Transverse Space Research Articles

D3+D6 solution and D4+D6 solution

Abstract We make the supergravity solutions describing the branes (D3 branes and D4 branes) localized within the D6 branes in the near core region of D6 brane. From the D=11 solutions (M3 branes and M4 branes with the ZN identifications in the transverse space) we obtain the D=10 supergravity solutions of D3 branes localized within D6 branes and D4 branes localized within D6 branes by reducing the dimension down to D=10 along a circular direction of S3 part of the transverse space. M3 brane solution leads to D=10 background representing D3 branes localized on D6 branes in the region close to the D6 branes core. M4 branes lead to the D4 branes localized on D6 branes in the region close to the D6 brane core.

Brane resolution through transgression

Modifications to the singularity structure of D3-branes that result from turning on a flux for the R-R and NS-NS 3-forms (fractional D3-branes) provide important gravity duals of four-dimensional N=1 super-Yang-Mills theories. We construct generalisations of these modified p-brane solutions in a variety of other cases, including heterotic 5-branes, dyonic strings, M2-branes, D2-branes, D4-branes and type IIA and type IIB strings, by replacing the flat transverse space with a Ricci-flat manifold M_n that admits covariantly constant spinors, and turning on a flux built from a harmonic form in M_n, thus deforming the original solution and introducing fractional branes. The construction makes essential use of the Chern-Simons or ``transgression'' terms in the Bianchi-identity or equation of motion of the field strength that supports the original undeformed solution. If the harmonic form is L^2 normalisable, this can result in a deformation of the brane solution that is free of singularities, thus providing viable gravity duals of field theories in diverse dimensions that have less than maximal supersymmetry. We obtain examples of non-singular heterotic 5-branes, dyonic strings, M2-branes, type IIA strings, and D2-branes.

Soft gluon resummation in transverse momentum space for electroweak boson production at hadron colliders

The distribution of W and Z bosons produced with small transverse momentum ( $p_{\rm T}$ ) at hadron colliders receives important contributions from large logarithms arising from soft gluon emission. Although conventionally the all-orders resummation of these ‘Sudakov’ logarithms is performed in impact parameter (Fourier transform) space, $p_{\rm T}$ -space resummation is also possible, and offers certain advantages. We present a detailed phenomenological analysis of W and Z production at small $p_{\rm T}$ at the Tevatron $p \bar p$ collider, using $p_{\rm T}$ -space resummation. A good description of the CDF and D0 data can be obtained provided a significant non-perturbative contribution is included. We also present predictions for the LHC.

Probing small length scales in heavy-ion collisions with event-by-event correlation analysis

I consider recent proposals of fluctuation suppression for certain global event variables in heavy-ion collisions as a signature of QGP formation. I relate these proposals to possible formation of a pion lattice at chemical freezeout due to rapid traversal of the QCD phase boundary reflecting the greater symmetry of a locally equilibrated prehadronic state. I then present a method to detect this structure in the transverse phase space of heavy-ion collisions which depends on a newly-identified effect of local transverse Hubble flow on two-particle distributions and suggest that such structure may have been observed already in the transverse phase space of Pb-Pb collisions at the SPS.

Scale factor in double parton collisions and parton densities in transverse space

The scale factor ${\ensuremath{\sigma}}_{\mathrm{eff}},$ which characterizes double parton collisions in high energy hadron interactions, is a direct manifestation of the distribution of the interacting partons in transverse space, in such a way that different distributions give rise to different values of ${\ensuremath{\sigma}}_{\mathrm{eff}}$ in different double parton collision processes. We work out the value of the scale factor in a few reactions of interest, in a correlated model of the multiparton density of the proton recently proposed.

Skewed parton distributions and the scale dependence of the transverse size parameter

We discuss the scale dependence of a skewed parton distribution of the pion obtained from a generalized light-cone wave function overlap formula. Using a simple ansatz for the transverse momentum dependence of the light-cone wave function and restricting ourselves to the case of a zero skewedness parameter, the skewed parton distribution can be expressed through an ordinary parton distribution multiplied by an exponential function. Matching the generalized and ordinary DGLAP evolution equations of the skewed and ordinary parton distributions, respectively, we derive a constraint for the scale dependence of the transverse size parameter, which describes the width of the pion wave function in transverse momentum space. This constraint has implications for the Fock state probability and valence distribution. We apply our results to the pion form factor.

