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We report measurements of the flux-integrated $\bar{\nu}_\mu$ and$\bar{\nu}_\mu+\nu_\mu$ charged-current cross-sections on water and hydrocarbontargets using the T2K anti-neutrino beam, with a mean neutrino energy of 0.86GeV. The signal is defined as the (anti-)neutrino charged-current interactionwith one induced $\mu^\pm$ and no detected charged pion nor proton. Thesemeasurements are performed using a new WAGASCI module recently added to the T2Ksetup in combination with the INGRID Proton module. The phase space of muons isrestricted to the high-detection efficiency region, $p_{\mu}>400~{\rm MeV}/c$and $\theta_{\mu}<30^{\circ}$, in the laboratory frame. Absence of pions andprotons in the detectable phase space of "$p_{\pi}>200~{\rm MeV}/c$ and$\theta_{\pi}<70^{\circ}$", and "$p_{\rm p}>600~{\rm MeV}/c$ and $\theta_{\rmp}<70^{\circ}$" is required. In this paper, both of the $\bar{\nu}_\mu$cross-sections and $\bar{\nu}_\mu+\nu_\mu$ cross-sections on water andhydrocarbon targets, and their ratios are provided by using D'Agostiniunfolding method. The results of the integrated $\bar{\nu}_\mu$ cross-sectionmeasurements over this phase space are $\sigma_{\rmH_{2}O}\,=\,(1.082\pm0.068(\rm stat.)^{+0.145}_{-0.128}(\rm syst.)) \times10^{-39}~{\rm cm^{2}/nucleon}$, $\sigma_{\rm CH}\,=\,(1.096\pm0.054(\rmstat.)^{+0.132}_{-0.117}(\rm syst.)) \times 10^{-39}~{\rm cm^{2}/nucleon}$, and$\sigma_{\rm H_{2}O}/\sigma_{\rm CH} = 0.987\pm0.078(\rmstat.)^{+0.093}_{-0.090}(\rm syst.)$. The $\bar{\nu}_\mu+\nu_\mu$ cross-sectionis $\sigma_{\rm H_{2}O} = (1.155\pm0.064(\rm stat.)^{+0.148}_{-0.129}(\rmsyst.)) \times 10^{-39}~{\rm cm^{2}/nucleon}$, $\sigma_{\rmCH}\,=\,(1.159\pm0.049(\rm stat.)^{+0.129}_{-0.115}(\rm syst.)) \times10^{-39}~{\rm cm^{2}/nucleon}$, and $\sigma_{\rm H_{2}O}/\sigma_{\rmCH}\,=\,0.996\pm0.069(\rm stat.)^{+0.083}_{-0.078}(\rm syst.)$.

progress of theoretical and experimental physics

Measurements of $\bar{\nu}_{\mu}$ and $\bar{\nu}_{\mu} + \nu_{\mu}$  charged-current cross-sections without detected pions nor protons on water  and hydrocarbon at mean antineutrino energy of 0.86 GeV