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Weak G-band (WGB) stars are a rare class of cool luminous stars that presenta strong depletion in carbon, but also lithium abundance anomalies that havebeen little explored in the literature since the first discovery of thesepeculiar objects in the early 50's. Here we focus on the Li-rich WGB stars andreport on their evolutionary status. We explore different paths to propose atentative explanation for the lithium anomaly. Using archive data, we derivethe fundamental parameters of WGB (Teff, log g, log(L/Lsun)) using Hipparcosparallaxes and recent temperature scales. From the equivalent widths of Liresonance line at 6707 {\AA}, we uniformly derive the lithium abundances andapply when possible NLTE corrections following the procedure described by Lindet al. (2009). We also compute dedicated stellar evolution models in the massrange 3.0 to 4.5 Msun, exploring the effects of rotation-induced andthermohaline mixing. These models are used to locate the WGB stars in the H-Rdiagram and to explore the origin of the abundance anomalies. The location ofWGB stars in the H-R diagram shows that these are intermediate mass stars ofmasses ranging from 3.0 to 4.5 Msun located at the clump, which implies adegeneracy of their evolutionary status between subgiant/red giant branch andcore helium burning phases. The atmospheres of a large proportion of WGB stars(more than 50%) exhibit lithium abundances A(Li) \geq 1.4 dex similar toLi-rich K giants. The position of WGB stars along with the Li-rich K giants inthe H-R diagram however indicates that both are well separated groups. Thecombined and tentatively consistent analysis of the abundance pattern forlithium, carbon and nitrogen of WGB stars seems to indicate that carbonunderabundance could be decorrelated from the lithium and nitrogenoverabundances.

Weak G-band stars on the H-R Diagram: Clues to the origin of Li anomaly