Fixed Momentum Transfer Research Articles

The High Energy Scattering Amplitude One-loop Gravitation in the Effective Field Theory

In this work, the Newton potential, together with the low-key corrective energy, an attractive loop of two large non-relativistic masses has been found. The asymptotic behavior of the scattering amplitude for two scalar particles at high energies with fixed momentum transfers was studied in the one-loop gravitation effective field theory.

The contribution of effective quantum gravity to the high energy scattering in the framework of modified perturbation theory and one loop approximation

The asymptotic behavior of the scattering amplitude for two scalar particles at high energies with fixed momentum transfers is studied. The study is done within the effective theory of quantum gravity based on quasi-potential equation. By using the modified perturbation theory, a systematic method is developed to find the leading eikonal scattering amplitudes together with corrections to them in the one-loop gravitational approximation. The relation is established and discussed between the solutions obtained by means of the operator and functional approaches applied to quasi-potential equation. The first non-leading corrections to the leading eikonal amplitude are found.

Overview of High Energy String Scattering Amplitudes and Symmetries of String Theory

In this paper, we studied symmetries of string scattering amplitudes in the high energy limits of both the fixed angle or Gross regime (GR) and the fixed momentum transfer or Regge regime (RR). We calculated high energy string scattering amplitudes (SSA) at arbitrary mass levels for both regimes. We discovered the infinite linear relations among fixed angle string amplitudes and the ifinite recurrence relations among Regge string amplitudes. The linear relations we obtained in the GR corrected the saddle point calculations by Gross, Gross and Mende. In addition, for the high energy closed string scatterings, our results differ from theirs by an oscillating prefactor which was crucial to recover the KLT relation valid for all energies. We showed that all the high energy string amplitudes can be solved using the linear or recurrence relations, so that all the string amplitudes can be expressed in terms of a single string amplitude. We further found that, at each mass level, the ratios among the fixed angle amplitudes can be extracted from the Regge string scattering amplitudes. Finally, we reviewed the recent developments on the discovery of infinite number of recurrence relations valid for all energies among Lauricella SSA. The symmetries or relations among SSA at various limits obtained previously can be exactly reproduced. It leads us to argue that the known S L ( K + 3 , C ) dynamical symmetry of the Lauricella function may be crucial to probe spacetime symmetry of string theory.

Separation of single-and two-center interference in ionization of H2 by proton impact

We present a triple differential experimental study of ionization of molecular hydrogen by proton impact. By comparing cross-sections obtained for coherent and incoherent projectile beams we were able to extract contributions from interference. Two types of distinctly different interferences could be identified. We demonstrate that both types can be separated in the same data set by analyzing triple differential cross-sections for fixed momentum transfer and for fixed recoil-ion momentum.

Vector meson production at low x from gauge/gravity duality

We use gauge/gravity duality to study vector meson (J/{\Psi}, {\rho}_0, {\Omega}, {\Phi}) production in electron-proton scattering, in the limit of high center of mass energy at fixed momentum transfer, corresponding to the limit of low Bjorken x, where the process is dominated by pomeron exchange. Our approach considers the pomeron at strong coupling, described by the graviton Regge trajectory in AdS space with a hard-wall to mimic confinement effects. Both the proton and vector mesons are described by simple holographic wave functions in AdS. This model agrees with HERA H1 data with a {\chi}^2 per degree of freedom below one on total cross-sections, and below two on differential cross-sections, confirming the success of previous studies that model low x DIS and DVCS using gauge/gravity duality.

Integrabilty of the BFKL dynamics and Pomeron trajectories in a thermostat

We consider scattering amplitudes in QCD at high energies \(\sqrt s \) and fixed momentum transfers \(q = \sqrt { - t} \) with a non-zero temperature T in the t-channel. In the s-channel the temperature leads to a compactification of the impact parameter plane. We find that the thermal BFKL Hamiltonian in the leading logarithmic approximation proceeds to have the property of the holomorphic separability. Moreover, there exists an integral of motion allowing one to construct the Pomeron wave function for arbitrary T in the coordinate and momentum representations. The holomorphic Hamiltonian for n-reggeized gluons at T ≠ 0 in the multicolour limit Nc → ∞ turns out to be equal to the local Hamiltonian for an integrable Heisenberg spin model. Further, the two-gluon Baxter function coincides with the corresponding wave function in the momentum representation. We calculate the spectrum of the Pomeron Regge trajectories at a finite temperature with taking into account the QCD running coupling. The important effect of the t-channel temperature is the appearence of a confining potential between gluons.