HARMONIC SIGNAL EXTRACTION FROM STRONG CHAOTIC INTERFERENCE

The problem of signal extraction from received data contaminated with strong chaotic interference has been investigated and a novel approach to this problem is proposed based on the geometry of chaotic interference. According to this approach, chaotic attractor is first reconstructed from the received data, then in the way of projecting chaotic interference and harmonic signals into the local tangent space and its transverse space of the manifold in which the attractor lies, the two signals are successfully separated. Excellent results were achieved from the computer simulation experiments, which verify the effectiveness of the approach.

Perturbative color transparency in electroproduction experiments

We calculate quasi-exclusive scattering of a virtual photon and a proton or pion in nuclear targets. This is the first complete calculation of ``color transparency'' and ``nuclear filtering'' in perturbative QCD. The calculation includes full integrations over hard interaction kernels and distribution amplitudes in Feynman-$x$ fractions and transverse spatial separation space b. Sudakov effects depending on b and the momentum transfer ${Q}^{2}$ are included. Attenuation of the hadronic states propagating through the medium is calculated using an eikonal Glauber formalism. Nuclear correlations are included explicitly. We find that the color transparency ratio is comparatively insensitive to theoretical uncertainties inherent in perturbative formalism, such as choice of infrared cutoff scales. However, the ${Q}^{2}$ dependence of the transparency ratio is found to depend sensitively on the model of the distribution amplitude, with end-point-dominated models failing to be dominated by short distance. Color transparency experiments should provide an excellent test of the underlying theoretical assumptions used in the PQCD calculations.

HARD JET PROBES IN TERMS OF COLORLESS QCD DIPOLES

The forward jet playing the role of a hard probe in high energy QCD scattering is analyzed in terms of QCD dipole (color-singlet [Formula: see text]) configurations in the transverse position space. There are sizable differences with the analogous [Formula: see text] configurations of a hard photon probe which may lead to significant phenomenological consequences on the analysis of hard processes using a forward jet probe, e.g. at the Tevatron. A geometrical interpretation of the resulting distribution in terms of black disk diffraction is proposed.

Quantum Statistical Entropy of Spherical Black Holes in Higher Dimensions

The free energy and entropy of a general spherically symmetry black hole are calculated by quantum statistic method with brick wall model. Two different kinds of approximation are used to calculate the number of states in transverse spatial space. The final results are approximately equal except a rational numerical constant. The formulas of free energy and entropy, evaluated by each one of the two different kinds of approximation, are the same except some numerical constants. The free energy and entropy are dependent on the spacetime dimensions D. When D = 4, they reduce to the usual well known results.

A critical cosmological constant from millimeter extra dimensions

We consider `brane universe' scenarios with standard-model fields localized on a 3-brane in 6 spacetime dimensions. We show that if the spacetime is rotationally symmetric about the brane, local quantities in the bulk are insensitive to the couplings on the brane. This potentially allows compactifications where the effective 4-dimensional cosmological constant is independent of the couplings on the 3-brane. We consider several possible singularity-free compactification mechanisms, and find that they do not maintain this property. We also find solutions with naked spacetime singularities, and we speculate that new short-distance physics can become important near the singularities and allow a compactification with the desired properties. The picture that emerges is that standard-model loop contributions to the effective 4-dimensional cosmological constant can be cut off at distances shorter than the compactification scale. At shorter distance scales, renormalization effects due to standard-model fields renormalize the 3-brane tension, which changes a deficit angle in the transverse space without affecting local quantities in the bulk. For a compactification scale of order 10^{-2} mm, this gives a standard-model contribution to the cosmological constant in the range favored by cosmology.

Angular collection using solenoids

Pion collection after the target is considered using solenoids. Two collection systems, involving solenoids, the quarter wave transformer and the Adiabatic lens, widely used for the positron collection in linear accelerators, are described. Their main features, as the acceptance volume in transverse phase space, the maximum source radius, the maximum transverse momentum accepted, are provided. The results are presented for the phase space associated to the canonical variables as for the trace space concerning the geometrical variables. The energy acceptances for both systems are presented and compared. Some special properties of the solenoids are then outlined.

