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We report the recent progress on the determination of three-nucleon forces (3NF) in lattice QCD. We utilize the Nambu-Bethe-Salpeter (NBS) wave function to define the potential in quantum field theory, and extract two-nucleon forces (2NF) and 3NF on equal footing. The enormous computational cost for calculating multi-baryon correlators on the lattice is drastically reduced by developing a novel contraction algorithm (the unified contraction algorithm). Quantum numbers of the three-nucleon (3N) system are chosen to be (I, J^P)=(1/2,1/2^+) (the triton channel), and we extract 3NF in which three nucleons are aligned linearly with an equal spacing. Lattice QCD simulations are performed using N_f=2 dynamical clover fermion configurations at the lattice spacing of a = 0.156 fm on a 16^3 x 32 lattice with a large quark mass corresponding to m(pi)= 1.13 GeV. Repulsive 3NF is found at short distance.
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In this article, we review the HAL QCD method to investigate baryon-baryon interactions such as nuclear forces in lattice QCD. We first explain our strategy in detail to investigate baryon-baryon interactions by defining potentials in field theories such as QCD. We introduce the Nambu-Bethe-Salpeter (NBS) wave functions in QCD for two baryons below the inelastic threshold. We then define the potential from NBS wave functions in terms of the derivative expansion, which is shown to reproduce the scattering phase shifts correctly below the inelastic threshold. Using this definition, we formulate a method to extract the potential in lattice QCD. Secondly, we discuss pros and cons of the HAL QCD method, by comparing it with the conventional method, where one directly extracts the scattering phase shifts from the finite volume energies through the Luschers formula. We give several theoretical and numerical evidences that the conventional method combined with the naive plateau fitting for the finite volume energies in the literature so far fails to work on baryon-baryon interactions due to contaminations of elastic excited states. On the other hand, we show that such a serious problem can be avoided in the HAL QCD method by defining the potential in an energy-independent way. We also discuss systematics of the HAL QCD method, in particular errors associated with a truncation of the derivative expansion. Thirdly, we present several results obtained from the HAL QCD method, which include (central) nuclear force, tensor force, spin-orbital force, and three nucleon force. We finally show the latest results calculated at the nearly physical pion mass, $m_pi simeq 146$ MeV, including hyperon forces which lead to form $OmegaOmega$ and $NOmega$ dibaryons.
Single state saturation of the temporal correlation function is a key condition to extract physical observables such as energies and matrix elements of hadrons from lattice QCD simulations. A method commonly employed to check the saturation is to seek for a plateau of the observables for large Euclidean time. Identifying the plateau in the cases having nearby states, however, is non-trivial and one may even be misled by a fake plateau. Such a situation takes place typically for the system with two or more baryons. In this study, we demonstrate explicitly the danger from a possible fake plateau in the temporal correlation functions mainly for two baryons ($XiXi$ and $NN$), and three and four baryons ($^3{rm He}$ and $^4{rm He})$ as well, employing (2+1)-flavor lattice QCD at $m_{pi}=0.51$ GeV on four lattice volumes with $L=$ 2.9, 3.6, 4.3 and 5.8 fm. Caution is given for drawing conclusion on the bound $NN$, $3N$ and $4N$ systems only based on the temporal correlation functions.
Nuclear forces and hyperon forces are studied by lattice QCD. Simulations are performed with (almost) physical quark masses, $m_pi simeq 146$ MeV and $m_K simeq 525$ MeV, where $N_f=2+1$ 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. In this report, we give the overview of the theoretical framework and present the numerical results for two-nucleon forces ($S=0$) and two-$Xi$ forces ($S=-4$). Central forces are studied in $^1S_0$ channel, and central and tensor forces are obtained in $^3S_1$-$^3D_1$ coupled channel analysis.
Precision experimental tests of the Standard Model of particle physics (SM) are one of our best hopes for discovering what new physics lies beyond the SM (BSM). Key in the search for new physics is the connection between theory and experiment. Forging this connection for searches involving low-energy hadronic or nuclear environments requires the use of a non-perturbative theoretical tool, lattice QCD. We present two recent lattice QCD calculations by the CalLat collaboration relevant for new physics searches: the nucleon axial coupling, $g_A$, whose precise value as predicted by the SM could help point to new physics contributions to the so-called neutron lifetime puzzle, and hadronic matrix elements of short-ranged operators relevant for neutrinoless double beta decay searches.
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.
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