Deeply virtual Compton scattering from gauge/gravity duality

We use gauge/gravity duality to study deeply virtual Compton scattering (DVCS) in the limit of high center of mass energy at fixed momentum transfer, corresponding to the limit of low Bjorken x, where the process is dominated by the exchange of the pomeron. Using conformal Regge theory we review the form of the amplitude for pomeron exchange, both at strong and weak 't Hooft coupling. At strong coupling, the pomeron is described as the graviton Regge trajectory in AdS space, with a hard wall to mimic confinement effects. This model agrees with HERA data in a large kinematical range. The behavior of the DVCS cross section for very high energies, inside saturation, can be explained by a simple AdS black disk model. In a restricted kinematical window, this model agrees with HERA data as well.

HIGH ENERGY SCATTERING IN THE QUASIPOTENTIAL APPROACH

Asymptotic behavior of the scattering amplitude for two scalar particles by scalar, vector and tensor exchanges at high energy and fixed momentum transfers is reconsidered in quantum field theory. In the framework of the quasipotential approach and the modified perturbation theory a systematic scheme of finding the leading eikonal scattering amplitudes and its corrections are developed and constructed. The connection between the solutions obtained by quasipotential and functional approaches is also discussed. The first correction to leading eikonal amplitude is found.

Resolution of infrared divergences in gluon-gluon scattering regulated on a lightcone worldsheet lattice

We improve and update the discussion, given some years ago by my collaborators and me, of infrared divergences and Bremsstrahlung in one-loop gluon scattering probabilities in lightcone gauge. In that work, we showed that adding soft and collinear gluon radiation, satisfying simple Lorentz invariant constraints, not only cancelled all IR divergences, but resulted in compact expressions for the consequent scattering probabilities. Here we impose less restrictive (albeit noncovariant) constraints on the unobserved radiation, which increases the high energy (s) fixed momentum transfer (t) behavior of the total probabilities from -ln^2s to ln s ln t, a behavior shared by the (IR divergent) elastic probabilities. Using this new treatment we also make a much more detailed comparison of the lightcone results to covariant calculations using dimensional regularization, finding complete agreement between the two styles of calculation.

Soft X-ray resonant scattering study of single-crystal LaSr2Mn2O7

Soft X-ray resonant scattering studies at the Mn $L_{\texttt{II, III}}$- and the La $M_{\texttt{IV, V}}$- edges of single-crystal LaSr$_2$Mn$_2$O$_7$ are reported. At low temperatures, below $T_\texttt{N} \approx 160$ K, energy scans with a fixed momentum transfer at the \emph{A}-type antiferromagnetic (0 0 1) reflection around the Mn $L_{\texttt{II, III}}$-edges with incident linear $\sigma$ and $\pi$ polarizations show strong resonant enhancements. The splitting of the energy spectra around the Mn $L_{\texttt{II, III}}$-edges may indicate the presence of a mixed valence state, e.g., Mn$^{3+}$/Mn$^{4+}$. The relative intensities of the resonance and the clear shoulder-feature as well as the strong incident $\sigma$ and $\pi$ polarization dependences strongly indicate its complex electronic origin. Unexpected enhancement of the charge Bragg (0 0 2) reflection at the La $M_{\texttt{IV, V}}$-edges with $\sigma$ polarization has been observed up to 300 K, with an anomaly appearing around the orbital-ordering transition temperature, $T_{\texttt{OO}} \approx 220$ K, suggesting a strong coupling (competition) between them.

Multi-band spectroscopy of inhomogeneous Mott-insulator states of ultracold bosons

In this work, we use inelastic scattering of light to study the response of inhomogeneous Mott-insulator gases to external excitations. The experimental setup and procedure to probe the atomic Mott states are presented in detail. We discuss the link between the energy absorbed by the gases and accessible experimental parameters as well as the linearity of the response to the scattering of light. We investigate the excitations of the system in multiple energy bands and a band-mapping technique allows us to identify band and momentum of the excited atoms. In addition, the momentum distribution in the Mott states that is spread over the entire first Brillouin zone enables us to reconstruct the dispersion relation in the high energy bands using a single Bragg excitation with a fixed momentum transfer.

