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.
The lattice QCD simulation with the lattice chiral symmetry is very attractive, however, it is difficult to maintain the symmetry at a modest numerical computation cost. A candidate to reduce the computational cost during the configuration generation
with the HMC algorithm is to relax the requirement of the chiral symmetry and to use the reweighing method recovering the symmetry at the measurement phase. In this talk, we presented the reweighing method to restore the chiral symmetry of the truncated overlap fermion operator. In order to avoid the large discrepancy between the truncated overlap operator and the exact overlap operator, we split the reweighting factor into several steps gradually increasing the order of truncation. We investigated the truncation dependence of the reweighting factor on a set of quenched $8^3times 32$ lattice configurations generated with the DBW2 gauge action. We found that a large fluctuation on the reweighting factor between a high-order truncated overlap operator and the exact overlap operator on a couple of configurations. The origin of the large fluctuation seems to be due to a small eigenvalue of the overlap kernel on these configurations.
Hattori-Itakura have recently derived the full Landau-level summation form for the photon vacuum polarization tensor in constant external magnetic fields at the one-loop level. The Landau-level summation form is essential when the photon momentum exc
eeds the threshold of the pair creation of charged particles in a magnetic field stronger than the squared mass of the charged particle. The tensor has three different form factors depending on the tensor direction with respect to the external magnetic field. The renormalization is nontrivial because these form factors are expressed in terms of double or triple summation forms. We give a numerical UV subtraction method which can be applied to numerically evaluate the form factors in constant external magnetic fields. We numerically investigate the photon vacuum polarization tensor in the form of the Landau-level summation and estimate the systematic errors coming from truncation of the Landau-level summation in a parameter region realized in heavy ion collision experiments. We find that the error is practically controllable at an $O(10^{-2})$ level for electrons and muons in strong magnetic fields expected in heavy ion collisions in the experimentally feasible kinematic parameter regions.
