Relativistic Distorted-wave Impulse Approximation Research Articles

Flux-integrated semiexclusive cross sections for charged-current quasielastic and neutral-current elastic neutrino scattering off Ar40 and a sterile neutrino oscillation study

Flux-integrated semiexclusive differential cross sections for charged-current quasielastic and neutral-current elastic neutrino scattering on argon are analyzed. The cross sections are calculated using the relativistic distorted-wave impulse approximation with values of the nucleon axial mass ${M}_{A}=1\text{ }\text{ }\mathrm{GeV}$ and 1.2 GeV. The elastic scattering cross sections are also computed for different strange quark contributions to the neutral-current axial form factor. The flux-integrated differential cross sections as functions of reconstructed neutrino energy are evaluated for the far detector of the SBN experiment. The effects of the short baseline neutrino oscillations are taken into account in a $3+1$ framework. We found that cross sections depend on oscillation parameters and the ratio of the measured and predicted cross sections can be used in a sterile neutrino oscillation study.

Assessing the theory-data tension in neutrino-induced charged pion production: The effect of final-state nucleon distortion

Pion production on nuclei constitutes a significant part of the total cross section in experiments involving few-GeV neutrinos. Combined analyses of data on deuterium and heavier nuclei points to tensions between the bubble-chamber data and the data of the $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$ experiment, which are often ascribed to unspecified nuclear effects. In experimental analysis use is made of approximate treatments of nuclear dynamics, usually in a Fermi gas approach with classical treatments of the reaction mechanism, and fits are often performed by simply rescaling cross sections. To understand the origin of these tensions, check the validity of approximations, and to further advance the description of neutrino pion production on nuclei, a microscopic quantum mechanical framework is needed to compute nuclear matrix elements. We use the local approximation to the relativistic distorted wave impulse approximation to calculate the nuclear matrix elements. We include the distortion of wave functions of the final-state nucleon in a real energy-dependent potential. We compare results with and without distortion. To perform this comparison under conditions relevant to neutrino experiments, we compute cross sections for the $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$ and T2K charged-pion production datasets. The inclusion of nucleon distortion leads to a reduction of the cross section up to 10%, but to no significant change in shape of the flux-averaged cross sections. Results with and without distortion compare favorably to experimental data, with the exception of the low-${Q}^{2}$ $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$ ${\ensuremath{\pi}}^{+}$ data. We point out that hydrogen target data from BEBC is also overpredicted at low ${Q}^{2}$, and the data-model discrepancy is similar in shape and magnitude as what is found in comparison to $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$ data. Including nucleon distortion alone cannot explain the overprediction of low-${Q}^{2}$ cross sections measured by $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$. The similar overprediction of BEBC data on hydrogen means that it is impossible to ascribe this discrepancy solely to a nuclear effect. Axial form factors might not be constrained in a satisfactory way by the Argonne and Brookhaven National Laboratories (ANL/BNL) data alone. Axial couplings and their ${Q}^{2}$ dependence should ideally be derived from more precise data on hydrogen and deuterium. Nuclear matrix elements should be tested with e.g., electron scattering data for which nucleon level physics is better constrained.

Final state interactions in semi-inclusive neutrino-nucleus scattering: Applications to the T2K and MINERνA experiments

We present a complete comparison of semi-inclusive ${\ensuremath{\nu}}_{\ensuremath{\mu}}\text{\ensuremath{-}}^{12}\mathrm{C}$ cross section measurements by T2K and $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$ collaborations with the predictions from the SuSAv2-MEC model implemented in the neutrino-nucleus event generator GENIE and an unfactorized approach based on the relativistic distorted wave impulse approximation. Results, that include cross sections as function of the final muon and proton kinematics and correlations between both, show that the agreement with data obtained by the relativistic distorted wave impulse approximation approach, that accounts for final-state interactions, matches or improves GENIE-SuSAv2 predictions for very forward angles where scaling violations are relevant.

