Abstract: We carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass in pure Yang-Mills theory, without quark effects taken into account. A detailed, all-order analysis of the complete kernel appearing in this particular equation, derived in the Landau gauge, reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained solutions, for which the deviations from the correct behavior are best quantified by resorting to appropriately defined renormalization-group invariant quantities. This analysis, in turn, provides a solid guiding principle for improving the form of the kernel, and furnishes a well-defined criterion for discriminating between various possibilities. Certain renormalization-group inspired Ansatze for the kernel are then proposed, and their numerical implications are explored in detail. One of the solutions obtained fulfills the theoretical expectations to a high degree of accuracy, yielding a gluon mass that is positive definite throughout the entire range of physical momenta, and displays in the ultraviolet the so-called “power-law” running, in agreement with standard arguments based on the operator product expansion. Some of the technical difficulties thwarting a more rigorous determination of the kernel are discussed, and possible future directions are briefly mentioned.

Abstract: We study the f(+) form factor for the semileptonic (B) over bar (s) -> K+ l(-) (V) over bar (l) decay in a constituent quark model. The valence quark estimate is supplemented with the contribution from the (B) over bar* pole that dominates the high q(2) region. We use a multiply-subtracted Omnes dispersion relation to extend the quark model predictions from its region of applicability near q(max)(2) = (M-Bs – M-K)(2) similar to 23.75 GeV2 to all q(2) values accessible in the physical decay. To better constrain the dependence of f(+) on q(2), we fit the subtraction constants to a combined input from previous light cone sum rule by Duplancic and Melic (2008) [11] and the present quark model results. From this analysis, we obtain Gamma ( (B) over bar (s) -> K+ l(-) (V) over bar (l)) = (5.47(-0.46)(+0.54)) vertical bar Vub vertical bar(2) x 10(-9) MeV, which is about 10% and 20% higher than the predictions based on Lattice QCD and QCD light cone sum rules respectively. The former predictions, for both the form factor f(+) (q(2)) and the differential decay width, lie within the 1 sigma band of our estimated uncertainties for all q(2) values accessible in the physical decay, except for a quite small region very close to q(max)(2). Differences with the light cone sum results for the form factor f(+) are larger than 20% in the region above q(2) = 15 GeV2.