Abstract In this paper, we compute the renormalization factors for the gluino and gluon fields, the gauge parameter, the coupling constant, as well as the scalar, pseudoscalar, and axial-vector gluino bilinear operators in $${\mathcal {N}} =1$$ N = 1 supersymmetric Yang–Mills (SYM) theory, using improved lattice actions. Our lattice formulation employs clover fermions, a Symanzik-improved gauge action, and stout-smeared links, which suppress ultraviolet fluctuations and thus enable more accurate determinations of renormalization factors. Our methodology involves computing gauge-variant two-point and three-point Green’s functions at one-loop order in lattice perturbation theory, in order to extract the multiplicative renormalization factors and the critical gluino mass. By analyzing lattice discretization effects on the axial current and their dependence on the stout-smearing and clover parameters, we identify a value of the smearing parameter that ensures axial-current conservation at one loop. The results presented in this work provide practical guidance for the fine-tuning procedures required to set up and calibrate lattice simulations of SYM.

We compute the electromagnetic form factors of the proton and neutron using lattice QCD. We employ Nf = 2 + 1 + 1 twisted mass clover-improved fermions with quark masses tuned to their physical values. Three ensembles with lattice spacings of a = 0.080 fm, 0.068 fm, and 0.057 fm and approximately the same physical volume allow us to obtain the continuum limit directly at the physical pion mass. For each ensemble, we use several values of the sink-source time separation, ranging from 0.5 to 1.5 fm, to allow for a thorough analysis of excited-state effects via multistate fits. The disconnected contributions are also analyzed using high statistics combined with techniques to mitigate stochastic noise in the estimation of the fermion loop. These techniques include low-mode deflation, dilution in the color and spin components, and hierarchical probing. We study the momentum-transfer dependence of the form factors using the z-expansion and dipole Ans & auml;tze, thereby enabling the extraction of the electric and magnetic radii and the magnetic moments, as well as the Zemach and Friar radii in the continuum limit. Results for the proton and neutron electric and magnetic mean square radii are p ffiffiffiffiffiffiffiffiffiffiffi p ffiffiffiffiffiffiffiffiffiffiffi (r2 E)n = -0.147(48) fm2, (r2 M)p = 0.870(53)(15) fm, and (r2M)n = 0.913(67)(19) fm, and for the proton and neutron magnetic moments, mu p = 2.849(92)(52) and mu n= -1.819(76)(29), respectively. In all cases, the first error is statistical, and the second is systematic, where the latter includes an estimate of the error from the fits to the momentum dependence of the form factors and from the continuum extrapolation.

In this paper we study a complete set of scalar and pseudoscalar four-quark operators, with a particular emphasis on their renormalization within a gauge-invariant renormalization scheme (GIRS). We focus on operators that do not mix with lower-dimensional operators by virtue of their transformation properties under the flavor-symmetry group. This class includes all Delta F = 2 operators, as well as their partners that transform under the same irreducible representations of the flavor group. These encompass a substantial subset of Delta F = 1 and Delta F = 0 operators. The present analysis provides a detailed classification of all four-quark operators, exploring their Fierz identities, symmetry properties, and mixing patterns. Different variants of GIRS are explored, including a "democratic" version that treats all mixing operators uniformly. For selected variants, which exhibit smaller mixing effects, we present the conversion matrices from GIRS to the MS scheme at next-to-leading order.

We present the strange electromagnetic form factors of the nucleon using lattice QCD with N_f=2+1+1 twisted mass clover-improved fermions and quark masses tuned to their physical values. Using four ensembles with lattice spacings of a=0.080 fm, 0.068 fm, 0.057 fm and 0.049 fm, and similar physical volume, we obtain the continuum limit directly at the physical pion mass. The disconnected strange contributions are computed using high statistics two-point functions combined with stochastic noise mitigation techniques, such as spin-color dilution and hierarchical probing in the estimation of the quark loop. From the momentum dependence of the form factors, we provide the strange electric and magnetic radii, as well as the strange magnetic moment in the continuum limit.

