PoS - Proceedings of Science
Volume 451 - European network for Particle physics, Lattice field theory and Extreme computing (EuroPLEx2023) - Plenary Session
Lattice QCD input for neutrino-nucleus scattering
R. Gupta
Full text: Not available
I present an overview of the calculations of the isovector
axial vector form factor of the nucleon, $G_A(Q^2)$, using lattice QCD. Based on a comparison of results from various collaborations, a case is made that lattice results are now consistent within 10\%. A similar level of uncertainty is found also in the axial charge $g_A^{u-d}$, the mean squared axial charge radius, $\langle r_A^2 \rangle$, the induced pseudoscalar charge $g_P^\ast$, and the pion-nucleon coupling $g_{\pi NN}$. These lattice results for $G_A(Q^2)$ are already compatible with those obtained from the recent MINER$\nu$A experiment but lie 2-3$\sigma$ higher than the phenomenological extraction from the old $\nu$-deuterium bubble chamber scattering data for $Q^2 > 0.3$~GeV${}^2$. Fits to our data show that the dipole ansatz does not have enough parameters to parameterize the form factor over the range $0 \le Q^2 \le 1$~GeV${}^2$, whereas even a $z^2$ truncation of the $z$-expansion or a low order Pad\'e are sufficient. Looking ahead, lattice QCD calculations will provide increasingly precise results over the range $0 \le Q^2 \lesssim 1$~GeV${}^2$, and MINER$\nu$A-like experiments will extend the range to $Q^2 \sim 2$~GeV${}^2$ or higher. To increase precision of lattice data to the percent level,
new developments are needed to address two related issues: the exponentially falling signal-to-noise ratio in all nucleon correlation functions and removing excited state contributions. Nevertheless, even with the current methodology, significant reduction in errors is expected over the next few years with higher statistics data on more ensembles closer to the physical point.
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