Pensieve header: A bad interaction of Series and degree bounds.

f=((Cosh[ℏ(((ϵ-t)/2)+ϵ a)]-Cosh[ℏ(Sqrt[(((((t-ϵ)/2)))^2)+ϵ ω])])/(ℏ Sinh[((-ϵ ℏ)/2)](ω-ϵ (a^2)+(t-ϵ)a)));
Series[f, {ℏ,0,2}]

ϵ /: (ϵ^(d_. ))/; d>2 :=0;
Series[f, {ℏ,0,2}]

?ϵ

Clear[ϵ]; ?ϵ

Series[((1/24) ((t^2)-2 t ϵ-2 a t ϵ+2 a (ϵ^2)+2 (a^2) (ϵ^2)+2 ϵ ω) (ℏ^2))-((((-a (t^3)+3 a (t^2) ϵ+3 (a^2) (t^2) ϵ-(t^2) ω+2 t ϵ ω-2 ϵ (ω^2)) (ℏ^2))/(24 (-a t+a ϵ+(a^2) ϵ-ω)))), {ϵ,0,2}] // Normal // Simplify