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Register a new userThe impact of $a_0^0(980)-f_0(980)$ mixing on the localized $CP$ violations of the $B^-rightarrow K^- pi^+pi^-$ decay
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In the framework of the QCD factorization approach, we study the localized $CP$ violations of the $B^-rightarrow K^- pi^+pi^-$ decay with and without $a_0^0(980)-f_0(980)$ mixing mechanism, respectively, and find that the localized $CP$ violation can be enhanced by this mixing effect when the mass of the $pi^+pi^-$ pair is in the vicinity of the $f_0(980)$ resonance. The corresponding theoretical prediction results are $mathcal{A}_{CP}(B^-rightarrow K f_0 rightarrow K^-pi^+pi^-)=[0.24, 0.36]$ and $mathcal{A}_{CP}(B^-rightarrow K^- f_0(a_0) rightarrow K^-pi^+pi^-)=[0.33, 0.52]$, respectively. Meanwhile, we also calculate the branching fraction of the $B^-rightarrow K^-f_0(980)rightarrow K^-pi^+pi^-$ decay, which is consistent with the experimental results. We suggest that $a_0^0(980)-f_0(980)$ mixing mechanism should be considered when studying the $CP$ violation of the $B$ or $D$ mesons decays theoretically and experimentally.
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The $a_0^0(980)-f_0(980)$ mixing is one of the most potential tools to learn about the nature of $a_0^0(980)$ and $f_0(980)$. Using the $f_0(980)$-$a_0^0(980)$ mixing intensity $xi_{af}$ measured recently at BESIII, we calculate the the branching ratio of the the isospin violation decay $J/psi rightarrowgammaeta_c rightarrow gamma pi^0 a_0^0(1450)rightarrow gamma pi^0 a_0^0(980)f_0(500)rightarrow gamma pi^0 f_0(980) f_0(500) rightarrow gamma pi^0 pi^+pi^- pi^+pi^-$. The value of the branching ratio is found to be $O(10^{-6})$, which can be observed with $10^{10}$ $J/psi$ events collected at BESIII. The narrow peak from the $f_0(980)$-$a_0^0(980)$ mixing in the $pi^+pi^-$ mass square spectrum can also be observed. In addition, we study the non-resonant decay $a_0^0(1450)rightarrow f_0(980) pi^+pi^-(text{non-resonant})$, which is dominated by the $a_0^0(980)$-$f_{0}(980)$ mixing. We find that the non-resonant decay $a_0^0(1450)rightarrow f_0(980) pi^+pi^-$ and the decay $a_0^0(1450)rightarrow f_0(980) f_0(500)$ can be combined to measure the mixing intensity $xi_{af}$ in experiment. These decays are the perfect complement to the decay $chi_{c1}rightarrow f_{0}(980)pi^{0}topi^{+}pi^{-}pi^{0}$ which had been observed at BESIII, the observations of them will make the measurement of the mixing intensity $xi_{af}$ more precisely.
We make a theoretical study of the $eta(1405) to pi^{0} f_0(980)$ and $eta(1405) to pi^{0} a_0(980)$ reactions with an aim to determine the isospin violation and the mixing of the $f_0(980)$ and $a_0(980)$ resonances. We make use of the chiral unitary approach where these two resonances appear as composite states of two mesons, dynamically generated by the meson-meson interaction provided by chiral Lagrangians. We obtain a very narrow shape for the $f_0(980)$ production in agreement with a BES experiment. As to the amount of isospin violation, or $f_0(980)$ and $a_0(980)$ mixing, assuming constant vertices for the primary $eta(1405)rightarrow pi^{0}Kbar{K}$ and $eta(1405)rightarrow pi^{0}pi^{0}eta$ production, we find results which are much smaller than found in the recent experimental BES paper, but consistent with results found in two other related BES experiments. We have tried to understand this anomaly by assuming an I=1 mixture in the $eta(1405)$ wave function, but this leads to a much bigger width of the $f_0(980)$ mass distribution than observed experimentally. The problem is solved by using the primary production driven by $eta to K^* bar K$ followed by $K^* to K pi$, which induces an extra singularity in the loop functions needed to produce the $f_0(980)$ and $a_0(980)$ resonances. Improving upon earlier work along the same lines, and using the chiral unitary approach, we can now predict absolute values for the ratio $Gamma(pi^0, pi^+ pi^-)/Gamma(pi^0, pi^0 eta)$ which are in fair agreement with experiment. We also show that the same results hold if we had the $eta(1475)$ resonance or a mixture of these two states, as seems to be the case in the BES experiment.
