On the generalized eigenvalue method for energies and matrix elements in lattice field theory

Abstract

We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as $\exp (-(E_{N+1}-E_n)t)$. The gap $E_{N+1}-E_n$ can be made large by increasing the number $N$ of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order $1/m_b$ in HQET.

(1+28) pages, 9 figures; minor corrections to table 1 and figures, main results unaffected

References in corpus (24)

• Flavor Symmetry and the Static Potential with Hypercubic Blocking
• Non-perturbative O(a) improvement of lattice QCD
• Observation of String Breaking in QCD
• Practical all-to-all propagators for lattice QCD
• Charmonium excited state spectrum in lattice QCD
• String Breaking in Non-Abelian Gauge Theories with Fundamental Matter Fields
• On lattice actions for static quarks
• Lattice QCD determination of patterns of excited baryon states
• Excited State Nucleon Spectrum with Two Flavors of Dynamical Fermions
• String breaking in SU(2) gauge theory with scalar matter fields
• Hadron Spectroscopy with Dynamical Chirally Improved Fermions
• Universality and scaling behavior of RG gauge actions
• A lattice study of light scalar tetraquarks
• Fixed Point Gauge Actions with Fat Links: Scaling and Glueballs
• Excitations of single-beauty hadrons
• Lattice Gauge Theory Approach to Spontaneous Symmetry Breaking from an Extra Dimension
• Derivative sources in lattice spectroscopy of excited light-quark mesons
• String Breaking as a Mixing Phenomenon in the SU(2) Higgs Model
• Heavy Quark Effective Theory computation of the mass of the bottom quark
• Mesons at large Nc from lattice QCD
• Radial and orbital excitations of static-light mesons
• Couplings of hybrid operators to ground and excited states of bottomonia
• Efficient use of the Generalized Eigenvalue Problem
• Charmonium spectrum including higher spin and exotic states

Cited by in corpus (225)

• Pentaquark and Tetraquark states
• FLAG Review 2019
• FLAG Review 2021
• Excited state baryon spectroscopy from lattice QCD
• Scattering processes and resonances from lattice QCD
• Toward the excited meson spectrum of dynamical QCD
• Coupled $\pi \pi ,K\overline{K}$ scattering in $P$-wave and the $\rho$ resonance from lattice QCD
• S and D-wave phase shifts in isospin-2 pi pi scattering from lattice QCD
• $D_{s0}^{\ast }(2317)$ Meson and $D$-Meson-Kaon Scattering from Lattice QCD
• Study of doubly heavy tetraquarks in Lattice QCD
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• Toward the excited isoscalar meson spectrum from lattice QCD
• $D_s$ mesons with $DK$ and $D^{\ast }K$ scattering near threshold
• Light Hadron Masses from Lattice QCD
• Resonances in coupled $\pi K,\eta K$ scattering from lattice QCD
• An $a_0$ resonance in strongly coupled $\pi \eta$, $K\overline{K}$ scattering from lattice QCD
• D Pi scattering and D meson resonances from lattice QCD
• Evidence for X(3872) from DD* scattering on the lattice
• QCD with Two Light Dynamical Chirally Improved Quarks: Baryons
• Lattice QCD investigation of a doubly-bottom $\bar{b}\bar{b}ud$ tetraquark with quantum numbers $I(J^P)=0(1^{+})$
• BB interactions with static bottom quarks from Lattice QCD
• Meson masses in electromagnetic fields with Wilson fermions
• $I=1$ and $I=2$ $\pi -\pi$ scattering phase shifts from $N_{\mathrm{f}}=2+1$ lattice QCD
• Resonance parameters of the rho-meson from asymmetrical lattices
• Hybrid Baryons in QCD
• Charmed baryon spectroscopy and light flavour symmetry from lattice QCD
• Scattering in the pion-nucleon negative parity channel in lattice QCD
• Two- and three-pion finite-volume spectra at maximal isospin from lattice QCD
• Excited and exotic charmonium, $D_s$ and $D$ meson spectra for two light quark masses from lattice QCD
