A solution of the DGLAP equation for gluon at low x

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate εF ₂(x,Q)²/ε In Q ² using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.     

Robust linear optimization under general norms

We explicitly characterize the robust counterpart of a linear programming problem with uncertainty set described by an arbitrary norm. Our approach encompasses several approaches from the literature and provides guarantees for constraint violation under probabilistic models that allow arbitrary dependencies in the distribution of the uncertain coefficients.     

Working group report: Neutrino and astroparticle physics

This is the report of neutrino and astroparticle physics working group at WHEPP-7. Discussions and work on CP violation in long baseline neutrino experiments, ultra high energy neutrinos, supernova neutrinos and water Cerenkov detectors are discussed.     

Search for Resolution of Chiral Fluorohalogenomethanes and Parity‐Violation Effects at the Molecular Level

The first observation of a parity‐violation effect in molecules induced by weak interactions is still a dream that requires the synthesis and, eventually, the resolution of the enantiomers of well‐chosen simple chiral molecules together with an appropriate experimental set‐up for high‐resolution spectroscopy. Performing IR spectroscopy on highly enantiomerically enriched samples of bromochlorofluoromethane succeeded in giving an upper limit of 10^?13 for the relative vibrational energy difference between the two enantiomers. These results led us to conceive a new experimental set‐up based on a supersonic molecular beam and to work on other chiral molecules, such as chlorofluoroiodomethane. A synthesis of (±)‐CHClFI from racemic chlorofluoroiodoacetic acid should, in the near future permit the preparation of optically active samples of this haloform. The development of molecular beam spectroscopy using a two‐photon Ramsey‐fringes experiment should allow us to reach the precision needed to observe parity violation. These experimental challenges, which stimulate a close collaboration between chemists and physicists, are presented. The success of these projects would open the route to new information on the molecular Hamiltonian, a better knowledge of the electroweak interaction, and a better control of the various chirality‐related properties of simple molecules.     

Algebraic spatial correlations in lattice gas automata violating detailed balance

In this paper we discuss the existence of generic long-range correlations in spatially homogeneous and stable equilibrium states of closed lattice gas automata whose stochastic collision rules violate the symmetry conditions of detailed balance and in addition satisfy local conservation laws. Such correlations occur even though the collision rules are strictly local and invariant under all symmetries of the lattice. First a phenomenological (Langevin equation) approach is discussed. Next we present a theoretical analysis on the basis of an approximate microscopic (ring kinetic) theory. This theory is used to calculate the amplitude ofr ^– tails in the spatial correlations, and the result is compared with computer simulations.     

Gravity and CP violation

The non-conservation of CP symmetry in the decay of neutralK mesons was discovered almost three decades ago. The origin of this unique phenomenon is still not well understood. There have been attempts to link it with energy splitting of theK and in the earth's gravitational field. In this essay we examine these attempts critically. A more natural way in which a gravitational field can couple asymmetrically to the system is through torsion, which coupling to isospin can, in addition to parity violation, also give rise to a C violation. The magnitude of this effect is estimated in the vicinity of a kaon and found to give a CP-violating parameter of the right value. Moreover, it is predicted that the CP violating parameter for the new system is much smaller 10^–6. Implications for baryogenesis in the early universe is also studied. In this paper we work not with the Newtonian gravitational constantG but with a torsion coupling constant, which is energy-dependent and can be related to the Fermi weak interaction constant.     

Isospin violation, light quark masses, and all that

Isospin violation is driven through the light quark mass difference and electromagnetic effects. I review recent progress in extracting the light quark mass difference and tests of the chiral dynamics of Quantum Chromodynamics in various reactions involving light as well as heavy quarks.     

Entropic information for travelling solitons in Lorentz and CPT breaking systems

In this work we group four research topics apparently disconnected, namely solitons, Lorentz symmetry breaking, supersymmetry, and entropy. Following a recent work (Gleiser and Stamatopoulos, 2012), we show that it is possible to construct in the context of travelling wave solutions a configurational entropy measure in functional space, from the field configurations. Thus, we investigate the existence and properties of travelling solitons in Lorentz and CPT breaking scenarios for a class of models with two interacting scalar fields. Here, we obtain a complete set of exact solutions for the model studied which display both double and single-kink configurations. In fact, such models are very important in applications that include Bloch branes, Skyrmions, Yang–Mills, Q-balls, oscillons and various superstring-motivated theories. We find that the so-called Configurational Entropy (CE) for travelling solitons shows that the best value of parameter responsible to break the Lorentz symmetry is one where the energy density is distributed equally around the origin. In this way, the information-theoretical measure of travelling solitons in Lorentz symmetry violation scenarios opens a new window to probe situations where the parameters responsible for breaking the symmetries are arbitrary. In this case, the CE selects the best value of the parameter in the model.