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High energy string-brane scattering for massive states

William Black, Cristina Monni

TL;DR

This work analyzes high-energy, small-angle scattering of NS-NS states on the leading Regge trajectory off a stack of D$p$-branes using disk amplitudes and OPE-based effective vertices. It reveals a universal Regge behaviour in the Regge limit, with amplitudes scaling as $(oldsymbol{\alpha'} s)^{oldsymbol{ rac{oldsymbol{t}}{4}+1}}$ modulated by a mass-level dependent kinematic factor and a pomeron propagator. The authors show exact agreement between the disk-tree amplitudes and the eikonal operator description of the string S-matrix, extending previous massless-state results to massive external states. They develop a systematic OPE-based pomeron framework to compute inelastic transitions within the leading Regge trajectory and discuss implications for large impact parameter scattering and potential loop corrections. The study enhances understanding of string-brane interactions at high energy and provides tools for analyzing inelastic massive-string processes within a universal Regge framework.

Abstract

String-brane interactions provide an ideal framework to study the dynamics of the massive states of the string spectrum in a non-trivial background. We present here an analysis of tree-level amplitudes for processes in which an NS-NS string state from the leading Regge trajectory scatters from a D-brane into another state from the leading Regge trajectory, in general of a different mass, at high energies and small scattering angles. This is done by using world-sheet OPE methods and effective vertex operators. We find that this class of processes has a universal dependence on the energy of the projectile and that the tree-level amplitudes are in agreement with the eikonal operator form of the string S-matrix.

High energy string-brane scattering for massive states

TL;DR

This work analyzes high-energy, small-angle scattering of NS-NS states on the leading Regge trajectory off a stack of D-branes using disk amplitudes and OPE-based effective vertices. It reveals a universal Regge behaviour in the Regge limit, with amplitudes scaling as modulated by a mass-level dependent kinematic factor and a pomeron propagator. The authors show exact agreement between the disk-tree amplitudes and the eikonal operator description of the string S-matrix, extending previous massless-state results to massive external states. They develop a systematic OPE-based pomeron framework to compute inelastic transitions within the leading Regge trajectory and discuss implications for large impact parameter scattering and potential loop corrections. The study enhances understanding of string-brane interactions at high energy and provides tools for analyzing inelastic massive-string processes within a universal Regge framework.

Abstract

String-brane interactions provide an ideal framework to study the dynamics of the massive states of the string spectrum in a non-trivial background. We present here an analysis of tree-level amplitudes for processes in which an NS-NS string state from the leading Regge trajectory scatters from a D-brane into another state from the leading Regge trajectory, in general of a different mass, at high energies and small scattering angles. This is done by using world-sheet OPE methods and effective vertex operators. We find that this class of processes has a universal dependence on the energy of the projectile and that the tree-level amplitudes are in agreement with the eikonal operator form of the string S-matrix.

Paper Structure

This paper contains 10 sections, 77 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Kinematics of a string scattering from a D$p$-brane
  3. Massive spectrum of the NS-NS superstring on the leading Regge trajectory
  4. Computation of the amplitudes on the disk in the high energy limit
  5. Computation via OPE methods
  6. Graviton-massive state transitions
  7. Transitions from the lowest massive state
  8. Transitions within the leading Regge trajectory
  9. Comparison with the eikonal analysis
  10. Conclusions

Figures (2)

  • Figure 1: Diagrammatic depiction of the type II string spectrum indicating the mass and spin of each physical state, represented by circles. Filled circles show states on the leading Regge trajectory.
  • Figure 2: (a) The pomeron vertex operator given by two physical vertices $W^{n}$ and $W^{n'}$ on the infinite cylinder. (b) The addition of a boundary gives the process in which these states interact with a D-brane.