We present the nucleon strange electromagnetic form factors using four lattice QCD ensembles with N_f=2+1+1 twisted mass clover-improved fermions and quark masses tuned to approximately their physical values. The four ensembles have similar physical volume and lattice spacings of a=0.080 fm, 0.068 fm, 0.057 fm and 0.049 fm allowing us to take the continuum limit directly at the physical pion mass point. We compute nucleon three-point correlation functions with high statistics, where the disconnected fermion loops are evaluated stochastically with spin-color dilution and hierarchical probing. We find non-zero values for both electric and magnetic form factors. We extract the strange electric and magnetic radii, as well as the strange magnetic moment in the continuum limit by studying the momentum dependence of the form factors. We also compute the charm electromagnetic form factors within the same setup, which we find to be consistent with zero within the statistical precision of our data.

We present the strange electromagnetic form factors of the nucleon using lattice QCD simulations with degenerate light, a strange, and a charm quark in the sea with masses tuned to their physical values. For the first time, the strange electromagnetic form factors are computed at the continuum limit using only ensembles simulated with physical quark masses, eliminating the need for chiral extrapolations and their associated systematic uncertainty. We obtain the momentum transfer dependence of the form factors using the z-expansion and provide the strange electric and magnetic radii, as well as the strange magnetic moment. When combining our statistical errors and systematic uncertainties stemming from the momentum transfer dependence fit, our errors are an order of magnitude smaller than those associated with experimental determinations of the strange electromagnetic form factor.

Discretization artifacts proportional to the quark mass can limit the precision of strong-coupling determinations in lattice QCD, especially in the presence of heavy quarks. In this work, we perform a lattice perturbative analysis of such $\mathcal{O}(a m)$ effects in the running coupling by computing its two-loop renormalization factor $Z_g$. Using the background field method together with clover-improved Wilson fermions and Symanzik-improved gauge actions, we determine the mass-dependent components of the relevant two-point Green's functions and obtain the improvement coefficients needed to remove $\mathcal{O}(a m)$ artifacts in mass-independent renormalization schemes. Our results are presented for general values of the number of colors $N_c$, the number of quark flavors $N_f$, and the clover coefficient $c_{\mathrm sw}$, and satisfy all symmetry and consistency constraints. Numerical values are provided for widely used instances of the above gauge actions, allowing improved control of mass-related cutoff effects in high-precision determinations of the strong coupling constant from lattice QCD. Full derivations and extended numerical results can be found in Ref. [arXiv:2503.00463].

Nucleon Mellin moments of parton distribution are computed up to the fourth order in lattice QCD. The computation is performed using one ensemble of twisted mass fermions at the physical pion mass point. We employ boosted frames to access the higher-order Mellin moments of generalized parton distributions. We also extract the forward-limit Mellin moments ⟨ x^n-1⟩ for n=2,3,4. These Mellin moments are used to construct unpolarized parton distribution functions and compare to phenomenological extractions.

We determine the momentum fraction and angular momentum carried by quarks and gluons in the proton in lattice QCD. We use four ensembles simulated with up, down, strange and charm quarks with their masses tuned to their physical values. These ensembles have similar physical volume and different lattice spacings allowing us to take the continuum limit directly at the physical pion mass point. We extract the quark and gluon momentum fractions and total angular momentum in the continuum limit as well as the intrinsic quark spin and orbital angular momentum contributions to the proton spin. We find the total momentum fraction ⟨ x_N ⟩= 0.995(60)(29) and the total spin J_N = 0.507(43)(65), showing that both the momentum and spin sum rules are satisfied. We compare our results to those extracted from phenomenological analyses.

We present results on the Mellin moments of the unpolarized parton distribution function (PDF) of the pion and kaon up to the fourth order. The computation is done using one N_f=2+1+1 gauge ensemble of twisted mass fermions with quark masses tuned to approximately their physical values. We reconstruct the valence pion and kaon PDFs using the connected contributions to the three Mellin moments. We compare our results on the Mellin moments and the reconstructed PDFs with other lattice QCD and phenomenological determinations.