In this work, we have investigated the process $D_s^+to K^+ K^- pi^+$, taking into account the contributions from the $S$-wave pseudoscalar-pseudoscalar interaction within the chiral unitary approach, and also the intermediate $phi$ resonance. By analyzing the BESIII and {it BABAR} measurements, we conclude that the $f_0(980)$ state, dynamically generated from the $S$-wave pseudoscalar-pseudoscalar interaction, gives the dominant contribution close to the $K^+K^-$ threshold in the $K^+K^-$ invariant mass distribution of the decay $D_s^+to K^+ K^- pi^+$ in $S$-wave. On the other hand, our results imply that the lineshape adopted by BESIII and {it BABAR} for the resonances $a_0(980)$ and $f_0(980)$ is not advisable in the fit to the data close to the $K^+K^-$ threshold.
The decay $D^{+}_{s}rightarrow pi^{+}pi^{+}pi^{-}eta$ is observed for the first time, using $e^+e^-$ collision data corresponding to an integrated luminosity of 6.32 fb$^{-1}$, collected by the BESIII detector at center-of-mass energies between 4.178 and 4.226 GeV. The absolute branching fraction for this decay is measured to be $mathcal{B}(D^+_s to pi^+ pi^+ pi^- eta) = (3.12pm0.13_{rm stat.}pm0.09_{rm syst.})$%. The first amplitude analysis of this decay reveals the sub-structures in $D^{+}_{s}rightarrow pi^{+}pi^{+}pi^{-}eta$ and determines the relative fractions and the phases among these sub-structures. The dominant intermediate process is $D^{+}_{s}rightarrow a_1(1260)^+ eta, a_1(1260)^+ rightarrow rho(770)^0pi^+$ with a branching fraction of $(1.73 pm 0.14_{rm stat.} pm 0.08_{rm syst.})$%. We also observe the W-annihilation process $D^{+}_{s}rightarrow a_0(980)^+rho(770)^0$, $a_0(980)^+ to pi^+ eta$ with a branching fraction of $(0.21pm0.08_{rm stat.}pm0.05_{rm syst.})$%, which is larger than the branching fractions of other measured pure W-annihilation decays by one order of magnitude.
From the amplitude analysis of the $D^+_s to pi^+ pi^0 eta$ decay, the BESIII Collaboration firstly observed the $D^+_s to a_0(980)^+pi^0$ and $D^+_s to a_0(980)^0pi^+$ decay modes, which are expected to occur through the pure $W$-annihilation processes. The measured branching fraction $mathcal{B}[D_{s}^{+}to a_{0}(980)^{+(0)}pi^{0(+)},a_{0}(980)^{+(0)}to pi^{+(0)}eta]$ is, however, found to be larger than those of known $W$-annihilation decays by one order of magnitude. This apparent contradiction can be reconciled if the two decays are induced by internal $W$-conversion or external $W$-emission mechanisms instead of $W$-annihilation mechanism. In this work, we propose that the $D^+_s$ decay proceeds via both the external and internal $W$-emission instead of $W$-annihilation mechanisms. In such a scenario, we perform a study of the $D^+_s to pi^+pi^0eta$ decay by taking into account the contributions from the tree diagram $D^+_s to rho^+ eta to pi^+ pi^0 eta$ and the intermediate $rho^+ eta$ and $K^*bar{K}/Kbar{K}^*$ triangle diagrams. The intermediate $a_0(980)$ state can be dynamically generated from the final state interactions of coupled $K bar{K}$ and $pi eta$ channels, and it is shown that the experimental data can be described fairly well, which supports the interpretation of $a_0(980)$ as a molecular state.
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