Probing for high-momentum protons in He4 via the He4(e,e′p)X reactions

Experimental cross sections for the He4(e,e′p)X reactions in the missing energy range from 0.017 to 0.022 GeV and up to a missing momentum of 0.632 GeV/c at xB=1.24 and Q2=2 (GeV/c)2 are reported. The data are compared to relativistic distorted-wave impulse approximation calculations for the He4(e,e′p)H3 channel. Significantly more events are observed for pm≥0.45 GeV/c than are predicted by the theoretical model, and striking fluctuations in the ratio of data to the theoretical model around pm=0.3GeV/c are possible signals of initial-state multinucleon correlations.5 MoreReceived 11 May 2019Revised 13 March 2022Accepted 14 April 2022DOI:https://doi.org/10.1103/PhysRevC.105.064003©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBreakup reactionsFew-body systemsNucleon-nucleon interactionsPropertiesA ≤ 5Nuclear Physics

Benchmarking intranuclear cascade models for neutrino scattering with relativistic optical potentials

The description of final-state interactions (FSI) in the large phase space probed in neutrino experiments poses a great challenge. In neutrino experiments, which operate under semi-inclusive conditions, cascade models are commonly used for this task, while under exclusive conditions FSI can be treated with relativistic optical potentials (ROP). We formulate conditions under which the ROP approach and cascade model can be directly compared. We feed the NEUT cascade with events from a relativistic distorted-wave impulse approximation calculation that uses the real part of an optical potential. Cuts on the missing energy of the resulting events are applied to define a set of events that can be directly compared to RDWIA calculations with the full optical potential. The NEUT cascade and ROP agree for proton kinetic energies $T_p > 150$ MeV for carbon, oxygen and calcium nuclei when a realistic nuclear density is used to introduce events in the cascade. For $T_p < 100$ MeV the ROP and NEUT cross sections differ in shape and differences in magnitude are larger than 50 \%. Single transverse variables allow to distinguish different approaches to FSI, but due to a large non-QE contribution the comparison to T2K data does not give an unambiguous view of FSI. We discuss electron scattering and argue that with a cut in missing energy FSI can be studied with minimal confounding factors in e.g. $e4\nu$. The agreement of the ROP and NEUT for T2K conditions lends confidence to these models as a tool in oscillation analyses for sufficiently large nucleon kinetic energies. These results urge for caution when a cascade model is applied for small nucleon energies. The assessment of model assumptions relevant to this region are strongly encouraged. This paper provides novel constraints on cascade models from proton-nucleus scattering that can be easily applied to other neutrino event generators.

Analysis of flux-integrated semiexclusive cross sections for charged-current quasielastic neutrino scattering off Ar40 at energies available at the MicroBooNE experiment

Flux-integrated semiexclusive differential and integral cross sections for quasielastic neutrino charged-current scattering on argon are analyzed. The cross sections are calculated using the relativistic distorted-wave impulse approximation and compare with recent MicroBooNE data. I found that the measured cross sections can be described well within the experimental uncertainties with value of the nucleon axial mass $1&lt;{M}_{A}&lt;1.2\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}$. The contribution of the exclusive channel $({\mathbf{\ensuremath{\nu}}}_{\mathbf{\ensuremath{\mu}}},\mathbf{\ensuremath{\mu}}p)$ to the flux-integrated inclusive cross sections is about 50%.

Comparison of recoil polarization in the [formula omitted] process for protons extracted from s and p shells

We present the first measurements of the double ratio of the polarization-transfer components (Px′/Pz′)p/(Px′/Pz′)s for knock-out protons from the s and p shells in C12 measured by the C12(e→,e′p→) reaction in quasi-elastic kinematics. The data are compared to theoretical predictions in the relativistic distorted-wave impulse approximation. Our results show that the differences between s- and p-shell protons, observed when compared at the same initial momentum (missing momentum), largely disappear when the comparison is done at the same proton virtuality. We observe no difference in medium modifications between protons from the s and p shells with the same virtuality in spite of the large differences in the respective nuclear densities.

