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Register a new userSystematic errors in partially-quenched QCD plus QED lattice simulations
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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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Form factors of the nucleon have been extracted from experiment with high precision. However, lattice calculations have failed so far to reproduce the observed dependence of form factors on the momentum transfer. We have embarked on a program to thoroughly investigate systematic effects in lattice calculation of the required three-point correlation functions. Here we focus on the possible contamination from higher excited states and present a method which is designed to suppress them. Its effectiveness is tested for several baryonic matrix elements, different lattice sizes and pion masses.
Using the infinite-volume photon propagator, we developed a method which allows us to calculate electromagnetic corrections to stable hadron masses with only exponentially suppressed finite-volume effects. The key idea is that the infinite volume hadronic current-current correlation function with large time separation between the two currents can be reconstructed by its value at modest time separation, which can be evaluated in finite volume with only exponentially suppressed errors. This approach can be extended to other possible applications such as QED corrections to (semi-)leptonic decays and some rare decays.
We present results for the binding energies for He and ^3He nuclei calculated in quenched lattice QCD at the lattice spacing of a = 0.128 fm with a heavy quark mass corresponding to m_pi = 0.8 GeV. Enormous computational cost for the nucleus correlation functions is reduced by avoiding redundancy of equivalent contractions stemming from permutation symmetry of protons or neutrons in the nucleus and various other symmetries. To distinguish a bound state from an attractive scattering state, we investigate the volume dependence of the energy difference between the nucleus and the free multi-nucleon states by changing the spatial extent of the lattice from 3.1 fm to 12.3 fm. A finite energy difference left in the infinite spatial volume limit leads to the conclusion that the measured ground states are bounded. It is also encouraging that the measured binding energies and the experimental ones show the same order of magnitude.
Since gluons in QCD are interacting fundamental constituents just as quarks are, we expect that in addition to mesons made from a quark and an antiquark, there should also be glueballs and hybrids (bound states of quarks, antiquarks and gluons). In general, these states would mix strongly with the conventional q-bar-q mesons. However, they can also have exotic quantum numbers inaccessible to q-bar-q mesons. Confirmation of such states would give information on the role of dynamical color in low energy QCD. In the quenched approximation we present a lattice calculation of the masses of mesons with exotic quantum numbers. These hybrid mesons can mix with four quark (q-bar-q-bar-q-q) states. The quenched approximation partially suppresses this mixing. Nonetheless, our hybrid interpolating fields also couple to four quark states. Using a four quark source operator, we demonstrate this mixing for the 1-+ meson. Using the conventional Wilson quark action, we calculate both at reasonably light quark masses, intending to extrapolate to small quark mass, and near the charmed quark mass, where we calculate the masses of some c-bar-c-g hybrid mesons. The hybrid meson masses are large --- over 4 GeV for charmonium and more than twice the vector meson mass at our smallest quark mass, which is near the strange quark mass.
We address the issue of bound state in the two-nucleon system in lattice QCD. Our study is made in the quenched approximation at the lattice spacing of a = 0.128 fm with a heavy quark mass corresponding to m_pi = 0.8 GeV. To distinguish a bound state from an attractive scattering state, we investigate the volume dependence of the energy difference between the ground state and the free two-nucleon state by changing the spatial extent of the lattice from 3.1 fm to 12.3 fm. A finite energy difference left in the infinite spatial volume limit leads us to the conclusion that the measured ground states for not only spin triplet but also singlet channels are bounded. Furthermore the existence of the bound state is confirmed by investigating the properties of the energy for the first excited state obtained by 2x2 diagonalization method. The scattering lengths for both channels are evaluated by applying the finite volume formula derived by Luscher to the energy of the first excited states.
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