Explicit Form of the Isgur-Wise function in the BPS limit

Abstract

Using previously formulated sum rules in the heavy quark limit of QCD, we demonstrate that if the slope 2 ÿ 0 1 of the Isgur-Wise (IW) function w attains its lower bound 3 4 , then all the derivatives ÿ1 L L 1 attain their lower bounds 2L1!! 2L, obtained by Le Yaouanc et al. This implies that the IW function is completely determined, given by the function w 2 w1 3=2 . Since the so-called BPS condition proposed by Uraltsev implies 2 3 4 , it implies also that the IW function is given by the preceding expression.

Memorino on the ‘1/2 versus 3/2 puzzle’ in B̄→lν̄Xc – a year later and a bit wiser

“…(19,20). On the quantitative level it is not a priori clear, at which scale µ these sum rules are saturated and by which kind of states.…”

DecaysB¯→D**πand the Isgur-Wise functionsτ1/2Jugeau1, Yaouanc2, Oliver3 et al. 2005Phys. Rev. DSelf Cite

“…In what follows there is some unavoidable overlap with our Appendix B of ref. [13] from which some points are worth to be recalled.…”

“…the subindex 0 denoting the value of w for q 2 = m It is interesting to notice that the rates (12), (13) are given, assuming the D * * for a given j = to be degenerate, by the expressions…”

The Isgur-Wise Function in the BPS Limit

“…We have demonstrated [10], using the above SR, that if the slope reaches its lower bound (1), as happens in the BPS limit, then all derivatives reach their lower bounds (2), and then the Isgur-Wise function is completely fixed, namely…”

“…Using the formalism of Leibovich et al [13], we have demonstrated in [10], using translational invariance, the equations of motion and the BPS condition (15) that the slope and the curvature of the IW function satisfy :…”