Constraints in modeling the quasielastic response in inclusive lepton-nucleus scattering

We show that the quasielastic (QE) response calculated with the SuSAv2 (superscaling approach) model, that relies on the scaling phenomenon observed in the analysis of (e,e') data and on the relativistic mean-field theory, is very similar to that from a relativistic distorted wave impulse approximation model when only the real part of the optical potentials is employed. The coincidence between the results from these two completely independent approaches, which satisfactorily agree with the inclusive data, reinforces the reliability of the quasielastic predictions stemming from both models and sets constraints for the QE response. We also study the low energy and momentum transfer region of the inclusive response by confronting the results of the relativistic mean-field model with those of the Hartree-Fock continuum random-phase approximation model, which accounts for nuclear long-range correlations. Finally, we present a comparison of our results with the recent JLab (e,e') data for argon, titanium and carbon, finding good agreement with the three data sets.

Testing of quasi-elastic neutrino charged-current and two-body meson exchange current models with the MiniBooNE neutrino data and analysis of these processes at energies available at the NOvA experiment

The charged-current quasi-elastic (CCQE) scattering of muon neutrinos on a carbon target is analyzed using the relativistic distorted-wave impulse approximation (RDWIA) taking into account the contribution of the two-particle and two-hole meson exchange current ($2p-2h$ MEC) to the weak response functions. A fit the RDWIA+MEC model to the MiniBooNE neutrino data is performed and the best fit value of nucleon axial mass $M_A=1.2 \pm 0.06$ GeV is obtained. We also extract the values of the axial form factor $F_A(Q^2)$ as a function of the squared momentum transfer $Q^2$ from the measured $d\sigma/dQ^2$ cross section. The flux-integrated CCQE-like differential cross sections for neutrino scattering at energies of the NOvA experiment are estimated within the RDWIA+MEC approach.

Quasielastic neutrino charged-current scattering off C12 : Effects of the meson exchange currents and large nucleon axial mass

The quasi-elastic scattering of muon neutrino and electrons on a carbon target are analyzed using the relativistic distorted-wave impulse approximation (RDWIA). We also evaluate the contribution of the two-particle and two-hole meson exchange current ($2p-2h$ MEC) to electroweak response functions. The nuclear model dependence of the (anti)neutrino cross sections is studied within the RDWIA+MEC approach and RDWIA model with the large nucleon axial mass. It is shown that the results for the squared momentum transfer distribution $d\sigma/dQ^2$ and for invariant mass of the final hadronic system distribution $d\sigma/dW$ obtained within these models are substantially different.

The (p,2p) reaction in finite range relativistic distorted-wave impulse approximation

The [Formula: see text] reaction on [Formula: see text] at incident proton energy of 300[Formula: see text]MeV is examined in the formalism of finite-range relativistic distorted-wave impulse approximation (FR-RDWIA). In comparison to conventional t-matrix model of Love–Franey, a new form of nucleon–nucleon t-matrix effective interaction is derived at 300[Formula: see text]MeV using Reid soft core potentials for isotopic spin one and taking into account the finite-range effects in the [Formula: see text] interaction at knockout vertex. In comparison to the conventional finite range nonrelativistic and relativistic formalism, the present formalism with a new version of [Formula: see text] t-matrix is effectively reproducing the shape of cross-section energy distributions for [Formula: see text], [Formula: see text] and [Formula: see text] states for asymmetric angle pair of [Formula: see text]–[Formula: see text]. Discrepancies between the experimental cross-section data and finite range theoretical calculations at [Formula: see text][Formula: see text]MeV are reasonably resolved in the present approach. Without any adjustable parameter of bound state, the obtained spectroscopic factors are in reasonably good agreement with the relativistic and nonrelativistic theoretical predictions by [Formula: see text], [Formula: see text] and [Formula: see text] analysis.