Implementation of the Duality between Wilson Loops and Scattering Amplitudes in QCD

We generalize modern ideas about the duality between Wilson loops and scattering amplitudes in N=4 super Yang-Mills theory to large-N (or quenched) QCD. We show that the area-law behavior of asymptotically large Wilson loops is dual to the Regge-Veneziano behavior of scattering amplitudes at high energies and fixed momentum transfer, when the quark mass is small and/or the number of particles is large. We elaborate on this duality for string theory in flat space, identifying the asymptotes of the disk amplitude and the Wilson loop of large-N QCD.

Local two-photon couplings and theJ=0fixed pole in real and virtual Compton scattering

The local coupling of two photons to the fundamental quark currents of a hadron gives an energy-independent contribution to the Compton amplitude proportional to the charge squared of the struck quark, a contribution which has no analog in hadron scattering reactions. We show that this local contribution has a real phase and is universal, giving the same contribution for real or virtual Compton scattering for any photon virtuality and skewness at fixed momentum transfer squared t. The t-dependence of this J=0 fixed Regge pole is parameterized by a yet unmeasured even charge-conjugation form factor of the target nucleon. The t=0 limit gives an important constraint on the dependence of the nucleon mass on the quark mass through the Weisberger relation. We discuss how this 1/x form factor can be extracted from high energy deeply virtual Compton scattering and examine predictions given by models of the H generalized parton distribution.

Two-photon exchange contribution to proton form factors in the time-like region

We estimate the two-photon exchange contribution to the process ${e}^{+}+{e}^{\ensuremath{-}}\ensuremath{\rightarrow}p+\overline{p} $. The two-photon exchange corrections to double spin polarization observables and form factors in the time-like region are calculated. The corrections are found to be small in magnitude but with a strong angular dependence at fixed momentum transfer. These two features are the same as those in the space-like region. In future experiments, the double spin polarization observable ${P}_{z}$ deserves to be considered.

Image contrast in X-ray reflection interface microscopy: comparison of data with model calculations and simulations

The contrast mechanism for imaging molecular-scale features on solid surfaces is described for X-ray reflection interface microscopy (XRIM) through comparison of experimental images with model calculations and simulated measurements. Images of elementary steps show that image contrast is controlled by changes in the incident angle of the X-ray beam with respect to the sample surface. Systematic changes in the magnitude and sign of image contrast are asymmetric for angular deviations of the sample from the specular reflection condition. No changes in image contrast are observed when defocusing the condenser or objective lenses. These data are explained with model structure-factor calculations that reproduce all of the qualitative features observed in the experimental data. These results provide new insights into the image contrast mechanism, including contrast reversal as a function of incident angle, the sensitivity of image contrast to step direction (i.e. up versus down), and the ability to maximize image contrast at almost any scattering condition defined by the vertical momentum transfer, Q(z). The full surface topography can then, in principle, be recovered by a series of images as a function of incident angle at fixed momentum transfer. Inclusion of relevant experimental details shows that the image contrast magnitude is controlled by the intersection of the reciprocal-space resolution function (i.e. controlled by numerical aperture of the condenser and objective lenses) and the spatially resolved interfacial structure factor of the object being imaged. Together these factors reduce the nominal contrast for a step near the specular reflection condition to a value similar to that observed experimentally. This formalism demonstrates that the XRIM images derive from limited aperture contrast, and explains how non-zero image contrast can be obtained when imaging a pure phase object corresponding to the interfacial topography.

Holographic double diffractive scattering

The holographic description of Pomeron exchange in a strongly-coupled gauge theory with an AdS dual is extended to the case of two to three scattering. We study the production event of a central particle via hadron-hadron scattering in the double Regge kinematic regime of large center-of-momentum energy and fixed momentum transfer. The computation reduces to the overlap of a holographic wave function for the central particle with a source function for the Pomerons. The formalism is applied to scalar glueball production and the resulting amplitude is studied in various kinematic limits.