We evaluate the Collins-Soper kernel and the reduced soft function in lattice QCD, incorporating O(alpha s) matching corrections. The calculation relies on the evaluation of the quasitransverse momentum-dependent wave function with asymmetric staple-shaped quark bilinear operators and four-point meson form factors. These quantities are computed nonperturbatively using two Nf = 2 + 1 + 1 twisted-mass fermion ensembles with the same lattice spacing of a = 0.093 fm: the first ensemble has a lattice size of 243 & times; 48 and a pion mass of 346 MeV, and the second one has a lattice size of 323 & times; 64 and a pion mass of 261 MeV. The Collins-Soper kernel and the soft function are needed for the determination of the transverse momentum-dependent parton distribution functions.

We compute the matrix elements of the energy-momentum tensor of the nucleon using four ensembles of twisted mass clover-improved fermions with the up, down, strange and charm quark masses tuned to approximately their physical values. The four ensembles have similar physical volume and lattice spacings a=0.080 fm, 0.068 fm, 0.057 fm, and 0.049 fm, allowing us to take the continuum limit directly at the physical pion mass point. We compute both connected and disconnected quark contributions as well as gluon contributions. All renormalization functions, including the mixing of the quark singlet with the gluon, are determined non-perturbatively. We extract the gravitational form factors in the continuum limit at Q^2=0 and evaluate the contribution of quarks and gluons to the momentum and angular momentum of the proton. Using the values of the intrinsic quark spin computed using the same gauge ensembles we also determine the orbital angular momentum for each quark flavor.

We compute the electromagnetic form factors of the proton and neutron using lattice QCD. We employ N_f=2+1+1 twisted mass clover-improved fermions with quark masses tuned to their physical values. Three ensembles with lattice spacings of a=0.080 fm, 0.068 fm, and 0.057 fm, and approximately the same physical volume allow us to obtain the continuum limit directly at the physical pion mass. For each ensemble, we use several values of the sink-source time separation, ranging from 0.5 fm to 1.5 fm, to allow for a thorough analysis of excited state effects via multi-state fits. The disconnected contributions are also analyzed using high statistics combined with techniques to mitigate stochastic noise in the estimation of the fermion loop. These techniques include low-mode deflation, dilution in the color and spin components, and hierarchical probing. We study the momentum transfer dependence of the form factors using the z-expansion and dipole Ansätze, thereby enabling the extraction of the electric and magnetic radii and the magnetic moments, as well as the Zemach and Friar radii in the continuum limit. Results for the proton and neutron electric and magnetic mean square radii are √(⟨ r_E^2⟩^p) = 0.860(38)(23) fm, ⟨ r_E^2⟩^n = -0.147(48) fm^2, √(⟨ r_M^2⟩^p) = 0.870(53)(15) fm and √(⟨ r_M^2⟩^n) = 0.913(67)(19) fm, and for the proton and neutron magnetic moments μ^p=2.849(92)(52) and μ^n=-1.819(76)(29), respectively. In all cases, the first error is statistical and the second systematic, where the latter includes an estimate of the error from the fits to the momentum dependence of the form factors and from the continuum extrapolation.

We determine the nucleon axial, scalar, and tensor charges and the nucleon sigma-terms using twisted mass fermions. We employ three ensembles with approximately equal physical volume of about 5.5 fm, three values of the lattice spacing, approximately 0.06, 0.07, and 0.08 fm, and with the mass of the degenerate up and down, strange and charm quarks tuned to approximately their physical values. We compute both isovector and isoscalar charges and sigma-terms and their flavor decomposition including the disconnected contributions. We use the Akaike information criterion to evaluate systematic errors due to excited states and the continuum extrapolation. For the nucleon isovector axial charge we find gu-dA = 1.250(24), in agreement with the experimental value. Moreover, we extract the nucleon sigma-terms and find for the light quark content sigma pi N = 41.9(8.1) MeV and for the strange sigma s = 30(17) MeV.

