudoscalar nonets with deltaS=1 in QCD factorization approach