Determination of the axial nucleon form factor from the MiniBooNE data

Both neutrino and antineutrino charged-current quasielastic scattering on a carbon target are studied to investigate the nuclear effect on the determination of the axial form factor ${F}_{A}({Q}^{2})$. A method for extraction of ${F}_{A}({Q}^{2})$ from the flux-integrated $d\ensuremath{\sigma}/d{Q}^{2}$ cross section of (anti)neutrino scattering on nuclei is presented. Data from the MiniBooNE experiment are analyzed in the relativistic distorted-wave impulse approximation, the Fermi gas model, and the Fermi gas model with enhancements in the transverse cross section. We found that the values of the axial form factor, extracted in the impulse approximation and predicted by the dipole approximation with the axial mass ${M}_{A}\ensuremath{\approx}1.37\text{ }\mathrm{GeV}$, are in good agreement. The agreement between the extracted form factor and meson-dominance ansatz also is good. On the other hand, the ${Q}^{2}$ dependence of ${F}_{A}$ extracted in the approach with the transverse enhancement is found to differ significantly from the dipole approximation.

Quasi-elastic neutrino charged-current scattering off medium-heavy nuclei:40Ca and40Ar

The charged-current quasi-elastic scattering of muon neutrinos on calcium and argon targets is calculated for neutrino energy up to 2.8 GeV. The calculations are done within the framework of the relativistic distorted-wave impulse approximation, which was earlier successfully applied to describe electron-nucleus data. The model is first tested against experimental data for electron scattering off calcium and then it is applied to calculate (anti)neutrino cross sections on 40Ca and 40Ar. We show that reduced exclusive cross sections for neutrino and electron scattering are similar. A significant nuclear model dependence of both inclusive and total cross sections for energy about 1 GeV was found. From the comparison of the (anti)neutrino differential and total cross sections per (proton)neutron, calculated for the carbon, oxygen, and argon targets it is evident that the cross sections decrease slowly with the mass-number of the target due to nuclear effects.

Electron-induced proton knockout from neutron rich nuclei

We study the evolution of the (e,e'p) cross section on nuclei with increasing asymmetry between the number of neutrons and protons. The calculations are done within the framework of the nonrelativistic and relativistic distorted-wave impulse approximation. In the nonrelativistic model phenomenological Woods-Saxon and Hartree-Fock wave functions are used for the proton bound-state wave functions, in the relativistic model the wave functions are solutions of Dirac-Hartree equations. The models are first tested against experimental data on 40 Ca and 48Ca nuclei, and then they are applied to a set of spherical calcium isotopes.

Relativistic descriptions of final-state interactions in neutral-current neutrino-nucleus scattering at MiniBooNE kinematics

The analysis of the recent neutral-current neutrino-nucleus scattering cross sections measured by the MiniBooNE Collaboration requires relativistic theoretical descriptions also accounting for the role of final state interactions. In this work we evaluate differential cross sections with the relativistic distorted-wave impulse-approximation and with the relativistic Green's function model to investigate the sensitivity to final state interactions. The role of the strange-quark content of the nucleon form factors is also discussed.

Neutrino neutral-current elastic scattering on12C

The neutral current elastic scattering of neutrinos on Carbon and $CH_2$ targets is computed using the relativistic distorted-wave impulse approximation with relativistic optical potential. Results for exclusive and inclusive neutrino reactions on ${}^{12}$C target are presented. We show that the nuclear effects on the shape of four-momentum transferred squared distribution $d\sigma/dQ^2_{QE}$ in neutrino neutral-current and charged-current quasi-elastic scattering are similar. We also calculate flux-averaged neutral current elastic differential cross section $d\sigma/dQ^2_{QE}$ for neutrino scattering from $CH_2$, as well as, the neutral-current to charged-current cross section ratio as functions of $Q^2_{QE}$. The value of axial mass $M_A$ is extracted from a fit of $d\sigma/dQ^2_{QE}$ cross section measured in MiniBooNE experiment. The extracted value of $M_A=1.28\pm 0.05$ GeV is consistent within errors with the MiniBooNE result. Additionally, for proton kinetic energies above the Cherenkov threshold, the strange quark contribution to the neutral current axial vector form factor at $Q^2_{QE}=0$, $\Delta s$, was extracted from a fit of MiniBoone data for $\nu p \to \nu p$ to $\nu N \to \nu N$ cross section ratio. This value is found to be $\Delta s=-0.11\pm 0.36$