• Predicting positive parity $B_s$ mesons from lattice QCD
• Masses and decay constants of the $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$ from $N_f=2$ lattice QCD close to the physical point
• X(3872) and Y(4140) using diquark-antidiquark operators with lattice QCD
• Towards a theory of hadron resonances
• The $I=1$ pion-pion scattering amplitude and timelike pion form factor from $N_{\mathrm{f}}=2+1$ lattice QCD
• Pion-nucleon scattering in the Roper channel from lattice QCD
• Meson and baryon spectrum for QCD with two light dynamical quarks
• $P$-wave $\pi \pi$ scattering and the $\rho$ resonance from lattice QCD
• Rho resonance parameters from lattice QCD
• Nucleon electromagnetic form factors from lattice QCD using a nearly physical pion mass
• Isolating the Λ(1405) in Lattice QCD
• Study of the $Z_c^{+}$ channel using lattice QCD
• Three pion spectrum in the $I=3$ channel from lattice QCD
• Lattice QCD study of the $H$ dibaryon using hexaquark and two-baryon interpolators
• String breaking by light and strange quarks in QCD
• $\rho$ and $K^{\ast }$ resonances on the lattice at nearly physical quark masses and $N_f=2$
• First Physics Results at the Physical Pion Mass from $N_f=2$ Wilson Twisted Mass Fermions at Maximal Twist
• Tetraquark operators in lattice QCD and exotic flavour states in the charm sector
• Decays of an exotic $1^{-+}$ hybrid meson resonance in QCD
• Second Moment of the Pion Light-cone Distribution Amplitude from Lattice QCD
• A lattice investigation of exotic tetraquark channels
• Towards grounding nuclear physics in QCD
• FLAG Review 2024
• Computing K and D meson masses with N_f = 2+1+1 twisted mass lattice QCD
• K pi scattering for isospin 1/2 and 3/2 in lattice QCD
• Precision computation of hybrid static potentials in SU(3) lattice gauge theory
• Roper Resonance in 2+1 Flavor QCD
• K pi scattering and the K* decay width from lattice QCD
• Finite-volume energy spectrum of the $K^{-}{K}^{-}{K}^{-}$ system
• Weakly bound $H$ dibaryon from SU(3)-flavor-symmetric QCD
• Nucleon electromagnetic form factors in two-flavour QCD
• Search for Z_c^+(3900) in the 1^+- channel on the lattice
• On the computation of hadron-to-hadron transition matrix elements in lattice QCD
• Mass of the b-quark and B-decay constants from Nf=2+1+1 twisted-mass Lattice QCD
• Scattering amplitudes from finite-volume spectral functions
• Extraction of isoscalar $\pi \pi$ phase-shifts from lattice QCD
• Quark masses using twisted mass fermion gauge ensembles
• Masses and decay constants of the $\eta$ and ${\eta }^{\prime }$ mesons from lattice QCD
• The energy-dependent ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ scattering amplitude from QCD
• Excited bottomonia in quark-gluon plasma from lattice QCD
• Extended hadron and two-hadron operators of definite momentum for spectrum calculations in lattice QCD
• Determination of the Static Potential with Dynamical Fermions
• The quark-mass dependence of elastic $\pi K$ scattering from QCD
• Structure and Flow of the Nucleon Eigenstates in Lattice QCD
• Scattering of two and three physical pions at maximal isospin from lattice QCD
• Studying the $\rho$ resonance parameters with staggered fermions
• Glueball mass measurements from improved staggered fermion simulations
• A cross-channel study of pion scattering from lattice QCD
• The $\pi \gamma \to \pi \pi$ transition and the $\rho$ radiative decay width from lattice QCD
• Effective string description of confining flux tubes
• Lattice investigation of the scalar mesons a_0(980) and κ using four-quark operators
• Extraction of HQE parameters from unquenched lattice data on pseudoscalar and vector heavy-light meson masses
