SMuK 2023 – wissenschaftliches Programm
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T: Fachverband Teilchenphysik
T 78: Flavor VII
T 78.1: Vortrag
Mittwoch, 22. März 2023, 17:30–17:45, HSZ/0304
Completing the Heavy Quark Expansion — •Ilija Sibin Milutin1, Thomas Mannel1, and Keri Vos2 — 1Siegen University, Siegen, Germany — 2Maastricht University, Maastricht, The Netherlands
The Heavy Quark Expansion (HQE) has become the major tool to perform precision calculations for inclusive rates and spectra of heavy hadron decays. The HQE is an expansion in powers of the inverse mass of the heavy quark 1/mb and introduces HQE matrix elements which need to be extracted from data. Recently, moments of the dilepton spectrum of inclusive semileptonic B→ Xcℓν have been used to extract the CKM matrix element Vcb with incredible percent-level precision and in agreement with the world’s best determination of Vcb.
The HQE for the inclusive semileptonic B→ Xcℓν decay is usually set up in such a way that one assumes that the charm quark is also a heavy quark. Therefore, one will also have contributions of order ΛQCDn/mcn.
At dimension six, i.e. at 1/mb3, a coefficient function behaving as lnmc2 appears and at dimension eight, terms with 1/mc2 appear. A consistent power counting therefore needs to be set up. Numerically, we find that mc2∼ mbΛQCD and therefore two powers of mc should be counted as one power of mb. Consequently, in order to complete the existing calculation at order 1/mb4, we need to include contributions of order 1/mb3· 1/mc2 that may be numerically relevant.
In this talk, we present how we determine these contributions and the results for the moments of the leptonic invariant mass spectrum.