Ground-state energy and matrix elements are reconstructed from correlators in lattice QCD by diagonalizing transfer matrix <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi mathvariant="script">T</mi><mo stretchy="false">^</mo></mover></math> within the Krylov subspace spanned by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi mathvariant="script">T</mi><mo stretchy="false">^</mo></mover><mi>n</mi></msup><mo stretchy="false">|</mo><mi>χ</mi><mo stretchy="false">⟩</mo></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><mi>χ</mi><mo stretchy="false">⟩</mo></math> is a state generated by an interpolating field on the lattice. In numerical applications, this strategy is spoiled by statistical noise. To circumvent the problem, we introduce a low-rank approximation based on a singular-value decomposition of a matrix made of the correlators. The associated bias is eliminated by an extrapolation to the limit of vanishing variance of energy eigenvalues. The strategy is tested using a set of mock data as well as real data of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub></math> meson correlators.

Japan

Ryutaro Tsuji

Shoji Hashimoto

Ryan Kellermann

Unbiased Krylov subspace method for the extraction of ground states from lattice correlators

Lattice QCD calculations of inclusive semileptonic decay rates involve new types of systematic effects, such as truncation errors in the estimation of energy integrals, or finite-volume effects for multibody final states. We investigate them for the lattice data of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">→</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>ℓ</mo><mi>ν</mi></mrow></math> decays, obtained using Möbius domain-wall fermions. Separating the ground-state and excited-state contributions results in better control over these systematic effects. With the Chebyshev polynomial approximation, the truncation error is under control, while the finite-volume effects are estimated using a model to describe two-body final states.

Zhi Hu

Germany

Alessandro Barone

United Kingdom

Ahmed Elgaziari

Takashi Kaneko

CERN

Andreas Jüttner

Inclusive semileptonic decays from lattice QCD: Analysis of systematic effects

The low-energy spectrum relevant to the lattice calculation of the hadronic vacuum polarization contribution to muon anomalous magnetic moment <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>a</mi><mi>μ</mi><mrow><mi>HVP</mi><mo>,</mo><mi>LO</mi></mrow></msubsup></math> is dominantly given by two-pion states satisfying Lüscher’s finite-volume quantization condition. Finite-volume effects from those states may exhibit power-law dependence on the volume, contrary to an exponential suppression as suggested by chiral effective theory. Employing the finite-volume state decomposition of Euclidean correlators, we systematically investigate the volume dependence and identify the different volume scalings depending on the volume and Euclidean-time region. Using phenomenological inputs for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math> phase shift and the timelike pion form factor, we obtain an estimate for the finite-volume effects on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>a</mi><mi>μ</mi><mrow><mi>HVP</mi><mo>,</mo><mi>LO</mi></mrow></msubsup></math>, which is consistent with previous works. Numerical results are given for the “window” observables of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>μ</mi></msub></math>.

Sakura Itatani

Hidenori Fukaya

Anatomy of finite-volume effects on the hadronic vacuum polarization contribution to the muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math>

We address the nonperturbative calculation of the inclusive decay rate of semileptonic B (s)-meson decays from lattice QCD. Precise Standard-Model predictions are key ingredients in searches for new physics, and this type of computation may eventually provide new insight into the long-standing tension between the inclusive and exclusive determinations of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements |V  cb | and |V  ub |. We present results from a pilot lattice computation for B  s  → X  c  lν  l , where the initial b quark described by the relativistic-heavy-quark (RHQ) formalism on the lattice and the other valence quarks discretised with domain-wall fermions are simulated approximately at their physical quark masses. We compare two different methods for computing the decay rate from lattice data of Euclidean n-point functions, namely Chebyshev and Backus-Gilbert approaches. We further study how much the ground-state meson dominates the inclusive decay rate and indicate our strategy towards a computation with a more comprehensive systematic error budget.

Approaches to inclusive semileptonic B (s)-meson decays from Lattice QCD

Using a fully relativistic lattice fermion action, we compute the form factors of the semileptonic decay <math><mrow><mi>B</mi><mo>→</mo><mi>π</mi><mo>ℓ</mo><mi>ν</mi></mrow></math>, which is required for the determination of the Cabibbo-Kobayashi-Maskawa matrix element <math><mo>|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>b</mi></mrow></msub><mo>|</mo></math>. We employ the Möbius domain-wall fermion formalism for the generation of lattice ensembles with <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> sea quark flavors as well as for the valence heavy and light quarks. We compute the form factors at various values of the lattice spacing and multiple light and heavy quark masses, and extrapolate the results to the physical point. We combine our lattice results with the available experimental data to obtain <math><mo>|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>b</mi></mrow></msub><mo>|</mo><mo>=</mo><mo>(</mo><mn>3.93</mn><mo>±</mo><mn>0.41</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>.

