We investigate the combination of a two-level sampling algorithm with distillation techniques to compute disconnected fermionic correlation functions. The method relies on a factorization of the quark propagator into domain-local contributions that depend only on the gauge fields within overlapping temporal regions, enabling independent submeasurements of each term through a two-level sampling strategy. The statistical uncertainty follows the expected inverse scaling with the number of second-level submeasurements, up to exponential boundary effects, in contrast to the inverse square-root scaling of standard sampling. This leads to an exponential reduction of statistical errors at negligible additional computational cost compared to the gain in statistical precision. The method is tested on pure gauge ensembles, providing a controlled benchmark for its forthcoming application to dynamical QCD studies.

Germany

Lorenzo Barca

Stefan Schaefer

CERN

Jacob Finkenrath

Investigating a two-level algorithm for fermionic observables

We investigate the mixing between flavor-singlet light meson and charmonium operators in the S-wave channels, i.e., pseudoscalar and vector channel, at two different pion masses. We measure statistically significant nonzero correlations between operators with different quark content corresponding to off-diagonal entries of a flavor-singlet mixing correlation matrix. By solving a Generalized Eigenvalue Problem (GEVP) we extract the low-lying energy spectrum and compare it with the one obtained by the different types of operators separately. We also calculate the overlaps between the states created by different operators and the energy eigenstates of the theory and find that all types of operators contribute to resolve the states of interest.

Juan Andrés Urrea-Niño

Roman Höllwieser

Francesco Knechtli

Tomasz Korzec

Ireland

Michael Peardon

S-wave flavor-singlet meson mixing in QCD with light and charm quarks

We present the full decomposition of the momentum fraction carried by quarks and gluons in the pion and the kaon. We employ three gauge ensembles generated with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></math> Wilson twisted-mass clover-improved fermions at the physical quark masses. For both mesons we perform a continuum extrapolation directly at the physical pion mass, which allows us to determine for the first time the momentum decomposition at the physical point. We find that the total momentum fraction carried by quarks is 0.575(79) and 0.683(50) and by gluons 0.402(53) and 0.422(67) in the pion and in the kaon, respectively, in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>MS</mi><mo stretchy="true">¯</mo></mover></math> scheme and at the renormalization scale of 2 GeV. Having computed both the quark and gluon contributions in the continuum limit, we find that the momentum sum is 0.984(89) for the pion and 1.13(11) for the kaon, verifying the momentum sum rule.

Cyprus

Constantia Alexandrou

Simone Bacchio

United States

Martha Constantinou

Joseph Delmar

Bartosz Kostrzewa

Marcus Petschlies

Italy

Luis Alberto Rodriguez Chacon

Gregoris Spanoudes

Fernanda Steffens

Carsten Urbach

Switzerland

Urs Wenger

Quark and Gluon Momentum Fractions in the Pion and in the Kaon

We study the <math><mover><mi>b</mi><mo>¯</mo></mover><mover><mi>b</mi><mo>¯</mo></mover><mi>u</mi><mi>d</mi></math> tetraquark with quantum numbers <math><mi>I</mi><mo>(</mo><msup><mi>J</mi><mi>P</mi></msup><mo>)</mo><mo>=</mo><mn>0</mn><mo>(</mo><msup><mn>1</mn><mo>+</mo></msup><mo>)</mo></math> as well as the <math><mover><mi>b</mi><mo>¯</mo></mover><mover><mi>b</mi><mo>¯</mo></mover><mi>u</mi><mi>s</mi></math> tetraquark with quantum numbers <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></math> using lattice QCD. We improve on existing work by including both local and scattering interpolating operators on both sides of the correlation functions and use symmetric correlation matrices. This allows not only a reliable determination of the energies of QCD-stable tetraquark ground states, but also of low-lying excited states, which are meson-meson scattering states. The latter is particularly important for future finite-volume scattering analyses. Here, we perform chiral and continuum extrapolations of just the ground-state energies, for which finite-volume effects are expected to be small. Our resulting tetraquark binding energies, <math><mrow><mo>−</mo><mn>100</mn><mo>±</mo><msubsup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>51</mn></mrow><mrow><mo>+</mo><mn>36</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math> for <math><mover><mi>b</mi><mo>¯</mo></mover><mover><mi>b</mi><mo>¯</mo></mover><mi>u</mi><mi>d</mi></math> and <math><mrow><mo>−</mo><mn>30</mn><mo>±</mo><msubsup><mn>3</mn><mrow><mo>−</mo><mn>31</mn></mrow><mrow><mo>+</mo><mn>11</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math> for <math><mover><mi>b</mi><mo>¯</mo></mover><mover><mi>b</mi><mo>¯</mo></mover><mi>u</mi><mi>s</mi></math>, are consistent with other recent lattice-QCD predictions.

