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We propose a detailed stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs in whispering gallery mode resonators pumped in the normal dispersion regime. We analyze the spatial bifurcation structure of the stationary states depending on two parameters that are experimentally tunable, namely the pump power and the cavity detuning. Our study demonstrates that the non-trivial equilibria play an important role in this bifurcation map, as their associated eigenvalues undergo critical bifurcations that are foreshadowing the existence of localized spatial structures. In particular, we show that in the normal dispersion regime, dark cavity solitons can emerge in the system, and thereby generate a Kerr comb. We also show how these solitons can coexist in the resonator as long as they do not interact with each other. The Kerr combs created by these (sets of) dark solitons are also analyzed, and their stability is discussed as well., Comment: 11 pages, 9 figures, 1 table

We present a stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs in whispering gallery mode resonators pumped in the anomalous dispersion regime. This article is the second part of a research work whose first part was devoted to the regime of normal dispersion, and was presented in ref. \cite{Part_I}. The case of anomalous dispersion is indeed the most interesting from the theoretical point of view, because of the considerable variety of dynamical behaviors that can be observed. From a technological point of view, it is also the most relevant because it corresponds to the regime where Kerr combs are predominantly generated, studied, and used for different applications. In this article, we analyze the connection between the spatial patterns and the bifurcation structure of the eigenvalues associated to the various equilibria of the system. The bifurcation map evidences a considerable richness from a dynamical standpoint. We study in detail the emergence of super- and sub-critical Turing patterns in the system. We determine the areas were bright isolated cavity solitons emerge, and we show that soliton molecules can emerge as well. Very complex temporal patterns can actually be observed in the system, where solitons (or soliton complexes) co-exist with or without mutual interactions. Our investigations also unveil the mechanism leading to the phenomenon of breathing solitons. Two routes to chaos in the system are identified, namely a route via the so called secondary combs, and another via soliton breathers. The Kerr combs corresponding to all these temporal patterns are analyzed in detail, and a discussion is led about the possibility to gain synthetic comprehension of the observed spectra out of the dynamical complexity of the system., Comment: 13 pages, 14 figures, 1 table

By means of QCD sum rules in local-duality limit, we analyze the behaviour of the form factors for the transitions of a real and a virtual photon to some pseudoscalar meson as functions of the involved momentum transfer. Except for the findings of BaBar for the neutral-pion form factor, the experimental data for all these transition form factors are compatible with saturation for large momentum transfer predicted by pQCD factorization. For light pseudoscalar mesons, saturation is observed already at relatively small momentum transfer, whereas for the eta-c meson it sets in only at larger momentum transfer. A recent measurement of the neutral-pion transition form factor by Belle seems to resolve this disturbing puzzle as its outcome is compatible with both saturation for relatively small momentum transfer and the behaviour of the eta and eta' transition form factors at large momentum transfer., Comment: 7 pages, 3 figures, talk presented at "Quark Confinement and the Hadron Spectrum X" (8 - 12 October 2012, TUM Campus Garching, Munich, Germany), to appear in the proceedings

Confronted with some surprising claims about experimentally measured or theoretically expected dependencies on the involved momentum transfer of various form factors of pseudoscalar mesons, we reassess the present status of these quantities by means of QCD sum rules. This approach provides well-developed and very efficient tools to relate in an analytical manner the parameters of QCD to the empirical properties of hadrons. Within this framework, we show that a few theoretical findings for the pion elastic form factor and one experimental result for the pion-to-photon transition form factor are at odds with rather general fundamental considerations., Comment: 3 pages, 3 figures, contributed to "Quark Confinement and the Hadron Spectrum X" (8 - 12 October 2012, TUM Campus Garching, Munich, Germany), to appear in the proceedings

We present the results of our recent analysis of the meson-photon transition form factors $F_{P\gamma}(Q^2)$ for the pseudoscalar mesons $P = \pi^0,\eta,\eta',\eta_c$, using the local-duality version of QCD sum rules., Comment: 7 pages, 4 figures, talk presented at "QCD@Work 2012 - International Workshop on Quantum Chromodynamics: Theory and Experiment" (18 - 21 June 2012, Lecce, Italy), to appear in the proceedings

