Some consequences of GUP induced ultraviolet wavevector cutoff in one-dimensional Quantum Mechanics

A projection method is proposed to treat the one-dimensional Schrodinger equation for a single particle when the Generalized Uncertainty Principle (GUP) generates an ultraviolet (UV) wavevector cutoff. The existence of a unique coordinate representation called the naive one is derived from the one-parameter family of discrete coordinate representations. In this bandlimited Quantum Mechanics a continuous potential is reconstructed from discrete sampled values observed by means of a particle in maximally localized states. It is shown that bandlimitation modifies the speed of the center and the spreading time of a Gaussian wavepacket moving in free space. Indication is found that GUP accompanied by bandlimitation may cause departures of the low-lying energy levels of a particle in a box from those in ordinary Quantum Mechanics much less suppressed than commonly thought when GUP without bandlimitation is in work.Comment: 20 pages, 2 figure

Phase structure of the O(2)O(2) ghost model with higher-order gradient term

The phase structure and the infrared behaviour of the Euclidean 3-dimensional $O(2)$ symmetric ghost scalar field model with higher-order derivative term has been investigated in Wegner and Houghton's renormalization group framework. The symmetric phase in which no ghost condensation occurs and the phase with restored symmetry but with a transient presence of a ghost condensate have been identified. Finiteness of the correlation length at the phase boundary hints to a phase transition of first order. The results are compared with those for the ordinary $O(2)$ symmetric scalar field model.Comment: 15 pages, 13 figure

Ordering variable for parton showers

The parton splittings in a parton shower are ordered according to an ordering variable, for example the transverse momentum of the daughter partons relative to the direction of the mother, the virtuality of the splitting, or the angle between the daughter partons. We analyze the choice of the ordering variable and conclude that one particular choice has the advantage of factoring softer splittings from harder splittings graph by graph in a physical gauge.Comment: 28 pages, 5 figure

Multi-jet cross sections in deep inelastic scattering at next-to-leading order

We present the perturbative prediction for three-jet production cross section in DIS at the NLO accuracy. We study the dependence on the renormalization and factorization scales of exclusive three-jet cross section. The perturbative prediction for the three-jet differential distribution as a function of the momentum transfer is compared to the corresponding data obtained by the H1 collaboration at HERA.Comment: 5 pages, 3 figure

Three-jet cross sections in hadron-hadron collisions at next-to-leading order

We present a new QCD event generator for hadron collider which can calculate one-, two- and three-jet cross sections at next-to-leading order accuracy. In this letter we study the transverse energy spectrum of three-jet hadronic events using the kT algorithm. We show that the next-to-leading order correction significantly reduces the renormalization and factorization scale dependence of the three-jet cross section.Comment: 4 pages, 4 figures, REVTEX

QCD corrections to e+ e- --> 4 jets

We report on the next-to-leading order QCD calculation for e+ e- --> 4 jets. We explain some modern techniques which have been used to calculate the one-loop amplitudes efficiently. We further report on the general purpose numerical program ``Mercutio'', which can be used to calculate any infrared safe four-jet quantity in electron-positron annihilation at next-to-leading order.Comment: 4 pages, talk given at the UK Phenomenology Workshop on Collider Physics, Durham, 19-24 September 199

C2_2H observations toward the Orion Bar

C$_2$H is one of the first radicals to be detected in the interstellar medium. Its higher rotational transitions have recently become available with the Herschel Space Observatory. We aim to constrain the physical parameters of the C$_2$H emitting gas toward the Orion Bar. We analyse the C$_2$H line intensities measured toward the Orion Bar CO$^+$ Peak and Herschel/HIFI maps of C$_2$H, CH, and HCO$^+$, and a NANTEN map of [CI]. We interpret the observed C$_2$H emission using radiative transfer and PDR models. Five rotational transitions of C$_2$H have been detected in the HIFI frequency range toward the CO$^+$ peak. A single component rotational diagram gives a rotation temperature of ~64 K and a beam-averaged C$_2$H column density of 4$\times$10$^{13}$ cm$^{-2}$. The measured transitions cannot be explained by any single parameter model. According to a non-LTE model, most of the C$_2$H column density produces the lower-$N$ C$_2$H transitions and traces a warm ($T_{\rm{kin}}$ ~ 100-150 K) and dense ($n$(H$_2$)~10$^5$-10$^6$ cm$^{-3}$) gas. A small fraction of the C$_2$H column density is required to reproduce the intensity of the highest-$N$ transitions ($N$=9-8 and N=10-9) originating from a high density ($n$(H$_2$)~5$\times$10$^6$ cm$^{-3}$) hot ($T_{\rm{kin}}$ ~ 400 K) gas. The total beam-averaged C$_2$H column density in the model is 10$^{14}$ cm$^{-2}$. Both the non-LTE radiative transfer model and a simple PDR model representing the Orion Bar with a plane-parallel slab of gas and dust suggest, that C$_2$H cannot be described by a single pressure component, unlike the reactive ion CH$^+$, which was previously analysed toward the Orion Bar CO$^+$ peak. The physical parameters traced by the higher rotational transitions ($N$=6-5,...,10-9) of C$_2$H may be consistent with the edges of dense clumps exposed to UV radiation near the ionization front of the Orion Bar.Comment: Proposed for acceptance in A&A, abstract abridge