Lattice Field Theory

The set-up of the QCD Schrödinger functional (SF) on the lattice with staggered quarks requires an even number of points L/a in the spatial directions, while the Euclidean time extent of the lattice, T /a, must be odd. Identifying a unique renormalisation scale, L = T , is then only possible up to O(a) lattice artefacts. In this article we study such lattices in the pure SU(3) gauge theory, where we can also compare to the standard set-up. We consider the SF coupling as obtained from the variation of an SU(3) Abelian and spatially constant background field. The O(a) lattice artefacts can be cancelled by the existing O(a) boundary counterterm. However, its coefficient, c t , differs at the tree-level from its standard value, so that one first needs to re-determine the induced background gauge field. The perturbative one-loop correction to the coupling allows to determine c t to one-loop order. A few numerical simulations serve to demonstrate that residual cutoff effects in the step scaling function are small in both cases, T = L ± a and comparable to the standard case with T = L. 1 For staggered quarks we here use the traditional term "flavour" rather than "taste".

In this report, we analyze the photon and gluon within the M o framework using the particle mass relation equation. By assigning both particles a parameter value of t =-ln(2), their calculated masses reduce exactly to zero, consistent with the Standard Model. This demonstrates that the M o framework naturally incorporates massless gauge bosons, while still unifying mass relations across massive fermions and bosons.

We describe new measurements of the inclusive and exclusive branching fractions for 2S transitions to J= using e e ÿ collision data collected with the CLEO detector operating at CESR. All branching fractions and ratios of branching fractions reported here represent either the most precise measurements to date or the first direct measurements. Indirectly and in combination with other CLEO measurements, we determine B cJ ! J= and B 2S ! light hadrons.

We explore gauge actions for lattice QCD, which are constructed such that the occurrence of small plaquette values is strongly suppressed. Such actions originate from the admissibility condition in order to conserve the topological charge. The suppression of small plaquette values is expected to be advantageous for numerical studies in the ε-regime and also for simulations with dynamical quarks. Performing simulations at a lattice spacing of about 0.1 fm, we present numerical results for the static potential, the physical scale r 0 , the stability of the topological charge history, the condition number of the kernel of the overlap operator and the acceptance rate against the step size in the local HMC algorithm.

Quantum Chromo Dynamics is considered in a setup where the light mesons are squeezed into unphysically small boxes. We show how such a situation can be used to determine the couplings of the low energy chiral Lagrangian from lattice simulations, applying chirally invariant formulations of lattice fermions.

We explore gauge actions for lattice QCD, which are constructed such that the occurrence of small plaquette values is strongly suppressed. By choosing strong bare gauge couplings we arrive at values for the physical lattice spacings of O(0.1 fm). Such gauge actions tend to confine the Monte Carlo history to a single topological sector. This topological stability facilitates the collection of a large set of configurations in a specific sector, which is profitable for numerical studies in the ǫ-regime. The suppression of small plaquette values is also expected to be favourable for simulations with dynamical quarks. We use a local Hybrid Monte Carlo algorithm to simulate such actions, and we present numerical results for the static potential, the physical scale, the topological stability and the kernel condition number of the overlap Dirac operator. In addition we discuss the question of reflection positivity for a class of such gauge actions.

We present simulation results employing overlap fermions for the axial correlation functions in the -regime of chiral perturbation theory. In this regime, finite size effects and topology play a dominant rôle. Their description by quenched chiral perturbation theory is compared to our numerical results in quenched QCD. We show that lattices with a linear extent L > 1.1 fm are necessary to interpret the numerical data obtained in distinct topological sectors in terms of the -expansion. Such lattices are, however, still substantially smaller than the ones needed in standard chiral perturbation theory. However, we also observe severe difficulties at very low values of the quark mass, in particular in the topologically trivial sector.