We scrutinize recent findings on the charged-pion elastic form factor and the form factors entering in neutral-meson-to-photons transition amplitudes within the framework of QCD sum rules., Comment: 4 pages, 4 figures, contributed to "QCD@Work 2012 - International Workshop on Quantum Chromodynamics: Theory and Experiment" (18 - 21 June 2012, Lecce, Italy), to appear in the proceedings

We revisit $F_\pi(Q^2)$ and $F_{P\gamma}(Q^2)$, $P=\pi,\eta,\eta'$, making use of the local-duality (LD) version of QCD sum rules. We give arguments, that the LD sum rule provides reliable predictions for these form factors at $Q^2 \ge 5-6$ GeV$^2$, the accuracy of the method increasing with $Q^2$ in this region. For the pion elastic form factor, the well-measured data at small $Q^2$ give a hint that the LD limit may be reached already at relatively low values of momentum transfers, $Q^2\approx 4-8$ GeV$^2$; we therefore conclude that large deviations from LD in the region $Q^2=20-50$ GeV$^2$ seem very unlikely. The data on the ($\eta,\eta')\to\gamma\gamma^*$ form factors meet the expectations from the LD model. However, the {\sc BaBar} results for the $\pi^0\to\gamma\gamma^*$ form factor imply a violation of LD growing with $Q^2$ even at $Q^2\approx 40$ GeV$^2$, at odds with the $\eta,\eta'$ case and with the general properties expected for the LD sum rule., Comment: 17 pages. arXiv admin note: substantial text overlap with arXiv:1103.3781 and arXiv:1110.6904

The local-duality formulation of QCD sum rules allows for the prediction of hadronic form factors without knowledge of the subtle details of their structure. With the aid of this formalism, we take a fresh look at the behaviours of the charged-pion elastic form factor and of the form factors entering in the transitions of the ground-state neutral unflavoured pseudoscalar mesons pi^0, eta, eta' to one real and one virtual photon within a broad range of momentum transfers Q^2. The uncertainties induced by the approximations inherent to this local-duality approach are estimated by studying, in parallel to QCD, quantum-mechanical potential models, where the exact form factors, obtained by solving the Schr\"odinger equation, may be compared with the corresponding local-duality sum-rule results. For Q^2 larger than 5-6 GeV^2, we judge the predictions of the simplest local-duality model to be reliable and expect their accuracy to improve very fast with increasing Q^2. The large-Q^2 prediction for the pion elastic form factor should be approached already at moderate momentum transfer squared of approximately 4-8 GeV^2; large deviations from its local-duality behaviour for Q^2 = 20-50 GeV^2, predicted by some hadron-structure models, seem rather unlikely. The (eta, eta') to gamma + gamma* form factors deduced from the simplest local-duality approach exhibit excellent agreement with experiment. In startling contrast, BaBar measurements of the pi^0 to gamma + gamma* form factor imply local-duality violations which even rise with Q^2., Comment: 8 pages, talk presented at the "XXth International Workshop on High Energy Physics and Quantum Field Theory", 24 September - 1 October 2011, Sochi, Russia, to appear in the proceedings

We analyze $F_\pi(Q^2)$ and $F_{P\gamma}(Q^2)$, $P=\pi,\eta,\eta'$, within the local-duality (LD) version of QCD sum rules, which allows one to obtain predictions for hadron form factors in a broad range of momentum transfers. To probe the accuracy of this approximate method, we consider, in parallel to QCD, a potential model: in this case, the exact form factors may be calculated from the solutions of the Schr\"odinger equation and confronted with the results from the quantum-mechanical LD sum rule. On the basis of our quantum-mechanical analysis we conclude that the LD sum rule is expected to give reliable predictions for $F_\pi(Q^2)$ and $F_{\pi\gamma}(Q^2)$ in the region $Q^2 \ge 5-6$ GeV$^2$. Moreover, the accuracy of the method improves rather fast with growing $Q^2$ in this region. For the pion elastic form factor, the data at small $Q^2$ indicate that the LD limit may be reached already at relatively low values of momentum transfers, $Q^2\approx 4-8$ GeV$^2$; we therefore conclude that large deviations from LD in the region $Q^2=20-50$ GeV$^2$ reported in some recent theoretical analyses seem unlikely. The data on the ($\eta,\eta')\to\gamma\gamma^*$ form factors meet very well the expectations from the LD model. Surprisingly, the {\sc BaBar} results for the $\pi^0\to\gamma\gamma^*$ form factor imply a violation of LD growing with $Q^2$ even at $Q^2\approx 40$ GeV$^2$, at odds with the $\eta,\eta'$ case and the experience from quantum mechanics., Comment: 8 pages

