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The positive-parity nucleon spectrum is explored in $2 + 1$-flavour lattice QCD in a search for new low-lying energy eigenstates near the energy regime of the Roper resonance. In addition to conventional three-quark operators, we consider novel, local five-quark meson-baryon type interpolating fields that hold the promise to reveal new eigenstates that may have been missed in previous analyses. Drawing on phenomenological insight, five-quark operators based on $sigma{N}$, $pi{N}$ and $a_0{N}$ channels are constructed. Spectra are produced in a high-statistics analysis on the PACS-CS dynamical gauge-field configurations with $m_{pi} = 411textrm{ MeV}$ via variational analyses of several operator combinations. Despite the introduction of qualitatively different interpolating fields, no new states are observed in the energy regime of the Roper resonance. This result provides further evidence that the low-lying finite-volume scattering states are not localised, and strengthens the interpretation of the Roper as a coupled-channel, dynamically-generated meson-baryon resonance.
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We investigate the effects of low-lying fermion eigenmodes on the QCD partition function in the $epsilon$-regime. The fermion determinant is approximated by a truncated product of low-lying eigenvalues of the overlap-Dirac operator. With two flavors of dynamical quarks, we observe that the lattice results for the lowest eigenvalue distribution, eigenvalue sum rules and partition function reproduce the analytic predictions made by Leutwyler and Smilga, which strongly depend on the topological charge of the background gauge configuration. The value of chiral condensate extracted from these measurements are consistent with each other. For one dynamical quark flavor, on the other hand, we find an apparent disagreement among different determinations of the chiral condensate, which may suggest the failure of the $epsilon$-expansion in the absence of massless Nambu-Goldstone boson.
We present a lattice QCD study of $Npi$ scattering in the positive-parity nucleon channel, where the puzzling Roper resonance $N^*(1440)$ resides in experiment. The study is based on the PACS-CS ensemble of gauge configurations with $N_f=2+1$ Wilson-clover dynamical fermions, $m_pi simeq 156~$MeV and $Lsimeq 2.9~$fm. In addition to a number of $qqq$ interpolating fields, we implement operators for $Npi$ in $p$-wave and $Nsigma$ in $s$-wave. In the center-of-momentum frame we find three eigenstates below 1.65 GeV. They are dominated by $N(0)$, $N(0)pi(0)pi(0)$ (mixed with $N(0)sigma(0)$) and $N(p)pi(-p)$ with $psimeq 2pi/L$, where momenta are given in parentheses. This is the first simulation where the expected multi-hadron states are found in this channel. The experimental $Npi$ phase-shift would -- in the approximation of purely elastic $Npi$ scattering -- imply an additional eigenstate near the Roper mass $m_Rsimeq 1.43~$GeV for our lattice size. We do not observe any such additional eigenstate, which indicates that $Npi$ elastic scattering alone does not render a low-lying Roper. Coupling with other channels, most notably with $Npipi$, seems to be important for generating the Roper resonance, reinforcing the notion that this state could be a dynamically generated resonance. Our results are in line with most of previous lattice studies based just on $qqq$ interpolators, that did not find a Roper eigenstate below $1.65~$GeV. The study of the coupled-channel scattering including a three-particle decay $Npipi$ remains a challenge.
We investigate the effects of low-lying fermion modes on the QCD partition function in the epsilon-regime. With the overlap Dirac operator we calculate several tens of low-lying fermion eigenvalues on the quenched lattice. By partially incorporating the fermion determinant through the truncated determinant approximation, we calculate the partition function and other related quantities for Nf = 1 and compare them with the theoretical predictions obtained by Leutwyler and Smilga.
We present preliminary results from a lattice QCD calculation of the H-dibaryon using two flavors of $mathcal{O}(a)$ improved Wilson fermions. We employ local six-quark interpolating operators at the source with a combination of local six-quark and two-baryon operators at the sink with the appropriate quantum numbers of the H-dibaryon and its coupling to the two-baryon channels. We find that the two-baryon operators provide an improved overlap onto the ground state in comparison to the local six-quark operators. We also apply Luschers finite volume formalism to obtain information on the nature of the infinite-volume interaction of two particles. Further, the momentum projection to three moving frames enables the isolation of the pole in the infinite-volume scattering amplitude. Preliminary results at pion masses of 450 MeV and 1 GeV clearly indicate the presence of states below the $Lambda Lambda$ threshold while a finite-volume analysis fails to conclusively show the existence of an infinite-volume bound state.
We compute the low-lying spectrum of the staggered Dirac operator above and below the finite temperature phase transition in both quenched QCD and in dynamical four flavor QCD. In both cases we find, in the high temperature phase, a density with close to square root behavior, $rho(lambda) sim (lambda-lambda_0)^{1/2}$. In the quenched simulations we find, in addition, a volume independent tail of small eigenvalues extending down to zero. In the dynamical simulations we also find a tail, decreasing with decreasing mass, at the small end of the spectrum. However, the tail falls off quite quickly and does not seem to extend to zero at these couplings. We find that the distribution of the smallest Dirac operator eigenvalues provides an efficient observable for an accurate determination of the location of the chiral phase transition, as first suggested by Jackson and Verbaarschot.
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