Reducing Hadronic Uncertainty in Low-Energy Neutral-Current Processes

Abstract

We analyze the hadronic uncertainty from light-quark loops coupled to (anti)neutrino in low-energy neutral-current (anti)neutrino scattering, estimated at the $3$-$4$ permille level. This uncertainty arises from limited knowledge of the charge-isospin correlation function of quark currents. We study the charge-charge and charge-isospin correlators within $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$ chiral perturbation theory (ChPT). In $\mathrm{SU}(2)$ ChPT, the two correlators are identical to all orders in the chiral and electromagnetic expansions. We further perform a leading-order $\mathrm{SU}(3)$ ChPT calculation and discuss the relevant counterterms. Our findings reduce the hadronic uncertainty in neutral-current processes such as (anti)neutrino-electron and coherent elastic (anti)neutrino-nucleus scattering by a factor $\sim 35$.

Figures (2)

• Figure 1: Non-perturbative flavor-independent closed fermion loop contribution to neutral-current (anti)neutrino scattering that involves light quarks is illustrated.
• Figure 2: Error sources in the relative difference between charge-charge and charge-isospin correlation functions, $\frac{\mathrm{\Pi}_{3 \gamma} \left( 0 \right) - \mathrm{\Pi}_{\gamma \gamma} \left( 0 \right)}{\mathrm{\Pi}_{\gamma \gamma} \left( 0 \right)}$, at one loop in $\mathrm{SU}\left( 3 \right)$ ChPT analysis are shown as functions of the renormalization scale $\mu_\chi$. The relative error from the pion(kaon) mass splitting is shown as a green dash-dotted(dotted) line, respectively. The higher-order error is represented by a red dashed line. The total uncertainty, shown as a black solid line, is computed by summing the errors in quadrature. It is automatically reduced to zero in $\mathrm{SU}\left( 2 \right)$ ChPT analysis.