We discuss the eigenvalue distribution of the overlap Dirac operator in quenched QCD on lattices of size 8 4 , 10 4 and 12 4 at β = 5.85 and β = 6. We distinguish the topological sectors and study the distributions of the leading non-zero eigenvalues, which are stereographically mapped onto the imaginary axis. Thus they can be compared to the predictions of random matrix theory applied to the ǫ-expansion of chiral perturbation theory. We find a satisfactory agreement, if the physical volume exceeds about (1.2 fm) 4 . For the unfolded level spacing distribution we find an accurate agreement with the random matrix conjecture on all volumes that we considered.

We compare the behavior of overlap fermions, which are chirally invariant, and of Wilson twisted mass fermions at full twist in the approach to the chiral limit. Our quenched simulations reveal that with both formulations of lattice fermions pion masses of O(250 MeV) can be reached in practical applications. Our comparison is done at a fixed value of the lattice spacing a ≃ 0.123 fm. A number of quantities are measured such as hadron masses, pseudoscalar decay constants and quark masses obtained from Ward identities. We also determine the axial vector renormalization constants in the case of overlap fermions.

We provide a method for (i) performing deterministic imaginary time evolution and (ii) computing the thermal average of gauge-invariant models. We assess scalability on quantum computers, employing a circuit-based formulation. We validate our framework by numerical simulations of two-and three-particle chains. Results show that the method is correct within a finitetemperature regime and may be used to approximate groundstate energies.

We review recent results from studies of the dynamics of classical Yang-Mills fields on a lattice. We discuss the numerical techniques employed in solving the classical lattice Yang-Mills equations in real time, and present results exhibiting the universal chaotic behavior of nonabelian gauge theories. The complete spectrum of Lyapunov exponents is determined for the gauge group SU(2). We survey results obtained for the SU(3) gauge theory and other nonlinear field theories. We also discuss the relevance of these results to the problem of thermalization in gauge theories.

We determine numerically the full complex Lyapunov spectrum of SU(2) Yang-Mills fields on a 3-dimensional lattice from the classical chaotic dynamics using eigenvalues of the monodromy matrix. The microcanonical equation of state is determined as the entropy -energy relation utilizing the Kolmogorov-Sinai entropy extrapolated to the large size limit.

This paper presents a comprehensive and corrected analysis of two fundamental phenomena in modern physics: the Lamb Shift in hydrogen atoms and Einstein's quadrupole formula for gravitational wave luminosity.

This work systematically derives the accurate master equations governing these phenomena, provides detailed mathematical frameworks, and explores their experimental validations.

The Lamb Shift represents a cornerstone achievement in quantum electrodynamics (QED), demonstrating the influence of vacuum fluctuations on atomic spectra, while gravitational wave luminosity calculations have revolutionized our understanding of cosmic phenomena and enabled gravitational wave astronomy.

Through rigorous mathematical analysis and corrected numerical computations, this study elucidates the theoretical foundations underlying these pivotal discoveries in 20th and 21st-century physics.

The sPHENIX experiment at RHIC aims to precisely characterize the properties of the Quark-Gluon Plasma (QGP). The Standard Model describes this state as a deconfined soup of quarks and gluons. The Helix-Light-Vortex (HLV) theory offers an alternative interpretation: a geometric phase transition of the discrete, dodecahedral spacetime lattice itself. In this state, the localized resonances that constitute baryons "melt" into a delocalized, liquid-like phase of the fundamental Φ-field. This paper derives three unique, testable predictions from this model for the sPHENIX experiment.

It is popular to probe the structure of the QCD vacuum indirectly by studying individual fermion eigenmodes, because this provides a natural way to filter out UV fluctuations. The double-peaking in the distribution of the local chiral orientation parameter (X) has been offered as evidence, by some, in support of a particular model of the vacuum. Here we caution that the X-distribution peaking varies significantly with various versions of the definition of X. Furthermore, each distribution varies little from that resulting from a random reshuffling of the left-handed (and independently the right-handed) fields, which destroys any QCD-induced left-right correlation; that is, the double-peaking is mostly a phase-space effect. We propose a new universal definition of the X parameter whose distribution is uniform for randomly reshuffled fields. Any deviations from uniformity for actual data can then be directly attributable to QCD-induced dynamics. We find that the familiar double peak disappears.

