Axial and pseudoscalar form factors from charged current quasielastic neutrino-nucleon scattering

We study the scattering of neutrinos on polarized nucleons or detecting the polarization of recoil particles. In contrast to electromagnetic processes, the parity-violating weak interaction does not suppress spin asymmetries contributing sizably at leading order. The future measurements with polarized particles could provide independent access to the proton axial structure and allow us the first extraction of the pseudoscalar form factor from neutrino data without assumptions regarding its form. Limited by charged lepton mass suppression, the latter is possible scattering muon (anti)neutrinos with hundreds of $\mathrm{MeV}$ energy but requires a percent or even sub-percent measurement of spin asymmetries or scattering tau (anti)neutrinos. Axial form factor can be extracted from all energies of accelerator neutrinos.

We study the scattering of neutrinos on polarized nucleons or detecting the polarization of recoil particles. In contrast to electromagnetic processes, the parity-violating weak interaction does not suppress spin asymmetries contributing sizably at leading order. The future measurements with polarized particles could provide independent access to the proton axial structure and allow us the first extraction of the pseudoscalar form factor from neutrino data without assumptions regarding its form. Limited by charged lepton mass suppression, the latter is possible scattering muon (anti)neutrinos with hundreds of MeV energy but requires a percent or even sub-percent measurement of spin asymmetries or scattering tau (anti)neutrinos. Axial form factor can be extracted from all energies of accelerator neutrinos.
In this work, we study the sensitivity of single-spin asymmetries in neutrino-nucleon charged current quasielastic scattering to axial and pseudoscalar form factors. We determine neutrino beam energies suitable for the simultaneous extraction of both form factors in one experiment and identify single-spin asymmetries sensitive to the axial contributions at GeV energies.
At energies of accelerator experiments, charged current neutrino-quark scattering is described by four-fermion interaction: with projection operator on the left-handed chiral states P L = 1−γ5 2 . At leading order, Wilson coefficients are determined by the Fermi coupling constant G F and CKM matrix elements V qq as c qq = 2 √ 2G F V qq . More precise determination is given in Ref. [68].
The matrix element of the quark current inside the nucleon can be expressed in terms of Sachs electric G V E and magnetic G V M isovector, axial F A and pseudoscalar F P form factors as To evaluate transverse to the recoil nucleon asymmetry R t with spin direction in the scattering plane, we substitute (p · S) = 0 and (k · S) = − τ ν 2 − (1 + τ )(τ + r 2 ) 2 / τ (1 + τ ). To evaluate longitudinal to the recoil nucleon asymmetry R l with spin direction in the scattering plane, we substitute (p · S) = 2 τ (1 + τ ) and (k · S) = τ ν − (1 + τ )(τ + r 2 ) / τ (1 + τ ).
The asymmetry L in the neutrino scattering with determination of the recoil lepton spin S is determined by the following structure-dependent factors A L , B L , and C L : To evaluate transverse to the recoil lepton asymmetry L t with spin direction in the scattering plane, we substitute To evaluate longitudinal to the recoil lepton asymmetry L l with spin direction in the scattering plane, we substitute 2 (p · rS) Asymmetries provide a complementary way of accessing the nucleon structure. Contrary to asymmetries in electromagnetic and strong interactions, spin-dependent contributions in weak interaction enter observables with similar to unpolarized cross-section weights. In the experiment, flux normalization errors and detector systematics can be significantly reduced on the level of asymmetry.
Pseudoscalar contribution in the scattering of ν e andν e is suppressed by factors m 2 e /E 2 ν , m 2 e /M 2 and m 2 e / (M E ν ) and therefore negligible at energies of accelerator experiments. Pseudoscalar contribution in the scattering of ν µ and ν µ is negligible at energies above E ν M . However, it becomes sizable at neutrino beam energies of hundreds MeV and rises approaching the muon production threshold in asymmetries with polarized nucleons and unpolarized cross section while event rates decrease. In the following Figs. (1-6), we present all non-vanishing at leading order single-spin asymmetries in muon (anti)neutrino scattering substituting nucleon form factors from Refs. [69,70] in the assumption of the partial conservation of the axial-vector current and pion-pole dominance (PCAC ansatz) for pseudoscalar form factor: F P (Q 2 ) = 2M 2 / m 2 π + Q 2 F A (Q 2 ) (though PCAC ansatz can be valid only at Q 2 Λ 2 QCD ). We also compare central values varying the axial form factor by 20 % versus varying pseudoscalar form factor from PCAC value by 20 %. 2 Both axial and pseudoscalar form factors can be accessed with the muon (anti)neutrino beam of a few hundred MeV energy.  The contribution of axial form factor to unpolarized cross section and spin asymmetries is sizable at all beam energies. Though asymmetries at GeV energies require a few percent or sub-percent precision to add a complementary information regarding the axial structure, besides T l , R t , R l inν p → + n, see Fig. 7 with asymmetries of practical interest. Averaging over the anticipated flux profiles of the DUNE Near Detector [64,71] at Fermilab and neglecting detector details, we present a closer to experiment result in Fig. 8. Adding high-energy flux components, the asymmetry R t loses sensitivity to the axial structure. However, T l and R t require just a factor of a few more statistics to be equally useful as the unpolarized cross section. Contrary to the unpolarized cross sections, spin asymmetries in the scattering of tau (anti)neutrino are sensitive to the pseudoscalar form factor, see Figs. (9)(10)(11)(12)(13)(14) for details. Above the τ -production threshold, recoil and target asymmetries at low Q 2 are more sensitive to pseudoscalar than to axial form factor. Asymmetries L l and L t are sensitive only to the axial form factor. An improved dataset with ν τ ,ν τ could allow us to access the pseudoscalar form factor from the neutrino scattering data. In this work, we study the sensitivity of single-spin asymmetries in (anti)neutrino-nucleon charged current quasielastic scattering to axial and pseudoscalar form factors. Such asymmetries provide independent access to the nucleon axial structure. Pseudoscalar form factor can be accessed either from asymmetries scattering muon (anti)neutrino at hundreds of MeV energies or from asymmetries scattering tau (anti)neutrino above the tau production threshold E ν 3.5 GeV. Axial structure contributes significantly to recoil and transverse longitudinal electron and muon antineutrino-proton charged current quasielastic scattering at the GeV energy range. The first measurement of polarized observables in neutrino-nucleon scattering experiments could provide another confirmation of the Standard Model of particle physics, complementary information on the axial form factor, and the way to access pseudoscalar form factor independently.