Fully differential ionization cross sections in fast ion-atom collisions

Fully differential cross sections for helium ionization by fast ion collisions are analyzed. The emitted-electron angular distributions for fixed momentum transfer and electron energies are described theoretically and compared to the experiment. The effect of uncertainties in the determination of the momentum is considered within the theoretical model. The cross sections are found to be extremely sensitive to the inclusion of the uncertainties. Important quantitative and qualitative modifications of the calculated cross sections are obtained by including small uncertainties in the determination of the momentum transferred by the projectile to the target.

Phasing of resonant anomalous X-ray reflectivity spectra and direct Fourier synthesis of element-specific partial structures at buried interfaces

A formalism for model-independent determination of element-specific partial structures at buried interfaces using the phase-dependent behavior of resonant anomalous X-ray reflectivity (RAXR) data is described. Each RAXR spectrum (i.e.reflectivityversusenergy at a fixed momentum transfer near the absorption edge of interest) is uniquely constrained by the amplitude and phase of the resonant partial structure factor with pre-determined non-resonant total structure factor and anomalous dispersion corrections of the resonant species. The element-specific partial density distribution is then imaged by discrete Fourier synthesis with the partial structure factor. The utility of this approach is demonstrated in the comparison of Rb+and Sr2+distributions at muscovite (001)–aqueous solution interfaces derived by model-independent and model-dependent approaches. This imaging method is useful for rapid determination of complex buried interfacial structures where element-specific atomic distributions are poorly constrained by conventional X-ray reflectivity analysis.

BFKL pomeron in string models

We consider scattering amplitudes in string models in the Regge limit of high energies and fixed momentum transfers with the use of the unitarity in direct channels. Intermediate states are taken in the multi-Regge kinematics corresponding to the production of resonances with fixed invariant masses and large relative rapidities. In QCD such kinematics leads to the BFKL equation for the pomeron wave function in the leading logarithmic approximation. We derive a similar equation in the string theory and discuss its properties. The purpose of this investigation is to find a generalization of the BFKL approach to the region of small momentum transfers where non-perturbative corrections to the gluon Regge trajectory and reggeon couplings are essential. The BFKL equation in the string theory contains additional contributions coming from a linear part of the Regge trajectory and from the soft pomeron singularity appearing already in the tree approximation. In higher dimensions in addition, a non-multi-Regge kinematics corresponding to production of particles with large masses is important. We solve the equation for the pomeron wave function in the string theory for D = 4 and discuss integrability properties of analogous equations for composite states of several reggeized gluons in the multi-colour limit.maren.stein@desy.de.

Precise numerical evaluation of the two loop sunrise graph Master Integrals in the equal mass case

We present a double precision routine in Fortran for the precise and fast numerical evaluation of the two Master Integrals (MIs) of the equal mass two-loop sunrise graph for arbitrary momentum transfer in d = 2 and d = 4 dimensions. The routine implements the accelerated power series expansions obtained by solving the corresponding differential equations for the MIs at their singular points. With a maximum of 22 terms for the worst case expansion a relative precision of better than a part in 10 15 is achieved for arbitrary real values of the momentum transfer. Program summary Title of program: sunem Version: 1.0 Release: 1 Catalogue identifier: ADYC_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADYC_v1_0 Program obtainable from: http://www-ttp.physik.uni-karlsruhe.de/Progdata/ Computers: all Operating system: all Program language used: FORTRAN77 No. of lines in distributed program, including test data, etc.:1080 No. of bytes in distributed program, including test data, etc.: 11 835 Memory required to execute: Size: 1532K No. of bits in a word: up to 32 No. of processors used: 1 Distribution format: tar.gz Other programs called: none External files needed: none Nature of the physical problem: Numerical evaluation of the two Master Integrals of the equal mass two-loop sunrise Feynman graph for arbitrary momentum transfer in d = 2 and d = 4 dimensions. Method of solution: Accelerated power series expansions obtained by solving the differential equations for the MIs at their singular points. With a maximum of 22 terms for the worse case expansion a relative precision of better than a part in 10 15 is achieved for arbitrary real values of the momentum transfer. Restrictions on complexity of the problem: Limited to real momentum transfer and equal internal masses. Typical running time: Approximately 1 μs to evaluate the four Master integrals for a fixed momentum transfer value on a Pentium IV/3 GHz Linux PC.