The mass spectrum of baryons in the spin-3/2 sector is computed in quenched lattice QCD using a tadpole-improved anisotropic action. Both isospin 1/2 and 3/2 (the traditional decuplet) are considered, as well as members that contain strange quarks. States with positive and negative parities are isolated by parity projection, while states with spin-3/2 and spin-1/2 are separated by spin projection. The extent to which spin projection is needed is examined. The issue of optimal interpolating field is also investigated. The results are discussed in relation to previous calculations and experiment.

This report examines the hadronic energy in the framework of Mo-theory and its connection to the mass gap observed in pure Yang-Mills theory. Using Motheory's formulation of the Hagedorn energy, we show how the fundamental Mo parameter M o provides a natural scale for hadron formation and the emergence of the Yang-Mills mass gap.

We propose a lattice version of Chern-Simons gravity and show that the partition function coincides with Ponzano-Regge model and the action leads to the Chern-Simons gravity in the continuum limit. The action is explicitly constructed by lattice dreibein and spin connection and is shown to be invariant under lattice local Lorentz transformation and gauge diffeomorphism. The action includes the constraint which can be interpreted as a gauge fixing condition of the lattice gauge diffeomorphism.

We study the phase diagram of quark matter at finite temperature (T) and chemical potential () in the strong coupling limit of lattice QCD for color SU(3). We derive an analytical expression of the effective free energy as a function of T and , including baryon effects. The finite temperature effects are evaluated by integrating over the temporal link variable exactly in the Polyakov gauge with an antiperiodic boundary condition for fermions. The obtained phase diagram shows the first and the second order phase transition at low and high temperatures, respectively, and those are separated by the tricritical point in the chiral limit. Baryon has effects to reduce the effective free energy and to extend the hadron phase to a larger direction at low temperatures.

Supersymmetric lattice Ward-Takahashi identities are investigated perturbatively up to two-loop corrections for super doubler approach of N = 2 lattice Wess-Zumino models in 1-and 2-dimensions. In this approach notorious chiral fermion doublers are treated as physical particles and momentum conservation is modified in such a way that lattice Leibniz rule is satisfied. The two major difficulties to keep exact lattice supersymmetry are overcome. This formulation defines, however, nonlocal field theory. Nevertheless we confirm that exact supersymmetry on the lattice is realized for all supercharges at the quantum level. Delicate issues of associativity are also discussed.

Abelian gauge theories formulated on a space-time lattice can be used as a prototype for investigating the confinement mechanism. In U (1) lattice gauge theory it is possible to perform a dual transformation of the path integral. Simulating the obtained dual theory (which corresponds to a certain limit of a dual Higgs model) including external sources, we perform a very accurate analysis of flux tubes with respect to the dual superconductor picture. Dual flux tube simulations are also performed in the full Abelian Higgs model, in order to obtain non-perturbative control over quantum and string fluctuations, and for a comparison to the results of dual QCD.

Starting from the strong-coupling SU(2) Wilson action in D = 3 dimensions, we derive an effective, semi-local action on a lattice of spacing L times the spacing of the original lattice. It is shown that beyond the adjoint color-screening distance, i.e. for L ≥ 5, thin center vortices are stable saddlepoints of the corresponding effective action. Since the entropy of these stable objects exceeds their energy, center vortices percolate throughout the lattice, and confine color charge in half-integer representations of the SU(2) gauge group. This result contradicts the folklore that confinement in strong-coupling lattice gauge theory, for D > 2 dimensions, is simply due to plaquette disorder, as is the case in D = 2 dimensions. It also demonstrates explicitly how the emergence and stability of center vortices is related to the existence of color screening by gluon fields.

