Using a sample of
( 2712 ± 14 ) × 10 6 ψ ( 3686 ) events collected with the BESIII detector, we perform partial wave analyses of the decays
ψ ( 3686 ) → p p ¯ π 0 and
ψ ( 3686 ) → p p ¯ η . The branching fractions of
ψ ( 3686 ) → p p ¯ π 0 and
ψ ( 3686 ) → p p ¯ η are determined to be
( 133.9 ± 11.2 ± 2.3 ) × 10 − 6 or
( 183.7 ± 13.7 ± 3.2 ) × 10 − 6 and
( 61.5 ± 6.5 ± 1.1 ) × 10 − 6 or
( 84.4 ± 6.9 ± 1.4 ) × 10 − 6 , respectively, where the two solutions are caused by an ambiguous phase angle between resonant and continuum processes. Several well-established
N * states are observed in the
p π 0 and
p η systems, and the corresponding branching fractions are measured. The ratio of decay widths
Γ N ( 1535 ) → N η / Γ N ( 1535 ) → N π is determined to be
0.99 ± 0.05 ± 0.19 .