Precision quantum chromodynamics from heavy quark expansions

The heavy quark expansion is applied to the semileptonic width of b → c and b → u transitions along with the moments of various decay distributions in the semileptonic b → c transitions. The resulting expressions can be used to improve the precision with which we can extract the values of the CKM matrix elements Vcb and Vub from the data. Heavy quark parameters like mb and m2p are also obtained with values that are completely consistent with theoretical expectations. The observed agreement between the theoretical predictions of the heavy quark expansion and the experimental data tightly constrain the theoretical uncertainty. The heavy quark expansion can also be applied to the photon energy moments in B → Xsgamma. The first two of these moments are directly related to mb and m2p . The experimentally imposed cuts on the photon energy spectrum introduce biases into the extracted values of these parameters. Correcting for these biases generates a remarkable agreement with the experimental data.