|Vcb | and |Vub|: Theoretical Developments 1

Since sin 2β, the CP asymmetry in B → ψKS and related modes [1], is consistent with ǫK , |Vub|, and Bd,s mixing, searching for new flavor physics will require a combination of “redundant” and precise measurements that relate in the Standard Model (SM) to the same CKM elements. The determination of |Vcb| is important because the uncertainties in ǫK and in K → πνν̄ are proportional to |Vcb| , while the uncertainty of |Vub| dominates the error of a side of the unitarity triangle. Some of the best strategies to look for new physics include comparing angles and sides of the unitarity triangle, and results from tree and loop processes, and semileptonic decays are crucial for this. Processes mediated by flavor-changing neutral currents, such as b → q γ, b → q ll, and b → q νν̄ (q = s, d) are sensitive probes of the SM, and the theoretical tools to analyze these are the same as for |Vxb|. It is the accuracy of the theory that ultimately limits the sensitivity to new physics [2]. To illustrate where the future might take us, Fig. 1 shows CKM fits assuming that sin 2β equals its present central value with half the error, and that |Vub| is about 1.5σ lower [higher] than its central value with 5% experimental and theoretical errors: |Vub| = (3.0±0.15±0.15)× 10 [(5.0 ± 0.25 ± 0.25) × 10]. These fits are motivated by the fact that recent exclusive [inclusive] measurements of |Vub| appear to be on the low [high] side [3]. The resulting central values of the angle γ differ by 25, and the SM value of ∆ms is near the minimum [maximum] of its presently allowed range. Clearly, an accuracy of σ(|Vub|) ∼ 5% is very desirable. To believe at some point in the future that a discrepancy between measurements is due to new physics, model independent predictions are crucial. Results that depend on modeling nonperturbative strong interaction effects cannot prove that there is new flavor physics beyond the SM. Model independent predictions are those where the theoretical uncertainties are suppressed by powers of small parameters, typically ΛQCD/mb, ms/ΛχSB, αs(mb), etc. Still, in most cases, there are uncertainties at some order, which cannot be estimated model independently. If the goal is to test the Standard Model, one must assign sizable uncertainties to such “small corrections” not known from first principles.