We present the results of our recent analyses of the form factors F_pi(Q^2) and F_{P gamma}(Q^2), P = pi, eta, eta', within the local-duality version of QCD sum rules. To probe the expected accuracy of this method, we consider, in parallel to QCD, a quantum-mechanical potential model. In the latter case, the exact form factor may be calculated from the solutions of the Schr\"odinger equation and confronted with the result from the quantum-mechanical local-duality sum rule. We find that the local-duality sum rule is expected to yield reliable predictions for both F_pi(Q^2) and F_{pi gamma}(Q^2) in the region Q^2 > 5-6 GeV^2. Moreover, in this region the accuracy of this approach improves rather fast with increasing Q^2. For the elastic form factor F_pi(Q^2), we are therefore forced to conclude that large deviations from the local-duality limit in the region Q^2 = 20-50 GeV^2 reported in some recent theoretical studies seem to us unlikely. The data on the eta, eta' to gamma gamma* transition form factors meet pretty well the predictions of a "local-duality model." Interestingly, recent results for the pi to gamma gamma* transition form factor hint at a violation of local duality rising with Q^2; this is at odds with the eta and eta' cases and all our experience from quantum mechanics., Comment: talk presented at the "2011 Europhysics Conference on High Energy Physics - EPS-HEP 2011", 21 - 27 July 2011, Grenoble, Rhone-Alpes, France, to appear in the proceedings

Revisiting, within QCD sum rules, the relevance of local duality for the pion elastic form factor gives rise to optimism., Comment: 4 pages, 1 figure, talk presented at the "XIV International Conference on Hadron Spectroscopy", 13 - 17 June 2011, Munich, Germany, to appear in the proceedings

We analyze the accuracy of the pion elastic form factor predicted by a local-duality (LD) version of dispersive sum rules. To probe the precision of this theoretical approach, we adopt potential models with interactions that involve both Coulomb and confining terms. In this case, the exact form factor may be obtained from the solution of the Schroedinger equation and confronted with the LD sum rule results. We use parameter values appropriate for hadron physics and observe that, independently of the details of the confining interaction, the deviation of the LD form factor from the exact form factor culminates in the region Q^2~4-6 GeV^2. For larger Q^2, the accuracy of the LD description increases rather fast with Q^2. A similar picture is expected for QCD. For the pion form factor, existing data suggest that the LD limit may be reached already at the relatively low values Q^2=4-10 GeV^2. Thus, large deviations of the pion form factor from the behaviour predicted by LD QCD sum rules for higher values of Q^2, as found by some recent analyses, appear to us quite improbable. New accurate data on the pion form factor at Q^2=4-10 GeV^2 expected soon from JLab will have important implications for the behaviour of the pion form factor in a broad Q^2 range up to asymptotically large values of Q^2., Comment: 12 pages, extended version, conclusions remain unchanged

This work presents the results of our analysis of the accuracy of the pion form factor derived from the local-duality version of QCD sum rules., Comment: Presented at the International Conference "Quark Confinement and the Hadron Spectrum IX", August 30th - September 3rd, Madrid, Spain

We study the accuracy of the pion form factor, obtained with a local-duality version of dispersive sum rules. To probe this accuracy, we make use of a potential model, where the exact form factor may be calculated from the solution of the Schroedinger equation and confronted with the local-duality form factor. The deviation between these quantities is found to be below 20% in the region of momentum transfers Q > 2 - 3 GeV, independently of the specific form of the confining potential. We argue that the local-duality model for elastic form factors in QCD has at least this level of accuracy., Comment: 7 pages, Talk given at The XIXth International Workshop High Energy Physics and Quantum Field Theory (QFTHEP2010) 8-15 September 2010, Golitsyno, Moscow, Russia

We study the forward-backward and the CP-violating asymmetries (both time-independent and time-dependent) in rare semileptonic $B_d\to\rho^0 l^+l^-$, $B_s\to\phi l^+l^-$, and radiative leptonic $B_{d,s}\to \gamma l^+l^-$ decays and investigate the sensitivity of these asymmetries to the extensions of the Standard model., Comment: Revised version: plots for A_CP corrected, discussion of B_d\to \rho^0 l^+l^- added