We present the perturbative results of the discretization errors proportional to the quark mass [O(am)] on the QCD running coupling within lattice perturbation theory. Our analysis involves calculating the twoloop renormalization factor Z(g) using improved lattice actions for the SU(N-c) gauge group and Nf multiplets of fermions with a finite quark mass. We employ the background field method to compute Zg, by calculating quantum corrections on both the background and quantum gluon propagator, respecting the O(a) improvement. This allows us to evaluate the perturbative OoamTHORN lattice errors which affect the determination of the running coupling. Eliminating these O(am) effects is crucial for the nonperturbative studies of precision determinations of the strong coupling constant using lattice field theory.

We compute the electromagnetic form factors of the proton and neutron using lattice QCD with $N_f = 2 + 1 + 1$ twisted mass clover-improved fermions and quark masses tuned to their physical values. Three ensembles with lattice spacings of $a$=0.080 fm, 0.068 fm, and 0.057 fm, and approximately the same physical volume allow us to obtain the continuum limit directly at the physical pion mass. Several values of the source-sink time separation ranging from 0.5 fm to 1.5 fm are used, enabling a thorough analysis of excited state effects via multi-state fits. The disconnected contributions are analyzed using high statistics for the two-point functions combined with low-mode deflation and hierarchical probing for the fermion loop estimation. We study the momentum dependence of the form factors using the z-expansion and dipole Ansaetze, thereby enabling the extraction of the electric and magnetic radii, as well as the magnetic moments in the continuum limit, for which we provide preliminary results.

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 N_{f}=2+1+1 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 MS[over ¯] 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.

In this study, we explore the renormalization of a comprehensive set of gauge-invariant gluon nonlocal operators on the lattice. We calculate the renormalization factors for these operators in the modified Minimal Subtraction $(\rm \overline{MS})$ scheme up to one-loop, using both dimensional and lattice regularizations in the Wilson gluon action. To facilitate a non-perturbative renormalization approach, we examine an appropriate version of the modified regularization-invariant (${\rm RI}'$) scheme and determine the conversion factors from this scheme to $\rm \overline{MS}$. As an integral part of this procedure, by employing symmetry arguments on the lattice, we identify the mixing pattern of these operators under renormalization.

We present the isovector axial, induced pseudoscalar, and pseudoscalar form factors of the nucleon using three twisted-mass fermion ensembles with degenerate up- and down-, strange-, and charm-quarks with masses tuned to their physical values (physical point). The three ensembles have lattice spacing $a$=0.08, 0.068, and 0.057 fm and approximately equal physical volume allowing for the continuum limit to be taken at the physical point. Excited-state contributions to the matrix elements are evaluated using several sink-source separations from 0.5 fm to 1.5 fm and multistate fits. We check the partially conserved axial-vector current (PCAC) hypothesis and the pion pole dominance (PPD) and show that in the continuum limit both relations are satisfied. We provide results at the continuum limit for the isovector nucleon axial charge, axial radius, pion-nucleon coupling constant, and for the induced pseudoscalar form factor at the muon capture point.

We determine the nucleon axial, scalar and tensor charges at the continuum limit by analyzing three N_f=2+1+1 twisted mass fermion ensembles with all quark masses tuned to approximately their physical values. We include all contributions from valence and sea quarks. We use the Akaike Information Criterion to evaluate systematic errors due to excited states and the continuum extrapolation. For the nucleon isovector axial charge we find g_A^u-d=1.250(24), in agreement with the experimental value. We compute the axial, tensor and scalar charges for each quark flavor. The axial charge provides crucial information on the intrinsic spin carried by quark in the nucleon and the the latter two provide input for experimental searches of physics beyond the standard model. Moreover, we extract the nucleon σ-terms and find σ_π N=41.9(8.1) MeV, for the strange σ_s=30(17) MeV and for the charm σ_c=82(29) MeV. We also present preliminary results on the isovector quantities using a fourth ensemble at smaller lattice spacing.