Leading-order Amplitude Research Articles

Patterns of high energy massive string scatterings in the Regge regime

We calculate high energy massive string scattering amplitudes of open bosonic string in the Regge regime (RR). We found that the number of high energy amplitudes for each fixed mass level in the RR is much more numerous than that of Gross regime (GR) calculated previously. Moreover, we discover that the leading order amplitudes in the RR can be expressed in terms of the Kummer function of the second kind. In particular, based on a summation algorithm for Stirling number identities developed recently, we discover that the ratios calculated previously among scattering amplitudes in the GR can be extracted from this Kummer function in the RR. We conjecture and give evidences that the existence of these GR ratios in the RR persists to subleading orders in the Regge expansion of all string scattering amplitudes. Finally, we demonstrate the universal power-law behavior for all massive string scattering amplitudes in the RR.

Two-nucleon problem in semi-relativistic baryon chiral perturbation theory

We consider a symmetry-preserving approach to the nucleon-nucleon scattering problem in the framework of the higher-derivative formulation of baryon chiral perturbation theory. Within this framework the leading-order amplitude is calculated by solving renormalizable equations and corrections are taken into account perturbatively.

NN scattering in higher-derivative formulation of baryon chiral perturbation theory

We consider a new approach to the nucleon-nucleon scattering problem in the framework of the higher-derivative formulation of baryon chiral perturbation theory. Starting with a Lorentz-invariant form of the effective Lagrangian we work out a new symmetry-preserving framework where the leading-order amplitude is calculated by solving renormalizable equations and corrections are taken into account perturbatively. Analogously to the KSW approach, the (leading) renormalization scale dependence to any finite order is absorbed in the redefinition of a finite number of parameters of the effective potential at given order. On the other hand, analogously to Weinberg's power counting, the one-pion-exchange potential is of leading order and is treated non-perturbatively.

The large Nc baryon–meson It=Jt rule holds for three flavors

It has long been known that nonstrange baryon-meson scattering in the 1/N_c expansion of QCD greatly simplifies when expressed in terms of t-channel exchanges: The leading-order amplitudes satisfy the selection rule I_t = J_t. We show that I_t = J_t, as well as Y_t = 0, also hold for the leading amplitudes when the baryon and/or meson contain strange quarks, and also characterize their 1/N_c corrections, thus opening a new front in the phenomenological study of baryon-meson scattering and baryon resonances.

High-Energy Zero-Norm States and Symmetries of String Theory

High-energy limit of zero-norm states in the old covariant first quantized spectrum of the 26D open bosonic string, together with the assumption of a smooth behavior of string theory in this limit, are used to derive infinitely many linear relations among the leading high-energy, fixed-angle behavior of four-point functions of different string states. As a result, ratios among all high-energy scattering amplitudes of four arbitrary string states can be calculated algebraically and the leading order amplitudes can be expressed in terms of that of four tachyons as conjectured by Gross in 1988. A dual calculation can also be performed and equivalent results are obtained by taking the high-energy limit of Virasoro constraints. Finally, we compute all high-energy scattering amplitudes of three tachyons and one massive state at the leading order by saddle-point approximation to verify our results.

Nonlinear internal waves in the upper atmosphere

This article considers the large-scale dynamics generated in the upper atmosphere by the destabilization of a linear internal gravity wave and its eventual restabilization through nonlinear processes into a coherent pattern. The assumption of a strongly dissipative medium is relevant to wave propagation in the thermosphere range above 100 km. A parametric instability analysis is carried out involving the Froude, Reynolds and Prandtl numbers, and the following parameters: friction, wave incidence and disturbance periodicity. A solution of the motion is sought with the help of a multiscale technique based upon the hypothesis of large-scale flow. The leading-order amplitude equation governing this dynamics contains the Cahn–Hilliard equation, but also possesses a dispersive term depending on the Prandtl number, a large-scale damping proportional to the overall Richardson number and a quadratic term modelling the incidence effects. A numerical and analytical study of this equation is given. An internal-wave stability criterion is obtained which shows the possibility of obtaining coherent structures for large Froude numbers.

