Production cross sections of b quarks measured with data collected during the Run I Tevatron collider are generally appreciably larger than the QCD prediction at Next to Leading Order.
This has stimulated improvements of the theoretical calculation (FONLL) that, together with a consistent derivation of the Fragmentation functions and improved PDF, is now closer to experimental results.

However, the theoretical prediction is still affected by large uncertainties due to the choice of renormalization and factorization scale.

Unfortunately, different measurements of single and correlated production cross sections also appeared to be inconsistent among themselves. This is a major problem in comparing to theoretical predictions and has even suggested hints of new physics.

Data collected during the Tevatron Run II provide large samples of b hadrons that have been used by the CDF collaboration to perform high precision measurements of the single and correlated b quark production cross sections which resolve previously observed
disagreements.