Mean curvature flow of monotone Lagrangian submanifolds

We use holomorphic disks to describe the formation of singularities in the mean curvature flow of monotone Lagrangian submanifolds in $\mathbb C^{n}$.Comment: 37 pages, 3 figure

Coherent pion production by neutrinos on nuclei

The main part of coherent pion production by neutrinos on nuclei is essentially determined by PCAC, provided that the leptonic momentum transferred square Q^2 remains sufficiently small. We give the formulas for the charged and neutral current cross sections, including also the small non-PCAC transverse current contributions and taking into account the effect of the \mu^- mass. Our results are compared with the experimental ones and other theoretical treatments.Comment: 18 pages, 4 figure

From the Birkhoff-Gustavson normalization to the Bertrand-Darboux integrability condition

The Bertrand-Darboux integrability condition for a certain class of perturbed harmonic oscillators is studied from the viewpoint of the Birkhoff-Gustavson(BG)-normalization: By solving an inverse problem of the BG-normalization on computer algebra, it is shown that if the perturbed harmonic oscillators with a homogeneous-{\it cubic} polynomial potential and with a homogeneous-{\it quartic} polynomial potentials admit the same BG-normalization up to degree-4 then both oscillators satisfy the Bertrand-Darboux integrability condition.Comment: 23 pages, LaTeX (iop.sty), typos and Appendix adde

Light Gluino Constituents of Hadrons and a Global Analysis of Hadron Scattering Data

Light strongly interacting supersymmetric particles may be treated as partonic constituents of nucleons in high energy scattering processes. We construct parton distribution functions for protons in which a light gluino is included along with standard model quark, antiquark, and gluon constituents. A global analysis is performed of a large set of data from deep-inelastic lepton scattering, massive lepton pair and vector boson production, and hadron jet production at large values of transverse momentum. Constraints are obtained on the allowed range of gluino mass as a function of the value of the strong coupling strength alpha_s(M_Z) determined at the scale of the Z boson mass. We find that gluino masses as small as 10 GeV are admissible provided that alpha_s(M_Z) \ge 0.12. Current hadron scattering data are insensitive to the presence of gluinos heavier than ~ 100 - 150 GeV.Comment: 31 pages, 12 figures, RevTe

Stein structures: existence and flexibility

This survey on the topology of Stein manifolds is an extract from our recent joint book. It is compiled from two short lecture series given by the first author in 2012 at the Institute for Advanced Study, Princeton, and the Alfred Renyi Institute of Mathematics, Budapest.Comment: 29 pages, 11 figure

Factorization Breaking in Dijet Photoproduction with a Leading Neutron

The production of dijets with a leading neutron in ep-interactions at HERA is calculated in leading order and next-to-leading order of perturbative QCD using a pion-exchange model. Differential cross sections for deep-inelastic scattering (DIS) and photoproduction are presented as a function of several kinematic variables. By comparing the theoretical predictions for DIS dijets to recent H1 data, the pion flux factor together with the parton distribution functions of the pion is determined. The dijet cross sections in photoproduction show factorization breaking if compared to the H1 photoproduction data. The suppression factor is S = 0.48 (0.64) for resolved (global) suppression.Comment: 16 pages, 5 figure

LHC as πp\pi p and ππ\pi\pi Collider

We propose an experiment at the LHC with leading neutron production.The latter can be used to extract from it the total $\pi^+ p$ cross-sections. With two leading neutrons we can get access to the total $\pi^+\pi^+$ cross-sections. In this note we give some estimates and discuss related problems and prospects.Comment: 22 pages, 18 figures, 8 tables, to be publishe

The energy dependence of the hard exclusive diffractive processes in pQCD as the function of momentum transfer

We predict the dependence on energy of photo(electro) production processes: $\gamma(\gamma^*)+p\to V+ X$ with large rapidity gap at small x and large momentum $-t$ transferred to $V$ in pQCD. Here V is a heavy quarkonium ($J/\psi, \Upsilon$) or longitudinally polarized light vector meson (in the electroproduction processes), etc. In the kinematics of HERA we calculate the dependence on energy of cross sections of these processes as the function of momentum transfer $t$, photon virtuality $Q^2$ and/or quarkonium mass. In the kinematical region $Q_0^2\le -t\ll Q^2+M^2_V$ the nontrivial energy dependence of the cross section for the vector meson production due to the photon scattering off a parton follows within QCD from the summing of the double logarithmic terms. In the second regime $-t\ge Q^2+M^2_V$ within DGLAP approximation in all orders of perturbation theory the $q\bar q - {\rm parton}$ elastic cross section is energy independent. We show that the correct account of the double logarithmic terms and of the gluon radiation including kinematical constraints removes the disagreement between pQCD calculations and recent HERA experimental data. The explicit formula for the dependence of the differential cross section$\displaystyle{\frac{d^2\sigma}{dtdx_J}}$ of these processes on $s_{\gamma^*N}$ is obtained. We show that perturbative Pomeron type behavior may reveal itself only at energies significantly larger than those available at HERA. In addition we evaluate the energy dependence of DCVS processes.Comment: 22 pages, 4 figure

Testing the dynamics of high energy scattering using vector meson production

I review work on diffractive vector meson production in photon-proton collisions at high energy and large momentum transfer, accompanied by proton dissociation and a large rapidity gap. This process provides a test of the high energy scattering dynamics, but is also sensitive to the details of the treatment of the vector meson vertex. The emphasis is on the description of the process by a solution of the non-forward BFKL equation, i.e. the equation describing the evolution of scattering amplitudes in the high-energy limit of QCD. The formation of the vector meson and the non-perturbative modeling needed is also briefly discussed.Comment: 17 pages, 8 figures. Brief review to appear in Mod. Phys. Lett.