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Register a new userTwo-particle Correlation Functions with Distilled Propagators
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Correlation functions of the simplest multi-particle state will be presented using distilled quark propagators. The I=2 pi-pi state can be simulated without computing disconnected diagrams and thus is the simplest two-particle state that can be studied with quark sources placed on a single time-slice. We study the quality of the signals of this pi-pi correlation function using the quark-smearing guided distillation method. Results will be presented for pi-pi correlation functions computed on dynamical, anisotropic lattices.
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We present first results for two-baryon correlation functions, computed using $N_f=2$ flavours of O($a$) improved Wilson quarks, with the aim of explaining potential dibaryon bound states, specifically the H-dibaryon. In particular, we use a GEVP to isolate the groundstate using two-baryon (hyperon-hyperon) correlation functions $big(langle C_{XY}(t)C_{XY}(0) rangle$, where $XY=LambdaLambda, SigmaSigma, NXi, cdotsbig)$, each of which has an overlap with the H-dibaryon. We employ a `blocking algorithm to handle the large number of contractions, which may easily be extended to N-baryon correlation functions. We also comment on its application to the analysis of single baryon masses ($n$, $Lambda$, $Xi$, $cdots$). This study is performed on an isotropic lattice with $m_pi = 460$ MeV, $m_pi L = 4.7$ and $a = 0.063$ fm.
The pion-pion scattering phase shift is computed using LapH propagators. The LapH method for computing quark propagators is used to form two-particle correlation functions with a number of different operators. Excited state energies of two-particle states on 2+1 dynamical, anisotropic lattices (Mpi=390 MeV) are computed to determine the phase shift in the isospin-2 channel. The signal for t-to-t diagrams for the isospin-0 channel are also presented to demonstrate the efficacy of the stochastic LapH method which combines LapH with diluted Z4 noise sources.
We explore the possibility to make use of cosmological data to look for signatures of unknown heavy particles whose masses are on the order of the Hubble parameter during the time of inflation. To be more specific we take up the quasi-single field inflation model, in which the isocurvaton $sigma $ is supposed to be the heavy particle. We study correlation functions involving both scalar ($zeta $) and tensor ($gamma $) perturbations and search for imprints of the $sigma$-particle effects. We make use of the technique of the effective field theory for inflation to derive the $zeta sigma $ and $gamma zeta sigma $ couplings. With these couplings we compute the effects due to $sigma $ to the power spectrum $langle zeta zeta rangle $ and correlations $langle gamma^{s} zeta zeta rangle$ and $langle gamma^{s_{1}} gamma ^{s_{2}} zeta zeta rangle $, where $s$, $s_{1}$ and $s_{2}$ are the polarization indices of gravitons. Numerical analyses of the $sigma$-mass effects to these corrlations are presented. It is argued that future precise observations of these correlations could make it possible to measure the $sigma$-mass and the strength of the $zeta sigma$ and $gamma zeta sigma$ couplings. As an extension to the $N$-graviton case we also compute the correlations $langle gamma ^{s_{1}} cdots gamma ^{s_{N}} zeta zeta rangle $ and $langle gamma ^{s_{1}} cdots cdots gamma ^{s_{2N}} zeta zeta rangle $ and their $sigma$-mass effects. It is suggested that larger $N$ correlation functions are useful to probe larger $sigma$-mass .
Cluster Perturbation Theory (CPT) is a computationally economic method commonly used to estimate the momentum and energy resolved single-particle Greens function. It has been used extensively in direct comparisons with experiments that effectively measure the single-particle Greens function, e.g., angle-resolved photoemission spectroscopy. However, many experimental observables are given by two-particle correlation functions. CPT can be extended to compute two-particle correlation functions by approximately solving the Bethe-Salpeter equation. We implement this method and focus on the transverse spin-susceptibility, measurable via inelastic neutron scattering or with optical probes of atomic gases in optical lattices. We benchmark the method with the one-dimensional Fermi-Hubbard model at half filling by comparing with known results.
Momentum-space derivatives of matrix elements can be related to their coordinate-space moments through the Fourier transform. We derive these expressions as a function of momentum transfer $Q^2$ for asymptotic in/out states consisting of a single hadron. We calculate corrections to the finite volume moments by studying the spatial dependence of the lattice correlation functions. This method permits the computation of not only the values of matrix elements at momenta accessible on the lattice, but also the momentum-space derivatives, providing {it a priori} information about the $Q^2$ dependence of form factors. As a specific application we use the method, at a single lattice spacing and with unphysically heavy quarks, to directly obtain the slope of the isovector form factor at various $Q^2$, whence the isovector charge radius. The method has potential application in the calculation of any hadronic matrix element with momentum transfer, including those relevant to hadronic weak decays.
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