• Masses and decay constants of D(s)* and B(s)* mesons with Nf = 2 + 1 + 1 twisted mass fermions
• Masses and decay constants of $D_{(s)}^{\ast }$ and $B_{(s)}^{\ast }$ mesons in Lattice QCD with $N_f=2+1+1$ twisted-mass fermions
• A variational study of two-nucleon systems with lattice QCD
• Precision Study of Excited State Effects in Nucleon Matrix Elements
• Symmetries of mesons after unbreaking of chiral symmetry and their string interpretation
• Flavor-singlet meson decay constants from $N_f=2+1+1$ twisted mass lattice QCD
• Nucleon-$J/\psi$ and nucleon-${\eta }_c$ scattering in $P_c$ pentaquark channels from LQCD
• Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives
• A study of the eta and eta' mesons with improved staggered fermions
• Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarisation
• HQET at order 1/m: I. Non-perturbative parameters in the quenched approximation
• Pion scattering in the isospin I=2 channel from elongated lattices
• Isoscalar mesons upon unbreaking of chiral symmetry
• Precision lattice QCD computation of the $B^{\ast }B\pi$ coupling
• Decay constants of B-mesons from non-perturbative HQET with two light dynamical quarks
• Axial resonances a1(1260), b1(1235) and their decays from the lattice
• Towards glueball masses of large-$N$ $\mathrm{SU}(N)$ pure-gauge theories without topological freezing
• Masses of $D$ mesons, $D_s$ mesons and charmonium states from twisted mass lattice QCD
• Low-energy Scattering and Effective Interactions of Two Baryons at $m_{\pi }\sim 450$ MeV from Lattice Quantum Chromodynamics
• Multiple-particle interaction in $1+1$ dimensional lattice model
• Exotic Tetraquark states with two $\bar{b}$-quarks and $J^P=0^{+}$ and $1^{+}$ $B_s$ states in a nonperturbatively-tuned Lattice NRQCD setup
• Lattice QCD study of $\pi \Sigma -\bar{K}N$ scattering and the $\Lambda (1405)$ resonance
• η and η' mesons from Nf=2+1+1 twisted mass lattice QCD
• Accelerating lattice quantum field theory calculations via interpolator optimization using NISQ-era quantum computing
• Lattice studies of the $Sp(4)$ gauge theory with two fundamental and three antisymmetric Dirac fermions
• Elastic nucleon-pion scattering at $m_{\pi }=200\mathrm{MeV}$ from lattice QCD
• Nucleon-pion-state contribution to nucleon two-point correlation functions
• Non-perturbative Test of the Witten-Veneziano Formula from Lattice QCD
• Towards the determination of the gluon helicity distribution in the nucleon from lattice quantum chromodynamics
• P-wave nucleon-pion scattering amplitude in the $\Delta (1232)$ channel from lattice QCD
• Nucleon matrix elements using the variational method in lattice QCD
• HQET at order $1/m$: II. Spectroscopy in the quenched approximation
• Three-body dynamics of the $a_1(1260)$ resonance from lattice QCD
• $B_s{\pi }^{+}$ scattering and search for X(5568) with lattice QCD
• Tetraquark interpolating fields in a lattice QCD investigation of the $D_{s0}^{\ast }(2317)$ meson
• Importance of meson-meson and of diquark-antidiquark creation operators for a $\bar{b}\bar{b}ud$ tetraquark
• Continuum limit of the $D$ meson, $D_s$ meson and charmonium spectrum from $N_f=2+1+1$ twisted mass lattice QCD
• The continuum limit of the static-light meson spectrum
• Shallow Bound States and Hints for Broad Resonances with Quark Content $\bar{b}\bar{c}ud$ in $B$-$\bar{D}$ and $B^{\ast }$-$\bar{D}$ Scattering from Lattice QCD
• Coupled-channel scattering in 1+1 dimensional lattice model
• $\omega$ meson from lattice QCD
• Charmonium resonances with $J^{PC}=1^{--}$ and $3^{--}$ from $\bar{D}D$ scattering on the lattice
• Constraining $1+\mathcal{J}\to 2$ coupled-channel amplitudes in finite-volume
• On the generalised eigenvalue method and its relation to Prony and generalised pencil of function methods
