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/).

Causal amplitudes in the Schwinger model at finite temperature

We show, in the imaginary time formalism, that the temperature dependent parts of all the retarded (advanced) amplitudes vanish in the Schwinger model. We trace this behavior to the CPT invariance of the theory and give a physical interpretation of this result in terms of forward scattering amplitudes of on-shell thermal particles.

Towards a data-driven analysis of hadronic light-by-light scattering

The hadronic light-by-light contribution to the anomalous magnetic moment of the muon was recently analyzed in the framework of dispersion theory, providing a systematic formalism where all input quantities are expressed in terms of on-shell form factors and scattering amplitudes that are in principle accessible in experiment. We briefly review the main ideas behind this framework and discuss the various experimental ingredients needed for the evaluation of one- and two-pion intermediate states. In particular, we identify processes that in the absence of data for doubly-virtual pion–photon interactions can help constrain parameters in the dispersive reconstruction of the relevant input quantities, the pion transition form factor and the helicity partial waves for γ⁎γ⁎→ππ.

Dispersive approach to hadronic light-by-light scattering

Based on dispersion theory, we present a formalism for a model-independent evaluation of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon. In particular, we comment on the definition of the pion pole in this framework and provide a master formula that relates the effect from ππ intermediate states to the partial waves for the process γ * γ * → ππ. All contributions are expressed in terms of on-shell form factors and scattering amplitudes, and as such amenable to an experimental determination.

The electron-furfural scattering dynamics for 63 energetically open electronic states

We report on integral-, momentum transfer-and differential cross sections for elastic and electronically inelastic electron collisions with furfural (C5H4O2). The calculations were performed with two different theoretical methodologies, the Schwinger multichannel method with pseudopotentials (SMCPP) and the independent atom method with screening corrected additivity rule (IAM-SCAR) that now incorporates a further interference (I) term. The SMCPP with N energetically open electronic states (N-open) at either the static-exchange (N-open ch-SE) or the static-exchange-plus-polarisation (N-open ch-SEP) approximation was employed to calculate the scattering amplitudes at impact energies lying between 5 eV and 50 eV, using a channel coupling scheme that ranges from the 1ch-SEP up to the 63ch-SE level of approximation depending on the energy considered. For elastic scattering, we found very good overall agreement at higher energies among our SMCPP cross sections, our IAM-SCAR+I cross sections and the experimental data for furan (a molecule that differs from furfural only by the substitution of a hydrogen atom in furan with an aldehyde functional group). This is a good indication that our elastic cross sections are converged with respect to the multichannel coupling effect for most of the investigated intermediate energies. However, although the present application represents the most sophisticated calculation performed with the SMCPP method thus far, the inelastic cross sections, even for the low lying energy states, are still not completely converged for intermediate and higher energies. We discuss possible reasons leading to this discrepancy and point out what further steps need to be undertaken in order to improve the agreement between the calculated and measured cross sections. (C) 2016 AIP Publishing LLC.

Spontaneous symmetry breaking in twisted noncommutative quantum theories

We analyze aspects of symmetry breaking for Moyal spacetimes within a quantization scheme which preserves the twisted Poincare´ symmetry. Towards this purpose, we develop the Lehmann-Symanzik- Zimmermann (LSZ) approach for Moyal spacetimes. The latter gives a formula for scattering amplitudes on these spacetimes which can be obtained from the corresponding ones on the commutative spacetime. This formula applies in the presence of spontaneous breakdown of symmetries as well. We also derive Goldstone’s theorem on Moyal spacetime. The formalism developed here can be directly applied to the twisted standard model.

Rolling tachyons, random matrices, and Coulomb gas thermodynamics

Time-dependent backgrounds in string theory provide a natural testing ground for physics concerning dynamical phenomena which cannot be reliably addressed in usual quantum field theories and cosmology. A good, tractable example to study is the rolling tachyon background, which describes the decay of an unstable brane in bosonic and supersymmetric Type II string theories. In this thesis I use boundary conformal field theory along with random matrix theory and Coulomb gas thermodynamics techniques to study open and closed string scattering amplitudes off the decaying brane. The calculation of the simplest example, the tree-level amplitude of n open strings, would give us the emission rate of the open strings. However, even this has been unknown. I will organize the open string scattering computations in a more coherent manner and will argue how to make further progress.

Low tension strings on a cosmological singularity

It has recently been argued that the singularity of the Milne orbifold can be resolved in higher spin theories. In string theory scattering amplitudes, however, the Milne singularity gives rise to ultraviolet divergences that signal uncontrolled backreaction. Since string theory in the low tension limit is expected to be a higher spin theory (although precise proposals only exist in special cases), we investigate what happens to these scattering amplitudes in the low tension limit. We point out that the known problematic ultraviolet divergences disappear in this limit. In addition we systematically identify all divergences of the simplest 2-to-2 tree-level string scattering amplitude on the Milne orbifold, and argue that the divergences that survive in the low tension limit have sensible infrared interpretations.

Improvements to the Froissart bound from AdS/CFT

In this paper we consider the issue of the Froissart bound on the high energy behaviour of total cross sections. This bound, originally derived using principles of analyticity of scattering amplitudes, is seen to be satisfied by all the available experimental data on total hadronic cross sections. At strong coupling, gauge/gravity duality has been used to provide some insights into this behaviour. In this work, we find the subleading terms to the so-derived Froissart bound from AdS/CFT. We find that a (ln s/s0) term is obtained, with a negative coefficient. We see that the fits to the currently available data confirm improvement in the fits due to the inclusion of such a term, with the appropriate sign. (C) 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license.

The complex angular momentum theory of the production of three particles in collisions of two strongly interacting particles at high energy

The problem of the continuation to complex values of the angular momentum of the partial wave amplitude is examined for the simplest production process, that of two particles → three particles. The presence of so-called "anomalous singularities" complicates the procedure followed relative to that used for quasi two-body scattering amplitudes. The anomalous singularities are shown to lead to exchange degenerate amplitudes with possible poles in much the same way as "normal" singularities lead to the usual signatured amplitudes. The resulting exchange-degenerate trajectories would also be expected to occur in two-body amplitudes.

The representation of the production amplitude in terms of the singularities of the partial wave amplitude is then developed and applied to the high energy region, with attention being paid to the emergence of "double Regge" terms. Certain new results are obtained for the behavior of the amplitude at zero momentum transfer, and some predictions of polarization and minima in momentum transfer distributions are made. A calculation of the polarization of the ρ^o meson in the reaction π ^- p → π ^- ρ^op at high energy with small momentum transfer to the proton is compared with data taken at 25 Gev by W. D. Walker and collaborators. The result is favorable, although limited by the statistics of the available data.