Final Nucleon Research Articles

Nucleon helicity parton distribution function in the continuum limit with self-renormalization

We present the first lattice calculation of the nucleon isovector helicity parton distribution function (PDF) in the framework of large-momentum effective theory (LaMET) that uses the hybrid scheme with self-renormalization. We use ensembles generated by the MILC collaboration at lattice spacings a={0.1207,0.0888,0.0582} fm, with Nf=2+1+1 flavors of highly improved staggered quarks at sea pion mass of Mπ≈315 MeV. We use clover-improved action for our valence quarks with nucleon boost momentum Pz≈1.75 GeV and high-statistics measurements for the LaMET matrix elements. We perform an extrapolation to the continuum limit and improve the handling of systematic errors using renormalization-group resummation (RGR) and leading-renormalon resummation (LRR). Our final nucleon helicity PDF is renormalized in the MS‾ scheme at energy scale μ=2.0 GeV. We compare our results with and without the two systematic improvements of RGR and LRR at each lattice spacing as well as the continuum limit, and we see that the application of RGR and LRR greatly reduces the systematic errors across the whole x range. Our continuum results with both RGR and LRR show a small positive antiquark region for the nucleon helicity PDF as well as a change of as much as a factor of two in the central values compared to results with neither RGR or LRR. By contrast, the application of RGR and LRR only changes the central values by about 5% in the quark region. We compare our lattice results with the global fits by the JAM, NNPDF and DSSV collaborations, and we observe some tension between our results.

Weak Neutrino (Antineutrino) Charged-Current Responses and Scaling for Nuclear Matter in the Relativistic Mean Field

A systematic analysis of the weak responses for charged-current quasielastic neutrino-nucleus reactions is presented within the scheme of a fully relativistic microscopic model considering momentum-dependent scalar and vector mean field potentials in both the initial and final nucleon states. The responses obtained are compared with the ones corresponding to simpler approaches: energy-independent potentials and the relativistic plane wave limit in the final state, i.e., no potentials applied to the outgoing particle. The analysis is also extended to the scaling phenomenon, which provides additional information regarding nuclear dynamics. Results for the scaling function are shown for various nuclei and different values of the transferred momentum in order to analyze the behavior of the relativistic scalar and vector mean field potentials.

Deeply Virtual Compton Scattering Cross Section at High Bjorken xB

We report high-precision measurements of the deeply virtual Compton scattering (DVCS) cross section at high values of the Bjorken variable x_{B}. DVCS is sensitive to the generalized parton distributions of the nucleon, which provide a three-dimensional description of its internal constituents. Using the exact analytic expression of the DVCS cross section for all possible polarization states of the initial and final electron and nucleon, and final state photon, we present the first experimental extraction of all four helicity-conserving Compton form factors (CFFs) of the nucleon as a function of x_{B}, while systematically including helicity flip amplitudes. In particular, the high accuracy of the present data demonstrates sensitivity to some very poorly known CFFs.

General Analysis of the Reaction e^+ + e^- → N + Ñ + π^0

The general analysis of the reaction , in the case of longitudinally polarized electron beam, has been performed in the one-photon-nnihilation approximation, accounting for the polarization states of the final nucleon. This analysis is useful for the description of the continuum (non-resonant) and resonant (with different possible vector mesons or excited baryons in the intermediate virtual states of the Feynman diagrams) contributions. The conservation of the hadron electromagnetic currents and P-invariance of the hadron electromagnetic interaction were used to express the matrix element in terms of the six complex independent invariant amplitudes. The general structure of the hadronic tensor for the case of unpolarized final hadrons and polarized nucleon has been derived. The spin-independent part of the hadronic tensor is determined by five structure functions and the spin-dependent one by 13 structure functions. The transversal, longitudinal and normal components of the nucleon polarization four-vector are expressed by means of the four-vectors of the particle momenta. The five independent invariant variables which describe the reaction have been introduced. The limits of the changing of these variables have been considered. The kinematical double invariant variables regions are given in the figure. The kinematics, suitable to study the invariant mass distributions, is investigated.

