Numerical analytic continuation arises frequently in lattice field theory, particularly in spectroscopy problems. This work shows the equivalence of common spectroscopic problems to certain classes of moment problems that have been studied thoroughly in the mathematical literature. Mathematical results due to Kovalishina enable rigorous bounds on smeared matrix-valued spectral functions, which are implemented numerically for the first time. The required input is a positive-definite matrix of Euclidean-time correlation functions; such matrices are routinely computed in variational spectrum studies using lattice quantum chromodynamics. This work connects the moment-problem perspective to recent developments using the Rayleigh--Ritz method and Lanczos algorithm. Possible limitations due to finite numerical precision are discussed.

Neutrinoless double-beta ($0\nu\beta\beta$) decays provide an excellent probe for determining whether neutrinos are Dirac or Majorana fermions. The short-range matrix elements associated with the $\pi^- \to \pi^+ ee$ process contribute at leading order in the $0\nu\beta\beta$ decay channel $nn \to ppee$ through pion exchange between nucleons. However, current lattice calculations show notable discrepancies in predicting these short-range contributions. To address this issue, we perform a lattice QCD calculation of the $\pi^- \to \pi^+ ee$ matrix elements using domain wall fermion ensembles at the physical pion mass generated by the RBC and UKQCD Collaborations. To mitigate contamination from around-the-world effects, we develop a new method to reconstruct and subtract them directly from lattice data. We then perform a nonperturbative renormalization using the RI/SMOM scheme. Compared with previous studies, this work reduces the uncertainties in the matrix elements and provides an independent cross-check that helps to reconcile the discrepancies among previous lattice calculations.

Higher rank gauge theories are generalizations of electromagnetism where, in addition to overall charge conservation, there is also conservation of higher rank multipoles such as the total dipole moment. In this work we study a four dimensional lattice tensor gauge theory coupled to bosonic matter which has second rank tensor electric and magnetic fields and charge conservation on individual planes. Starting from the Hamiltonian, we derive the lattice action for the gauge fields coupled to $q=1,2$ charged scalars. We use the action formulation to carry out Monte Carlo simulations to map the phase diagram as a function of the gauge ($\beta$) and matter ($\kappa$) couplings. We compute the nature of correlators at strong and weak coupling in the pure gauge theory and compare the results to numerical simulations. Simulations show that the naive weak coupling regime (small $\kappa$, large $\beta$) does not survive in the thermodynamic limit. Instead, the strong coupling confined phase, spans the whole phase diagram. It is a proliferation of instantons that destroys the weak coupling phase and we show, via a duality transformation, that the expected strong confinement is present in the analog of Wilson line correlators. For finite matter coupling at $q=1$ we find a single thermodynamic phase albeit with a first order phase transition terminating in a critical this http URL $q=2$ it is known that the the X-cube model with $\mathbb{Z}_2$ fractonic topological order is recovered deep in the Higgs regime. The simulations indeed reveal a distinct Higgs phase in this case.

We calculate the nucleon mass within a manifestly relativistic formulation of baryon chiral perturbation theory (BChPT), extending the framework to leading two-loop order ($\mathcal{O}(p^5)$). By employing dimensional counting analysis and rigorously verifying the extended on-mass-shell scheme at this order, we obtain a complete chiral representation of the nucleon mass that preserves analyticity, respects proper power counting, and maintains renormalization-scale independence. The resulting expression exhibits excellent convergence, with $\mathcal{O}(p^5)$ contributions remaining small ($\sim 8~\rm{MeV}$). This formulation provides a robust foundation for chiral extrapolation, demonstrating remarkable agreement with lattice QCD data across a wide range of pion masses ($M_\pi \lesssim 300~\rm{MeV}$). The success of this calculation establishes two-loop relativistic BChPT as a precision tool for studying nucleon structure and related properties.

The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is an efficient and versatile algorithm that simultaneously mitigates both the sign problem and the ergodicity problem -- the latter being intrinsic to algorithms based on Lefschetz thimbles. We consider a situation in which the maximum flow time can be set to a small value, as occurs when WV-HMC is applied to the doped Hubbard model using a nonphysical redundant parameter. An optimal choice of this parameter significantly reduces the sign problem on the original integration surface and allows the maximum flow time to remain small, a feature that facilitates increasing the system size while keeping the computation time modest. However, as the worldvolume becomes a thin layer, it becomes increasingly difficult to explore it efficiently, leading to potential ergodicity issues. To overcome this limitation, we propose embedding the Generalized-thimble HMC (GT-HMC) into the WV-HMC framework. GT-HMC performs HMC updates on a deformed surface at a fixed flow time. Although it suffers from ergodicity issues due to infinitely high potential barriers at the zeros of the Boltzmann weight, it enables more efficient exploration within the allowed region. Furthermore, its molecular dynamics step size can typically be taken to be larger than in WV-HMC. GT-HMC is thus better suited for sampling regions where ergodicity issues are not serious. We provide a proof that GT-HMC can be embedded within the WV-HMC algorithm, and verify that the two methods -- the pure WV-HMC and the combined version -- yield consistent results within statistical errors for the two-dimensional doped Hubbard model on a $6 \times 6$ spatial lattice at $T/\kappa = 1/6.4\simeq 0.156$ and $U/\kappa = 8.0$ with Trotter number $N_t = 20$ ($\kappa$: hopping parameter).

