We investigate the formation of light nuclei with the nuclear mass number less than or equal to four in 2+1 flavor QCD using a non-perturbative improved Wilson quark and Iwasaki gauge actions. The quark mass is decreased from our previous work to the
one corresponding to the pion mass of 0.30 GeV. In each multi-nucleon channel, the energy shift of the ground state relative to the assembly of free nucleons is calculated on two volumes, whose spatial extents are 4.3 fm and 5.8 fm. From the volume dependence of the energy shift, we distinguish a bound state of multi nucleons from an attractive scattering state. We find that all the ground states measured in this calculation are bound states. As in the previous studies at larger $m_pi$, our result indicates that at $m_pi = 0.30$ GeV the effective interaction between nucleons in the light nuclei is relatively stronger than the one in nature, since the results for the binding energies are larger than the experimental values and a bound state appears in the dineutron channel, which is not observed in experiment. Possible sources of systematic error in this calculation are discussed.
We report our numerical lattice QCD calculations of the isovector nucleon form factors for the vector and axialvector currents: the vector, induced tensor, axialvector, and induced pseudoscalar form factors. The calculation is carried out with the ga
uge configurations generated with N_f=2+1 dynamical domain wall fermions and Iwasaki gauge actions at beta = 2.13, corresponding to a cutoff 1/a = 1.73 GeV, and a spatial volume of (2.7 fm)^3. The up and down quark masses are varied so the pion mass lies between 0.33 and 0.67 GeV while the strange quark mass is about 12% heavier than the physical one. We calculate the form factors in the range of momentum transfers, 0.2 < q^2 < 0.75 GeV^2. The vector and induced tensor form factors are well described by the conventional dipole forms and result in significant underestimation of the Dirac and Pauli mean-squared radii and the anomalous magnetic moment compared to the respective experimental values. We show that the axialvector form factor is significantly affected by the finite spatial volume of the lattice. In particular in the axial charge, g_A/g_V, the finite volume effect scales with a single dimensionless quantity, m_pi L, the product of the calculated pion mass and the spatial lattice extent. Our results indicate that for this quantity, m_pi L > 6 is required to ensure that finite volume effects are below 1%.
We present a quenched lattice calculation of all six form factors: vector [f_1(q^2)], weak magnetism [f_2(q^2)], induced scalar [f_3(q^2)], axial-vector [g_1(q^2)], weak electricity [g_2(q^2)] and induce pseudoscalar [g_3(q^2)] form factors in hypero
n semileptonic decay Xi^0 -> Sigma^{+} l nu using domain wall fermions. The q^2 dependences of all form factors in the relatively low q^2 region are examined in order to evaluate their values at zero momentum transfer. The Xi^0 -> Sigma^+ transition is highly sensitive to flavor SU(3) breaking since this decay corresponds to the direct analogue of neutron beta decay under the exchange of the down quark with the strange quark. The pattern of flavor SU(3) breaking effects in the hyperon beta decay is easily exposed in a comparison to results for neutron beta decay. We measure SU(3)-breaking corrections to f_1(0), f_2(0)/f_1(0) and g_1(0)/f_1(0). A sign of the leading order corrections, of which the size is less than a few %, on f_1(0) is likely negative, while f_2(0)/f_1(0) and g_1(0)/f_1(0) receive positive corrections of order 16% and 5% respectively. The observed patterns of the deviation from the values in the exact SU(3) limit does not support some of model estimates. We show that there are nonzero second-class form factors in the Xi^0 -> Sigma^+ decay, measuring f_3(0)/f_1(0)=0.14(10) and g_2(0)/g_1(0)=0.68(18), which are comparable to the size of first-order SU(3) breaking. It is also found that the SU(3) breaking effect on g_3(0)/g_1(0) agree with the prediction of the generalized pion-pole dominance.
We present a quenched lattice calculation of the weak nucleon form factors: vector (F_V(q^2)), induced tensor (F_T(q^2)), axial-vector (F_A(q^2)) and induced pseudo-scalar (F_P(q^2)) form factors. Our simulations are performed on three different latt
ice sizes L^3 x T=24^3 x 32, 16^3 x 32 and 12^3 x 32 with a lattice cutoff of 1/a = 1.3 GeV and light quark masses down to about 1/4 the strange quark mass (m_{pi} = 390 MeV) using a combination of the DBW2 gauge action and domain wall fermions. The physical volume of our largest lattice is about (3.6 fm)^3, where the finite volume effects on form factors become negligible and the lower momentum transfers (q^2 = 0.1 GeV^2) are accessible. The q^2-dependences of form factors in the low q^2 region are examined. It is found that the vector, induced tensor, axial-vector form factors are well described by the dipole form, while the induced pseudo-scalar form factor is consistent with pion-pole dominance. We obtain the ratio of axial to vector coupling g_A/g_V=F_A(0)/F_V(0)=1.219(38) and the pseudo-scalar coupling g_P=m_{mu}F_P(0.88m_{mu}^2)=8.15(54), where the errors are statistical erros only. These values agree with experimental values from neutron beta decay and muon capture on the proton. However, the root mean squared radii of the vector, induced tensor and axial-vector underestimate the known experimental values by about 20%. We also calculate the pseudo-scalar nucleon matrix element in order to verify the axial Ward-Takahashi identity in terms of the nucleon matrix elements, which may be called as the generalized Goldberger-Treiman relation.
We discuss signatures of bound-state formation in finite volume via the Luscher finite size method. Assuming that the phase-shift formula in this method inherits all aspects of the quantum scattering theory, we may expect that the bound-state formati
on induces the sign of the scattering length to be changed. If it were true, this fact provides us a distinctive identification of a shallow bound state even in finite volume through determination of whether the second lowest energy state appears just above the threshold. We also consider the bound-state pole condition in finite volume, based on Luschers phase-shift formula and then find that the condition is fulfilled only in the infinite volume limit, but its modification by finite size corrections is exponentially suppressed by the spatial lattice size L. These theoretical considerations are also numerically checked through lattice simulations to calculate the positronium spectrum in compact scalar QED, where the short-range interaction between an electron and a positron is realized in the Higgs phase.
