Quasielastic electromagnetic scattering cross sections and world data comparisons in the GENIE Monte Carlo event generator

The usage of Monte Carlo neutrino event generators ($\mathrm{MC}\nu \mathrm{EG}\mathrm{s}$) is a norm within the high-energy $\nu$ scattering community. The relevance of quasielastic (QE) energy regimes to $\nu$ oscillation experiments implies that accurate calculations of $\nu A$ cross sections in this regime will be a key contributor to reducing the systematic uncertainties affecting the extraction of oscillation parameters. In spite of this, many $\mathrm{MC}\nu \mathrm{EG}\mathrm{s}$ utilize highly phenomenological, parametrized models of QE scattering cross sections. Moreover, a culture of validation of $\mathrm{MC}\nu \mathrm{EG}$s against prolific electron ($e$) scattering data has been historically lacking. In this work, we implement new $eA$ cross sections obtained from nuclear ab initio approaches in GENIE, the primary $\mathrm{MC}\nu \mathrm{EG}$ utilized by the FNAL community. In particular, we utilize results from quantum MC methods which solve the many-body nuclear problem in the short-time approximation (STA), allowing consistent retention of two-nucleon dynamics which are crucial to explain available nuclear electromagnetic (electroweak) data over a wide range of energy and momentum transfers. This new implementation in GENIE is fully tested against the world QE electromagnetic data, finding agreement with available data below $\sim 2\mathrm{GeV}$ of beam energy with the aid of a scaling function formalism. The STA is currently limited to study $A\le 12$ nuclei, however, its semi-inclusive multibody identity components are exportable to other many-body computational techniques such as auxiliary field diffusion MC which can reach $A\le 40$ systems while continuing to realize the factorization contained within the STA’s multinucleon dynamics. Together, these developments promise to make future experiments such as DUNE more accurate in their assessment of $\mathrm{MC}\nu \mathrm{EG}$ systematics, $\nu$ properties, and potentially empower the discovery of physics beyond the Standard Model.

Figure 1

The ${}^4\mathrm{He}$ transverse response density is shown for $|\mathbf{q}|=500\mathrm{MeV}/\mathrm{c}$. The surface plot shows the response density as functions of relative energy $e$ and center-of-mass energy $E_{\text{c.m}}$. of pairs of nucleons being actively scattered upon by the incoming electron, leading to microscopic knowledge of semifinal states before intranuclear transport and final state interactions.

Figure 2

The interpolated nonrelativistic nuclear response surfaces $\{R_{\alpha },q,\omega \}$ are shown with sub-MeV grid-spacing. The underlying $\sim 1\mathrm{MeV}$-spaced $\{|\mathbf{q}|,\omega \}$ grid forms the fundamental objects cast in tabulated form which GENIE then dynamically bilinearly interpolates upon to form all subsequent double differential cross sections for QE EM scattering. Lines along the surfaces serve as visual aides only.

Figure 3

Nuclear responses comparisons between QMC STA theory outputs [3] and available empirical data [24, 67]. Many response components are shown, including but not limited to interference and one-body off-diagonal terms, whose destructive qualities within particularly the longitudinal response limit the strength of the pure one-body contribution. Thresholds refer to a small, free shift-parameter which has been simplistically tuned in post-processing to better fit available response data.

Figure 4

A series of ${}_2{}^4\mathrm{He}$ double differential leptonic cross sections are shown for various beam energies and angles, derived from the scaled responses coming from the average scaling function. Behavior is good overall, with all curves properly and consistently undershooting the QE-peak due to lack of resonant production. This is especially true for beam energies $<2\mathrm{GeV}$ and more forward angles, though even highly transverse cross sections appear quite consistent with data. However, one can see that strength is missing from the top-most plot at low energy and high angle, due to the current averaging scheme of scaled nuclear responses.

Figure 5

A prediction of total inclusive double differential electron scattering cross sections. The $pp$ and $nn$ channels are also shown.

Figure 6

Two kinematics are shown for double differential cross sections showing data, scaled theoretical curves, and GENIE generator outputs. Great consistency in all three is observed throughout the QE regime.

Figure 7

Approximate scaling is observed for both the one-body diagonal term (“1bdiag”) and total ($“\mathrm{Tot}\mathrm{.}”=\text{one body diagonal}+\text{one-body off-diagonal}+\text{interference}+\text{two-body}$) electromagnetic response contributions across longitudinal and transverse components; this appears particularly strong in the total transverse response. Note the respective (marginal) destructive and (strongly) constructive behavior of the longitudinal and transverse components when moving from a one-body diagonal to total response paradigm by adding additional interference and two-body terms. The average scaling function is calculated from all shown total responses. Though computed, responses for $|\mathbf{q}|=\{300,350\}\mathrm{MeV}/\mathrm{c}$ are currently not included in this analysis due to presence of the elastic peak, thus spoiling scaling across all components. The longitudinal component of $|\mathbf{q}|=1000\mathrm{MeV}/\mathrm{c}$ has not yet been computed.

Figure 8

Comparisons between newly created scaled (dashed) and originally computed (solid) one-body diagonal and total nuclear response functions are shown. Note the excellent agreement of the transverse responses due to the lack of strength of the elastic peak in this particular component, while the reduced strength of the scaled longitudinal responses removes the elastic strength due to higher momentum transfer responses outweighing the average scaling function; however, too much strength is lost here due to the averaging scheme in both the longitudinal and transverse responses. Other methods may be pursued in future work.

Figure 9

The interpolated nuclear response are shown. Lines along the $\{R,q,\omega \}$ surfaces are visual aides only.

Figure 10

The original [3] and scaled two-body particle identity-specific nuclear reponse functions are shown for $pp$ and $nn$ pairs, mirroring Fig. 8. We show only $|\mathbf{q}|=\{500,600,700\}\mathrm{MeV}/\mathrm{c}$ responses here; in principle, the number of known responses can increase, allowing for better-behaved and expansive interpolation for a densifying of the two-body $\{R_{NN},|\mathbf{q}|,\omega \}$-surface; from this, more robust double differential cross sections could be derived. Note the different ranges (strengths) of the different components of each channel due to differences in underlying pairing dynamics; the $nn$ longitudinal responses are not shown due to low values.

Figure 11

Alignment of form factor normalized response functions is shown when graphing against the nonrelativistic dimensional parameter ${\psi }_{nr}^{\prime }$.