Stringy scaling of multi-tensor hard string scattering amplitudes and the K-identities

TL;DR

This paper explores the scaling behavior of multi-tensor string scattering amplitudes, revealing a stringy scaling pattern and introducing K-identities that underpin this behavior, with proofs for specific cases.

Contribution

It introduces a novel set of K-identities and demonstrates their role in explaining the stringy scaling of multi-tensor scattering amplitudes at arbitrary mass levels.

Findings

Discovered stringy scaling behavior in n-point HSSA.

Proposed and proved K-identities crucial for scaling analysis.

Numerical validation of K-identities for higher point HSSA.

Abstract

We calculate n-point hard string scattering amplitudes (HSSA) with n-2 tachyons and 2 tensor states at arbitrary mass levels. We discover the stringy scaling behavior of these HSSA. It is found that for HSSA with more than 2 transverse directions, the degree of stringy scaling dimM2 decreases comparing to the degree of stringy scaling dimM1 of the n-1 tachyons and 1 tensor HSSA calculated previously. Moreover, we propose a set of K-identities which is the key to demonstrate the stringy scaling behavior of HSSA. We explicitly prove both the diagonal and off-diagonal K-identities for the 4-point HSSA and give numerical proofs of these K-identities for some higher point HSSA.