2006/09/30 by Stephan Stieberger, Tomasz R. Taylor
Mathematics · Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Gluon #Helicity #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Order (exchange) #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Scattering amplitude #String (physics) #String theory #Superstring theory #Supersymmetry #hep-ph #hep-th #math.NT
paper · pdf · doi:10.1103/physrevd.74.126007
published as Phys.Rev.D74:126007,2006 · 34 pages, REVTeX, 2 figs
arxiv created 2006/10/06 · openalex publication_date 2006/12/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 (\ensuremathα^\ensuremath'\ensuremath→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\ensuremath≥6 correspond to multiple hypergeometric series (generalized Kamp'e de F'eriet functions). Their \ensuremathα^\ensuremath' expansions lead to Euler-Zagier sums. For arbitrary N, we show that the leading string corrections to the Yang-Mills amplitude, of order O(\ensuremathα^\ensuremath'2), originate from the well-known \ensuremathα^\ensuremath'2 TrF4 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 \ensuremathα^\ensuremath'. If nature gracefully picked a sufficiently low string mass scale, our results would be important for studying string effects in multijet production at the Large Hadron Collider (LHC).