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Register a new user$K_{l3}$ form factors at the physical point on (10.9 fm)$^3$ volume
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We present the calculation of the $K_{l3}$ form factors with $N_f = 2 + 1$ nonperturbatively $O(a)$-improved Wilson quark action and Iwasaki gauge action at the physical point on a large volume of (10.9 fm)$^3$ at one lattice spacing of $a = 0.085$ fm. We extract the form factors from 3-point functions with three different time separations between the source and sink operators to confirm suppression of excited state contributions. The form factors are calculated in very close to the zero momentum transfer, $q^2 = 0$, thanks to the large volume, so that stable interpolations to $q^2 = 0$ are carried out. Using our form factors, we obtain the form factor at $q^2 = 0$, $f_+(0) = 0.9603(16)(^{+14}_{ -4})(44)(19)(1)$, where the first, second, and fifth errors are statistical, systematic errors from fit functions and the isospin breaking effect, respectively. The third and fourth errors denote the finite lattice spacing effects estimated from the renormalization factor and contribution beyond the leading order SU(3) chiral perturbation theory (ChPT). The result of $f_+(0)$ yields the Cabibbo-Kobayashi-Maskawa (CKM) matrix element, $|V_{us}| = 0.2255(13)(4)$, where the first error comes from our calculation and the second from the experiment. This value is consistent with the ones determined from the unitarity of the CKM matrix and the $K_{l2}$ decay within one standard deviation, while it is slightly larger than recent lattice calculations by at most 1.5 $sigma$. Furthermore, we evaluate the shape of the form factors and the phase space integral from our results. We confirm that those results are consistent with the experiment, and also $|V_{us}|$ determined with our phase space integral agrees with the one in the above.
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We present our results of the $K_{l3}$ form factors on the volume whose spatial extent is more than $L=$10 fm, with the physical pion and kaon masses using the stout-smearing clover $N_f = 2+1$ quark action and Iwasaki gauge action at $a^{-1}approx2.3$ GeV. The $K_{l3}$ form factor at zero momentum transfer is obtained from fit based on the next-to-leading (NLO) formula in SU(3) chiral perturbation theory. We estimate systematic errors of the form factor, mainly coming from the finite lattice spacing effect. We also determine the value of $|V_{us}|$ by combining our result with the experiment and check the consistency with the standard model prediction. The result is compared with the previous lattice calculations.
We present the nucleon form factors and root-mean-square (RMS) radii measured on a (10.8 fm$)^4$ lattice at the physical point. We compute the form factors at small momentum transfer region in $q^2le 0.102$ GeV$^2$ with the standard plateau method choosing four source-sink separation times $t_{rm sep}$ from 0.84 to 1.35 fm to examine the possible excited state contamination. We obtain the electric and magnetic form factors and their RMS radii for not only the isovector channel but also the proton and neutron ones without the disconnected diagram. We also obtain the axial-vector coupling and the axial radius from the axial-vector form factor. We find that these three form factors do not show large $t_{rm sep}$ dependence in our lattice setup. On the other hand, the induced pseudoscalar and pseudoscalar form factors show the clear effects of the excited state contamination, which affect the generalized Goldberger-Treiman relation.
We present results for the nucleon electromagnetic form factors using an ensemble of maximally twisted mass clover-improved fermions with pion mass of about 130 MeV. We use multiple sink-source separations and three analysis methods to probe ground-state dominance. We evaluate both the connected and disconnected contributions to the nucleon matrix elements. We find that the disconnected quark loop contributions to the isoscalar matrix elements are small, giving an upper bound of up to 2$%$ of the connected contribution and smaller than its statistical error. We present results for the isovector and isoscalar electric and magnetic Sachs form factors and the corresponding proton and neutron form factors. By fitting the momentum dependence of the form factors to a dipole form or to the z-expansion we extract the nucleon electric and magnetic radii, as well as, the magnetic moment. We compare our results to experiment as well as to other recent lattice QCD calculations.
We present results for the isovector nucleon form factors measured on a $96^4$ lattice at almost the physical pion mass with a lattice spacing of 0.085 fm in 2+1 flavor QCD. The configurations are generated with the stout-smeared $O(a)$-improved Wilson quark action and the Iwasaki gauge action at $beta$=1.82. The pion mass at the simulation point is about 146 MeV. A large spatial volume of $(8.1~{rm fm})^3$ allows us to investigate the form factors in the small momentum transfer region. We determine the isovector electric radius and magnetic moment from nucleon electric ($G_E$) and magnetic ($G_M$) form factors as well as the axial-vector coupling $g_A$. We also report on the results of the axial-vector ($F_A$), induced pseudoscalar ($F_P$) and pseudoscalar ($G_P$) form factors in order to verify the axial Ward-Takahashi identity in terms of the nucleon matrix elements, which may be called the generalized Goldberger-Treiman relation.
We present a direct calculation for the first derivative of the isovector nucleon form factors with respect to the momentum transfer $q^2$ using the lower moments of the nucleon 3-point function in the coordinate space. Our numerical simulations are performed using the $N_f = 2 + 1$ nonperturbatively $O(a)$-improved Wilson quark action and Iwasaki gauge action near the physical point, corresponding to the pion mass $M_pi =138$ MeV, on a (5.5 fm)$^4$ lattice at a single lattice spacing of $a = 0.085$ fm. In the momentum derivative approach, we can directly evaluate the mean square radii for the electric, magnetic, and axial-vector form factors, and also the magnetic moment without the $q^2$ extrapolation to the zero momentum point. These results are compared with the ones determined by the standard method, where the $q^2$ extrapolations of the corresponding form factors are carried out by fitting models. We find that the new results from the momentum derivative method are obtained with a larger statistical error than the standard method, but with a smaller systematic error associated with the data analysis. Within the total error range of the statistical and systematic errors combined, the two results are in good agreement. On the other hand, two variations of the momentum derivative of the induced pseudoscalar form factor at the zero momentum point show some discrepancy. It seems to be caused by a finite volume effect, since a similar trend is not observed on a large volume, but seen on a small volume in our pilot calculations at a heavier pion mass of $M_{pi}= 510$ MeV. Furthermore, we discuss an equivalence between the momentum derivative method and the similar approach with the point splitting vector current.
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