We compare U (1) lattice gauge theory to an effective model of Maxwell and London equations. In the effective model there is only one free parameter, the London penetration depth λ. It turns out that one can get good agreement between both models if one modifies the usual definition of magnetic monopole currents in U (1) lattice gauge theory. This comparison also shows that already at small distances fluctuations of the occuring string are important. Further, we investigate the β-dependence of the penetration depth and determine the suppression of the monopole condensate in flux tubes.

The dually transformed path integral of four-dimensional U (1) lattice gauge theory is used for the calculation of expectation values in the presence of external charges. Applying the dual simulation to flux tubes for charge distances up to around 20 lattice spacings, we find a deviation from the behaviour of a dual type-II superconductor in the London limit at large distances. The roughening of the flux tube agrees with the effective string picture of confinement. Further we show that finite temperature effects are negligible for time extents larger than the charge distance. Finally we analyze the different contributions to the total energy of the electromagnetic field. The parallel component of the magnetic field turns out to have the strongest influence on the deviation from the linear behaviour at small charge distances.

We investigate singly and doubly charged flux tubes in U (1) lattice gauge theory. By simulating the dually transformed path integral we are able to consider large flux tube lengths, low temperatures, and multiply charged systems without loss of numerical precision. We simulate flux tubes between static sources as well as periodically closed flux tubes, calculating flux tube profiles, the total field energy and the free energy. Our main results are that the string tension in both three and four dimensions scales proportionally to the charge -which is in contrast to previous lattice results -and that in four-dimensional U (1) there is an attractive interaction between flux tubes for β approaching the phase transition.

This study introduces a new theoretical framework called the "Theory of Nature," which unifies magnetism, electricity, and light under a single energy form termed "pothu." The theory posits unique properties, such as real-time energy transfer once electricity or light reaches its destination. It addresses fundamental questions about magnetic attraction, repulsion, field line formation, and the instantaneous nature of light and electricity post-transfer. Experimental implications and comparisons with classical physics are discussed, offering a novel perspective on energy interactions. • Why do magnets stick? • Why do magnetic poles repel each other? • Why is the magnetic field stronger in elongated regions? • Why do magnetic fields form lines? • Light takes time to reach its destination, but once it arrives, it operates in real time. The same applies to electricity.

This study introduces a new theoretical framework called the "Theory of Nature," which unifies magnetism, electricity, and light under a single energy form termed "pothu." The theory posits unique properties, such as real-time energy transfer once electricity or light reaches its destination. It addresses fundamental questions about magnetic attraction, repulsion, field line formation, and the instantaneous nature of light and electricity post-transfer. Experimental implications and comparisons with classical physics are discussed, offering a novel perspective on energy interactions. Key Questions • Why do magnets stick? • Why do magnetic poles repel each other? • Why is the magnetic field stronger in elongated regions? • Why do magnetic fields form lines? • Light takes time to reach its destination, but once it arrives, it operates in real time. The same applies to electricity.

We address the problems of fermions in light front QCD on a transverse lattice. We propose and numerically investigate different approaches of formulating fermions on the light front transverse lattice. In one approach we use forward and backward derivatives. There is no fermion doubling and the helicity flip term proportional to the fermion mass in the full light front QCD becomes an irrelevant term in the free field limit. In the second approach with symmetric derivative (which has been employed previously in the literature), doublers appear and their occurrence is due to the decoupling of even and odd lattice sites. We study their removal from the spectrum in two ways namely, light front staggered formulation and the Wilson fermion formulation. The numerical calculations in free field limit are carried out with both fixed and periodic boundary conditions on the transverse lattice and finite volume effects are studied. We find that an even-odd helicity flip symmetry on the light front transverse lattice is relevant for fermion doubling.