Model dependence of the polarization asymmetries in weak pion production off the nucleon

The work presents the study of the polarization observables in the single pion production (SPP) induced by the interaction of the muon neutrino (antineutrino) with nucleons. The SPP cross sections and spin asymmetries are computed within two phenomenological models. One is based on the nonlinear sigma model [E. Hernandez, J. Nieves, and M. Valverde, Phys. Rev. D 76, 033005 (2007)] and the other has origin in the linear sigma model [G. L. Fogli and G. Nardulli, Nucl. Phys. B160, 116 (1979)]. First, we show that the final nucleon polarization and target spin asymmetries are good observables to obtain information about the ${C}_{5}^{A}$ axial form factor. Second, we demonstrate that the nucleon polarization and the target spin asymmetries are sensitive to the relative phase between resonance and nonresonance amplitudes. We conclude that the polarization of the final nucleon and the target spin asymmetry are promising observables for testing SPP models, including studies of the axial content of $\mathrm{\ensuremath{\Delta}}(1232)$ resonance and unitarization procedures.

Quasielastic lepton scattering and back-to-back nucleons in the short-time approximation

Understanding quasielastic electron- and neutrino-scattering from nuclei has taken on new urgency with current and planned neutrino oscillation experiments, and with electron scattering experiments measuring specific final states, such as those involving nucleon pairs in ``back-to-back'' configurations. Accurate many-body methods are available for calculating the response of light ($A \leq 12$) nuclei to electromagnetic and weak probes, but they are computationally intensive and only applicable to the inclusive response. In the present work we introduce a novel approach, based on realistic models of nuclear interactions and currents, to evaluate the short-time (high-energy) inclusive and exclusive response of nuclei. The approach accounts reliably for crucial two-nucleon dynamics, including correlations and currents, and provides information on back-to-back nucleons observed in electron and neutrino scattering experiments. We demonstrate that in the quasielastic regime and at moderate momentum transfers both initial- and final-state correlations, and two-nucleon currents are important for a quantitatively successful description of the inclusive response and final state nucleons. Finally, the approach can be extended to include relativistic---kinematical and dynamical---effects, at least approximately in the two-nucleon sector, and to describe the response in the resonance-excitation region.

Analysis of quasielastic (e,e′) electromagnetic responses and scaling for nuclear matter in the relativistic mean field model

A detailed study of the electromagnetic responses for quasielastic (e,e′) reactions from nuclear matter is presented within the framework of a relativistic model including momentum dependent scalar and vector mean field potentials in both the initial and final nucleon wave function states. The effects ascribed to the use of energy-dependent potentials are carefully analyzed by comparing their predictions with the responses obtained in the case of constant, i.e., energy-independent, potentials, as well as with the plane wave limit in the final state. The study is extended to the scaling phenomenon. Results are provided for the scaling functions corresponding to different nuclear systems evaluated at several kinematics ranging from intermediate to high values of the momentum transfer. Emphasis is placed on scaling of the first and second kinds and the role played by the relativistic scalar and vector mean field potentials.

Nuclear effects in electron-nucleus and neutrino-nucleus scattering within a relativistic quantum mechanical framework

We study the impact of the description of the knockout nucleon wave function on electron- and neutrino-induced quasielastic and single-pion production cross sections. We work in a fully relativistic and quantum mechanical framework, where the relativistic mean-field model is used to describe the target nucleus. The focus is on Pauli blocking and the distortion of the final nucleon, these two nuclear effects are separated and analyzed in detail. We find that a proper quantum mechanical treatment of these effects is crucial to provide the correct magnitude and shape of the inclusive cross section. Also, this seems to be key to predict the right ratio of muon- to electron-neutrino cross sections at very forward scattering angles.

Electron versus Muon Neutrino Induced Cross Sections in Charged Current Quasielastic Processes.

Differences between ν_{e} and ν_{μ} quasielastic cross sections are essential in neutrino oscillation analyses and CP violation searches for experiments such as DUNE and T2HK. The ratio of these is however poorly known experimentally and for certain kinematic regions theoretical models give contradictory answers. We use two independent mean-field based models to investigate this ratio using ^{40}Ar and ^{12}C targets. We demonstrate that a proper treatment of the final nucleon's wave function confirms the dominance of ν_{μ} over ν_{e} induced cross sections at forward lepton scattering.