Exclusive production of pentaquarks in the scaling regime

We investigate two exclusive reactions with a Theta+ pentaquark in the final state: electroproduction of a K meson on the nucleon, and K+ scattering on a neutron target producing a lepton pair. These reactions offer unique opportunities to investigate the structure of pentaquark baryons at parton level. We discuss the generalized parton distributions for the N --> Theta+ transition and give the leading order amplitude for these processes in the Bjorken regime.

Vector analyzing power in elastic electron-proton scattering

We compute the vector analyzing power (VAP) for the elastic scattering of transversely polarized electrons from protons at low energies using an effective theory of electrons, protons, and photons. We study all contributions through second order in $E∕M$, where $E$ and $M$ are the electron energy and nucleon mass, respectively. The leading-order VAP arises from the imaginary part of the interference of one- and two-photon exchange amplitudes. Subleading contributions are generated by the nucleon magnetic moment and charge radius as well as recoil corrections to the leading-order amplitude. Working to $O{(E∕M)}^{2}$, we obtain a prediction for ${A}_{n}$ that is free of unknown parameters and that agrees with the recent measurement of the VAP in backward angle $ep$ scattering.

Deep electroproduction of exotic hybrid mesons

We evaluate the leading order amplitude for the deep exclusive electroproduction of an exotic hybrid meson in the Bjorken regime. We show that, contrary to naive expectation, this amplitude factorizes at the twist 2 level and thus scales like usual meson electroproduction when the virtual photon and the hybrid meson are longitidinally polarized. Exotic hybrid mesons may thus be studied in electroproduction experiments at JLAB, HERA (HERMES) or CERN (COMPASS).

Probing the partonic structure of pentaquarks in hard electroproduction

Exclusive electroproduction of a K or K∗ meson on the nucleon can give a Θ+ pentaquark in the final state. This reaction offers an opportunity to investigate the structure of pentaquark baryons at parton level. We discuss the generalized parton distributions for the N→Θ+ transition and give the leading order amplitude for electroproduction in the Bjorken regime. Different production channels contain complementary information about the distribution of partons in a pentaquark compared with their distribution in the nucleon. Measurement of these processes may thus provide deeper insight into the very nature of pentaquarks.

Weak non-linear analysis of moderate Stefan number stationary convection in rotating mushy layers

The effects of rotation on a mushy layer, during the solidification of binary alloys, is considered. A near-eutectic approximation and large far-field temperature are employed in order to decouple the mushy layer from the overlying liquid melt. The current study employs a new moderate time scale for mushy layers exhibiting Stefan numbers of unit order of magnitude. The weak non-linear theory is used to evaluate the leading order amplitude. The results of the weak non-linear theory are then used to establish the nature of the bifurcation, that is whether the bifurcation is forward or inverse.

Angular distributions in hard exclusive production of pion pairs

Using the leading order amplitudes of hard exclusive electroproduction of pion pairs we have analyzed the angular distribution of the two produced particles. At leading twist a pion pair can be produced only in an isovector or an isoscalar state. We show that certain components of the angular distribution only get contributions from the interference of the I=1 and the (much smaller) I=0 amplitude. Therefore our predictions prove to be a good probe of isospin zero pion pair production. We predict effects of a measurable size that could be observed at experiments like HERMES. We also discuss how hard exclusive pion pair production can provide us with new information on the effective chiral Lagrangian.

On nonlinearly detuned third harmonic ripples between two stratified fluids

The problem of two semi-infinite fluids in uniform horizontal motion parallel to their interface is studied. Attention is focused on the interfacial disturbances that are caused by the interaction between a fundamental mode and its third harmonic. A series expansion for the disturbance profile is obtained in which the leading-order amplitudes are assumed to be slowly varying functions in time and space. By use of this expression we are able to derive a pair of coupled nonlinear Schrödinger-type equations which model the evolution of the interface. Solutions to this system are found and thus we are able to describe the possible wave profiles, which turn out to be tripleor quintuple-dimpled. We also find that at perfect resonance three profiles are always possible but that at near-resonance there may be one or three profiles depending on the values of the parameters present in the problem.

