Bound on the curvature of the Isgur-Wise function of the baryon semileptonic decay Lambda_b -> Lambda_c + l + nu

In the heavy quark limit of QCD, using the Operator Product Expansion, the formalism of Falk for hadrons or arbitrary spin, and the non-forward amplitude, as proposed by Uraltsev, we formulate sum rules involving the Isgur-Wise function $\xi_{\Lambda} (w)$ of the baryon transition $\Lambda_b \to \Lambda_c \ell \overline{\nu}_{\ell}$, where the light cloud has $j^P=0^+$ for both initial and final baryons. We recover the lower bound for the slope $\rho_\Lambda^2 = - \xi '_\Lambda (1) \geq 0$ obtained by Isgur et al., and we generalize it by demonstrating that the IW function $\xi_{\Lambda} (w)$ is an alternate series in powers of $(w-1)$, i.e. $(-1)^n \xi_{\Lambda}^{(n)} (1) \geq 0$. Moreover, exploiting systematically the sum rules, we get an improved lower bound for the curvature in terms of the slope, $\sigma_\Lambda^2 = \xi "_\Lambda (1) \geq {3 \over 5} [\rho_\Lambda^2 + (\rho_\Lambda^2)^2]$. This bound constrains the shape of the Isgur-Wise function and it will be compelling in the analysis of future precise data on the differential rate of the baryon semileptonic decay $\Lambda_b \to \Lambda_c \ell \overline{\nu}_{\ell}$, that has a large measured branching ratio, of about 5%.Comment: 16 page

Assessing functional novelty of PSI structures via structure-function analysis of large and diverse superfamilies

The structural genomics initiatives have had as one of their aims to improve our understanding of protein function by providing representative structures for many structurally uncharacterised protein families. As suggested by the recent assessment of the Protein Structure Initiative (Structural Genomics Initiative, funded by the NIH), doubts have arisen as to whether Structural Genomics as initially planned were really beneficial to our understanding of biological issues, and in particular of protein function.
A few protein domain superfamilies have been shown to account for unexpectedly large numbers of proteins encoded in fully sequenced genomes. These large superfamilies are generally very diverse, spanning a wide range of functions, both in terms of molecular activities and biological processes. Some of these superfamilies, such as the Rossmann-fold P-loop nucleotide hydrolases or the TIM-barrel glycosidases, have been the subject of extensive structural studies which in turn have shed light on how evolution of the sequence and structure properties produce functional diversity amongst homologues. Recently, the Structure-Function Linkage Database (SFLD) has been setup with the aim of helping the study of structure-function correlations in such superfamilies. Since the evolutionary success of these large superfamilies suggests biological importance, several Structural Genomics Centers have focused on providing full structural coverage for representatives of all sequence families in these superfamilies.
In this work we evaluate structure/function diversity in a set of these large superfamilies and attempt to assess the quality and quantity of biological information gained from Structural Genomics.
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Magnetic anisotropy effects on quantum impurities in superconducting host

We study the magnetic anisotropy effects on the localized sub-gap excitations induced by quantum impurities coupled to a superconducting host. We establish the ground-state phase diagrams for single-channel and two-channel high-spin Kondo impurities; they unveil surprising complexity that results from the (multi-stage) Kondo screening in competition with the superconducting correlations and the magnetic anisotropy splitting of the spin multiplets. We discuss the possibility of detecting the Zeeman splitting of the sub-gap states, which would provide an interesting spectroscopic tool for studying the magnetism on the single-atom level. We also study the problem of two impurities coupled by the Heisenberg exchange interaction, and we follow the evolution of the sub-gap states for both antiferromagnetic and ferromagnetic coupling. For sufficiently strong antiferromagnetic coupling, the impurities bind into a singlet state that is non-magnetic, thus the sub-gap states move to the edge of the gap and can no longer be discerned. For ferromagnetic coupling, some excited states remain present inside the gap.Comment: 14 pages, 16 figures (significantly extended version, includes a section on the two-impurity effects

The Isgur-Wise function in the BPS limit

From sum rules in the heavy quark limit of QCD, using the non-forward amplitude, we demonstrate that if the slope rho^2 = -xsi'(1) of the Isgur-Wise function xsi(w) attains its lower bound 3/4 (as happens in the BPS limit proposed by Uraltsev), the IW function is completely determined, given by the function xsi(w) = [2/(w+1)]^(3/2)