Based on the published mitochondrial phylogeny of Gill et al (2005), the genus
Poecile consists of all North American chickadees plus various similar Old World species like those you mentioned. The Old World species are the basal members of this group, while the seven North American species (Carolina, Black-capped, Mexican, Mountain, Boreal, Chestnut-backed, and Gray-headed (Siberian)) form a group within the genus. The mtDNA places Carolina as sister species to Mexican, Black-capped as sister to Mountain, and the other three brownish species as a group. However, some friends in my lab are working on an exhaustive study of these relationships using a large number of nuclear markers that changes up the species tree for the North American chickadees. See the abstract below, from the 2009 AOU meeting, but note that those were preliminary results and further analysis and loci continues to change the picture. I can't wait for the publication
Harris, R. B., Carling, M. D., Lovette, I. J.,
A PHYLOGENOMIC STUDY OF CHICKADEES REVEALS THEIR EVOLUTIONARY HISTORY
Abstract: The behavior and ecology of the New World chickadees have been studied extensively, but there is still no well-resolved molecular phylogeny for this model avian group. A previous mtDNA-based phylogeny found that Carolina Chickadees and Black-capped Chickadees are not each other’s closest relatives despite forming a well-studied hybrid zone where their breeding ranges overlap along a contact zone stretching across much of North America. Furthermore, the mtDNA–based phylogeny was unable to resolve the relationship between Mexican Chickadees and Mountain Chickadees. To further elucidate these relationships, we reconstructed a phylogeny of the New World chickadees using DNA sequence data from 25 nuclear loci. Trees constructed using both Bayesian and Maximum Likelihood methods supported the same topology. We found a sister species relationship between Carolina Chickadees and Black-capped Chickadees, which is discordant with the previous phylogenic hypothesis between these species. In addition, we found strong support for the placement of Mexican Chickadee as sister to Mountain Chickadee. These results underscore the value of using multiple loci to infer phylogenetic relationships between closely related species.
Gill, F.B., Slikas, B., Sheldon, F.H. 2005. Phylogeny of titmice (Paridae): II. Species relationships based on sequences of the mitochondrial cytochrome-B gene. Auk 122(1):121-143.
Abstract: We present a phylogenetic hypothesis for 40 species in the bird family Paridae, based on comparisons of nucleotide sequences of the mitochondrial cytochrome-b gene. Parids, including tits and chickadees, are an older group than their morphological stereotypy suggests. The longest cytochrome-b distances between species reach 12% in uncorrected divergence. With the exception of one thrasher-like terrestrial tit species of the Tibetan plateau (Pseudopodoces humilis), morphological and ecological stasis have prevailed since the initial parid radiation in the Old World during the mid-Tertiary.
All trees support monophyly of the family Paridae, which includes Parus (sensu lato) and the monotypic Oriental genera Sylviparus, Melanochlora, and Pseudopodoces. Within the clade of chickadees and gray tits (Parus, subgenus Poecile), three Old World species, Parus lugubris of the eastern Mediterranean and Balkan regions, P. superciliosus of high elevations in the Himalayas of western China, and P. varius of the Orient are sisters to all other species. The Eurasian crested titmice (subgenus Lophophanes) and North American crested titmice (subgenus Baeolophus) are sister groups. Our data suggest two colonizations of the New World by parids in the late Tertiary. The ancestor of modern Baeolophus colonized North America ∼4 mya, and the ancestor of all North American chickadees colonized North America ∼3.5 mya.