We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These states allow for the efficient computation of all local observables (e. g. energy) and include states with diverging correlation length and unbounded multi-particle entanglement. As a demonstration we apply our approach to the Ising model on 1D, 2D and 3D square-lattices. We also present generalizations to higher spins and continuous-variable systems, which allows for the investigation of lattice field theories.

The light-front holographic mapping of classical gravity in anti-de Sitter space, modified by a positive-sign dilaton background, leads to a nonperturbative effective coupling α AdS s (Q 2 ). It agrees with hadron physics data extracted from different observables, such as the effective charge defined by the Bjorken sum rule, as well as with the predictions of models with built-in confinement and lattice simulations. It also displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale ∼ 1 GeV. The resulting β function appears to capture the essential characteristics of the full β function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD. Commensurate scale relations relate observables to each other without scheme or scale ambiguity. In this paper we extrapolate these relations to the nonperturbative domain, thus extending the range of predictions based on α AdS s (Q 2 ).

In order to study the fate of mesons in thermal QCD at finite baryon chemical potential, we consider light mesonic correlation functions using the Taylor expansion to O((µ/T ) 2 ), in both the hadronic and quark-gluon plasma phases. We use the FASTSUM anisotropic fixed-scale lattices with N f = 2 + 1 flavours of Wilson fermion. We find that mesonic correlators are sensitive to finite-density corrections and that the second-order terms indicate the chiral crossover in the vector and axial-vector channels.

We study what happens to the N , ∆ and Ω baryons in the hadronic gas and the quark-gluon plasma, with particular interest in parity doubling and its emergence as the plasma is heated. This is done using simulations of lattice QCD, employing the FASTSUM anisotropic N f = 2 + 1 ensembles, with four temperatures below and four above the deconfinement transition temperature. Below T c we find that the positive-parity groundstate masses are largely temperature independent, whereas the negative-parity ones are reduced considerably as the temperature increases. This may be of interest for heavyion phenomenology. Close to the transition, the masses are nearly degenerate, in line with the expectation from chiral symmetry restoration. Above T c we find a clear signal of parity doubling in all three channels, with the effect of the heavier s quark visible.

Since distribution shifts are common in real-world applications, there is a pressing need to develop prediction models that are robust against such shifts. Existing frameworks, such as empirical risk minimization or distributionally robust optimization, either lack generalizability for unseen distributions or rely on postulated distance measures. Alternatively, causality offers a data-driven and structural perspective to robust predictions. However, the assumptions necessary for causal inference can be overly stringent, and the robustness offered by such causal models often lacks flexibility. In this paper, we focus on causality-oriented robustness and propose Distributional Robustness via Invariant Gradients (DRIG), a method that exploits general noise interventions in training data for robust predictions against unseen interventions, and naturally interpolates between in-distribution prediction and causality. In a linear setting, we prove that DRIG yields predictions that are robust among a data-dependent class of distribution shifts. Furthermore, we show that our framework includes anchor regression as a special case, and that it yields prediction models that protect against more diverse perturbations. We establish finite-sample results and extend our approach to semi-supervised domain adaptation to further improve prediction performance. Finally, we empirically validate our methods on synthetic simulations and on single-cell and intensive health care datasets.

A lattice study of the quenched QCD quark propagator in Landau and Coulomb gauges is reported. We find that m£ itical . the value of the quark propagator pole in the chiral limit, is 290 ± 20 MeV (/? = 5.7) and 350 ± 40 MeV (/? = 6.0). Scaling and gauge dependence of this quantity are discussed.

Spin asymmetries of semi-inclusive cross sections for the production of positively and negatively charged hadrons have been measured in deep-inelastic scattering of polarized positrons on polarized hydrogen and 3 He targets, in the kinematic range 0.023 < x < 0.6 and 1 GeV 2 < Q 2 < 10 GeV 2 . Polarized quark distributions are extracted as a function of x for up (u + ū) and down (d + d) flavors. The up quark polarization is positive and the down quark polarization is negative in the measured range. The polarization of the sea is compatible with zero. The first moments of the polarized quark distributions are presented. The isospin non-singlet combination ∆q3 is consistent with the prediction based on the Bjorken sum rule. The moments of the polarized quark distributions are compared to predictions based on SU(3) f flavor symmetry and to a prediction from lattice QCD.

