Determination of the Cabibbo-Kobayashi-Maskawa matrix element |𝑉𝑐𝑏| from inclusive observables in semileptonic B meson decays

Sumitted to PubDB: 2025-05-02

Category: Master Thesis

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Principal Authors Christoph Schwanda, Felix Troneberger
Date 2025-02-12
Belle II Number BELLE2-MTHESIS-2025-010
Abstract The Cabibbo-Kobayashi-Maskawa (CKM) matrix is the primary source of CP vi- olation in the Standard Model (SM) of particle physics, which is necessary for a matter-antimatter asymmetry. Precise measurements of the CKM matrix element |𝑉𝑐𝑏| play an important role in testing the SM and determining the CP violation pa- rameter. However, discrepancies between the determination of |𝑉𝑐𝑏| from exclusive and inclusive semileptonic decays suggest the existence of unknown effects. To gain further insight into this discrepancy, this thesis aims to determine |𝑉𝑐𝑏| by fitting recently computed theoretical predictions for π‘ž2 moments to experimental data from inclusive semileptonic decays 𝐡 β†’ π‘‹π‘π‘™πœˆπ‘™. The theoretical model is based on the operator product expansion (OPE), which allows for a product of operators at different points in spacetime to be expressed as a series of local operators. By performing a double expansion in the strong coupling constant 𝛼𝑠 and the inverse bottom quark mass Λ𝑄𝐢𝐷/π‘šπ‘, the moments depend on perturbative coefficients and non-perturbative matrix elements of these local operators. These matrix elements, known as the Heavy Quark Expansion (HQE) parameters, must be extracted by the fit. The experimental input consists of the squared momentum transfer of the lepton- neutrino pair π‘ž2 measured at the Belle and Belle II experiments. A key aspect of this study is the fitting procedure, which includes the theoretical errors of the calculations and external constraints to stabilize the fit. To validate the fitting procedure fits to the lepton energy 𝐸𝑙 and the hadron mass distribution π‘š2𝑋 as well as a fit including π‘ž2 data are performed and compared with published results. The π‘š2𝑋 and 𝐸𝑙 moments have been measured at the BaBar, Belle, CDF, CLEO, and DELPHI experiments. The global fits are performed using a maximum likelihood estimation technique implemented with the Minuit framework. The first extraction of |𝑉𝑐𝑏| led to large uncertainties since the π‘ž2 moments are insensitive to the HQE parameter πœ‡2πœ‹. With additional constraints obtained from other fits, the π‘ž2 fit could be stabilized. The final fit using only π‘ž2 moments results in |𝑉𝑐𝑏| = (42.15 Β± 0.54) Γ— 10βˆ’3. This result is consistent with previous inclusive determinations of |𝑉𝑐𝑏| and demonstrates that |𝑉𝑐𝑏| can be reliably determined using π‘ž2 moments. An analysis of the other HQE parameters reveals discrepancies between fit types. While the fit using only π‘ž2 moments yields compatible values for most of the HQE parameters, there are differences in the results for 𝜌3𝐷. This suggests potential the- oretical or experimental problems in the treatment of these moments that require further investigation.

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