Multi-Gluon Scattering in Open Superstring Theory

TL;DR

This paper derives explicit multi-gluon scattering amplitudes in open superstring theory for N=4,5,6 gluons, highlighting their structure, string corrections, and potential relevance for collider physics.

Contribution

It provides the full MHV disk amplitudes for N=4,5,6 gluons in superstring theory, expressed via boundary integrals and hypergeometric functions, and derives leading string corrections to Yang-Mills amplitudes.

Findings

Explicit N=4,5,6 gluon amplitudes in superstring theory.

Leading alpha' corrections to Yang-Mills are of order alpha'^2.

Derived a simple formula for string corrections applicable to all N.

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).