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Multi-Gluon Scattering in Open Superstring Theory

Stephan Stieberger, Tomasz R. Taylor

TL;DR

This work computes open-string disk-level N-gluon scattering amplitudes in type I superstring theory, focusing on maximally helicity violating (MHV) configurations. The authors show that the full MHV amplitudes for $N=4,5,6$ gluons can be expressed in terms of a small set of boundary integrals, which reduce to one-variable hypergeometric functions for $N=4$ and $N=5$ and to multi-variable Kampé de Fériet functions for $N=6$, with alpha' expansions giving Euler–Zagier sums. They demonstrate that all $O(\alpha'^2)$ string corrections to the YM amplitude originate from the $I_{F^4}$ effective interaction, and derive a simple, recursion-friendly formula for arbitrary $N$ through soft-limit iteration; Abelian limits further constrain the structure. These results suggest a remarkably organized string-level structure for multi-gluon scattering, potentially connecting to twistor-string ideas and offering a route to incorporating string corrections in high-multiplicity jet processes if the string scale is accessible at colliders.

Abstract

We discuss the amplitudes describing N-gluon scattering in type I superstring theory, on a disk world-sheet. After reviewing the general structure of amplitudes and the complications created by the presence of a large number of vertices at the boundary, we focus on the most promising case of maximally helicity violating (MHV) configurations because in this case, the zero Regge slope limit (alpha' -> 0) is particularly simple. We obtain the full-fledged MHV disk amplitudes for N=4,5 and N=6 gluons, expressed in terms of one, two and six functions of kinematic invariants, respectively. These functions represent certain boundary integrals - generalized Euler integrals - which for N>= 6 correspond to multiple hypergeometric series (generalized Kampe de Feriet functions). Their alpha'-expansions lead to Euler-Zagier sums. For arbitrary N, we show that the leading string corrections to the Yang-Mills amplitude, of order O(alpha'^2), originate from the well-known alpha'^2 Tr F^4 effective interactions of four gauge field strength tensors. By using iteration based on the soft gluon limit, we derive a simple formula valid to that order for arbitrary N. We argue that such a procedure can be extended to all orders in alpha'. If nature gracefully picked a sufficiently low string mass scale, our results would be important for studying string effects in multi-jet production at the Large Hadron Collider (LHC).

Multi-Gluon Scattering in Open Superstring Theory

TL;DR

This work computes open-string disk-level N-gluon scattering amplitudes in type I superstring theory, focusing on maximally helicity violating (MHV) configurations. The authors show that the full MHV amplitudes for gluons can be expressed in terms of a small set of boundary integrals, which reduce to one-variable hypergeometric functions for and and to multi-variable Kampé de Fériet functions for , with alpha' expansions giving Euler–Zagier sums. They demonstrate that all string corrections to the YM amplitude originate from the effective interaction, and derive a simple, recursion-friendly formula for arbitrary through soft-limit iteration; Abelian limits further constrain the structure. These results suggest a remarkably organized string-level structure for multi-gluon scattering, potentially connecting to twistor-string ideas and offering a route to incorporating string corrections in high-multiplicity jet processes if the string scale is accessible at colliders.

Abstract

We discuss the amplitudes describing N-gluon scattering in type I superstring theory, on a disk world-sheet. After reviewing the general structure of amplitudes and the complications created by the presence of a large number of vertices at the boundary, we focus on the most promising case of maximally helicity violating (MHV) configurations because in this case, the zero Regge slope limit (alpha' -> 0) is particularly simple. We obtain the full-fledged MHV disk amplitudes for N=4,5 and N=6 gluons, expressed in terms of one, two and six functions of kinematic invariants, respectively. These functions represent certain boundary integrals - generalized Euler integrals - which for N>= 6 correspond to multiple hypergeometric series (generalized Kampe de Feriet functions). Their alpha'-expansions lead to Euler-Zagier sums. For arbitrary N, we show that the leading string corrections to the Yang-Mills amplitude, of order O(alpha'^2), originate from the well-known alpha'^2 Tr F^4 effective interactions of four gauge field strength tensors. By using iteration based on the soft gluon limit, we derive a simple formula valid to that order for arbitrary N. We argue that such a procedure can be extended to all orders in alpha'. If nature gracefully picked a sufficiently low string mass scale, our results would be important for studying string effects in multi-jet production at the Large Hadron Collider (LHC).

Paper Structure

This paper contains 18 sections, 87 equations, 2 figures.

Table of Contents

  1. Introduction and review
  2. Multi--gluon scattering on the disk
  3. Five Gluons
  4. Six Gluons
  5. Six-Particle Kinematics
  6. Integrals and Their Six-Element Basis
  7. MHV Amplitude
  8. Reconstructing the Amplitude from First Principles
  9. $\bm{N}$ Gluons
  10. Conclusions
  11. Kinematic Invariants, Soft Limits and Collinear Limits
  12. Kinematic Invariants
  13. Soft Limits
  14. Collinear Limits
  15. $\bm{\alpha'}$ Expansions of Triple Hypergeometric Functions
  16. ...and 3 more sections

Figures (2)

  • Figure 1: Feynman diagrams contributing to the $A_{F^4}$ part of the five-gluon amplitude involve a single four- or five-gluon vertex due to the ${\cal I}_{F^4}$ effective interaction, represented here by the blob.
  • Figure 2: Feynman diagrams contributing the leading ${\cal O}(\alpha'^2)$ string corrections to $N$-gluon YM amplitudes involve one ${\cal I}_{F^4}$ effective interaction vertex, while the remaining vertices are due to the tree-level YM interactions.