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Register a new userKaon-Nucleon potential from lattice QCD
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Y. Ikeda
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We study the KN interactions in the I(J^{pi})=0(1/2^-) and 1(1/2^-) channels and associated exotic state Theta^+ from 2+1 flavor full lattice QCD simulation for relatively heavy quark mass corresponding to m_{pi}=871 MeV. The s-wave KN potentials are obtained from the Bethe-Salpeter wave function by using the method recently developed by HAL QCD (Hadrons to Atomic nuclei from Lattice QCD) Collaboration. Potentials in both channels reveal short range repulsions: Strength of the repulsion is stronger in the I=1 potential, which is consistent with the prediction of the Tomozawa-Weinberg term. The I=0 potential is found to have attractive well at mid range. From these potentials, the $KN$ scattering phase shifts are calculated and compared with the experimental data.
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We calculate $pXi^0$ potentials from the equal-time Bethe-Salpeter amplitude measured in the quenched QCD simulation with the spatial lattice volume, (4.4 fm)$^3$. The standard Wilson gauge action with the gauge coupling $beta=5.7$ on $32^4$ lattice together with the standard Wilson quark action are used. The hopping parameter $kappa_{ud}=0.1678$ is chosen for $u$ and $d$ quarks, which corresponds to $m_{pi}simeq 0.37$ GeV. The physical strange quark mass is used by taking the parameter $kappa_s=0.1643$ which is deduced from the physical $K$ meson mass. The lattice spacing $a=0.1420$ fm is determined by the physical $rho$ meson mass. We find that the $pXi^0$ potential has strong spin dependence. Strong repulsive core is found in $^1S_0$ channel while the effective central potential in the $^3S_1$ channel has relatively weak repulsive core. The potentials also have weak attractive parts in the medium to long distance region (0.6 fm $lsim r lsim 1.2$ fm) in both of the $^1S_0$ and $^3S_1$ channels.
We present a new analysis method that allows one to understand and model excited state contributions in observables that are dominated by a pion pole. We apply this method to extract axial and (induced) pseudoscalar nucleon isovector form factors, which satisfy the constraints due to the partial conservation of the axial current up to expected discretization effects. Effective field theory predicts that the leading contribution to the (induced) pseudoscalar form factor originates from an exchange of a virtual pion, and thus exhibits pion pole dominance. Using our new method, we can recover this behavior directly from lattice data. The numerical analysis is based on a large set of ensembles generated by the CLS effort, including physical pion masses, large volumes (with up to $96^3 times 192$ sites and $L m_pi = 6.4$), and lattice spacings down to $0.039 , text{fm}$, which allows us to take all the relevant limits. We find that some observables are much more sensitive to the choice of parametrization of the form factors than others. On the one hand, the $z$-expansion leads to significantly smaller values for the axial dipole mass than the dipole ansatz ($M_A^{text{$z$-exp}}=1.02(10) , text{GeV}$ versus $M_A^{text{dipole}} = 1.31(8) , text{GeV}$). On the other hand, we find that the result for the induced pseudoscalar coupling at the muon capture point is almost independent of the choice of parametrization ($g_P^{star text{$z$-exp}} = 8.68(45)$ and $g_P^{star text{dipole}} = 8.30(24)$), and is in good agreement with both, chiral perturbation theory predictions and experimental measurement via ordinary muon capture. We also determine the axial coupling constant $g_A$.
We present state-of-the-art results from a lattice QCD calculation of the nucleon axial coupling, $g_A$, using Mobius Domain-Wall fermions solved on the dynamical $N_f = 2 + 1 + 1$ HISQ ensembles after they are smeared using the gradient-flow algorithm. Relevant three-point correlation functions are calculated using a method inspired by the Feynman-Hellmann theorem, and demonstrate significant improvement in signal for fixed stochastic samples. The calculation is performed at five pion masses of $m_pisim {400, 350, 310, 220, 130}$~MeV, three lattice spacings of $asim{0.15, 0.12, 0.09}$~fm, and we do a dedicated volume study with $m_pi Lsim{3.22, 4.29, 5.36}$. Control over all relevant sources of systematic uncertainty are demonstrated and quantified. We achieve a preliminary value of $g_A = 1.285(17)$, with a relative uncertainty of 1.33%.
We present results on the nucleon axial form factors within lattice QCD using two flavors of degenerate twisted mass fermions. Volume effects are examined using simulations at two volumes of spatial length $L=2.1$ fm and $L=2.8$ fm. Cut-off effects are investigated using three different values of the lattice spacings, namely $a=0.089$ fm, $a=0.070$ fm and $a=0.056$ fm. The nucleon axial charge is obtained in the continuum limit and chirally extrapolated to the physical pion mass enabling comparison with experiment.
We present a model-independent calculation of hadron matrix elements for all dimension-six operators associated with baryon number violating processes using lattice QCD. The calculation is performed with the Wilson quark action in the quenched approximation at $beta=6/g^2=6.0$ on a $28^2times 48times 80$ lattice. Our results cover all the matrix elements required to estimate the partial lifetimes of (proton,neutron)$to$($pi,K,eta$) +(${bar u},e^+,mu^+$) decay modes. We point out the necessity of disentangling two form factors that contribute to the matrix element; previous calculations did not make the separation, which led to an underestimate of the physical matrix elements. With a correct separation, we find that the matrix elements have values 3-5 times larger than the smallest estimates employed in phenomenological analyses of the nucleon decays, which could give strong constraints on several GUT models. We also find that the values of the matrix elements are comparable with the tree-level predictions of chiral lagrangian.
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