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We present a lattice QCD study for the cutoff effects on nuclear forces. Two-nucleon forces are determined from Nambu-Bethe-Salpeter (NBS) wave functions using the HAL QCD method. Lattice QCD simulations are performed employing N_f = 2 clover fermion configurations at three lattice spacings of a = 0.108, 0.156, 0.215 fm on a fixed physical volume of L^3 x T = (2.5 fm)^3 x 5 fm with a large quark mass corresponding to m_pi = 1.1 GeV. We observe that while the discretization artifact appears at the short range part of potentials, it is suppressed at the long distance region. The cutoff dependence of the phase shifts and scattering length is also presented.
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Recent progress of lattice QCD study of nuclear forces (potentials) is reviewed. Scattering phase shift is an important observable for two particle system. In lattice QCD, phase shifts are calculated from long distance behavior of Bethe-Salpeter (BS) wave functions by Lueschers finite volume method. For applications to nuclear physics of multi-nucleon system, it is more advantageous to convert the information of phase shifts in the form of potentials. We therefore extend the method so as to generate the potentials from BS wave functions. These potentials are faithful to scattering phase shift by construction, because they can reproduce BS wave functions in which the information of phase shift is embeded in the long distance part.The method was first applied to the central potential in NN system. It is now applied to many objects, such as tensor potential, hyperon potentials, energy dependence of nuclear potentials, and investigations of the repulsive core at short distance.
We present the latest lattice QCD results for baryon interactions obtained at nearly physical quark masses. $N_f = 2+1$ nonperturbatively ${cal O}(a)$-improved Wilson quark action with stout smearing and Iwasaki gauge action are employed on the lattice of $(96a)^4 simeq (8.1mbox{fm})^4$ with $a^{-1} simeq 2.3$ GeV, where $m_pi simeq 146$ MeV and $m_K simeq 525$ MeV. In this report, we study the two-nucleon systems and two-$Xi$ systems in $^1S_0$ channel and $^3S_1$-$^3D_1$ coupled channel, and extract central and tensor interactions by the HAL QCD method. We also present the results for the $NOmega$ interaction in $^5S_2$ channel which is relevant to the $NOmega$ pair-momentum correlation in heavy-ion collision experiments.
We investigate the cutoff effects in 2-d lattice O(N) models for a variety of lattice actions, and we identify a class of very simple actions for which the lattice artifacts are extremely small. One action agrees with the standard action, except that it constrains neighboring spins to a maximal relative angle delta. We fix delta by demanding that a particular value of the step scaling function agrees with its continuum result already on a rather coarse lattice. Remarkably, the cutoff effects of the entire step scaling function are then reduced to the per mille level. This also applies to the theta-vacuum effects of the step scaling function in the 2-d O(3) model. The cutoff effects of other physical observables including the renormalized coupling and the mass in the isotensor channel are also reduced drastically. Another choice, the mixed action, which combines the standard quadratic with an appropriately tuned large quartic term, also has extremely small cutoff effects. The size of cutoff effects is also investigated analytically in 1-d and at N = infinity in 2-d.
When analyzed in terms of the Symanzik expansion, lattice correlators of multi-local (gauge-invariant) operators with non-trivial continuum limit exhibit in maximally twisted lattice QCD ``infrared divergent cutoff effects of the type a^{2k}/(m_pi^2)^{h}, 2kgeq hgeq 1 (k,h integers), which tend to become numerically large when the pion mass gets small. We prove that, if the action is O(a) improved a` la Symanzik or, alternatively, the critical mass counter-term is chosen in some ``optimal way, these lattice artifacts are reduced to terms that are at worst of the order a^{2}(a^2/m_pi^2)^{k-1}, kgeq 1. This implies that the continuum extrapolation of lattice results is smooth at least down to values of the quark mass, m_q, satisfying the order of magnitude inequality m_q >a^2Lambda^3_{rm QCD}.
Discretization effects of lattice QCD are described by Symanziks effective theory when the lattice spacing, $a$, is small. Asymptotic freedom predicts that the leading asymptotic behavior is $sim a^n [bar g^2(a^{-1})]^{hatgamma_1} sim a^n left[frac{1}{-log(aLambda)}right]^{hatgamma_1}$. For spectral quantities, $n=d$ is given in terms of the (lowest) canonical dimension, $d+4$, of the operators in the local effective Lagrangian and $hatgamma_1$ is proportional to the leading eigenvalue of their one-loop anomalous dimension matrix $gamma^{(0)}$. We determine $gamma^{(0)}$ for Yang-Mills theory ($n=2$) and discuss consequences in general and for perturbatively improved short distance observables. With the help of results from the literature, we also discuss the $n=1$ case of Wilson fermions with perturbative O$(a)$ improvement and the discretization effects specific to the flavor currents. In all cases known so far, the discretization effects are found to disappear faster than the naive $sim a^n$ and the log-corrections are a rather weak modification -- in contrast to the two-dimensional O(3) sigma model.
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