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Register a new userSymmetries and Interactions from Lattice QCD
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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.
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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.
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.
On the basis of the Brueckner-Hartree-Fock method with the nucleon-nucleon forces obtained from lattice QCD simulations, the properties of the medium-heavy doubly-magic nuclei such as 16^O and 40^Ca are investigated. We found that those nuclei are bound for the pseudo-scalar meson mass M_PS ~ 470 MeV. The mass number dependence of the binding energies, single-particle spectra and density distributions are qualitatively consistent with those expected from empirical data at the physical point, although these hypothetical nuclei at heavy quark mass have smaller binding energies than the real nuclei.
The $S$-wave $LambdaLambda$ and $N Xi$ interactions are studied on the basis of the (2+1)-flavor lattice QCD simulations close to the physical point ($m_pi simeq 146{rm{MeV}}$ and $m_K simeq 525{rm{MeV}}$). Lattice QCD potentials in four different spin-isospin channels are extracted by using the coupled-channel HAL QCD method and are parametrized by analytic functions to calculate the scattering phase shifts. The $Lambda Lambda$ interaction at low energies shows only a weak attraction, which does not provide a bound or resonant dihyperon. The $NXi$ interaction in the spin-singlet and isospin-singlet channel is most attractive and lead the $NXi$ system near unitarity. Relevance to the strangeness=$-2$ hypernuclei as well as to two-baryon correlations in proton-proton, proton-nucleus and nucleus-nucleus collisions is also discussed.
We study two- and three-meson systems composed either of pions or kaons at maximal isospin using Monte Carlo simulations of lattice QCD. Utilizing the stochastic LapH method, we are able to determine hundreds of two- and three-particle energy levels, in nine different momentum frames, with high precision. We fit these levels using the relativistic finite-volume formalism based on a generic effective field theory in order to determine the parameters of the two- and three-particle K-matrices. We find that the statistical precision of our spectra is sufficient to probe not only the dominant $s$-wave interactions, but also those in $d$ waves. In particular, we determine for the first time a term in the three-particle K-matrix that contains two-particle $d$ waves. We use three $N_f=2+1$ CLS ensembles with pion masses of $200$, $280$, and $340;$MeV. This allows us to study the chiral dependence of the scattering observables, and compare to the expectations of chiral perturbation theory.
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