Removal energies and final state interaction in lepton nucleus scattering

We investigate the binding energy parameters that should be used in modeling electron and neutrino scattering from nucleons bound in a nucleus within the framework of the impulse approximation. We discuss the relation between binding energy, missing energy, removal energy (epsilon ), spectral functions and shell model energy levels and extract updated removal energy parameters from hbox {ee}^{prime }p spectral function data. We address the difference in parameters for scattering from bound protons and neutrons. We also use inclusive e-A data to extract an empirical parameter U_{FSI}( (varvec{q}_3+varvec{k})^2) to account for the interaction of final state nucleons (FSI) with the optical potential of the nucleus. Similarly we use V_{eff} to account for the Coulomb potential of the nucleus. With three parameters epsilon , U_{FSI}( (varvec{q}_3+varvec{k})^2) and V_{eff} we can describe the energy of final state electrons for all available electron QE scattering data. The use of the updated parameters in neutrino Monte Carlo generators reduces the systematic uncertainty in the combined removal energy (with FSI corrections) from ± 20 to ± 5 MeV.

Probing axial quark generalized parton distributions through exclusive photoproduction of a \u03b3\u03c0\xb1 pair with a large invariant mass

Exclusive photoproduction of a γπ± pair in the kinematics where the pair has a large invariant mass and the final nucleon has a small transverse momentum is described in the collinear factorization framework. The scattering amplitude is calculated at leading order in αs and the differential cross sections for the process are estimated in the kinematics of the JLab 12-GeV experiments. The order of magnitude of the predicted cross-sections seems sufficient for a dedicated experiment to be performed. The process turns out to be very sensitive to the axial generalized parton distribution combination {tilde{H}}_u-{tilde{H}}_d .

Erratum to: Exclusive photoproduction of a γ ρ pair with a large invariant mass

An unfortunate misprint in our numerical code has led to an overestimate of the cross section for the exclusive photoproduction of a γ ρL pair in the kinematics where the pair has a large invariant mass and the final nucleon has a small transverse momentum, described in the collinear factorization framework. The rates are thus expected to be smaller but the possibility to disentangle the transversity GPDs through the process where the ρ−meson is transversely polarized is enhanced.

Polarization transfer in weak pion production off the nucleon

Polarization transfer (PT) observables in the single pion production induced by the charged current interaction of the neutrino with the nucleon are examined. The polarization components of the final nucleon and the charged lepton are calculated within two models for the pion production. The predictions are made for neutrino energy of the order of 1~GeV as well as for the T2K energy distribution. It is demonstrated that the PT observables, the degree of polarization and the polarization components of outgoing fermions, are sensitive on assumptions about the nonresonant background model. In particular it is shown that the normal components of the polarization of the outgoing nucleon and the lepton are determined by the interference between the resonant (RES) and nonresonant (NB) amplitudes. Moreover the sign of the normal component of the polarization of the charged lepton is fixed by the relative sign between the RES and the NB amplitudes.

The frozen nucleon approximation in two-particle two-hole response functions

We present a fast and efficient method to compute the inclusive two-particle two-hole (2p–2h) electroweak responses in the neutrino and electron quasielastic inclusive cross sections. The method is based on two approximations. The first neglects the motion of the two initial nucleons below the Fermi momentum, which are considered to be at rest. This approximation, which is reasonable for high values of the momentum transfer, turns out also to be quite good for moderate values of the momentum transfer q≳kF. The second approximation involves using in the “frozen” meson-exchange currents (MEC) an effective Δ-propagator averaged over the Fermi sea. Within the resulting “frozen nucleon approximation”, the inclusive 2p–2h responses are accurately calculated with only a one-dimensional integral over the emission angle of one of the final nucleons, thus drastically simplifying the calculation and reducing the computational time. The latter makes this method especially well-suited for implementation in Monte Carlo neutrino event generators.

Exclusive photoproduction of a \u03b3 \u03c1 pair with a large invariant mass

Exclusive photoproduction of a γ ρ pair in the kinematics where the pair has a large invariant mass and the final nucleon has a small transverse momentum is described in the collinear factorization framework. The scattering amplitude is calculated at leading order in αs and the differential cross sections for the process where the ρ−meson is either longitudinally or transversely polarized are estimated in the kinematics of the JLab 12-GeV experiments.

On the polarization of the final nucleon in NC elastic $\nu _\mu (\bar \nu _\mu )$ -N scattering

New short baseline neutrino experiments open new possibilities of high precision study of different neutrino processes. We present here results of the calculation of the polarization of final nucleon in elastic NC \nu_\mu (\bar\nu_\mu)-nucleon scattering. In a numerical analysis the sensitivity to the different choices of the axial and axial strange form factors is examined. Measurements of the polarization of the final proton in elastic e-p scattering drastically changed our knowledge about the electromagnetic form factors of the proton. From measurement of the nucleon polarization in the NC elastic scattering a new additional information about the axial G_A(Q^2} and the strange axial G^s_A(Q^2) form factors of the nucleon could be inferred.

