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Register a new userScattering processes and resonances from lattice QCD
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The vast majority of hadrons observed in nature are not stable under the strong interaction, rather they are resonances whose existence is deduced from enhancements in the energy dependence of scattering amplitudes. The study of hadron resonances offers a window into the workings of quantum chromodynamics (QCD) in the low-energy non-perturbative region, and in addition, many probes of the limits of the electroweak sector of the Standard Model consider processes which feature hadron resonances. From a theoretical standpoint, this is a challenging field: the same dynamics that binds quarks and gluons into hadron resonances also controls their decay into lighter hadrons, so a complete approach to QCD is required. Presently, lattice QCD is the only available tool that provides the required non-perturbative evaluation of hadron observables. In this article, we review progress in the study of few-hadron reactions in which resonances and bound-states appear using lattice QCD techniques. We describe the leading approach which takes advantage of the periodic finite spatial volume used in lattice QCD calculations to extract scattering amplitudes from the discrete spectrum of QCD eigenstates in a box. We explain how from explicit lattice QCD calculations, one can rigorously garner information about a variety of resonance properties, including their masses, widths, decay couplings, and form factors. The challenges which currently limit the field are discussed along with the steps being taken to resolve them.
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We present a determination of nucleon-nucleon scattering phase shifts for l >= 0. The S, P, D and F phase shifts for both the spin-triplet and spin-singlet channels are computed with lattice Quantum ChromoDynamics. For l > 0, this is the first lattice QCD calculation using the Luscher finite-volume formalism. This required the design and implementation of novel lattice methods involving displaced sources and momentum-space cubic sinks. To demonstrate the utility of our approach, the calculations were performed in the SU(3)-flavor limit where the light quark masses have been tuned to the physical strange quark mass, corresponding to m_pi = m_K ~ 800 MeV. In this work, we have assumed that only the lowest partial waves contribute to each channel, ignoring the unphysical partial wave mixing that arises within the finite-volume formalism. This assumption is only valid for sufficiently low energies; we present evidence that it holds for our study using two different channels. Two spatial volumes of V ~ (3.5 fm)^3 and V ~ (4.6 fm)^3 were used. The finite-volume spectrum is extracted from the exponential falloff of the correlation functions. Said spectrum is mapped onto the infinite volume phase shifts using the generalization of the Luscher formalism for two-nucleon systems.
We calculate the parameters describing elastic $I=1$, $P$-wave $pipi$ scattering using lattice QCD with $2+1$ flavors of clover fermions. Our calculation is performed with a pion mass of $m_pi approx 320::{rm MeV}$ and a lattice size of $Lapprox 3.6$ fm. We construct the two-point correlation matrices with both quark-antiquark and two-hadron interpolating fields using a combination of smeared forward, sequential and stochastic propagators. The spectra in all relevant irreducible representations for total momenta $|vec{P}| leq sqrt{3} frac{2pi}{L}$ are extracted with two alternative methods: a variational analysis as well as multi-exponential matrix fits. We perform an analysis using Luschers formalism for the energies below the inelastic thresholds, and investigate several phase shift models, including possible nonresonant contributions. We find that our data are well described by the minimal Breit-Wigner form, with no statistically significant nonresonant component. In determining the $rho$ resonance mass and coupling we compare two different approaches: fitting the individually extracted phase shifts versus fitting the $t$-matrix model directly to the energy spectrum. We find that both methods give consistent results, and at a pion mass of $am_{pi}=0.18295(36)_{stat}$ obtain $g_{rhopipi} = 5.69(13)_{stat}(16)_{sys}$, $am_rho = 0.4609(16)_{stat}(14)_{sys}$, and $am_{rho}/am_{N} = 0.7476(38)_{stat}(23)_{sys} $, where the first uncertainty is statistical and the second is the systematic uncertainty due to the choice of fit ranges.
Over the last decade, numerical solutions of Quantum Chromodynamics (QCD) using the technique of lattice QCD have developed to a point where they are beginning to connect fundamental aspects of nuclear physics to the underlying degrees of freedom of the Standard Model. In this review, the progress of lattice QCD studies of nuclear matrix elements of electroweak currents and beyond-Standard-Model operators is summarized, and connections with effective field theories and nuclear models are outlined. Lattice QCD calculations of nuclear matrix elements can provide guidance for low-energy nuclear reactions in astrophysics, dark matter direct detection experiments, and experimental searches for violations of the symmetries of the Standard Model, including searches for additional CP violation in the hadronic and leptonic sectors, baryon-number violation, and lepton-number or flavor violation. Similarly, important inputs to neutrino experiments seeking to determine the neutrino-mass hierarchy and oscillation parameters, as well as other electroweak and beyond-Standard-Model processes can be determined. The phenomenological implications of existing studies of electroweak and beyond-Standard-Model matrix elements in light nuclear systems are discussed, and future prospects for the field toward precision studies of these matrix elements are outlined.
We summarize our lattice QCD determinations of the pion-pion, pion-kaon and kaon-kaon s-wave scattering lengths at maximal isospin with a particular focus on the extrapolation to the physical point and the usage of next-to-leading order chiral perturbation theory to do so. We employ data at three values of the lattice spacing and pion masses ranging from around 230 MeV to around 450 MeV, applying Lueschers finite volume method to compute the scattering lengths. We find that leading order chiral perturbation theory is surprisingly close to our data even in the kaon-kaon case for our entire range of pion masses.
We present the results of a lattice study of light-cone distribution amplitudes (DAs) of the nucleon and negative parity nucleon resonances using two flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to m_pi = 150 MeV. We find that the three valence quarks in the proton share their momentum in the proportion 37% : 31% : 31%, where the larger fraction corresponds to the u-quark that carries proton helicity, and determine the value of the wave function at the origin in position space, which turns out to be small compared to the existing estimates based on QCD sum rules. Higher-order moments are constrained by our data and are all compatible with zero within our uncertainties. We also calculate the normalization constants of the higher-twist DAs that are related to the distribution of quark angular momentum. Furthermore, we use the variational method and customized parity projection operators to study the states with negative parity. In this way we are able to separate the contributions of the two lowest states that, as we argue, possibly correspond to N*(1535) and a mixture of N*(1650) and the pion-nucleon continuum, respectively. It turns out that the state that we identify with N*(1535) has a very different DA as compared to both the second observed negative parity state and the nucleon, which may explain the difference in the decay patterns of N*(1535) and N*(1650) observed in experiment.
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