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Register a new userTheoretical Foundation of the Nuclear Force in QCD and its applications to Central and Tensor Forces in Quenched Lattice QCD Simulations
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Sinya Aoki
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We present full accounts of a method to extract nucleon-nucleon (NN) potentials from the Bethe-Salpter amplitude in lattice QCD. The method is applied to two nucleons on the lattice with quenched QCD simulations. By disentangling the mixing between the S-state and the D-state, we obtain central and tensor potentials in the leading order of the velocity expansion of the non-local NN potential. The spatial structure and the quark mass dependence of the potentials are analyzed in detail.
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We present our updated results of the nucleon-nucleon potential in quenched lattice QCD simulations with the plaquette gauge action and the Wilson quark action on the 32^4(simeq (4.4 fm)^4) lattice. From the equal-time Bethe-Salpeter (BS) wave function, the NN potential is constructed through the Schroedinger-type equation. Resulting NN potential has all the qualitative features which phenomenological potentials commonly have: the repulsive core at short distance and the attractive well at medium and long distances. In the L to infty limit, our NN potential is guaranteed to reproduce the scattering length obtained from the Lueschers formula. The quark mass dependence of the NN potential is studied with m_{pi} sim 380, 529, 731 MeV. The results suggest that both the repulsive core at short distance and the attractive well at medium distance are enhanced in the light quark mass region.
The first lattice QCD result on the nuclear force (the NN potential) is presented in the quenched level. The standard Wilson gauge action and the standard Wilson quark action are employed on the lattice of the size 16^3times 24 with the gauge coupling beta=5.7 and the hopping parameter kappa=0.1665. To obtain the NN potential, we adopt a method recently proposed by CP-PACS collaboration to study the pi pi scattering phase shift. It turns out that this method provides the NN potentials which are faithful to those obtained in the analysis of NN scattering data. By identifying the equal-time Bethe-Salpeter wave function with the Schroedinger wave function for the two nucleon system, the NN potential is reconstructed so that the wave function satisfies the time-independent Schroedinger equation. In this report, we restrict ourselves to the J^P=0^+ and I=1 channel, which enables us to pick up unambiguously the ``central NN potential V_{central}(r). The resulting potential is seen to posses a clear repulsive core of about 500 MeV at short distance (r < 0.5 fm). Although the attraction in the intermediate and long distance regions is still missing in the present lattice set-up, our method is appeared to be quite promising in reconstructing the NN potential with lattice QCD.
The reweighting method is widely used in numerical studies of QCD, in particular, for the cases in which the conventional Monte-Carlo method cannot be applied directly, e.g., finite density QCD. However, the application range of the reweighing method is restricted due to several problems. One of the most severe problems here is the overlap problem. To solve it, we examine a multipoint reweighting method in which simulations at several simulation points are combined in the data analyses. We systematically study the applicability and limitation of the multipoint reweighting method in two-flavor QCD at zero density. Measuring histograms of physical quantities at a series of simulation points, we apply the multipoint reweighting method to calculate the meson masses as continuous functions of the gauge coupling $beta$ and the hopping parameters $kappa$. We then determine lines of constant physics and beta functions, which are needed in a calculation of the equation of state at finite temperature.
Two of recent progress in lattice QCD approach to nuclear force are reported. (i) Tensor force from quenched lattice QCD: By truncating the derivative expansion of inter-nucleon potential to the strictly local terms, we obtain central force V_C(r) and tensor force V_T(r) separately from s-wave and d-wave components of Bethe-Salpeter wave function for two nucleon state with J^P=1^+. Numerical calculation is performed with quenched QCD on 32^4 lattice using the standard plaquette action at beta=5.7 with the standard Wilson quark action with kappa=0.1640, 0.1665, 0.1678. Preliminary results show that the depths of the resulting tensor force amount to 20 to 40 MeV, which is enhanced in the light quark mass region. (ii) Nuclear force from 2+1 flavor QCD with PACS-CS gauge configuration: Preliminary full QCD results are obtained by using 2+1 flavor gauge configurations generated by PACS-CS collaboration. The resulting potential has the midium range attraction of about 30 MeV similar to the preceding quenched calculations. However, the repulsive core at short distance is significantly stronger than the corresponding quenched QCD result.
At the precision reached in current lattice QCD calculations, electromagnetic effects are becoming numerically relevant. Here, electromagnetic effects are included by superimposing $mathrm{U}(1)$ degrees of freedom on $N_f = 2+1$ QCD configurations from the Budapest-Marseille-Wuppertal Collaboration. We present preliminary results for the electromagnetic corrections to light pseudoscalars mesons masses and discuss some of the associated systematic errors.
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