Theodoros Leontiou

Stefan Meinel

Martin Pflaumer

Marc Wagner

<math><mover><mi>b</mi><mo>¯</mo></mover><mover><mi>b</mi><mo>¯</mo></mover><mi>u</mi><mi>d</mi></math> and <math><mover><mi>b</mi><mo>¯</mo></mover><mover><mi>b</mi><mo>¯</mo></mover><mi>u</mi><mi>s</mi></math> tetraquarks from lattice QCD using symmetric correlation matrices with both local and scattering interpolating operators

We present a lattice determination of the inclusive decay rate of the process <math><mrow><mi>τ</mi><mo>↦</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>u</mi><mi>s</mi></mrow></msub><msub><mrow><mi>ν</mi></mrow><mrow><mi>τ</mi></mrow></msub></mrow></math> in which the <math><mi>τ</mi></math> lepton decays into a generic hadronic state <math><msub><mi>X</mi><mrow><mi>u</mi><mi>s</mi></mrow></msub></math> with <math><mover><mi>u</mi><mo>¯</mo></mover><mi>s</mi></math> flavor quantum numbers. Our results have been obtained in <math><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math> isosymmetric QCD with full nonperturbative accuracy, without any operator product expansion approximation and, except for the presently missing long-distance isospin-breaking corrections, include a solid estimate of all sources of theoretical uncertainties. This has been possible by using the Hansen-Lupo-Tantalo method [M. Hansen et al., Phys. Rev. D 99, 094508 (2019)] that we have already successfully applied [A. Evangelista et al., Phys. Rev. D 108, 074513 (2023)] to compute the inclusive decay rate of the process <math><mi>τ</mi><mo>↦</mo><msub><mi>X</mi><mrow><mi>u</mi><mi>d</mi></mrow></msub><msub><mi>ν</mi><mi>τ</mi></msub></math> in the <math><mover><mi>u</mi><mo>¯</mo></mover><mi>d</mi></math> flavor channel. By combining our first-principles theoretical results with the presently available experimental data, we extract the Cabibbo-Kobayashi-Maskawa matrix element <math><mo>|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>s</mi></mrow></msub><mo>|</mo></math>, the Cabibbo angle, with a 0.9% accuracy, dominated by the experimental error.

Alessandro De Santis

Antonio Evangelista

Roberto Frezzotti

Giuseppe Gagliardi

Marco Garofalo

Vittorio Lubicz

Simone Romiti

Francesco Sanfilippo

Silvano Simula

Nazario Tantalo

Inclusive Hadronic Decay Rate of the <math><mi>τ</mi></math> Lepton from Lattice QCD: The <math><mover><mi>u</mi><mo>¯</mo></mover><mi>s</mi></math> Flavor Channel and the Cabibbo Angle

We present the first determination of the energy dependence of the <math><mrow><mi>B</mi><mtext>−</mtext><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> and <math><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>*</mo></mrow></msup><mtext>−</mtext><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> isospin-0, <math><mi>S</mi></math>-wave scattering amplitudes both below and above the thresholds using lattice QCD, which allows us to investigate rigorously whether mixed bottom-charm <math><mrow><mover><mrow><mi>b</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>u</mi><mi>d</mi></mrow></math> tetraquarks exist as bound states or resonances. The scattering phase shifts are obtained using Lüscher’s method from the energy spectra in two different volumes. To ensure that no relevant energy level is missed, we use large, symmetric <math><mn>7</mn><mo>×</mo><mn>7</mn></math> and <math><mn>8</mn><mo>×</mo><mn>8</mn></math> correlation matrices that include, at both source and sink, <math><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mtext>−</mtext><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> scattering operators with the lowest three or four possible back-to-back momenta in addition to local <math><mover><mi>b</mi><mo>¯</mo></mover><mover><mi>c</mi><mo>¯</mo></mover><mi>u</mi><mi>d</mi></math> operators. We fit the energy dependence of the extracted scattering phase shifts using effective-range expansions. We observe sharp peaks in the <math><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mtext>−</mtext><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> scattering rates close to the thresholds, which are associated with shallow bound states, either genuine or virtual, a few MeV or less below the <math><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mtext>−</mtext><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> thresholds. In addition, we find hints for resonances with masses of order 100 MeV above the thresholds and decay widths of order 200 MeV.