Unstable periodic orbits in the presence of spatio-temporal chaos

In this paper we investigate spatio-temporal disorder in a liquid crystal light valve with two-dimensional feedback and modulated input. We focus on the specific case of an optical feedback with a 180° rotation. By modulating the input field with appropriate amplitude and frequency, chaotic domains are formed in different locations of the transverse space [1, 2]. Because of diffusion, a global description of the spatio-temporal dynamics requires a partial differential equation. However, the local dynamics of the chaotic domains can be embedded in low-dimensional manifolds. The detection of a variety of different unstable periodic orbits (UPOs) at different spatial locations and the presence of UPOs for different detector sizes are strong indications that the dimensionality of the model of spatio-temporal chaos in our system can be drastically reduced.

Exotic branes and non-perturbative seven branes

We construct the effective action of certain exotic branes in the Type II theories which are not predicted by their space-time supersymmetry algebras. We analyze in detail the case of the NS-7B brane, S-dual to the D7-brane, and connected by T-duality to other exotic branes in Type IIA: the KK-6A brane and the KK-8A brane (obtained by reduction of the M-theory Kaluza–Klein monopole and M9-brane, respectively). The NS-7B brane carries charge with respect to the S-dual of the RR 8-form, which we identify as a non-local combination of the electric–magnetic duals of the axion and the dilaton. The study of its effective action agrees with previous results in the literature showing that it transforms as an SL(2, Z) triplet together with the D7-brane. We discuss why this brane is not predicted by the Type IIB space-time supersymmetry algebra. In particular we show that the modular transformation relating the D7 and NS-7B brane solutions can be undone by a simple coordinate transformation in the two-dimensional transverse space, equivalent to choosing a different region to parametrize the SL(2, Z) moduli space. We discuss a similar relation between the D6 and KK-6A branes and the D8 and KK-8A branes.

T self-dual transverse space and gravity trapping

We advocate that the orbifold Z 2 symmetry of the gravity trapping model proposed by Randall and Sundrum can be seen, in appropriate coordinates, as a symmetry that exchanges the short distances with the large ones. Using diffeomorphism invariance, we construct extensions defined by patch glued together. A singularity occurs at the junction and it is interpreted as a brane, the jump brane, of codimension one. We give explicit realization in ten and eleven dimensional supergravity and show that the lower dimensional Planck scale on the brane is finite. The standard model would be trapped on a supersymmetric brane located at the origin whereas the jump brane would surround it at a finite distance. The bulk interactions could transmit the supersymmetry breaking from the jump brane to the SM brane.

Beam profile measurements and transverse phase-space reconstruction on the relativistic heavy-ion collider

The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Lab was commissioned during the summer of 1999. Transverse beam profiles on RHIC are measured with ionization profile monitors (IPMs). An IPM measures beam profiles by collecting the electrons liberated by residual gas ionization by the beam. The detector is placed in the gap of a dipole magnet to force the electrons to travel in straight lines from the beamline center to the collector. One IPM was tested and it measured the profiles of a single gold bunch containing 10 8 ions on consecutive turns. We show an example of one of these profiles giving transverse emittance. Several profiles are assembled into a mountain-range plot which shows betatron oscillations at injection. Finally, we use tomographic techniques to reconstruct the beam transverse phase space at two times in the early beam store.

A Paul trap configuration to simulate intense non-neutral beam propagation over large distances through a periodic focusing quadrupole magnetic field

This paper considers an intense non-neutral charged particle beam propagating in the z-direction through a periodic focusing quadrupole magnetic field with transverse focusing force, −κq(s)[xêx−yêy], on the beam particles. Here, s=βbct is the axial coordinate, (γb−1)mbc2 is the directed axial kinetic energy of the beam particles, qb and mb are the charge and rest mass, respectively, of a beam particle, and the oscillatory lattice coefficient satisfies κq(s+S)=κq(s), where S is the axial periodicity length of the focusing field. The particle motion in the beam frame is assumed to be nonrelativistic, and the Vlasov-Maxwell equations are employed to describe the nonlinear evolution of the distribution function fb(x,y,x′,y′,s) and the (normalized) self-field potential ψ(x,y,s)=qbφ(x,y,s)/γb3mbβb2c2 in the transverse laboratory-frame phase space (x,y,x′,y′), assuming a thin beam with characteristic radius rb≪S. It is shown that collective processes and the nonlinear transverse beam dynamics can be simulated in a compact Paul trap configuration in which a long non-neutral plasma column (L≫rp) is confined axially by applied dc voltages V̂=const on end cylinders at z=±L, and transverse confinement in the x−y plane is provided by segmented cylindrical electrodes (at radius rw) with applied oscillatory voltages ±V0(t) over 90° segments. Here, V0(t+T)=V0(t), where T=const is the oscillation period, and the oscillatory quadrupole focusing force on a particle with charge q and mass m near the cylinder axis is −mκq(t)[xêx−yêy], where κq(t)≡8qV0(t)/πmrw2.

