Measurements of and + charged-current cross-sections without detected pions or protons on water and hydrocarbon at a mean anti-neutrino energy of 0.86 GeV

We report measurements of the flux-integrated and + charged-current cross-sections on water and hydrocarbon targets using the T2K anti-neutrino beam with a mean beam energy of 0.86 GeV. The signal is defined as the (anti-)neutrino charged-current interaction with one induced and no detected charged pion or proton. These measurements are performed using a new WAGASCI module recently added to the T2K setup in combination with the INGRID Proton Module. The phase space of muons is restricted to the high-detection efficiency region, 400 and 30 , in the laboratory frame. An absence of pions and protons in the detectable phase spaces of 200, 70 and 600, 70 is required. In this paper, both the; cross-sections and +; cross-sections on water and hydrocarbon targets and their ratios are provided by using the D\u27Agostini unfolding method. The results of the integrated ; cross-section measurements over this phase space are ;\sigma{\rm H{2}O}=(1.082\pm0.068(\rm stat.) {+0.145}{-0.128}(\rm syst.)) \times 10 {-39}\,{\rm cm {2} / nucleon};, ;\sigma{\rm CH}=(1.096\pm0.054(\rm stat.) {+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(\rm stat.) {+0.093}{-0.090}(\rm syst.);. The +; cross-section is ;\sigma{\rm H{2}O} = (1.155\pm0.064(\rm stat.) {+0.148}{-0.129}(\rm syst.)) \times 10 {-39}\,{\rm cm {2} / nucleon};, ;\sigma{\rm CH}=(1.159\pm0.049(\rm stat.) {+0.129}{-0.115}(\rm syst.)) \times 10 {-39}\,{\rm cm {2} / nucleon};, and ;\sigma{\rm H{2}O}/\sigma{\rm CH}=0.996\pm0.069(\rm stat.) {+0.083}{-0.078}(\rm syst.);