Three-body system with short-range interactions

Within the framework of non-relativistic scalar effective field theory it is shown that the problem of the cutoff dependence of the leading order amplitude for a particle scattering off a two-body bound state can be solved without introducing three-body forces.

An asymptotic derivation of weakly nonlinear ray theory

Using a method of expansion similar to Chapman-Enskog expansion, a new formal perturbation scheme based on high frequency approximation has been constructed. The scheme leads to an eikonal equation in which the leading order amplitude appears. The transport equation for the amplitude has been deduced with an errorO(e2) where e is the small parameter appearing in the high frequency approximation. On a length scale over which Choquet-Bruhat’s theory is valid, this theory reduces to the former. The theory is valid on a much larger length scale and the leading order terms give the weakly nonlinear ray theory (WNLRT) of Prasad, which has been very successful in giving physically realistic results and also in showing that the caustic of a linear theory is resolved when nonlinear effects are included. The weak shock ray theory with infinite system of compatibility conditions also follows from this theory.

Deeply virtual compton scattering

We estimate the leading order amplitude for exclusive Deeply Virtual Compton Scattering in terms of modelised skewed parton distributions. The influence of the skewedness variable is found non negligible. We also estimate the power corrections due to the intrinsic transverse momentum of the partons and find that the onset of scaling is in the range 2 ÷ 10 GeV 2.

Hard exclusive electroproduction of two pions

We have calculated the leading order amplitude of hard exclusive production of two pions in lepton nucleon scattering. At leading twist a pion pair can be produced only in an isospin one or zero state. We have shown that isoscalar states are produced predominantly for x Bj>0.3 and with an invariant mass of the two pions close to the threshold (S-wave) and in the f 2 resonance region (D-wave). These isoscalar pion pairs are mostly produced by two collinear gluons. Hence, comparing the production of charged and neutral pion pairs as a function of x Bj and m ππ , one can get information about the gluonic component of two-pion distribution amplitudes.

Deeply virtual electroproduction of photons and mesons on the nucleon

We give predictions for the leading order amplitudes for deeply virtual Compton scattering and hard meson electroproduction reactions at large Q^2 in the valence region in terms of skewed quark distributions. We give first estimates for the power corrections to these leading order amplitudes. In particular, we outline examples of experimental opportunities to access the skewed parton distributions at the current high-energy lepton facilities : JLab, HERMES and COMPASS.

NLO corrections and contribution of a tensor gluon operator to the process [formula omitted

We have calculated the NLO corrections for the leading twist amplitude of the reaction γ ∗γ→ππ at large virtuality of the photon and at W 2≪ Q 2. With a simple model for the two-pion quark and gluon distribution amplitudes we have estimated that the NLO effects may reduce the leading-order amplitude by as much as 30%. We have found that besides the usual twist-2 quark and gluon operators the NLO amplitude receives contribution from a distribution associated with twist-2 tensor gluon operator. The new gluon distribution can be investigated by studying the azimuthal asymmetry of the cross section for e+ γ→ e′+ ππ.

Deeply virtual electroproduction of photons and mesons on the nucleon: Leading order amplitudes and power corrections

We estimate the leading order amplitudes for exclusive photon and meson electroproduction reactions at large Q^2 in the valence region in terms of skewed quark distributions. As experimental investigations can currently only be envisaged at moderate values of Q^2, we estimate power corrections due to the intrinsic transverse momentum of the partons in the meson wavefunction and in the nucleon. To this aim the skewed parton distribution formalism is generalized so as to include the parton intrinsic transverse momentum dependence. Furthermore, for the meson electroproduction reactions, we calculate the soft overlap type contributions and compare with the leading order amplitudes. We give first estimates for these different power corrections in kinematics which are relevant for experiments in the near future.