Polarization of the final nucleon in quasi-elastic neutrino scattering and the axial form factor of the nucleon

Measurements of the polarization of the final proton in elastic e–p scattering drastically changed our knowledge about the electromagnetic form factors of the proton. Here we present our results of the calculation of the polarization of the final nucleon in charged current quasi-elastic neutrino nucleon scattering. Relations which connect the axial form factor with the polarization, the cross section and the electromagnetic form factors of the nucleon are derived. Measurements of the polarization of the nucleon in high-statistics short baseline neutrino experiments (or in near detectors of long baseline experiments) could provide important information on the axial form factor of the nucleon.

Neutrino- and antineutrino-induced reactions with nuclei between 1 and 50 GeV

Background: Nuclear effects can have a significant impact on neutrino-nucleus interactions. In particular, data from neutrino experiments with broad energy distributions require complex theoretical models that are able to take all the relevant channels into account as well as incorporate nuclear effects in both initial and final-state interactions. Purpose: We investigate neutrino and antineutrino scattering on iron and carbon in the energy range from 1 to 30 GeV, which is relevant to current and coming experiments (MINOS, NOvA, and Minerva). Method: The Giessen Boltzmann--Uehling--Uhlenbeck (GiBUU) model, which implements all reaction channels relevant for neutrino energies under consideration, is used for an investigation of neutrino-nucleus reactions. Results: Our calculations are compared with the recent NOMAD and MINOS data for the integrated inclusive cross sections. Predictions are made for the differential cross sections for semiinclusive final states (pions, kaons, and nucleons) for the MINOS and NOvA beams. Conclusions: Nuclear effects in the initial-state interactions may slightly change the inclusive nuclear cross section as compared to the free nucleon ones. Final-state interactions noticeably change the spectra of the outgoing hadrons. In the Minerva and NOvA experiments these effects should be visible in the kinetic energy distributions of the final pions, kaons, and nucleons. Secondary interactions play an important role for strangeness production.

New ways to access the transverse spin content of the nucleon

We first describe a new way to access the chiral odd transversity parton distribution in the proton through the photoproduction of lepton pairs. The basic ingredient is the interference of the usual Bethe-Heitler or Drell-Yan amplitudes with the amplitude of a process, where the photon couples to quarks through its chiral-odd distribution amplitude, which is normalized to the magnetic susceptibility of the QCD vacuum. We also show how the chiral-odd transversity generalized parton distributions (GPDs) of the nucleon can be accessed experimentally through the exclusive electro - or photoproduction process of a meson pair with a large invariant mass and when the final nucleon has a small transverse momentum. We calculate perturbatively the scattering amplitude at leading order, both in the high energy domain which may be accessed in electron-ion colliders and in the medium energy range. Estimated rates are encouraging.

Inclusive charged-current neutrino-nucleus scattering in the quasielastic region

We study inclusive charged-current reaction through total cross sections of neutrino-nucleus scattering within the framework of a relativistic single-particle model in the quasielastic region. To describe the final-state interaction between knocked-out nucleons and the residual nucleus, a real potential of final nucleons, which is generated by a relativistic mean field, is used with the assumption of no loss of flux, which leads to current conservation and gauge invariance. We calculate $({\ensuremath{\nu}}_{\ensuremath{\mu}},{\ensuremath{\mu}}^{\ensuremath{-}})$ and $({\mathrm{\ensuremath{\nu}\ifmmode \bar{}\else \={}\fi{}}}_{\ensuremath{\mu}},{\ensuremath{\mu}}^{+})$ reactions. In these calculations, $^{12}\mathrm{C}$, $^{40}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$ are used as target nuclei and the incident neutrino (antineutrino) energies are exploited up to 4 GeV. We find that the effect of the final-state interaction by the real potential of the knocked-out nucleons reduces cross sections by about 15%, similar to the effect of electron scattering. Furthermore, the effect of the Coulomb distortion for the outgoing leptons is shown to be different from the electron scattering. Finally, our total cross sections by scaling number of participated nucleons are presented to compare with experimental data.