Jet evolution from weak to strong coupling

Recent studies, using the AdS/CFT correspondence, of the radiation produced by a decaying system or by an accelerated charge in the N=4 supersymmetric Yang-Mills theory, led to a striking result: the 'supergravity backreaction', which is supposed to describe the energy density at infinitely strong coupling, yields exactly the same result as at zero coupling, that is, it shows no trace of quantum broadening. We argue that this is not a real property of the radiation at strong coupling, but an artifact of the backreaction calculation, which is unable to faithfully capture the space-time distribution of the radiation. This becomes obvious in the case of a decaying system ('virtual photon'), for which the backreaction is tantamount to computing a three-point function in the conformal gauge theory, which is independent of the coupling since protected by symmetries. Whereas this non-renormalization property is specific to the conformal N=4 SYM theory, we argue that the failure of the three-point function to provide a local measurement is in fact generic: it holds in any field theory with non-trivial interactions. To properly study a localized distribution, one should rather compute a four-point function, as standard in deep inelastic scattering. We substantiate these considerations with studies of the radiation produced by the decay of a time-like photon at both weak and strong coupling. We show that by computing four-point functions, in perturbation theory at weak coupling and, respectively, from Witten diagrams at strong coupling, one can follow the quantum evolution and thus demonstrate the broadening of the energy distribution. This broadening is slow when the coupling is weak but it proceeds as fast as possible in the limit of a strong coupling.Comment: 49 pages, 6 figure

Resumming large higher-order corrections in non-linear QCD evolution

Linear and non-linear QCD evolutions at high energy suffer from severe issues related to convergence, due to higher order corrections enhanced by large double and single transverse logarithms. We resum double logarithms to all orders by taking into account successive soft gluon emissions strongly ordered in lifetime. We further resum single logarithms generated by the first non-singular part of the splitting functions and by the one-loop running of the coupling. The resulting collinearly improved BK equation admits stable solutions, which are used to successfully fit the HERA data at small-x for physically acceptable initial conditions and reasonable values of the fit parameters.Comment: 4 pages, 4 figures, based on talk given at Hard Probes 2015, 29 June - 3 July 2015, Montreal, Canad

Resummation of Large Logarithms in the Rapidity Evolution of Color Dipoles

Perturbative corrections beyond leading-log accuracy to BFKL and BK equations, describing the rapidity evolution of QCD scattering amplitudes at high energy, exhibit strong convergence problems due to radiative corrections enhanced by large single and double transverse logs. We identify explicitly the physical origin of double transverse logs and resum them directly in coordinate space as appropriate for BK equation, in terms of an improved local-in-rapidity evolution kernel. Numerical results show the crucial role of double-logarithmic resummation for BK evolution, which is stabilized and slowed down by roughly a factor of two.Comment: 6 pages, 4 figures; Proceedings of the XXIII International Workshop on Deep-Inelastic Scattering (27 April-May 1 2015, Dallas (USA)

Aspects of the UV/IR correspondence : energy broadening and string fluctuations

We show that a source which radiates in the vacuum of the strongly coupled N=4 SYM theory produces an energy distribution which, in the supergravity approximation, has the same space-time pattern as the corresponding classical distribution: the radiation propagates at the speed of light without broadening. We illustrate this on the basis of several examples: a small perturbation propagating down a steady string, a massless particle falling into AdS_5, and the decay of a time-like wave-packet. A similar observation was made in Phys. Rev. D81 (2010) 126001 for the case of a rotating string. In all these cases, the absence of broadening is related to the fact that the energy backreaction on the boundary arises exclusively from the bulk perturbation at, or near, the boundary. This is so since bulk sources which propagate in AdS_5 at the speed of light do not generate any energy on the boundary. We interpret these features as an artifact of the supergravity approximation, which fails to encode quantum mechanical fluctuations that should be present even in the strong coupling limit. We argue that such fluctuations should enter the dual string theory as longitudinal string fluctuations, which are not suppressed at strong coupling. We heuristically estimate the effects of such fluctuations and argue that they restore the broadening of the radiation, in agreement with expectations from both quantum mechanics and the ultraviolet/infrared correspondence.Comment: 47 page

