Determination of $|V_{cb}|$ using N$^3$LO perturbative corrections to $Γ(B \to X_c \ell ν)$ and 1S masses

Abstract

We determine |V cb | using the third-order perturbative series for the inclusive semileptonic B decay width and for the masses of the bottomonium 1S states. We use the masses of η b (1S) and Υ(1S) as short-distance masses and point out that there is a sizable difference of |V cb | between the two 1S mass schemes. This is the dominant error of our determination and stems from insufficiency to describe theoretically the observed mass splitting of the bottomonium 1S states. We also study the significance of the O(Λ 2 MS ) non-perturbative effects in HQET with respect to the current perturbative accuracy. Our result |V cb | = 0.0425( 11) is consistent with the PDG value determined from the inclusive decays and has a slightly larger error. G m 2 b + O((Λ MS /m b ) 3 ) . (1)

Higher QCD corrections for inclusive semileptonic B decays

“…In addition, a recent (non-fit) analysis using the 1S scheme found a value consistent with the above determinations, but exhibits a slightly larger uncertainty [5]. The recent improvements in precision of the inclusive |𝑉 𝑐𝑏 |, compared to previous determinations [6,7], have been achieved thanks to new calculations of the third order correction to the partonic 𝑏 → 𝑋 𝑐 ℓ νℓ decay rate [8], partially checked in [9], and the 𝑂 (𝛼 𝑠 ) corrections to the Wilson coefficient of 𝜌 𝐷 [10,11].…”