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Register a new user$Z to pi^+pi^-, K^+K^-$: A touchstone of the PQCD approach
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We study two rare decays, $Z to pi^+pi^-$ and $K^+K^-$, in the perturbative QCD approach up to the next-to-leading order of the strong coupling and the leading power of $1/m_Z$, $m_Z$ being the $Z$ boson mass. The branching ratios $mathcal{B}(Zto pi^+pi^-) = (0.83 pm 0.02 pm 0.02 pm 0.04)times 10^{-12}$ and $mathcal{B}(Zto K^+K^-) = (1.74^{+0.03}_{-0.05} pm 0.04 pm 0.02)times 10^{-12}$ are obtained and can be measured at a tera-$Z$ factory. Because the subleading-power contributions to the branching ratios are negligible, and the leading one does not depend on any free parameter, the two channels can serve as a touchstone for the applicability of the perturbative QCD approach.
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We present a model for the decay $D^+to K^-pi^+pi^+$. The weak interaction part of this reaction is described using the effective weak Hamiltonian in the factorisation approach. Hadronic final state interactions are taken into account through the $Kpi$ scalar and vector form factors fulfilling analyticity, unitarity and chiral symmetry constraints. Allowing for a global phase difference between the $S$ and $P$ waves of $-65^circ$, the Dalitz plot of the $D^+to K^-pi^+pi^+$ decay, the $Kpi$ invariant mass spectra and the total branching ratio due to $S$-wave interactions are well reproduced.
We extract the form factors relevant for semileptonic decays of D and B mesons from a relativistic computation on a fine lattice in the quenched approximation. The lattice spacing is a=0.04 fm (corresponding to a^{-1}=4.97 GeV), which allows us to run very close to the physical B meson mass, and to reduce the systematic errors associated with the extrapolation in terms of a heavy quark expansion. For decays of D and D_s mesons, our results for the physical form factors at q^2=0 are as follows: f_+^{D to pi}(0)= 0.74(6)(4), f_+^{D to K}(0)= 0.78(5)(4) and f_+^{D_s to K}(0)=0.68(4)(3). Similarly, for B and B_s we find: f_+^{B to pi}(0)=0.27(7)(5), f_+^{B to K}(0)=0.32(6)(6) and f_+^{B_s to K}(0)=0.23(5)(4). We compare our results with other quenched and unquenched lattice calculations, as well as with light-cone sum rule predictions, finding good agreement.
We report on a theoretical study of the newly observed $Omega(2012)$ resonance in the nonleptonic weak decays of $Omega_c^0 to pi^+ bar{K}Xi^*(1530) (eta Omega) to pi^+ (bar{K}Xi)^-$ and $pi^+ (bar{K}Xipi)^-$ via final-state interactions of the $bar{K}Xi^*(1530)$ and $eta Omega$ pairs. The weak interaction part is assumed to be dominated by the charm quark decay process: $c(ss) to (s + u + bar{d})(ss)$, while the hadronization part takes place between the $sss$ cluster from the weak decay and a quark-antiquark pair with the quantum numbers $J^{PC} = 0^{++}$ of the vacuum, produces a pair of $bar{K}Xi^*(1530)$ and $eta Omega$. Accordingly, the final $bar{K}Xi^*(1530)$ and $eta Omega$ states are in pure isospin $I= 0$ combinations, and the $Omega_c^0 to pi^+ bar{K}Xi^*(1530)(eta Omega) to pi^+ (bar{K}Xi)^-$ decay is an ideal process to study the $Omega(2012)$ resonance. With the final-state interaction described in the chiral unitary approach, up to an arbitrary normalization, the invariant mass distributions of the final state are calculated, assuming that the $Omega(2012)$ resonance with spin-parity $J^P = 3/2^-$ is a dynamically generated state from the coupled channels interactions of the $bar{K}Xi^*(1530)$ and $eta Omega$ in $s$-wave and $bar{K}Xi$ in $d$-wave. We also calculate the ratio, $R^{bar{K}Xipi}_{bar{K}Xi} = {rm Br}[Omega_c^0 to pi^+ Omega(2012)^- to pi^+ (bar{K}Xi pi)^-] / {rm Br}[Omega_c^0 to pi^+ Omega(2012)^- to pi^+ (bar{K}Xi)^-$]. The proposed mechanism can provide valuable information on the nature of the $Omega(2012)$ and can in principle be tested by future experiments.
Recent experimental data for the differential decay distribution of the decay $tau^-to u_tau K_Spi^-$ by the Belle collaboration are described by a theoretical model which is composed of the contributing vector and scalar form factors $F_+^{Kpi}(s)$ and $F_0^{Kpi}(s)$. Both form factors are constructed such that they fulfil constraints posed by analyticity and unitarity. A good description of the experimental measurement is achieved by incorporating two vector resonances and working with a three-times subtracted dispersion relation in order to suppress higher-energy contributions. The resonance parameters of the charged $K^*(892)$ meson, defined as the pole of $F_+^{Kpi}(s)$ in the complex $s$-plane, can be extracted, with the result $M_{K^*}=892.0 pm 0.9 $MeV and $Gamma_{K^*}=46.2 pm 0.4 $MeV. Finally, employing the three-subtracted dispersion relation allows to determine the slope and curvature parameters $lambda_+^{}=(24.7pm 0.8)cdot 10^{-3}$ and $lambda_+^{}=(12.0pm 0.2)cdot 10^{-4}$ of the vector form factor $F_+^{Kpi}(s)$ directly from the data.
We investigate the $D_{s}^{+} rightarrow K^{+} K^{-} pi^{+}$ decay theoretically with the final state interactions, which is based on the chiral unitary approach and takes into account the external and internal $W$-emission mechanisms at the quark level. Only considering three resonances contributions, the $f_0(980)$ in $S$-wave, the $bar {K}^{*}(892)^{0}$ and $phi(1020)$ in $P$-wave, one can make a good description of the recent experimental data from BESIII Collaboration, where the contribution from $S$-wave is found to be small. Besides, we also make a calculation of the corresponding branching fractions, which are consistent with the results of BESIII Collaboration and Particle Data Group.
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