QCD condensates and αₛ from τ-decay

We improve the determinations of the QCD condensates within the SVZ expansion in the axial-vector (A) channel using the ratio of Laplace sum rule (LSR) R₁₀A(τ) within stability criteria and τ-like higher moments Rn,A within stability for arbitrary τ-mass squared s₀. We find the same violation of the factorization by a factor 6 of the four-quark condensate as from e⁺e⁻ → Hadrons data. One can notice a systematic alternate sign and no exponential growth of the size of these condensates. Then, we extract αₛ from the lowest τ-decay like moment and find: αₛ(M_τ)V+A=0.3135(83) (FO) and 0.3322 (81) (CI) leading to: αₛ(MZ)V+A=0.1177(10)fit(3)evol. (FO) and 0.1200(9)fit(3)evol.\,(CI). We extend the analysis to the V+A channel and find: αₛ(M_τ)V+A=0.3135(83) (FO) and 0.3322 (81) (CI) leading to: αₛ(MZ)V+A=0.1177(10)fit(3)evol. (FO) and 0.1200(9)fit(3)evol.\,(CI). We observe that in different channels (e⁺e⁻→ Hadrons, \, A,\,V+A), the extraction of αₛ(M_τ) at the observed τ-mass leads to an overestimate of its value. Our determinations from these different channels lead to the mean: αₛ(M_τ)=0.3140(44) (FO) and 0.3346 (35) (CI) leading to: αₛ(MZ)=0.1178(6)fit(3)evol. (FO) and 0.1202(4)fit(3)evol.(CI). Comparisons with some other results are done.