QED radiative corrections to impact factors

We consider the radiative corrections to the impact factors of electron and photon. According to a generalized eikonal representation the e\bar e scattering amplitude at high energies and fixed momentum transfers is proportional to the electron form factor. But we show that this representation is violated due to the presence of non-planar diagrams. One loop correction to the photon impact factor for small virtualities of the exchanged photon is obtained using the known results for the cross section of the e\bar e production at photon-nuclei interactions.Comment: 8 pp, plain LaTe

Profiles of near-resonant population-imbalanced trapped Fermi gases

We investigate the density profiles of a partially polarized trapped Fermi gas in the BCS-BEC crossover region using mean field theory within the local density approximation. Within this approximation the gas is phase separated into concentric shells. We describe how the structure of these shells depends upon the polarization and the interaction strength. A Comparison with experiments yields insight into the possibility of a polarized superfluid phase.Comment: 4 pages, 5 Figures, Published versio

Method of variational calculation of influence of the propulsion plants of forestry machines upon the frozen and thawing soil grounds

The forests, which grow in the conditions of complete expansion of the perpetually frozen ground, are unique forests in accordance with their taxational characteristics, quality indicators of the felled timber, and the ecological functions, which these forests perform in the nature. They are characterised by the low biological productivity, as well as by the high vulnerability due to climatological changes and human economic activities. It is fair to say that conservation of the permafrost is one of the main functions of the forests, which grow within the cryolithozone. Because of this, it is necessary to ensure special regimes for the forestry management and forest exploitation within the forests of the cryolithozone. We formulated the variational problem in order to determine influence of the changeability of the physical and mechanical properties of the thawing soil ground at the boundary with the permafrost ground. © 2019 SERSC

A lithospheric cross-section through the Swiss Alps—I. Thermokinematic modelling of the Neoalpine orogeny

In this paper we develop a forward 2-D thermokinematic model to investigate the Neoalpine 35-0 Ma phase of orogeny along the European Geotraverse (EGT) through the Swiss Alps on a crustal and lithospheric scale. Using a divergence-free kinematic model (div v=0), we define mass displacements, which subsequently serve as input to a transient thermal model. the thermal model uses critically assessed material prorameters and accounts for the depth dependence of the thermal properties in processes such as crustal thickening and mantle-lithospheric subduction. Based on the presentday density pattern of the deep seismic image and estimated exhumation and shortening rates, we derive, in a first modelling step, a mass-displacement field describing the Neoalpine orogeny as a uniform process in time. In a second—thermal—modelling step, this kinematic scenario is further refined by modelling the non-uniform cooling histories of the southern Lepontine in the Penninic domain. For that purpose we adopt lithospheric shortening rates—and consequently exhumation rates—to agree with total Neoalpine shortening, while keeping the geometry of the kinematic model fixed. the resultant thermokinematic model reflects the main characteristics of Neoalpine tectonics, and shows a good overall agreement with combined geological and geophysical data. the asymmetric feature of the present-day tectonic structure along the profile is strongly reflected in the thermal structure of the lithosphere. This demonstrates the need for a kinematic model to investigate the deep-temperature field in active tectonic provinces. For further refinement of the model, the amounts of shortening have to be more precisely estimated, and a higher spatial density in geochronological and metamorphic data is required. Furthermore, surface heat-flow values are, up to now, too uncertain to constrain the predicted surface heat flow. In summary, our results show that we need, in particular, data constraining the horizontal component of the tectonic and thermal evolution. the results of the Neoalpine orogeny modelling demonstrate that the presented thermokinematic procedure yields a good first-order approximation to investigate crustal-scale and lithospheric processes. We conclude. therefore, that the approach presented provides the potential for application not only to continent-continent collision zones, but also to any active tectonic provinc