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Register a new userThe $pi f_0(500)$ decay of the $a_1(1260)$
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We evaluate the $a_1(1260) to pi sigma (f_0(500))$ decay width from the perspective that the $a_1(1260)$ resonance is dynamically generated from the pseudoscalar-vector interaction and the $sigma$ arises from the pseudoscalar-pseudoscalar interaction. A triangle mechanism with $a_1(1260) to rho pi$ followed by $rho to pi pi$ and a fusion of two pions within the loop to produce the $sigma$ provides the mechanism for this decay under these assumptions for the nature of the two resonances. We obtain widths of the order of $13-22$ MeV. Present experimental results differ substantially from each other, suggesting that extra efforts should be devoted to the precise extraction of this important partial decay width, which should provide valuable information on the nature of the axial vector and scalar meson resonances and help clarify the role of the $pisigma$ channel in recent lattice QCD calculations of the $a_1$.
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We show that the a_1-rho-pi Lagrangian is a decisive element for obtaining a good phenomenological description of the three-pion decays of the tau lepton. We choose it in a two-component form with a flexible mixing parameter sin(theta). In addition to the dominant a_1-> pho pi intermediate states, the a_1->pi sigma ones are included. When fitting the three-pion mass spectra, three data sets are explored: (1) ALEPH 2005 pi-pi-pi+ data, (2) ALEPH 2005 pi-pi0pi0 data, and (3) previous two sets combined and supplemented with the ARGUS 1993, OPAL 1997, and CLEO 2000 data. The corresponding confidence levels are (1) 28.3%, (2) 100%, and (3) 7.7%. After the inclusion of the a_1(1640) resonance, the agreement of the model with data greatly improves and the confidence level reaches 100% for each of the three data sets. From the fit to all five experiments [data set (3)] the following parameters of the a_1(1260) are obtained m_{a_1}=(1233+/-18) MeV, Gamma_{a_1}=(431+/-20) MeV. The optimal value of the Lagrangian mixing parameter sin(theta)= 0.459+/-0.004 agrees with the value obtained recently from the e+e- annihilation into four pions.
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.
In the present talk, we report a recent investigation on photoproduction of the $gamma N to f_0(500)N$ within a framework of the effective Lagrangian. We include the nucleon resonances with pin $1/2$ in the $s$ channel. The coupling constants have been etermined by assuming that the decay process $N^* to (pipi)_{I=0,J=0}N$ can be regarded as $N^* to f_0(500) N$. We discuss the numerical results for the total cross sections and possible extension of the present work.
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.
We investigate the rare radiative eta decay modes eta -> pi+ pi- gamma gamma and eta -> pi0 pi0 gamma gamma within the framework of chiral lagrangians at o(p^4) and present photon spectra for both processes.
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