Shallow Bound States and Hints for Broad Resonances with Quark Content <math><mover><mi>b</mi><mo>¯</mo></mover><mover><mi>c</mi><mo>¯</mo></mover><mi>u</mi><mi>d</mi></math> in <math><mrow><mi>B</mi><mtext>−</mtext><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> and <math><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>*</mo></mrow></msup><mtext>−</mtext><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> Scattering from Lattice QCD

We compute the nucleon axial and pseudoscalar form factors using three <math><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></math> twisted-mass fermion ensembles with all quark masses tuned to approximately their physical values. The values of the lattice spacings of these three physical point ensembles are 0.080, 0.068, and 0.057 fm and spatial sizes 5.1, 5.44, and 5.47 fm, respectively, yielding <math><msub><mi>m</mi><mi>π</mi></msub><mi>L</mi><mo>&gt;</mo><mn>3.6</mn></math>. Convergence to the ground-state matrix elements is assessed using multistate fits. We study the momentum dependence of the three form factors and check the partially conserved axial-vector current (PCAC) hypothesis and the pion pole dominance (PPD). We show that in the continuum limit, the PCAC and PPD relations are satisfied. We also show that the Goldberger-Treimann relation is approximately fulfilled and determine the Goldberger-Treiman discrepancy. Our final results are <math><msub><mi>g</mi><mi>A</mi></msub><mo>=</mo><mn>1.245</mn><mo>(</mo><mn>28</mn><mo>)</mo><mo>(</mo><mn>14</mn><mo>)</mo></math> for the nucleon axial charge, <math><mo>⟨</mo><msubsup><mi>r</mi><mi>A</mi><mn>2</mn></msubsup><mo>⟩</mo><mo>=</mo><mn>0.339</mn><mo>(</mo><mn>48</mn><mo>)</mo><mo>(</mo><mn>06</mn><mo>)</mo><msup><mtext>fm</mtext><mn>2</mn></msup></math> for the axial radius, <math><msub><mi>g</mi><mrow><mi>π</mi><mi>N</mi><mi>N</mi></mrow></msub><mo>≡</mo><munder><mo>lim</mo><mrow><msup><mi>Q</mi><mn>2</mn></msup><mo>→</mo><mo>−</mo><msubsup><mi>m</mi><mi>π</mi><mn>2</mn></msubsup></mrow></munder><msub><mi>G</mi><mrow><mi>π</mi><mi>N</mi><mi>N</mi></mrow></msub><mo>(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo><mo>=</mo><mn>13.25</mn><mo>(</mo><mn>67</mn><mo>)</mo><mo>(</mo><mn>69</mn><mo>)</mo></math> for the pion-nucleon coupling constant, and <math><msub><mi>G</mi><mi>P</mi></msub><mo>(</mo><mn>0.88</mn><msubsup><mi>m</mi><mi>μ</mi><mn>2</mn></msubsup><mo>)</mo><mo>≡</mo><msubsup><mi>g</mi><mi>P</mi><mo>*</mo></msubsup><mo>=</mo><mn>8.99</mn><mo>(</mo><mn>39</mn><mo>)</mo><mo>(</mo><mn>49</mn><mo>)</mo></math> for the induced pseudoscalar form factor at the muon capture point.

Giannis Koutsou

Nucleon axial and pseudoscalar form factors using twisted-mass fermion ensembles at the physical point

We investigate the low-lying baryon spectrum using three <math><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></math> ensembles simulated with physical values of the quark masses and lattice spacings of 0.080, 0.069 and 0.057 fm. The ensembles are generated using twisted mass clover-improved fermions and the Iwasaki gauge action. The spatial length is kept approximately the same at about 5.1 fm to 5.5 fm fulfilling the condition <math><msub><mi>m</mi><mi>π</mi></msub><mi>L</mi><mo>&gt;</mo><mn>3.6</mn></math>. We investigate isospin splitting within isospin multiples and verify that for most cases the isospin splitting for these lattice spacing is consistent with zero. In the couple of cases, for which there is a nonzero value, in the continuum limit, the mass splitting goes to zero. The baryon masses are extrapolated to the continuum limit using the three <math><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></math> ensembles and are compared to other recent lattice QCD results. For the strange and charm quark masses we find, respectively, <math><msub><mi>m</mi><mi>s</mi></msub><mo>(</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>)</mo><mo>=</mo><mn>99.2</mn><mo>(</mo><mn>2.7</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> and <math><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>3</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>)</mo><mo>=</mo><mn>1.015</mn><mo>(</mo><mn>39</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. The values predicted for the masses of the doubly charmed <math><msubsup><mi>Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>⋆</mo></msubsup></math>, <math><msub><mi>Ω</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> and <math><msubsup><mi>Ω</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>⋆</mo></msubsup></math> baryons are 3.676(55) GeV, 3.703(51) GeV and 3.803(50) GeV, respectively, and for the triply charmed <math><msub><mi>Ω</mi><mrow><mi>c</mi><mi>c</mi><mi>c</mi></mrow></msub></math> baryon is 4.785(71) GeV.