Relativistic distorted-wave analysis of quasielastic proton-nucleus scattering

A relativistic distorted-wave impulse approximation formalism is presented for the calculation of quasielastic proton-nucleus scattering. It is shown that the double differential cross section may be written as a contraction between the hadronic tensor (describing the projectile and ejectile) and the polarization tensor (describing the nuclear target) and that this mathematical structure also holds for the case where distortions are included. The eikonal approximation is used to introduce distortions in the wave functions, and the nuclear response is described using a Fermi gas model. The highly oscillatory nine-dimensional integrand contained in the expression for the double differential cross section is computed using a novel technique based on combining traditional Gaussian integration methods with the powerful fitting functions in the matlab programming language. This work has successfully calculated the distorted-wave quasielastic differential cross section for proton-nucleus scattering within a fully relativistic framework. It is found that the distortions lead to a reduction in the double differential cross section and have a negligible effect on the computed spin observables.

Relativistic description of inclusive quasielastic proton-nucleus scattering with relativistic distorted-wave impulse approximation and random-phase approximation

We present a fully relativistic model for polarized inclusive quasielastic proton-nucleus scattering that includes relativistic distorted waves for the projectile and ejectile (RDWIA), as well as the relativistic random-phase approximation (RPA) applied to the target nucleus. Using a standard relativistic impulse approximation treatment of quasielastic scattering and a two-body Scalar, Pseudoscalar, Vector, Axial vector, Tensor (SPVAT) form of the current operator, it is shown how the behavior of the projectile/ejectile and target can be decoupled. Distortion effects are included via a full partial-wave expansion of the relativistic wave functions. Target correlations are included via the relativistic RPA applied to mean-field theory in quantum hadrodynamics. A number of novel analytical and numerical techniques are employed to aid in this highly nontrivial calculation. A baseline plane-wave calculation is performed for the reaction $^{40}\mathrm{Ca}$$(\mathrm{pP\vec},\mathrm{pP\vec} {}^{\ensuremath{'}})$ at an energy of 500 MeV and an angle ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}={40}^{\ifmmode^\circ\else\textdegree\fi{}}$. Here it is found that the effect of isoscalar correlations is a quenching of the cross section that is expected to become more pronounced at lower energies or for higher-density targets. A RDWIA calculation shows additional reduction and if isoscalar target correlations are included this effect is enhanced.

Precise Extraction of the Induced Polarization in theHe4(e,e′p→)H3Reaction

We measured with unprecedented precision the induced polarization P(y) in (4)He(e,e'p)(3)H at Q(2)=0.8 and 1.3 (GeV/c)(2). The induced polarization is indicative of reaction-mechanism effects beyond the impulse approximation. Our results are in agreement with a relativistic distorted-wave impulse approximation calculation but are overestimated by a calculation with strong charge-exchange effects. Our data are used to constrain the strength of the spin-independent charge-exchange term in the latter calculation.

Relativistic Description of 3He (e, e′ p)2H

The Relativistic Distorted-Wave Impulse Approximation is used to describe the $^3$He($e,e^\prime p$)$^2$H process. We describe the $^3$He nucleus within the adiabatic hyperspherical expansion method with realistic nucleon-nucleon interactions. The overlap between the $^3$He and the deuteron wave functions can be accurately computed from a three-body calculation. The nucleons are described by solutions of the Dirac equation with scalar and vector (S-V) potentials. The wave function of the outgoing proton is obtained by solving the Dirac equation with a S-V optical potential fitted to elastic proton scattering data on the residual nucleus. Within this theoretical framework, we compute the cross section of the reaction and other observables like the transverse-longitudinal asymmetry, and compare them with the available experimental data measured at JLab.