Recently, a tetraquark mixing framework has been proposed for light mesons and applied more or less successfully to the isovector resonances, a 0 ð980Þ, a 0 ð1450Þ, as well as to the isodoublet resonances,. In this work, we present a more extensive view on the mixing framework and apply this framework to the isoscalar resonances, f 0 ð500Þ, f 0 ð980Þ, f 0 ð1370Þ, f 0 ð1500Þ. Tetraquarks in this framework can have two spin configurations containing either spin-0 diquark or spin-1 diquark and each configuration forms a nonet in flavor space. The two spin configurations are found to mix strongly through the color-spin interactions. Their mixtures, which diagonalize the hyperfine masses, can generate the physical resonances constituting two nonets, which, in fact, coincide roughly with the experimental observation. We identify that f 0 ð500Þ, f 0 ð980Þ are the isoscalar members in the light nonet, and f 0 ð1370Þ, f 0 ð1500Þ are the similar members in the heavy nonet. This means that the spin configuration mixing, as it relates the corresponding members in the two nonets, can generate f 0 ð500Þ, f 0 ð1370Þ among the members in light mass, and f 0 ð980Þ, f 0 ð1500Þ in heavy mass. The complication arises because the isoscalar members of each nonet are subject to an additional flavor mixing known as Okubo-Zweig-Iizuka rule so that f 0 ð500Þ, f 0 ð980Þ, and similarly f 0 ð1370Þ, f 0 ð1500Þ, are the mixture of two isoscalar members belonging to an octet and a singlet in SU f ð3Þ. The tetraquark mixing framework including the flavor mixing is tested for the isoscalar resonances in terms of the mass splitting and the fall-apart decay modes. The mass splitting among the isoscalar resonances is found to be consistent qualitatively with their hyperfine mass splitting strongly driven by the spin configuration mixing, which suggests that the tetraquark mixing framework works. The fall-apart modes from our tetraquarks also seem to be consistent with the experimental modes. We also discuss possible existence of the spin-1 tetraquarks that can be constructed by the spin-1 diquark.

We investigate medium effects due to density-dependent magnetic moments of baryons on neutron stars under strong magnetic fields. If we allow the variation of anomalous magnetic moments (AMMs) of baryons in dense matter under strong magnetic fields, AMMs of nucleons are enhanced to be larger than those of hyperons. The enhancement naturally affects the chemical potentials of baryons to be large and leads to the increase of a proton fraction. Consequently, it causes the suppression of hyperons, resulting in the stiffness of the equation of state. Under the presumed strong magnetic fields, we evaluate relevant particles' population, the equation of state and the maximum masses of neutron stars by including density-dependent AMMs and compare them with those obtained from AMMs in free space.

In the paper above, we have proposed a tetraquark picture with the mixing scheme for the I z = 1 members of the isovector (I = 1) resonances, a + 0 (980), a + 0 (1450). In particular, their mass splittings fit relatively well with the hyperfine mass splittings if they are viewed as mixtures of two spin-configurations of diquark-antidiquark constituents, |J, J 12 , J 34 = |000 , |011 , where J is the tetraquark spin, J 12 the diquark spin, J 34 the antidiquark spin. The second configuration involving the spin-1 diquark, |011 , is found to be an important ingredient in explaining the resonances of our concern in this tetraquark picture. However, the existence of the |011 component requires additional tetraquarks to be found in J = 1 and J = 2 resonances with the spin configurations, |J, J 12 , J 34 = |111 and |211 , respectively.In this erratum, we point out that our assignment of a + 1 (1260) as a candidate for the J = 1 tetraquark with the |111 configuration is incorrect because of the C-parity for its corresponding member in I z = 0. Specifically, we would like to demonstrate that the |111 state with I = 1, I z = 0 must have the C-parity odd and, in this regard, a relevant candidate for the |111 state should be b 0 1 (1235). So its charged member (I = 1, I z = 1), which in fact was considered in our paper, must be b To demonstrate that C|111 = −|111 for the isospin member of I = 1, I z = 0, we take the state with J = 1 and the spin projection M = 1 among three spin states in |111 , and we denote this state as |J M = |11 . The same proof can be done for the other spin states, |J M = |10 , |1 − 1 . The flavor structure of the member I = 1, Now it is straightforward to prove that the state above has C = − by applying the charge conjugation [Eq. (2) 123

We reinvestigate effects of neutrino oscillations on the production of 7 Li and 11 B in core-collapse supernovae (SNe). During the propagation of neutrinos from the proto-neutron star, their flavors change and the neutrino reaction rates for spallation of 12 C and 4 He are affected. In this work corrected neutrino spallation cross sections for 4 He and 12 C are adopted. Initial abundances involving heavy s-nuclei and other physical conditions are derived in a new calculation of the SN 1987A progenitor in which effects of the progenitor metallicity are included. A dependence of the SN nucleosynthesis and final yields of 7 Li and 11 B on the neutrino mass hierarchy are shown in several stellar locations. In the normal hierarchy case, the charged-current (CC) reaction rates of ν e are enhanced, and yields of proton-rich nuclei, along with 7 Be and 11 C, are increased. In the inverted hierarchy case, the CC reaction rates ofν e are enhanced, and yields of neutron-rich nuclei, along with 7 Li and 11 B, are increased. We find that variation of the metallicity modifies the yields of 7 Li, 7 Be, 11 B, and 11 C. This effect is caused by changes in the neutron abundance during SN nucleosynthesis. Therefore, accurate calculations of Li and B production in SNe should take into account the metallicity of progenitor stars.

Based on the recent proposal for the tetraquarks with the mixing scheme, we investigate fall-apart decays of a 0 (980), a 0 (1450) into two lowest-lying mesons. This mixing scheme suggests that a 0 (980) and a 0 (1450) are the tetraquarks with the mixtures of two spin configurations of diquark and antidiquark. Due to the relative sign differences in the mixtures, the couplings of fall-apart decays into two mesons are strongly enhanced for a 0 (980) but suppressed for a 0 (1450). We report that this expectation is supported by their experimental decays. In particular, the ratios of the associated partial decay widths, which depend on some kinematical factors and the couplings, are found to be around.52 − 0.89, which seems to agree with the experimental ratios reasonably well. This agreement can be interpreted as the tetraquark signatures for a 0 (980), a 0 (1450).