Georgios Christou

Low-lying baryon masses using twisted mass fermions ensembles at the physical pion mass

We calculate the double-virtual <math><mrow><mi>η</mi><mo>→</mo><msup><mrow><mi>γ</mi></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mi>γ</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> transition form factor <math><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>η</mi><mo>→</mo><msup><mrow><mi>γ</mi></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mi>γ</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></msub><mo>(</mo><msubsup><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></mrow></math> from first principles using a lattice QCD simulation with <math><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></math> quark flavors at the physical pion mass and at one lattice spacing and volume. The kinematic range covered by our calculation is complementary to the one accessible from experiment and is relevant for the <math><mi>η</mi></math>-pole contribution to the hadronic light-by-light scattering in the anomalous magnetic moment <math><msub><mi>a</mi><mi>μ</mi></msub><mo>=</mo><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><mo>)</mo><mo>/</mo><mn>2</mn></math> of the muon. From the form factor calculation we extract the partial decay width <math><mrow><mi>Γ</mi><mo>(</mo><mi>η</mi><mo>→</mo><mi>γ</mi><mi>γ</mi><mo>)</mo><mo>=</mo><mn>338</mn><mo>(</mo><mn>87</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mn>17</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>syst</mi></mrow></msub><mtext> </mtext><mtext> </mtext><mi>eV</mi></mrow></math> and the slope parameter <math><mrow><msub><mrow><mi>b</mi></mrow><mrow><mi>η</mi></mrow></msub><mo>=</mo><mn>1.34</mn><mo>(</mo><mn>28</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mn>14</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>syst</mi></mrow></msub><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></math>. For the <math><mi>η</mi></math>-pole contribution to <math><msub><mi>a</mi><mi>μ</mi></msub></math> we obtain <math><mrow><msubsup><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mi>η</mi><mtext>-pole</mtext></mrow></msubsup><mo>=</mo><mn>13.8</mn><mo>(</mo><mn>5.2</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mn>1.5</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>syst</mi></mrow></msub><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>11</mn></mrow></msup></mrow></math>.

Sebastian Burri

Andrew Gasbarro

Kyriakos Hadjiyiannakou

Karl Jansen

Gurtej Kanwar

Konstantin Ottnad

Ferenc Pittler

<math><mrow><mi>η</mi><mo>→</mo><msup><mrow><mi>γ</mi></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mi>γ</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> transition form factor and the hadronic light-by-light <math><mi>η</mi></math>-pole contribution to the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> from lattice QCD

We present a first-principles lattice QCD investigation of the <math><mi>R</mi></math> ratio between the <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> cross section into hadrons and into muons. By using the method of Ref. [1], that allows one to extract smeared spectral densities from Euclidean correlators, we compute the <math><mi>R</mi></math> ratio convoluted with Gaussian smearing kernels of widths of about 600 MeV and central energies from 220 MeV up to 2.5 GeV. Our theoretical results are compared with the corresponding quantities obtained by smearing the KNT19 compilation [2] of <math><mi>R</mi></math>-ratio experimental measurements with the same kernels and, by centering the Gaussians in the region around the <math><mi>ρ</mi></math>-resonance peak, a tension of about 3 standard deviations is observed. From the phenomenological perspective, we have not included yet in our calculation QED and strong isospin-breaking corrections, and this might affect the observed tension. From the methodological perspective, our calculation demonstrates that it is possible to study the <math><mi>R</mi></math> ratio in Gaussian energy bins on the lattice at the level of accuracy required in order to perform precision tests of the standard model.

Petros Dimopoulos

Probing the Energy-Smeared <math><mi>R</mi></math> Ratio Using Lattice QCD