LOW-ENERGY BEHAVIOR OF FEW-PARTICLE SCATTERING-AMPLITUDES IN 2 DIMENSIONS

A study of the analytic behavior of different few-particle scattering amplitudes at low energies in two space dimensions is presented. Such a study is of use in modeling and understanding different few-particle processes at low energies. A detailed discussion of the energy and the momentum dependence of the partial-wave on-the-energy-shell and off-the-energy-shell two-particle t matrices is given. These t-matrix elements tend to zero as the energy and momentum variables tend to zero. The multiple-scattering series is used to show that the connected three-to-three amplitudes diverge in the low-energy-momentum limit. Unitarity relations are used to show that the connected two-to-three and one-to-three amplitudes have specific logarithmic singularities at the m-particle breakup threshold. The subenergy singularity in the two-to-three amplitudes is also studied, and comments are made on some applications of the present study in different problems of ph cal interest.

Some mathematical aspects and scattering amplitudes in the pure spinor formalism

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Interpolating scattering amplitudes between the instant form and the front form of relativistic dynamics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Scattering Amplitudes Interpolating Between Instant Form and Front Form of Relativistic Dynamics

Among the three forms of relativistic Hamiltonian dynamics proposed by Dirac in 1949, the front form has the largest number of kinematic generators. This distinction provides useful consequences in the analysis of physical observables in hadron physics. Using the method of interpolation between the instant form and the front form, we introduce the interpolating scattering amplitude that links the corresponding time-ordered amplitudes between the two forms of dynamics and provide the physical meaning of the kinematic transformations as they allow the invariance of each individual time-ordered amplitude for an arbitrary interpolation angle. We discuss the rationale for using front form dynamics, nowadays known as light-front dynamics (LFD), and present a few explicit examples of hadron phenomenology that LFD uniquely can offer from first-principles quantum chromodynamics. In particular, model-independent constraints are provided for the analyses of deuteron form factors and the N Delta transition form factors at large momentum transfer squared Q(2). The swap of helicity amplitudes between the collinear and non-collinear kinematics is also discussed in deeply virtual Compton scattering.

gamma p and gamma gamma scattering from (p)over-bar-p, pp forward amplitudes in a QCD eikonal model with a dynamical gluon mass

We examine the gamma p photoproduction and the hadronic gamma gamma total cross sections by means of a QCD eikonal model with a dynamical infrared mass scale. In this model, where the dynamical gluon mass is the natural regulator for the tree level gluon-gluon scattering, the gamma p and gamma gamma total cross sections are derived from the pp and (p) over barp forward scattering amplitudes assuming vector meson dominance and the additive quark model. We show that the validity of the cross section factorization relation sigma(pp)/sigma(gamma p)=sigma(gamma p)/sigma(gamma gamma) is fulfilled depending on the Monte Carlo model used to unfold the hadronic gamma gamma cross section data, and we discuss in detail the case of sigma(gamma gamma -> hadrons) data with W-gamma gamma> 10 GeV unfolded by the Monte Carlo generators PYTHIA and PHOJET. The data seems to favor a mild dependence with the energy of the probability (P-had) that the photon interacts as a hadron.

Scattering equations, generating functions and all massless five point tree amplitudes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Multiloop superstring amplitudes from non-minimal pure spinor formalism

Using the non-minimal version of the pure spinor formalism, manifestly super-Poincare covariant superstring scattering amplitudes can be computed as in topological string theory without the need of picture-changing operators. The only subtlety comes from regularizing the functional integral over the pure spinor ghosts. In this paper, it is shown how to regularize this functional integral in a BRST-invariant manner, allowing the computation of arbitrary multiloop amplitudes. The regularization method simplifies for scattering amplitudes which contribute to ten-dimensional F-terms, i.e. terms in the ten-dimensional superspace action which do not involve integration over the maximum number of theta's.

Loop scattering in two-dimensional QCD

Using the integrability conditions that we recently obtained in two-dimensional QCD with massless fermions we arrive at a sufficient number of conservation laws to fix the scattering amplitudes involving a local version of the Wilson loop operator.

Consistency of super-poincaré covariant superstring tree amplitudes

Using pure spinors, the superstring was recently quantized in a manifestly ten-dimensional super-Poincaré covariant manner and a covariant prescription was given for tree-level scattering amplitudes. In this paper, we prove that this prescription is cyclically symmetric and, for the scattering of an arbitrary number of massless bosons and up to four massless fermions, it agrees with the standard Ramond-Neveu-Schwarz prescription.

Superstring Amplitudes in the Pure Spinor Formalism

Among other things, the pure spinor formalism has been used to rederive some particular superstring scattering amplitudes in the last few years. I will briefly review how the computations were done and show that the kinematical factors of these amplitudes can be simply written as integrals in a pure spinor superspace. © 2007 Elsevier B.V. All rights reserved.

N-point tree-level scattering amplitude in the new Berkovits' string

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A simpler prescription for MHV graviton tree amplitudes in superstring theory

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

All-loop infrared-divergent behavior of most-subleading-color gauge-theory amplitudes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Massless scattering at special kinematics as Jacobi polynomials

We study the scattering equations recently proposed by Cachazo, He and Yuan in the special kinematics where their solutions can be identified with the zeros of the Jacobi polynomials. This allows for a non-trivial two-parameter family of kinematics. We present explicit and compact formulas for the n-gluon and n-graviton partial scattering amplitudes for our special kinematics in terms of Jacobi polynomials. We also provide alternative expressions in terms of gamma functions. We give an interpretation of the common reduced determinant appearing in the amplitudes as the product of the squares of the eigenfrequencies of small oscillations of a system whose equilibrium is the solutions of the scattering equations.

RNS derivation of N-point disk amplitudes from the revisited S-matrix approach

Recently, in [7] we proposed a revisited S-matrix approach to efficiently find the bosonic terms of the open superstring low energy effective lagrangian (OSLEEL). This approach allows to compute the alpha'(N) terms of the OSLEEL using open superstring n-point amplitudes in which n is considerably lower than (N + 2) (which is the order of the required amplitude to obtain those alpha'(N) terms by means of the conventional S-matrix approach). In this work we use our revisited S-matrix approach to examine the structure of the scattering amplitudes, arriving at a closed form for them. This is a RNS derivation of the formula first found by Mafra, Schlotterer and Stieberger [21], using the pure spinor formalism. We have succeeded doing this for the 5, 6 and 7-point amplitudes. In order to achieve these results we have done a careful analysis of the kinematical structure of the amplitudes, finding as a by-product a purely kinematical derivation of the BCJ relations (for N = 4, 5, 6 and 7). Also, following the spirit of the revisited S-matrix approach, we have found the alpha' expansions for these amplitudes up to alpha'(6) order in some cases, by only using the well known open superstring 4-point amplitude, cyclic symmetry and tree level unitarity: we have not needed to compute any numerical series or any integral involving polylogarithms, at any moment. (C) 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/).