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Register a new userForm factors of the isovector scalar current and the $etapi$ scattering phase shifts
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A model for S-wave $etapi$ scattering is proposed which could be realistic in an energy range from threshold up to above one GeV, where inelasticity is dominated by the $Kbar{K}$ channel. The $T$-matrix, satisfying two-channel unitarity, is given in a form which matches the chiral expansion results at order $p^4$ exactly for the $etapitoetapi$, $etapito Kbar{K}$ amplitudes and approximately for $Kbar{K}to Kbar{K}$. It contains six phenomenological parameters. Asymptotic conditions are imposed which ensure a minimal solution of the Muskhelishvili-Omn`es problem, thus allowing to compute the $etapi$ and $Kbar{K}$ form factor matrix elements of the $I=1$ scalar current from the $T$-matrix. The phenomenological parameters are determined such as to reproduce the experimental properties of the $a_0(980)$, $a_0(1450)$ resonances, as well as the chiral results of the $etapi$ and $Kbar{K}$ scalar radii which are predicted to be remarkably small at $O(p^4)$. This $T$-matrix model could be used for a unified treatment of the $etapi$ final-state interaction problem in processes such as $etato eta pipi$, $phitoetapigamma$, or the $etapi$ initial-state interaction in $etato3pi$.
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We consider the evaluation of the $etapi$ isospin-violating vector and scalar form factors relying on a systematic application of analyticity and unitarity, combined with chiral expansion results. It is argued that the usual analyticity properties do hold (i.e. no anomalous thresholds are present) in spite of the instability of the $eta$ meson in QCD. Unitarity relates the vector form factor to the $etapi to pipi$ amplitude: we exploit progress in formulating and solving the Khuri-Treiman equations for $etato 3pi$ and in experimental measurements of the Dalitz plot parameters to evaluate the shape of the $rho$-meson peak. Observing this peak in the energy distribution of the $tauto eta pi u$ decay would be a background-free signature of a second-class amplitude. The scalar form factor is also estimated from a phase dispersive representation using a plausible model for the $etapi$ elastic scattering $S$-wave phase shift and a sum rule constraint in the inelastic region. We indicate how a possibly exotic nature of the $a_0(980)$ scalar meson manifests itself in a dispersive approach. A remark is finally made on a second-class amplitude in the $tautopipi u$ decay.
We compute the diagonal isovector axial-vector as well as induced pseudoscalar form factors of nucleon, $Sigma$ and $Xi$ baryons by employing the light-cone QCD sum rules to leading order in QCD and including distribution amplitudes up to twist 6. Extrapolating our sum-rules results to low-momentum transfers, we make a comparison with experimental and lattice-QCD results where we can achieve a nice qualitative and quantitative agreement.
We study the scattering of neutrinos on polarized and unpolarized free nucleons, and also the polarization of recoil particles in these scatters. In contrast to electromagnetic processes, the parity-violating weak interaction gives rise to large spin asymmetries at leading order. Future polarization measurements could provide independent access to the proton axial structure and allow the first extraction of the pseudoscalar form factor from neutrino data without the conventional partially conserved axial current (PCAC) ansatz and assumptions about the pion-pole dominance. The pseudoscalar form factor can be accessed with precise measurements with muon (anti)neutrinos of a few hundreds $mathrm{MeV}$ of energy or with tau (anti)neutrinos. The axial form factor can be extracted from scattering measurements using accelerator neutrinos of all energies.
We present results for the isovector electromagnetic form factors of the nucleon computed on the CLS ensembles with $N_f=2+1$ flavors of $mathcal{O}(a)$-improved Wilson fermions and an $mathcal{O}(a)$-improved vector current. The analysis includes ensembles with four lattice spacings and pion masses ranging from 130 MeV up to 350 MeV and mainly targets the low-$Q^2$ region. In order to remove any bias from unsuppressed excited-state contributions, we investigate several source-sink separations between 1.0 fm and 1.5 fm and apply the summation method as well as explicit two-state fits. The chiral interpolation is performed by applying covariant chiral perturbation theory including vector mesons directly to our form factor data, thus avoiding an auxiliary parametrization of the $Q^2$ dependence. At the physical point, we obtain $mu=4.71(11)_{mathrm{stat}}(13)_{mathrm{sys}}$ for the nucleon isovector magnetic moment, in good agreement with the experimental value and $langle r_mathrm{M}^2rangle~=~0.661(30)_{mathrm{stat}}(11)_{mathrm{sys}},~mathrm{fm}^2$ for the corresponding square-radius, again in good agreement with the value inferred from the $ep$-scattering determination [Bernauer et~al., Phys. Rev. Lett., 105, 242001 (2010)] of the proton radius. Our estimate for the isovector electric charge radius, $langle r_mathrm{E}^2rangle = 0.800(25)_{mathrm{stat}}(22)_{mathrm{sys}},~mathrm{fm}^2$, however, is in slight tension with the larger value inferred from the aforementioned $ep$-scattering data, while being in agreement with the value derived from the 2018 CODATA average for the proton charge radius.
The form-factors for the transition $ N^*(1535)to N $ induced by isovector and isoscalar axial currents within the framework of light-cone QCD sum rules by using the most general form of the interpolating current are calculated. In numerical calculations, we use two sets of values of input parameters. It is observed that the $ Q^2 $ dependence of the form-factor $ G_A $ can be described by the dipole form. Moreover, the form-factors $ G_P^{(S)} $ are found to be highly sensitive to the variations in the auxiliary parameter $ beta $.
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