Determination of $|V_{cb}|$ using N${}^3$LO perturbative corrections to $\Gamma (B\to X_c\ell \nu )$ 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 ${\eta }_b(1S)$ and ${\rm Y}(1S)$ 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 $\mathcal{O}({\Lambda }_{\overline{\mathrm{MS}}}^2)$ 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.

arXiv comment14pages, 2 figures, version to appear in PLB

References in corpus (42)

• QCD Predictions for Lepton Spectra in Inclusive Heavy Flavour Decays
• The three loop relation between the \bar {MS} and the pole quark masses
• Inclusive Semileptonic B and Polarized Lambda_b Decays from QCD
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2018
• Heavy Quark Effective Theory beyond Perturbation Theory: Renormalons, the Pole Mass and the Residual Mass Term
• Strong Coupling Constant with Flavour Thresholds at Four Loops in the MS-bar Scheme
• Differential Distributions in Semileptonic Decays of the Heavy Flavors in QCD
• The relation between the $\overline{\mathrm{MS}}$ and the on-shell quark mass at order ${\alpha }_s^3$
• Quark mass relations to four-loop order
• Resummation of $({\beta }_0{\alpha }_s{)}^n$ Corrections in QCD: Techniques and Applications to the $\tau$ Hadronic Width and the Heavy Quark Pole Mass
• The infrared behaviour of the static potential in perturbative QCD
• Sum Rules for Heavy Flavor Transitions in the SV Limit
• B decay and the Upsilon mass
• Short Distance Mass of a Heavy Quark at Order α_s^3
• Global analysis of inclusive B decays
• B decays in the upsilon expansion
• The three loop on-shell renormalization of QCD and QED
• Precision determination of the CKM element Vcb
• Mass effects in muon and semileptonic b -> c decays
• $\overline{\mathrm{MS}}$-on-shell quark mass relation up to four loops in QCD and a general SU$(N)$ gauge group
• Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD
• Imprecated, yet Impeccable: On the Theoretical Evaluation of Gamma(B -> X_c \ell ν)
• High Power n of m_b in Beauty Widths and n=5 -> oo Limit
• Three loop calculations and inclusive $V_{cb}$
• Perturbative corrections to semileptonic b decay distributions
• $M({\eta }_b)$ and ${\alpha }_s$ from Nonrelativistic Renormalization Group
• Three-Loop Chromomagnetic Interaction in HQET
• Standard-model prediction of ${\epsilon }_K$ with manifest CKM unitarity
• Resummation of Running Coupling Effects in Semileptonic B Meson Decays and Extraction of $|V_{cb}|$
• O(α_s^2) corrections to semileptonic decay b \to c l \bar ν_l
• Heavy-to-heavy quark decays at NNLO
• Third order corrections to the semi-leptonic \boldmath{$b\to c$} and the muon decays
• Fine and Hyperfine Splittings of Charmonium and Bottomonium: An Improved Perturbative QCD Approach
• Charm Mass Dependence of the $\CO(α_s^2 n_f)$ Correction to Inclusive $B\to X_{c}e{\bar{\nu }}_e$ Decay
• Improving Extractions of |Vcb| and mb from the Hadronic Invariant Mass Moments of Semileptonic Inclusive B decay
• Full Formula for Heavy Quarkonium Energy Levels at Next-to-next-to-next-to-leading Order
• Inclusive semileptonic B decays from QCD with NLO accuracy for power suppressed terms
• Pole mass renormalon and its ramifications
• Hyperasymptotic approximation to the top, bottom and charm pole mass
• Determination of $m_c$ and $m_b$ from quarkonium 1S energy levels in perturbative QCD
• Semileptonic decays in the limit of a heavy daughter quark
• HQE parameters from unquenched lattice data on pseudoscalar and vector heavy-light meson masses

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