We determine within lattice QCD the nucleon spin carried by valence and sea quarks and gluons. The calculation is performed using an ensemble of gauge configurations with two degenerate light quarks ...with mass fixed to approximately reproduce the physical pion mass. We find that the total angular momentum carried by the quarks in the nucleon is J_{u+d+s}=0.408(61)_{stat}(48)_{syst} and the gluon contribution is J_{g}=0.133(11)_{stat}(14)_{syst}, giving a total of J_{N}=0.54(6)_{stat}(5)_{syst} that is consistent with the spin sum. For the quark intrinsic spin contribution, we obtain 1/2ΔΣ_{u+d+s}=0.201(17)_{stat}(5)_{syst}. All quantities are given in the modified minimal subtraction scheme at 2 GeV. The quark and gluon momentum fractions are also computed and add up to ⟨x⟩_{u+d+s}+⟨x⟩_{g}=0.804(121)_{stat}(95)_{syst}+0.267(12)_{stat}(10)_{syst}=1.07(12)_{stat}(10)_{syst}, thus satisfying the momentum sum.
AbstractYielding can be emulated in a structural system by adding an adaptive negative stiffness device (NSD) and shifting the yielding away from the main structural system, leading to the new idea ...of apparent weakening that occurs, ensuring structural stability at all displacement amplitudes. This is achieved through an adaptive negative stiffness system (ANSS), a combination of NSD and a viscous damper. By engaging the NSD at an appropriate displacement (apparent yield displacement that is well below the actual yield displacement of the structural system) the composite structure-device assembly behaves like a yielding structure. The combined NSD-structure system presented in this study has a recentering mechanism that avoids permanent deformation in the composite structure-device assembly unless the main structure itself yields. Essentially, a yielding-structure is mimicked with no, or with minimal, permanent deformation or yielding in the main structure. As a result, the main structural system suffers less acceleration, less displacement, and less base shear, while the ANSS absorbs these effects. This paper presents comprehensive details on development and study of the ANSS/NSD. Through numerical simulations, the effectiveness and the superior performance of the ANSS/NSD as compared with a structural system with supplemental passive dampers is presented. A companion paper presents the NSD and its mechanics in detail.
AbstractStructural weakening and addition of damping is an approach previously proposed for the reduction of seismic forces and drifts in the retrofit of structures. It is also used in the design of ...new buildings with damping systems. While this approach is efficient, it does not significantly reduce and may even amplify inelastic excursions and permanent deformations of the structural system during a seismic event. This paper describes a negative stiffness device (NSD) that can emulate weakening of the structural system without inelastic excursions and permanent deformations. The NSD simulates yielding by engaging at a prescribed displacement and by applying a force at its installation level that opposes the structural restoring force. The NSD consists of (a) a self-contained highly compressed spring in a double negative stiffness magnification mechanism; and (b) a gap spring assembly (GSA) mechanism which delays the engagement of negative stiffness until the structural system undergoes a prescribed displacement. The NSD employs double chevron braces that self-contain the large vertical forces needed for the development of the horizontal negative stiffness without transferring these forces to the structure. This paper reports the development and operation of the NSD and presents analytical and computational tools that describe the behavior of the device. The principles of global control of structures using the NSD are presented in a companion paper. Additional papers present the results of testing of the device, and the results of analytical and experimental studies on the application of the device in a three-story conventional structure and a three-story seismically isolated structure.
We evaluate the light, strange, and charm scalar content of the nucleon using one lattice QCD ensemble generated with two degenerate light quarks with mass fixed to their physical value. We use ...improved techniques to evaluate the disconnected quark loops to sufficient accuracy to determine the strange and charm nucleon σ terms in addition to the light quark content σ_{πN}. We find σ_{πN}=37.2(2.6)(4.7/2.9) MeV, σ_{s}=41.1(8.2)(7.8/5.8) MeV, and σ_{c}=79(21)(12/8) MeV, where the first error is statistical and the second is the systematic error due to the determination of the lattice spacing, the assessment of finite volume, and residual excited state effects.
