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Register a new userProperties of the $pi^0$, $eta$, $eta$, $sigma$, $f_0(980)$ and $a_0(980)$ mesons and their relevance for the polarizabilities of the nucleon
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Authors
Martin Schumacher
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The signs and values of the two-photon couplings $F_{Mgammagamma}$ of mesons $(M)$ and their couplings $g_{MNN}$ to the nucleon as entering into the $t$-channel parts of the difference of the electromagnetic polarizabilities $(alpha-beta)$ and the backward angle spin polarizabilities $gamma_pi$ are determined. The excellent agreement achieved with the experimental polarizabilities of the proton makes it possible to make reliable predictions for the neutron. The results obtained are $alpha_n=13.4pm 1.0$, $beta_n=1.8mp 1.0$ ($10^{-4}$ fm$^3$), and $gamma^{(n)}_pi=57.6pm 1.8$ ($10^{-4}$ fm$^4$). New empirical information on the flavor wave functions of the $f_0(980)$ and the $a_0(980)$ meson is obtained.
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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.
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.
The two-photon decay widths of scalar mesons sigma(600), f_0(980) and a_0(980) are calculated in framework of the local Nambu-Jona-Lasinio model. The contributions of the quark loops (Hartree-Fock approximation) and the meson loops (next 1/N_c-approximation where N_c is the number of colors) are taken into account. These contributions, as we show, are the values of the same order of magnitude. For the f_0 decay the K-loop contribution turns out to play the dominant role. The results are in satisfactory agreement with modern experimental data.
The two-photon decay widths of scalar mesons sigma(600), f_0(980) and a_0(980) as well a_0 -> rho(omega)gamma and f_0 -> rho(omega)gamma are calculated in the framework of the local Nambu-Jona-Lasinio model. The contributions of the quark loops (Hartree-Fock approximation) and the meson loops (next 1/Nc -approximation where Nc is the number of colors) are taken into account. These contributions, as we show, are the values of the same order of magnitude. For the f_0 decay the K-loop contribution turns out to play the dominant role. The results for two-gamma decays are in satisfactory agreement with modern experimental data. The predictions for a_0 -> rho(omega)gamma and f_0 -> rho(omega)gamma widths are given.
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.
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