Progress on Excited Hadrons in Lattice QCD

The study of excited hadron spectra using Lattice QCD is currently evolving. An important step toward obtaining resonance parameters from Lattice QCD is the calculation of finite volume energy spectra. Somewhat more rigorous studies of finite volume spectra are currently possible and should be completed in the near future. The inclusion of disconnected diagrams is increasingly commonplace and the simplest systems which involve mixing between single- and multi-hadron interpolating fields are being studied. Advances in all-to-all algorithms which have been crucial in this progress are reviewed and a survey of current results is given. Nevertheless, such results are preliminary and a thorough discussion of systematic errors is required. We discuss several such sources of error, focusing on excited state contamination and the use of the generalized eigenvalue problem. Also, the calculation of matrix elements between finite volume Hamiltonian eigenstates is discussed.Comment: 14 pages, 13 figures, Proceedings from Lattice 2011, Lake Tahoe, CA, US

Scattering amplitudes from finite-volume spectral functions

A novel proposal is outlined to determine scattering amplitudes from finite-volume spectral functions. The method requires extracting smeared spectral functions from finite-volume Euclidean correlation functions, with a particular complex smearing kernel of width $\epsilon$ which implements the standard $i\epsilon$-prescription. In the $L \to \infty$ limit these smeared spectral functions are therefore equivalent to Minkowskian correlators with a specific time ordering to which a modified LSZ reduction formalism can be applied. The approach is presented for general $m \to n$ scattering amplitudes (above arbitrary inelastic thresholds) for a single-species real scalar field, although generalization to arbitrary spins and multiple coupled channels is likely straightforward. Processes mediated by the single insertion of an external current are also considered. Numerical determination of the finite-volume smeared spectral function is discussed briefly and the interplay between the finite volume, Euclidean signature, and time-ordered $i\epsilon$-prescription is illustrated perturbatively in a toy example.Comment: 22 pages, 2 figures, CERN-TH-2019-035, CP3-Origins-2019-006 DNRF9

Multi-hadron spectroscopy in a large physical volume

We demonstrate the efficacy of the stochastic LapH method to treat all-to-all quark propagation on a $N_f = 2+1$ CLS ensemble with large linear spatial extent $L = 5.5$ fm, allowing us to obtain the benchmark elastic isovector p-wave pion-pion scattering amplitude to good precision already on a relatively small number of gauge configurations. These results hold promise for multi-hadron spectroscopy at close-to-physical pion mass with exponential finite-volume effects under control.Comment: 8 pages, 4 figures. Presented at Lattice 2017, the 35th International Symposium on Lattice Field Theory, Granada, Spain, 18-24 June 201

Constraining a fourth generation of quarks: non-perturbative Higgs boson mass bounds

We present a non-perturbative determination of the upper and lower Higgs boson mass bounds with a heavy fourth generation of quarks from numerical lattice computations in a chirally symmetric Higgs-Yukawa model. We find that the upper bound only moderately rises with the quark mass while the lower bound increases significantly, providing additional constraints on the existence of a straight-forward fourth quark generation. We examine the stability of the lower bound under the addition of a higher dimensional operator to the scalar field potential using perturbation theory, demonstrating that it is not significantly altered for small values of the coupling of this operator. For a Higgs boson mass of $\sim125\mathrm{GeV}$ we find that the maximum value of the fourth generation quark mass is $\sim300\mathrm{GeV}$, which is already in conflict with bounds from direct searches.Comment: 6 pages, 2 figure

Spectral reconstruction of Euclidean correlator moments in lattice QCD

A novel application of lattice QCD spectral reconstruction is presented, in which euclidean correlation function data in a fixed time range are used to infer values outside the range, enabling a model-independent investigation of the asymptotic large-time behavior. Moments of the correlator are also determined, and reconstructed correlation matrices between different moments are included in a variational optimization similar to the standard Generalized Eigenvalue Problem (GEVP). These ideas are illustrated using a single-nucleon correlation function determined on an $N_{\rm}=2+1$ ensemble of gauge configurations at $m_{\pi} = 200{\rm MeV}$.Comment: 5 pages, 3 figures, proceedings from the HADRON2023 conferenc

The elastic I=3/2I=3/2 pp-wave nucleon-pion scattering amplitude and the Δ(1232)\Delta(1232) resonance from Nf=2+1N_{\mathrm{f}}=2+1 lattice QCD

We present the first direct determination of meson-baryon resonance parameters from a scattering amplitude calculated using lattice QCD. In particular, we calculate the elastic $I=3/2$, $p$-wave nucleon-pion amplitude on a single ensemble of $N_{\mathrm{f}}=2+1$ Wilson-clover fermions with $m_{\pi}=280\mathrm{MeV}$ and $m_{K}=460\mathrm{MeV}$. At these quark masses, the $\Delta(1232)$ resonance pole is found close to the $N-\pi$ threshold and a Breit-Wigner fit to the amplitude gives $g^{\mathrm{BW}}_{\Delta N\pi}=19.0(4.7)$ in agreement with phenomenological determinations.Comment: 7 pages, 2 figures. Agrees with published version, one additional phase shift point and clarification of different coupling convention

Non-perturbative improvement of the axial current in N_f=3 lattice QCD with Wilson fermions and tree-level improved gauge action

The coefficient c_A required for O(a) improvement of the axial current in lattice QCD with N_f=3 flavors of Wilson fermions and the tree-level Symanzik-improved gauge action is determined non-perturbatively. The standard improvement condition using Schroedinger functional boundary conditions is employed at constant physics for a range of couplings relevant for simulations at lattice spacings of ~ 0.09 fm and below. We define the improvement condition projected onto the zero topological charge sector of the theory, in order to avoid the problem of possibly insufficient tunneling between topological sectors in our simulations at the smallest bare coupling. An interpolation formula for c_A(g_0^2) is provided together with our final results.Comment: 16 pages including figures and tables, latex2e; version published in Nucl. Phys. B, small additions to the text and references added, results unchange

Non-perturbative renormalization of the axial current in Nf=3N_f = 3 lattice QCD with Wilson fermions and tree-level improved gauge action

We non-perturbatively determine the renormalization factor of the axial vector current in lattice QCD with $N_f=3$ flavors of Wilson-clover fermions and the tree-level Symanzik-improved gauge action. The (by now standard) renormalization condition is derived from the massive axial Ward identity and it is imposed among Schr\"{o}dinger functional states with large overlap on the lowest lying hadronic state in the pseudoscalar channel, in order to reduce kinematically enhanced cutoff effects. We explore a range of couplings relevant for simulations at lattice spacings of $\approx 0.09$ fm and below. An interpolation formula for $Z_A(g_0^2)$, smoothly connecting the non-perturbative values to the 1-loop expression, is provided together with our final results.Comment: 13 pages, 2 tables, 5 figures. Version accepted for publication in PRD. References added, results unchanged. arXiv admin note: text overlap with arXiv:1502.0499