We determine the nucleon axial, scalar and tensor charges within lattice quantum chromodynamics including all contributions from valence and sea quarks. We analyze three gauge ensembles simulated ...within the twisted mass formulation at approximately physical value of the pion mass. Two of these ensembles are simulated with two dynamical light quarks and lattice spacing a = 0.094 fm and the third with a = 0.08 fm includes in addition the strange and charm quarks in the sea. After comparing the results among these three ensembles, we quote as final values our most accurate analysis using the latter ensemble. For the nucleon isovector axial charge we find 1.286(23) in agreement with the experimental value. We provide the flavor decomposition of the intrinsic spin 1/2 ΔΣq carried by quarks in the nucleon obtaining for the up, down, strange and charm quarks 1/2 ΔΣu = 0.431 (8), 1/2 ΔΣd = − 0.212 (8) , 1/2 ΔΣs = − 0.023 (4) and 1/2 ΔΣc = − 0.005 (2) , respectively. The corresponding values of the tensor and scalar charges for each quark flavor are also evaluated providing valuable input for experimental searches for beyond the standard model physics. In addition, we extract the nucleon σ -terms and find for the light quark content σπN = 41.6 (3.8) MeV and for the strange σs = 45.6 (6.2) MeV . The y-parameter that is used in phenomenological studies we find y = 0.078 (7) .
We present results for the nucleon electromagnetic form factors using an ensemble of maximally twisted mass clover-improved fermions with pion mass of about 130 MeV. We use multiple sink-source ...separations and three analysis methods to probe ground-state dominance. We evaluate both the connected and disconnected contributions to the nucleon matrix elements. We find that the disconnected quark loop contributions to the isoscalar matrix elements are small, giving an upper bound of up to 2% of the connected and smaller than its statistical error. We present results for the isovector and isoscalar electric and magnetic Sachs form factors and the corresponding proton and neutron form factors. By fitting the momentum dependence of the form factors to a dipole form or to the z expansion, we extract the nucleon electric and magnetic radii, as well as the magnetic moment. We compare our results to experiment as well as to other recent lattice QCD calculations.
We present results on the nucleon axial and induced pseudoscalar form factors using an ensemble of two degenerate twisted mass clover-improved fermions with mass yielding a pion mass of mπ=130 MeV. ...We evaluate the isovector and the isoscalar, as well as the strange and the charm axial form factors. The disconnected contributions are evaluated using recently developed methods that include deflation of the lower eigenstates, allowing us to extract the isoscalar, strange, and charm axial form factors. We find that the disconnected quark loop contributions are nonzero and particularly large for the induced pseudoscalar form factor.
We present the first Monte Carlo based global QCD analysis of spin-averaged and spin-dependent parton distribution functions (PDFs) that includes nucleon isovector matrix elements in coordinate space ...from lattice QCD. We investigate the degree of universality of the extracted PDFs when the lattice and experimental data are treated under the same conditions within the Bayesian likelihood analysis. For the unpolarized sector, we find rather weak constraints from the current lattice data on the phenomenological PDFs, and difficulties in describing the lattice matrix elements at large spatial distances. In contrast, for the polarized PDFs we find good agreement between experiment and lattice data, with the latter providing significant constraints on the spin-dependent isovector quark and antiquark distributions.
The neutron is a cornerstone in our depiction of the visible universe. Despite the neutron zero-net electric charge, the asymmetric distribution of the positively- (up) and negatively-charged (down) ...quarks, a result of the complex quark-gluon dynamics, lead to a negative value for its squared charge radius, Formula: see text. The precise measurement of the neutron's charge radius thus emerges as an essential part of unraveling its structure. Here we report on a Formula: see text measurement, based on the extraction of the neutron electric form factor, Formula: see text, at low four-momentum transfer squared (Q
) by exploiting the long known connection between the N → Δ quadrupole transitions and the neutron electric form factor. Our result, Formula: see text, addresses long standing unresolved discrepancies in the Formula: see text determination. The dynamics of the strong nuclear force can be viewed through the precise picture of the neutron's constituent distributions that result into the non-zero Formula: see text value.
We present results on the light, strange and charm nucleon scalar and tensor charges from lattice QCD, using simulations with Nf=2 flavors of twisted mass clover-improved fermions with a physical ...value of the pion mass. Both connected and disconnected contributions are included, enabling us to extract the isoscalar, strange and charm charges for the first time directly at the physical point. Furthermore, the renormalization is computed nonperturbatively for both isovector and isoscalar quantities. We investigate excited state effects by analyzing several sink-source time separations and by employing a set of methods to probe ground state dominance. Our final results for the scalar charges are gSu=5.20(42)(15)(12), gSd=4.27(26)(15)(12), gSs=0.33(7)(1)(4), and gSc=0.062(13)(3)(5) and for the tensor charges gTu=0.794(16)(2)(13), gTd=−0.210(10)(2)(13), gTs=0.00032(24)(0), and gTc=0.00062(85)(0) in the MS¯ scheme at 2 GeV. The first error is statistical, the second is the systematic error due to the renormalization and the third the systematic arising from estimating the contamination due to the excited states, when our data are precise enough to probe the first excited state.
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