By basing physics on a growing universe of bit strings generated by a simple recursive algorithm quantum mechanics, S-momentum conservation, the Lorentz transformations for quantum events, the conserved quantum numbers of the first -generation of the standard model for quarks and leptons and a flat space “big bang” cosmology can be constructed.

In this paper we outline a program for physics using as basic mathematics counting, binary arithmetic and randomness. We believe this approach makes sense because the discretization of physics has replaced arbitrary continuum stan- dards of time, length and mass by counting the oscillations of an atomic clock, counting the number of wavelengths between two positions and counting the num- ber of atoms in a macroscopic mass. These digital dimensional standards can be used to specify three dimensional constants: the limiting velocity c, the unit of action h, and either a reference mass (eg mp) or a coupling constant (eg G related to the mass scale by hc/(2nGm$ 21 1.7 X 1038). The objective of our program is to provide an algorithmic construction which allows us to relate this connection to specific laboratory paradigms. As in constructive mathematics, we hold that counting must be understood as the practice of mathematics in order to avoid redundancy. We allow no completed infinities a...

We present the first lattice QCD calculation with realistic sea quark content of the D + -meson decay constant f D + . We use the MILC Collaboration's publicly available ensembles of lattice gauge fields, which have a quark sea with two flavors (up and down) much lighter than a third (strange). We obtain f D + = 201 ± 3 ± 17 MeV, where the errors are statistical and a combination of systematic errors. We also obtain fD s = 249 ± 3 ± 16 MeV for the Ds meson.

We study the effects of dynamical quarks on the static quark potential at distances shorter than those where string breaking is expected. Quenched calculations and calculations with three flavors of dynamical quarks are done on sets of lattices with the lattice spacings matched within about one percent. The effect of the sea quarks on the shape of the potential is clearly visible. We investigate the consequences of these effects in a very crude model, namely solving Schroedinger's equation in the resulting potential. 11.15Ha,12.38.G

We have extended our program of QCD simulations with an improved Kogut-Susskind quark action to a smaller lattice spacing, approximately 0.09 fm. Also, the simulations with a ≈ 0.12 fm have been extended to smaller quark masses. In this paper we describe the new simulations and computations of the static quark potential and light hadron spectrum. These results give information about the remaining dependences on the lattice spacing. We examine the dependence of computed quantities on the spatial size of the lattice, on the numerical precision in the computations, and on the step size used in the numerical integrations. We examine the effects of autocorrelations in "simulation time" on the potential and spectrum. We see effects of decays, or coupling to two-meson states, in the 0 ++ , 1 + , and 0 -meson propagators, and we make a preliminary mass computation for a radially excited 0 -meson.

We present both spin-independent and -dependent parts of a central interquark potential for charmonium states, which is calculated in 2+1 flavor dynamical lattice QCD using the PACS-CS gauge configurations with a lattice cutoff of a -1 ≈ 2.2 GeV. Our simulations are performed with a relativistic heavy-quark action for the charm quark at the lightest pion mass, Mπ = 156(7) MeV, in a spatial volume of (3 fm) 3 . We observe that the spin-independent charmonium potential obtained from lattice QCD with almost physical quark masses is quite similar to the Cornell potential used in nonrelativistic potential models. The spin-spin potential, which is calculated in full lattice QCD for the first time, properly exhibits a finite-range repulsive interaction. Its r-dependence is different from the Fermi-Breit type potential, which is widely adopted in quark potential models. Recently, many of the newly discovered charmoniumlike mesons have been announced by B-factories at KEK and SLAC, which are primarily devoted to the physics of CP violation. Such states named as "XY Z" mesons could not be simply explained by a constituent quark description in quark potential models . Thus, the charmoniumlike XY Z mesons are expected to be good candidates for nonstandard quarkonium mesons such as hadronic molecular states, diquark-antidiquark bound states (tetraquark states) or hybrid mesons . However, it seems to be still too early to judge whether we may discard the constituent quark description for such higher-mass charmonium states.