• Nucleon Excited States in N${}_f$=2 lattice QCD
• Signal/noise enhancement strategies for stochastically estimated correlation functions
• Uncertainty Quantification in Lattice QCD Calculations for Nuclear Physics
• Introduction to Non-perturbative Heavy Quark Effective Theory
• The b-quark mass from non-perturbative $N_f=2$ Heavy Quark Effective Theory at $O(1/m_h)$
• Isolating the Roper Resonance in Lattice QCD
• Ordering of Spin-$\frac{1}{2}$ Excitations of the Nucleon in Lattice QCD
• A lattice model of heavy-light three-body system
• $I=1/2$ $S$-wave and $P$-wave $K\pi$ scattering and the $\kappa$ and $K^{\ast }$ resonances from lattice QCD
• Power corrections from decoupling of the charm quark
• Tetraquark systems $\bar{b}b\bar{d}u$ in the static limit and lattice QCD
• Near-threshold states in coupled $D{D}^{\ast }-D^{\ast }{D}^{\ast }$ scattering from lattice QCD
• Toward $N$ to $N\pi$ matrix elements from lattice QCD
• Lattice QCD investigation of the structure of the $a_0(980)$ meson
• Decay constants of the pion and its excitations on the lattice
• Excited $J^{--}$ meson resonances at the SU(3) flavor point from lattice QCD
• Controlling Excited-State Contributions with Distillation in Lattice QCD Calculations of Nucleon Isovector Charges $g_S^{u-d}$, $g_A^{u-d}$, $g_T^{u-d}$
• Charmonium ${\chi }_{c0}$ and ${\chi }_{c2}$ resonances in coupled-channel scattering from lattice QCD
• Optimising creation operators for charmonium spectroscopy on the lattice
• Hidden-charm Hexaquarks from Lattice QCD
• Opposite-Parity Contaminations in Lattice Nucleon Form Factors
• Gauge-invariant screening masses and static quark free energies in $N_f=2+1$ QCD at non-zero baryon density
• Roper State from Overlap Fermions
• The Shape of Covariantly Smeared Sources in Lattice QCD
• Towards studying the structural differences between the pion and its radial excitation
• Identifying spin and parity of charmonia in flight with lattice QCD
• Scale setting in lattice QCD
• A Mixed Action Analysis of $\eta$ and ${\eta }^{\prime }$ Mesons
• Strategies for quantum-optimized construction of interpolating operators in classical simulations of lattice quantum field theories
• Variational method with staggered fermions
• Constraining beyond the Standard Model nucleon isovector charges
• Lattice determination of $I=0$ and 2 $\pi \pi$ scattering phase shifts with a physical pion mass
• Leptonic D_s decays in two-flavour lattice QCD
• On the equivalence of Prony and Lanczos methods for Euclidean correlation functions
• Splittings of low-lying charmonium masses at the physical point
• Axial-vector $D_1$ hadrons in $D^{\ast }\pi$ scattering from QCD
• The spectrum of 2+1 dimensional Yang-Mills theory on a twisted spatial torus
• Investigating efficient methods for computing four-quark correlation functions
• On internal structure of the heavy-light mesons
• $|V_{ub}|$ determination in lattice QCD
• Spectroscopy From The Lattice: The Scalar Glueball
• On the B*' --> B transition
• Nucleon Mass with Highly Improved Staggered Quarks
• Revisiting the flux tube spectrum of 3d SU(2) lattice gauge theory
• The shape of the static potential with dynamical fermions
• Pion couplings to the scalar B meson
• Isospin 0 and 2 two-pion scattering at physical pion mass using all-to-all propagators with periodic boundary conditions in lattice QCD
• Eight very excited spectra and one possible axion in SU(3) lattice gauge theory
• Expanding the Interpolator Basis in the Variational Method to Explicitly Account for Backward Running States
• Light and strange vector resonances from lattice QCD at physical quark masses
• Non-zero temperature study of spin 1/2 charmed baryons using lattice gauge theory