We numerically investigate the multicritical behavior of the three dimensional lattice system in which a SU(2) gauge field is coupled to two flavors of scalar fields transforming in the fundamental representation of the gauge group. In this system a multicritical point is present, where the global symmetry O(2)$\oplus$O(3) gets enlarged to O(5). Such a symmetry enlargement is hindered for generic systems by the instability of the O(5) multicritical point, but the SU(2) gauge symmetry prevents the appearance of the term triggering the instability. All the numerical results obtained in this lattice gauge model fully support the expectations coming from the O(2)$\oplus$O(3) multicritical Landau-Ginzburg-Wilson $\phi^4$ theory, and we discuss possible implications of these results for some models of deconfined quantum criticality.

We bootstrap the leading order hadronic contribution to $a_\mu$ using unitarity, analytic properties, crossing symmetry and finite energy sum rules (FESR) from quantum chromodynamics (QCD), establishing a lower bound. Combining this lower bound with the remaining precisely calculated contributions from quantum electrodynamics and electroweak interactions, we achieve a lower bound on muon anomaly $a_\mu$. Since the FESRs have uncertainties, our bound depends on the choices of FESRs within these uncertainties. A conservative choice of the FESR gives a conservative lower bound, consistent with Standard Model (SM) data-driven prediction. We show that there are other valid choices of FESRs within the uncertainties that lead to lower bounds, which are inconsistent with SM data-driven prediction but consistent with the measured values of the muon anomaly. The bootstrapped spectral density shows a $\rho$-resonance peak similar to experimental hadronic cross-ratio data, providing a bootstrap prediction for $\rho$-meson mass.

We investigate the charmed meson spectrum using a constituent quark model (CQM) with one-loop corrections applied to the one-gluon exchange (OGE) potential. The study aims to understand if the modified version of our CQM sufficiently account for the charmed meson spectrum observed experimentally, without invoking exotic quark and gluon configurations such as hybrid mesons or tetraquarks. Within this model, charmed mesons' masses are computed, comparing theoretical predictions to experimental data. The results, within uncertainties, suggest that our theoretical framework generally reproduces mass splittings and level ordering observed for charmed mesons. Particularly, large discrepancies between theory and experiment found in $P$-wave states are, at least, significantly ameliorated by incorporating higher-order interaction terms. Therefore, the findings emphasize that while the traditional quark model is limited in fully describing charmed mesons, enhanced potential terms may bridge the gap with experimental observations. The study contributes a framework for predicting excited charmed meson states for future experimental validation.

The charm quark density-density correlation is calculated for $1S$ and $1P$ conventional charmonia and $J^{PC}=1^{-+},0^{+-}$ charmoniumlike states from lattice QCD and are interpreted as spatial wave functions of these states with some approximations. The angular distributions of $c\bar{c}$ in conventional charmonia are found to be in accordance with the expectation of two-body systems, while that of the $1^{-+}$ state exhibits an $S$-wave feature. However, the $c\bar{c}$ radial distributions turn out to be strikingly different from the non-relativistic quark model and can be understood by the Dirac theory of two-body bound states. These results provide the first gauge invariant and model-independent three-dimensional portraits of charmonium(like) states.

In this talk, I revisit and present a more comprehensive estimate of the lowest order Hadronic Vacuum Polarization (HVP) contribution $a_\mu\vert_{hvp}^{lo}$ to the muon anomalous magnetic moment (muon anomaly) from $e^+e^-\to$ Hadrons obtained recently in Ref.[1]. New CMD-3 data on $e^+e^-\to 2\pi$ [2] and precise BABAR [3] and recent BELLE2 [4] $e^+e^-\to 3\pi$ data are usedto update the estimate of the $I=0$ isoscalar channel below the $\phi$-meson mass. Adding the data compiled by PDG22 [5] above 1 GeV and the QCD improved continuum used in Ref. [1], one deduces: $a_\mu\vert^{hvp}_{lo}=(7043\pm 37)\times 10^{-11} $.A comparison with previous data driven ($e^+e^-$ and $\tau$-decays) estimates is this http URL the Higher Order $a_\mu\vert_{hvp}^{ho}$ corrections, the phenomenological estimate of the Hadronic Light by Light scattering up to NLO and the QED and Electroweak (EW) contributions, one obtains: $\Delta a_\mu^{pheno}\equiv a_\mu^{exp}-a_{\mu}^{pheno}= (81\pm 41)\times 10^{-11}$ where the recent experimental value $a_\mu^{exp}$ [6] has been used. This result consolidates the previous one in Ref.[1], after adding the $\pi^0\gamma,\eta\gamma$ contributions, and can be compared with the one from the most precise Lattice result $\Delta a_\mu^{lattice}= (90\pm 56)\times 10^{-11}$. Then, we deduce the (tentative) SM prediction average : $\Delta a_\mu^{SM} = (87\pm 33)\times 10^{-11}$. We complete the paper by revising our predictions on the LO HVP contributions in adding the $\pi^0\gamma,\eta\gamma$ contributions to the ones in Ref.[1]. Then, we obtain: $a_\tau\vert^{hvp}_{lo}=(3516\pm 25)\times 10^{-11} $ and $\Delta \alpha^{(5)}_{had}(M_Z^2)=(2770.7\pm 4.5)\times 10^{-5}$ for 5 flavours.