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This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for lattice QCD calculations related to the structure and spectroscopy of hadrons and nuclei. An overview of recent lattice calculations of the structure of the proton and other hadrons is presented along with prospects for future extensions. Progress and prospects of hadronic spectroscopy and the study of resonances in the light, strange and heavy quark sectors is summarized. Finally, recent advances in the study of light nuclei from lattice QCD are addressed, and the scope of future investigations that are currently envisioned is outlined.
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We study three subjects on quark confinement in hadrons in SU(3)$_{rm c}$ lattice QCD. From the accurate lattice calculation for more than 300 different patterns of three-quark (3Q) systems, we find that the static 3Q potential is well described by Y-Ansatz, i.e., the Coulomb plus Y-type linear potential. We also study the multi-quark (4Q, 5Q) potentials in lattice QCD, and find that they are well described by the one-gluon-exchange (OGE) Coulomb plus string-theoretical linear potential, which supports the {it infrared string picture} even for the multi-quarks. The second subject is a lattice-QCD determination of the relevant gluonic momentum component for confinement. The string tension (confining force) is found to be almost unchanged even after cutting off the high-momentum gluon component above 1.5GeV in the Landau gauge. In fact, {it quark confinement originates from the low-momentum gluon below about 1.5GeV.} Finally, we consider a possible gauge of QCD for the quark potential model, by investigating instantaneous inter-quark potential in generalized Landau gauge, which describes a continuous change from the Landau gauge to the Coulomb gauge.
We study hadron correlators upon artificial restoration of the spontaneously broken chiral symmetry. In a dynamical lattice simulation we remove the lowest lying eigenmodes of the Dirac operator from the valence quark propagators and study evolution of the hadron masses obtained. All mesons and baryons in our study, except for a pion, survive unbreaking the chiral symmetry and their exponential decay signals become essentially better. From the analysis of the observed spectroscopic patterns we conclude that confinement still persists while the chiral symmetry is restored. All hadrons fall into different chiral multiplets. The broken U(1)_A symmetry does not get restored upon unbreaking the chiral symmetry. We also observe signals of some higher symmetry that includes chiral symmetry as a subgroup. Finally, from comparison of the Delta - N splitting before and after unbreaking of the chiral symmetry we conclude that both the color-magnetic and the flavor-spin quark-quark interactions are of equal importance.
A relation is presented between single-hadron long-range matrix elements defined in a finite Euclidean spacetime, and the corresponding infinite-volume Minkowski amplitudes. This relation is valid in the kinematic region where any number of two-hadron states can simultaneously go on shell, so that the effects of strongly-coupled intermediate channels are included. These channels can consist of non-identical particles with arbitrary intrinsic spins. The result accommodates general Lorentz structures as well as non-zero momentum transfer for the two external currents inserted between the single-hadron states. The formalism, therefore, generalizes the work by Christ et al.~[Phys.Rev. D91 114510 (2015)], and extends the reach of lattice quantum chromodynamics (QCD) to a wide class of new observables beyond meson mixing and rare decays. Applications include Compton scattering of the pion ($pi gamma^star to [pi pi, K overline K] to pi gamma^star$), kaon ($K gamma^star to [pi K, eta K] to K gamma^star$) and nucleon ($N gamma^star to N pi to N gamma^star$), as well as double-$beta$ decays, and radiative corrections to the single-$beta$ decay, of QCD-stable hadrons. The framework presented will further facilitate generalization of the result to studies of nuclear amplitudes involving two currents from lattice QCD.
The binding energies of a range of nuclei and hypernuclei with atomic number A <= 4 and strangeness |s| <= 2, including the deuteron, di-neutron, H-dibaryon, 3He, Lambda 3He, Lambda 4He, and Lambda Lambda 4He, are calculated in the limit of flavor-SU(3) symmetry at the physical strange quark mass with quantum chromodynamics (without electromagnetic interactions). The nuclear states are extracted from Lattice QCD calculations performed with n_f=3 dynamical light quarks using an isotropic clover discretization of the quark-action in three lattice volumes of spatial extent L ~ 3.4 fm, 4.5 fm and 6.7 fm, and with a single lattice spacing b ~ 0.145 fm.
We present the results of lattice QCD calculations of the magnetic moments of the lightest nuclei, the deuteron, the triton and ${}^3$He, along with those of the neutron and proton. These calculations, performed at quark masses corresponding to $m_pi sim 800$ MeV, reveal that the structure of these nuclei at unphysically heavy quark masses closely resembles that at the physical quark masses. In particular, we find that the magnetic moment of ${}^3$He differs only slightly from that of a free neutron, as is the case in nature, indicating that the shell-model configuration of two spin-paired protons and a valence neutron captures its dominant structure. Similarly a shell-model-like moment is found for the triton, $mu_{{}^3{rm H}} sim mu_p$. The deuteron magnetic moment is found to be equal to the nucleon isoscalar moment within the uncertainties of the calculations.
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