Six-Loop Anomalous Dimension of Twist-Three Operators in N=4 SYM

The result for the six-loop anomalous dimension of twist-three operators in the planar N=4 SYM theory is presented. The calculations were performed along the paper arXiv:0912.1624. This result provides a new data for testing the proposed spectral equations for planar AdS/CFT correspondence.Comment: 19 pages, typos corrected, details adde

Charm-loop effect in B→K(∗)ℓ+ℓ−B \to K^{(*)} \ell^{+} \ell^{-} and B→K∗γB\to K^*\gamma

We calculate the long-distance effect generated by the four-quark operators with $c$-quarks in the $B\to K^{(*)} \ell^+\ell^-$ decays. At the lepton-pair invariant masses far below the $\bar{c}c$-threshold, $q^2\ll 4m_c^2$, we use OPE near the light-cone. The nonfactorizable soft-gluon emission from $c$-quarks is cast in the form of a nonlocal effective operator. The $B\to K^{(*)}$ matrix elements of this operator are calculated from the QCD light-cone sum rules with the $B$-meson distribution amplitudes. As a byproduct, we also predict the charm-loop contribution to $B\to K^*\gamma$ beyond the local-operator approximation. To describe the charm-loop effect at large $q^2$, we employ the hadronic dispersion relation with $\psi=J/\psi,\psi (2S), ...$ contributions, where the measured $B\to K^{(*)}\psi$ amplitudes are used as inputs. Matching this relation to the result of QCD calculation reveals a destructive interference between the $J/\psi$ and $\psi(2S)$ contributions. The resulting charm-loop effect is represented as a $q^2$-dependent correction $\Delta C_9(q^2)$ to the Wilson coefficient $C_9$. Within uncertainties of our calculation, at $q^2$ below the charmonium region the predicted ratio $\Delta C_9(q^2)/C_9$ is $\leq 5$ for $B\to K \ell^+\ell^-$, but can reach as much as 20% for $B\to K^*\ell^+\ell^-$, the difference being mainly caused by the soft-gluon contribution.Comment: A few comments added, version to appear in JHE

QCD and strongly coupled gauge theories : challenges and perspectives

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.Peer reviewe