Exact calculations of vertex sˉγb\bar{s}\gamma b and sˉZb\bar{s} Z b in the unitary gauge

In this paper, we present the exact calculations for the vertex $\bar{s}\gamma b$ and $\bar{s} Z b$ in the unitary gauge. We found that (a) the divergent- and $\mu$-dependent terms are left in the effective vertex function $\Gamma^\gamma_\mu(p,k)$ for $b \to s \gamma$ transition even after we sum up the contributions from four related Feynman diagrams; (b) for an on-shell photon, such terms do not contribute et al; (c) for off-shell photon, these terms will be canceled when the contributions from both vertex $\bar{s}\gamma b$ and $\bar{s} Z b$ are taken into account simultaneously, and therefore the finite and gauge independent function $Z_0(x_t)=C_0(x_t)+ D_0(x_t)/4$, which governs the semi-leptonic decay $b \to s l^- l^+$, is derived in the unitary gauge.Comment: 13 pages, 2 figures, Revte

N,N′-Bis(6-methyl-2-pyrid­yl)oxamide

In the crystal structure of the title compound, C14H14N4O2, the mol­ecules are almost planar (mean deviation 0.028 Å) and a weak intra­molecular N—H⋯O hydrogen bond between the H atom bound to an oxamide N atom and a carbonyl O atom is found. The asymmetric unit consits of one half-mol­ecule which is located on a centre of inversion

When employees are ostracised, the whole organisation suffers

They stop helping colleagues, following the rules and offering ideas, write Chia-Huei Wu and colleague

Methyl 4-[(5-chloro­pyrimidin-2-yl)carbamo­yl]benzoate

Mol­ecules of the title compound, C13H10ClN3O3, form centrosymmetric dimers via inter­molecular N—H⋯N hydrogen bonds generating an R 2 2(8) motif. The dimers are further connected through an O⋯Cl—C halogen bond [O⋯Cl = 3.233 (1) Å and O⋯Cl—C = 167.33 (1)°] into a chain along [110]. The secondary amide group adopts a cis conformation. Weak C—H⋯N hydrogen bonds among the methyl benzoate and pyrimidyl rings are also observed in the crystal structure

5-Iodo­pyrimidin-2-amine

The mol­ecule of the title compound, C4H4IN3, has crystallographic mirror plane symmetry. In the crystal, the mol­ecules are connected through N—H⋯N hydrogen bonds into polymeric tapes extended along the a axis, which are typical of 2-amino­pyrimidines. Each mol­ecule acts as a double donor and a double acceptor in the hydrogen bonding

6,6′-Dimethyl-2,2′-[oxalylbis(aza­nedi­yl)]dipyridinium dichloride acetonitrile solvate

In the crystal structure of the title compound, C14H16N4O2 2+·2Cl−·CH3CN, weak inter­molecular N—H⋯Cl hydrogen bonds are found between the H atoms bound to the pyridine and amine N atoms and the chloride anions. The asymmetric unit consits of one half cationic mol­ecule which is located on a centre of inversion, one chloride anion in a general position and one half acetonitrile mol­ecule which is located on a twofold axis. Because of symmetry, the C—H hydrogens of the acetonitrile solvent mol­ecule are disordered over two orientations

N-(6-Methyl-2-pyrid­yl)formamide

The mol­ecule of the title compound, C7H8N2O, is essentially planar with a maximum deviation of 0.0439 (1) Å from the best plane. In the crystal, N—H⋯O hydrogen bonds between self-complementary amide groups join mol­ecules into centrosymmetric dimers

N 1,N 2-Bis(6-methyl-2-pyrid­yl)formamidine

In the crystal structure of the title mol­ecule, C13H14N4, the two pyridyl rings are not coplanar but twisted about the C—N bond with an inter­planar angle of 71.1 (1)°. In the crystal, the mol­ecules form dimers, situated on crystallographic centres of inversion, which are connected via a pair of N—H⋯N hydrogen bonds. C—H⋯π-electron ring inter­actions are also present in the crystal structure. The title mol­ecule adopts an s–cis–anti–s–cis conformation in the solid state

2-{5-[N-(2-Pyridyl)carbamo­yl]pentan­amido}pyridinium hexa­fluoro­phosphate

In the crystal structure of the title compound, C16H19N4O2 +·PF6 −, the cations and anions are situated on centres of inversion. Thus, the N—H H atom is disordered over both N atoms due to symmetry. In the crystal, mol­ecules are connected via N—H⋯F and N—H⋯O hydrogen bonds. The cation adopts the ⋯AAA⋯ trans conformation in the solid state