We study the decays B → D ( * ) τ ντ in light of the available data from BABAR, Belle and LHCb. We divide our analysis into two parts: in one part we fit the form-factors in these decays directly from the data without adding any additional new physics (NP) contributions and compare our fit results with those available from the decays B → D ( * ) ν . We find that the q 2 -distributions of the formfactors associated with the pseudo-vector current, obtained from B → D ( * ) τ ντ and B → D ( * ) ν respectively, do not agree with each other, whereas the other form-factors are consistent with each other. In the next part of our analysis, we look for possible new effective operators of dimension 6 amongst new vector, scalar, and tensor-type that can best explain the current data in the decays B → D ( * ) τ ντ . We use the information-theoretic approaches, especially of 'Second-order Akaike Information Criterion' (AICc) in the analysis of empirical data. Normality tests for the distribution of residuals are done after selecting the best possible scenarios, for cross-validation. We find that it is the contribution from the operator involving left or right-handed vector current that passes all the selection criteria defined for the best-fit scenario and can successfully accommodate all the available data set.

We study the nucleon propagator at finite temperature in the framework of finite energy QCD sum rules. We find that the nucleon mass is approximately constant over a wide range of temperature, increasing sharply near the critical temperature for deconfinement T~. The coupling of the nucleon to quarks is a monotonically decreasing function of T, vanishing at T= To.

We illustrate why color deconfines when chiral symmetry is restored in gauge theories with quarks in the fundamental representation, and while these transitions do not need to coincide when quarks are in the adjoint representation, entanglement between them is still present.

Perturbative expansions of QCD observables in powers of α s are believed to be asymptotic and non-Borel summable due to the existence of singularities in the Borel plane (renormalons). This fact is connected with the factorization of scales (which is inherent to QCD and asymptotic freedom) and jeopardizes the convergence of the perturbative expansion and the accurate determination of power-suppressed corrections. This problem is more acute for physical systems composed by one or more heavy quarks. In lattice regulations, it reflects on the appearance of power-like divergences in the inverse of the lattice spacing for a series of quantities ( Λ, gluelump masses, the singlet and hybrid potentials, ...) making that the continuum limit can not be reached for them. Nevertheless, all these problems are solved within the framework of effective field theories with renormalon substraction. This allows us to obtain convergent perturbative series and to unambiguously define power corrections. In particular, one can connect with lattice results. Remarkably enough the dependence on the lattice spacing can be predicted by perturbation theory. This framework has been applied to the prediction of the gluelump masses and the singlet and octet (hybrid) potentials at short distances, as well as to their comparison with lattice simulations. Overall, very good agreement with data is obtained.

Boltzmann distributions over lattices are pervasive in Computational Physics. Sampling them becomes increasingly difficult with increasing lattice-size, especially near critical regions, e.g., phase transitions in statistical systems and continuum limits in lattice field theory. Machine learning-based methods, such as normalizing flows, have demonstrated the ability to alleviate these issues for small lattices. However, scaling to large lattices is a major challenge. We present a novel approach called Parallelizable Block Metropolis-within-Gibbs (PBMG) for generating samples for any lattice model. It factorizes the joint distribution of the lattice into local parametric kernels, thereby allowing efficient sampling of very large lattices. We validate our approach on the XY model and the Scalar ϕ 4 theory. PBMG achieves high acceptance rates and less correlated samples, and the observable statistics estimated from the samples match the ground truth. Moreover, PBMG significantly speeds up inference for large lattices as compared to HMC and plain MCMC algorithms.