Canada

Brian Colquhoun

Jonna Koponen

Form factors of <math><mi>B</mi><mo>→</mo><mi>π</mi><mo>ℓ</mo><mi>ν</mi></math> and a determination of <math><mo>|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>b</mi></mrow></msub><mo>|</mo></math> with Möbius domain-wall fermions

We present an ab initio study of inclusive semileptonic decays of heavy mesons from lattice QCD. Our approach is based on a recently proposed method, that allows one to address the study of these decays from the analysis of smeared spectral functions extracted from four-point correlators on the lattice, where the smearing is defined in terms of the phase-space integration relevant to the inclusive decays. We present results obtained from gauge-field ensembles from the JLQCD and ETM collaborations, and discuss their relation with theoretical predictions from the operator-product expansion.

Italy

Paolo Gambino

Switzerland

Sandro Mächler

Marco Panero

Francesco Sanfilippo

Silvano Simula

Antonio Smecca

Nazario Tantalo

Lattice QCD study of inclusive semileptonic decays of heavy mesons

We propose a method to use lattice QCD to compute the Borel transform of the vacuum polarization function appearing in the Shifman-Vainshtein-Zakharov QCD sum rule. We construct the spectral sum corresponding to the Borel transform from two-point functions computed on the Euclidean lattice. As a proof of principle, we compute the <math><mi>s</mi><mover><mi>s</mi><mo>¯</mo></mover></math> correlators at three lattice spacings and take the continuum limit. We confirm that the method yields results that are consistent with the operator product expansion in the large Borel mass region. The method provides a ground on which the OPE analyses can be directly compared with nonperturbative lattice computations.

Tsutomu Ishikawa

Spectral sum of current correlators from lattice QCD

We perform a numerical computation of the anomalous magnetic moment (g − 2) of the electron in QED by using the stochastic perturbation theory. Formulating QED on the lattice, we develop a method to calculate the coefficients of the perturbative series of g − 2 without the use of the Feynman diagrams. We demonstrate the feasibility of the method by performing a computation up to the α 3 order and compare with the known results. This program provides us with a totally independent check of the results obtained by the Feynman diagrams and will be useful for the estimations of not-yet-calculated higher order values. This work provides an example of the application of the numerical stochastic perturbation theory to physical quantities, for which the external states have to be taken on-shell.

Ryuichiro Kitano

Hiromasa Takaura

Stochastic computation of g − 2 in QED

We propose a fully nonperturbative method to compute inelastic lepton-nucleon (<math><mo>ℓ</mo><mi>N</mi></math>) scattering cross sections using lattice quantum chromodynamics (QCD). The method is applicable even at low energies, such as the energy region relevant for the recent and future neutrino-nucleon scattering experiments, for which perturbative analysis is invalidated. The basic building block is the forward Compton-scattering amplitude, or the hadronic tensor, computed on a Euclidean lattice. A total cross section is constructed from the hadronic tensor by multiplying a phase space factor and integrating over the energy and momentum of final hadronic states. The energy integral that induces a sum over all possible final states is performed implicitly by promoting the phase space factor to an operator written in terms of the transfer matrix on the lattice. The formalism is imported from that of the inclusive semileptonic <math><mi>B</mi></math> meson decay [P. Gambino and S. Hashimoto, Phys. Rev. Lett. 125, 032001 (2020)] and generalized to compute the <math><mo>ℓ</mo><mi>N</mi></math> scattering cross sections and their moments, as well as the virtual correction to the nuclear <math><mi>β</mi></math> decay.

Hiroshi Ohki

Towards fully nonperturbative computations of inelastic <math><mo>ℓ</mo><mi>N</mi></math> scattering cross sections from lattice QCD

We develop a method to compute the inclusive semileptonic decay rate of hadrons fully nonperturbatively using lattice QCD simulations. The sum over all possible final states is achieved by a calculation of the forward-scattering matrix elements on the lattice, and the phase-space integral is evaluated using their dependence on the time separation between two inserted currents. We perform a pilot lattice computation for the <math><mrow><msub><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow></msub><mo>→</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>ℓ</mo><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> decay with an unphysical bottom quark mass and compare the results with the corresponding OPE calculation. The method to treat the inclusive processes on the lattice can be applied to other processes, such as the lepton-nucleon inelastic scattering.

Inclusive Semileptonic Decays from Lattice QCD