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Register a new userScalar mesons and polarizability of the nucleon
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Authors
Martin Schumacher
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It is shown that the scalar mesons $sigma$, $f_0(980)$ and $a_0(980)$ as $t$-channel exchanges quantitatively solve the problem of diamagnetism and give an explanation of the large missing part of the electric polarizability $alpha$ showing up when only the pion cloud is taken into account. The electric polarizability of the proton $alpha_p$ confirms a two-photon width of the $sigma$ meson of $Gamma_{sigmagammagamma}=(2.58pm 0.26)$ keV.
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The center-of-gravity rule is tested for heavy and light-quark mesons. In the heavy-meson sector, the rule is excellently satisfied. In the light-quark sector, the rule suggests that the $a_0(980)$ could be the spin-partner of $a_2(1320)$, $a_1(1260)$, and $b_1(1235)$; $f_0(500)$ the spin-partner of $f_2(1270)$, $f_1(1285)$, and $h_1(1170)$; and $f_0(980)$ the spin-partner of $f_2(1525)$, $f_1(1420)$, and $h_1(1415)$. From the decay and the production of light scalar mesons we find a consistent mixing angle $theta^{rm s}=(14pm4)^circ$. We conclude that $f_0(980)$ is likely octet-like in SU(3) with a slightly larger $sbar s$ content and $f_0(500)$ is SU(3) singlet-like with a larger $nbar n$ component. The $a_0(1450)$, $K^*_0(1430)$, $f_0(1500)$ and $f_0(1370)$ are suggested as nonet of radial excitations. The scalar glueball is discussed as part of the wave function of scalar isoscalar mesons and not as additional intruder. It seems not to cause supernumerosity.
We discuss the effect of the instanton induced, six-fermion effective Lagrangian on the decays of the lightest scalar mesons in the diquark--antidiquark picture. This addition allows for a remarkably good description of light scalar meson decays. The same effective Lagrangian produces a mixing of the lightest scalars with the positive parity q-qbar states. Comparing with previous work where the q-qbar mesons are identified with the nonet at 1200-1700 MeV, we find that the mixing required to fit the mass spectrum is in good agreement with the instanton coupling obtained from light scalar decays. A coherent picture of scalar mesons as a mixture of tetraquark states (dominating in the lightest mesons) and heavy q-qbar states (dominating in the heavier mesons) emerges.
Within the framework of covariant confined quark model, we compute the transition form factors of $D$ and $D_s$ mesons decaying to light scalar mesons $f_0(980)$ and $a_0(980)$. The transition form factors are then utilized to compute the semileptonic branching fractions. We study the channels namely, $D_{(s)}^+ to f_0(980) ell^+ u_ell$ and $D to a_0(980) ell^+ u_ell$ for $ell = e$ and $mu$. For computation of semileptonic branching fractions, we consider the $a_0(980)$ meson to be the conventional quark-antiquark structure and the $f_0(980)$ meson as the admixture of $sbar{s}$ and light quark-antiquark pairs. Our findings are found to support the recent BESIII data.
The strange particle production induced by (anti)neutrino off nucleon has been studied for $|Delta S|=0$ and $|Delta S|=1$ channels. The reactions those we have considered are for the production of single kaon/antikaon, eta and associated particle production processes. We have developed a microscopical model based on the SU(3) chiral Lagrangian. The basic parameters of the model are $f_pi$, the pion decay constant, Cabibbo angle, the proton and neutron magnetic moments and the axial vector coupling constants for the baryons octet. For antikaon production we have also included $Sigma^*$(1385) resonance and for eta production $S_{11}$(1535) and $S_{11}$(1650) resonances are included.
We suggest that the recently observed charmed scalar mesons $D_0^{0}(2308)$ (BELLE) and $D_0^{0,+}(2405)$ (FOCUS) are considered as different resonances. Using the QCD sum rule approach we investigate the possible four-quark structure of these mesons and also of the very narrow $D_{sJ}^{+}(2317)$, firstly observed by BABAR. We use diquak-antidiquark currents and work to the order of $m_s$ in full QCD, without relying on $1/m_c$ expansion. Our results indicate that a four-quark structure is acceptable for the resonances observed by BELLE and BABAR: $D_0^{0}(2308)$ and $D_{sJ}^{+}(2317)$ respectively, but not for the resonances observed by FOCUS: $D_0^{0,+}(2405)$.
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