Collinear Factorization at Subasymptotic Kinematics and Validation in a Diquark Spectator Model

We revisit the derivation of collinear factorization for Deep Inelastic Scattering at subasymptotic values of the four-momentum transfer squared, where the masses of the particles participating in the interaction cannot be neglected. By using an inclusive jet function to describe the scattered quark final state, we can restrict the needed parton kinematic approximations just to the four-momentum conservation of the hard scattering process, and explicitly expand the rest of the diagram in powers of the unobserved parton transverse momenta rather than neglecting those. This procedure provides one with more flexibility in fixing the virtuality of the scattered and recoiling partons than in the standard derivation, and naturally leads to scaling variables that more faithfully represent the partonic kinematic at subasymptotic energy than the Bjorken’s ᵡB variable. We then verify the validity of the obtained factorization formula by considering a diquark spectator model designed to reproduce the main features of electron-proton scattering at large ᵡB in Quantum Chromodynamics. In the model, the Deep Inelastic Scattering contribution to the cross section can be explicitly isolated and analytically calculated, then compared to the factorized approximation. Limiting ourselves to the leading twist contribution, we then show that use of the new scaling variables maximizes the kinematic range of validity of collinear factorization, and highlight the intrinsic limitations of this approach due to the unavoidably approximate treatment of four-momentum conservation in factorized diagrams. Finally, we briefly discuss how these limitations may be overcome by including higher-twist corrections to the factorized calculation

Prospects For ** → Via Lattice QCD

The ** → scattering amplitude plays a key role in a wide range of phenomena, including understanding the inner structure of scalar resonances as well as constraining the hadronic contributions to the anomalous magnetic moment of the muon. In this work, we explain how the infinite-volume Minkowski amplitude can be constrained from finite-volume Euclidean correlation functions. The relationship between the finite-volume Euclidean correlation functions and the desired amplitude holds up to energies where 3 states can go on shell, and is exact up to exponentially small corrections that scale like (e−mL), where L is the spatial extent of the cubic volume and m is the pion mass. In order to implement this formalism and remove all power-law finite volume errors, it is necessary to first obtain →, ⋆→, ⋆→, and ⋆→ amplitudes; all of which can be determined via lattice quantum chromodynamic calculations

The role of boundary conditions in quantum computations of scattering observables

Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. This would give access to Minkowski-signature correlators, in contrast to the Euclidean calculations routinely performed at present. However, as with present-day calculations, quantum computation strategies still require the restriction to a finite system size, including a finite, usually periodic, spatial volume. In this work, we investigate the consequences of this in the extraction of hadronic and Compton-like scattering amplitudes. Using the framework presented in Phys. Rev. D101 014509 (2020), we quantify the volume effects for various $1+1$D Minkowski-signature quantities and show that these can be a significant source of systematic uncertainty, even for volumes that are very large by the standards of present-day Euclidean calculations. We then present an improvement strategy, based in the fact that the finite volume has a reduced symmetry. This implies that kinematic points, which yield the same Lorentz invariants, may still be physically distinct in the finite-volume system. As we demonstrate, both numerically and analytically, averaging over such sets can significantly suppress the unwanted volume distortions and improve the extraction of the physical scattering amplitudes.Comment: 18 pages, 7 figure

PDFs in small boxes

PDFs can be studied directly using lattice QCD by evaluating matrix elements of non-local operators. A number of groups are pursuing numerical calculations and investigating possible systematic uncertainties. One systematic that has received less attention is the effect of calculating in a finite spacetime volume. Here we present first attempts to assess the role of the finite volume for spatially non-local operators. We find that these matrix elements may suffer from large finite-volume artifacts and more careful investigation is needed.Comment: 6 pages, 3 figures, Conference: The 36th Annual International Symposium on Lattice Field Theory - LATTICE2018, 22-28 July, 2018, Michigan State University, East Lansing, Michigan, US

Role of Boundary Conditions in Quantum Computations of Scattering Observables

Quantum computing may offer the opportunity to simulate strongly interacting field theories, such as quantum chromodynamics, with physical time evolution. This would give access to Minkowski-signature correlators, in contrast to the Euclidean calculations routinely performed at present. However, as with present-day calculations, quantum computation strategies still require the restriction to a finite system size, including a finite, usually periodic, spatial volume. In this work, we investigate the consequences of this in the extraction of hadronic and Compton-like scattering amplitudes. Using the framework presented in Briceno et al. [Phys. Rev. D 101, 014509 (2020)], we estimate the volume effects for various 1 + 1D Minkowski-signature quantities and show that these can be a significant source of systematic uncertainty, even for volumes that are very large by the standards of present-day Euclidean calculations. We then present an improvement strategy, based in the fact that the finite volume has a reduced symmetry. This implies that kinematic points, which yield the same Lorentz invariants, may still be physically distinct in the periodic system. As we demonstrate, both numerically and analytically, averaging over such sets can significantly suppress the unwanted volume distortions and improve the extraction of the physical scattering amplitudes. As the improvement strategy is based only in kinematics, it can be applied without detailed knowledge of the system

Estandarización de análisis de metilesteres de ácidos grasos por la técnica de cromatografía de gases acoplada a espectrometría de masas.

Se realizó la estandarización del análisis de metilésteres de ácidos grasos (FAME’s) por cromatografía de gases acoplada a espectrometría de masas (CG-EM) utilizando impacto electrónico (EI) e ionización química (CI). En este estudio se evaluaron los parámetros estadísticos: precisión, linealidad, límite de detección y cuantificación, sensibilidad y coeficiente de correlación. Los resultados mostraron que el análisis por impacto electrónico presentó valores estadísticos adecuados para la identificación y cuantificación de los metilesteres, sin embargo los espectros de masas de los FAME’s presentaron como ión molecular a [M 1]y no tienen iones comunes, luego es mas fácil la identificación mediante CI. La muestra real fue aceite de crisálida del Bombix mori Linn obtenidas de crisálidas del Hibrido Pilamo 1 cultivado en la región cafetera. El aceite mostró ácido oleico y ácido palmitico como componentes mayoritarios (43,752 y 26,300% respectivamente