Time evolution of pulsed supersonic jets of argon clusters

The correlation between cluster decomposition and the structure of pulsed supersonic jets of argon clusters is analysed. The longitudinal and transverse space structures of short supersonic pulses (0.5 ms) of argon clusters have been studied far from the skimmer, by a movable mass spectrometer and near the skimmer, by an electron impact ionizer, depending on the stagnation pressure. It has been found that the pulses consist of two distinct fractions of clusters, light and heavy, which are also differently localized in space. The heavy fraction is located inside the pulses and the light fraction is mainly found in the outlying area of the pulses. It has been shown that neutral clusters reveal instability for a long period of time (~0.6 ms) after condensation. This instability results in additional divergence of the cluster beam. Therefore, the change of the cluster beam cross section as a function of the pressure correlates with the corresponding change in the cluster instability.

A comparison of growth impairment and orthodontic results in adult patients with clefts of palate and unilateral clefts of lip, palate and alveolus

Objective: To evaluate and compare the long-term aesthetic and functional results of surgical and orthodontic treatment in patients with cleft palate and unilateral cleft lip, palate, and alveolus.Design: 30 patients with unilateral cleft lip, palate, and alveolus and 30 patients with isolated cleft palate, mean age of 18.9 years, were evaluated by cephalometric and model analysis a mean of 1.5 years after orthodontic treatment. In each group the surgical treatment has been similar.Results: Model analysis: The sum of every mesiodistal tooth diameter in the maxilla and in the mandible was recorded according to the Bolton analysis. Twenty patients with unilateral cleft lip, palate and alveolus had relatively large upper dental arches and nine had relatively large lower dental arches. Twenty-two patients with cleft palates had large upper dental arches and seven had large mandibular arches. Eleven patients with unilateral cleft lip, palate, and alveolus and 18 patients with cleft palate had a negative space supply (the sum of the mesiodistal tooth diameters compared with the sagittal length of the alveolar ridge) in the region of the lateral teeth. All patients had persistent transverse space deficits that were increased on the side of the cleft in patients with cleft lip, palate, and alveolus. These unilateral transversal space deficits were recorded in 22 patients with unilateral cleft lip, palate, and alveolus and in 8 patients with isolated cleft palate. Sagittal measurements were reduced in 26 patients with unilateral cleft lip, palate, and alveolus and in 23 patients with cleft palate alone. The alveolar midline of the maxilla and the mandible were displaced in 25 patients with unilateral cleft lip, palate, and alveolus and in 19 patients with isolated cleft palate. Lateral cephalometric analysis: The lateral cephalograms taken at the same time as the models showed a mean SNA of 76.8° and a NL-NSL angle of 8.7°, indications of a tendency towards maxillary retrognathia in patients with unilateral cleft lip, palate, and alveolus. Patients with cleft palate had a mean SNA of 79.6° and NL-NSL angle of 8.1°. The anterior facial vertical index was within normal limits in patients with cleft lip, palate, and alveolus (44% vs 56%). An anterior facial height index of 42% compared with 58% in patients with isolated cleft palate indicated a slight reduction in midface height with an increase in the lower face as a consequence.Conclusion: Orthodontic and surgical treatment can result in satisfactory results on model analysis. However, there is specific growth impairment of the maxilla 1.5 years after termination of orthodontic treatment and this influences the final cephalometric analysis, particularly in patients with cleft lip, palate, and alveolus.

On the resummation of subleading logarithms in the transverse momentum distribution of vector bosons produced at hadron colliders

The perturbation series for electroweak vector boson production at small transverse momentum is dominated by large double logarithms at each order in perturbation theory. An accurate theoretical prediction therefore requires a resummation of these logarithms. This can be performed either directly in transverse momentum space or in impact parameter (Fourier transform) space. While both approaches resum the same leading double logarithms, the subleading logarithms are, in general, treated differently. We comment on two recent approaches to this problem, emphasising the particular subleading logarithms resummed in each case and the numerical differences in the cross sections which result.