• Lattice investigation of the tetraquark candidates a0(980) and kappa
• Investigation of pion-nucleon contributions to nucleon matrix elements
• Semileptonic $B\to D^{\ast \ast }$ decays in Lattice QCD : a feasibility study and first results
• B-meson spectroscopy in HQET at order 1/m
• Physical-mass calculation of $\rho (770)$ and $K^{\ast }(892)$ resonance parameters via $\pi \pi$ and $K\pi$ scattering amplitudes from lattice QCD
• New extended interpolating fields built from three-dimensional fermions
• Spectrum of very excited ${\Sigma }_g^{+}$ flux tubes in SU(3) gauge theory
• Feynman--Hellmann approach to transition matrix elements and quasi-degenerate energy states
• $\Delta I=3/2$ and $\Delta I=1/2$ channels of $K\to \pi \pi$ decay at the physical point with periodic boundary conditions
• Extraction of multiple exponential signals from lattice correlation functions
• Elastic Nucleon-Pion scattering amplitudes in the $\Delta$ channel at physical pion mass from Lattice QCD
• State mixing and masses of the ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$ mesons from $n_f=1+1+1$ lattice QCD+QED
• Density distributions in the $B$ meson
• Constructing static quark-anti-quark creation operators from Laplacian eigenmodes
• Excited-state effects in nucleon structure on the lattice using hybrid interpolators
• Towards high partial waves in lattice QCD with a dumbbell-like operator
• Källén-Lehmann Spectral Representation of the Scalar SU(2) Glueball
• Meson-Nucleon Scattering Amplitudes from Lattice QCD
• Mixing of S-Wave Charmonia with $\mathrm{D}\overline{\mathrm{D}}$ Molecule States
• Twisted mass lattice computation of charmed mesons with focus on $D^{\ast \ast }$
• Di-nucleons do not form bound states at heavy pion mass
• Scattering phase shift and resonance properties on the lattice: an introduction
• Unexpected pattern of transitions to radial excitations by heavy quark current
• Properties of pseudoscalar flavour-singlet mesons from 2+1+1 twisted mass lattice QCD
• Recent Developments of Muon g-2 from Lattice QCD
• Lattice results on charmonium
• Coupled-channel scattering of $DD,D{D}^{\ast }$ and $D^{\ast }{D}^{\ast }$ in isospin-$1$ from lattice QCD
• B-physics with $N_f=2$ Wilson fermions
• S-wave flavor-singlet meson mixing in QCD with light and charm quarks
• Position-space sampling for local multiquark operators in lattice QCD using distillation and the importance of tetraquark operators for $T_{cc}(3875{)}^{+}$
• $N_f=2+1+1$ flavours of twisted mass quarks: cut-off effects at tree-level of perturbation theory
• The determination of potential scales in 2+1 flavor QCD
• Emergence of the $\pi (1300)$ Resonance from Lattice QCD
• Application of Laplace filters to the analysis of lattice time correlators
• The two-pion contribution to the hadronic vacuum polarization with staggered quarks
• Decoding Two-Particle States in QCD with Spatial Wavefunctions
• Accessing the Gluon Momentum Fraction of Nucleons through the Gradient Flow
• Binding energy of the $T_{bb}$ tetraquark from lattice QCD with relativistic and nonrelativistic heavy-quark actions
• Mass estimates of the SU(2) $0^{++}$ glueball from spectral methods
• Excited State Effects in Nucleon Matrix Element Calculations
• $DK$ and $D^{\ast }K$ scattering near threshold
• K pi scattering in moving frames
• Nonperturbative HQET at Order $1/m$
• Mesons upon low-lying Dirac mode exclusion
• Unpolarized gluon distribution in the nucleon from lattice quantum chromodynamics
• Low lying charmonium states at the physical point
• Handling Excited States on the Lattice: The GEVP Method
• Wavefunction-based operator optimization for two-hadron systems in lattice QCD
• Testing the stochastic LapH method in the twisted mass formulation