Veneziano amplitude

In theoretical physics, the Veneziano amplitude refers to the discovery made in 1968 by Italian theoretical physicist Gabriele Veneziano that the Euler beta function, when interpreted as a scattering amplitude, has many of the features needed to explain the physical properties of strongly interacting mesons, such as symmetry and duality.^[1] Conformal symmetry was soon discovered. This discovery can be considered the birth of string theory,^[2] as the invention of string theory came about as a search for a physical model which would give rise to such a scattering amplitude. In particular, the amplitude appears as the four tachyon scattering amplitude in oriented open bosonic string theory. Using Mandelstam variables and the beta function ${\displaystyle B(x,y)}$, the amplitude is given by^[3]

${\displaystyle S(k_{1},k_{2},k_{3},k_{4})={\frac {2ig_{o}^{2}}{\alpha '}}(2\pi )^{26}\delta ^{26}(\Sigma _{i}k_{i}){\big [}B(\alpha (s),\alpha (t))+B(\alpha (s),\alpha (u))+B(\alpha (t),\alpha (u)){\big ]}}$

where ${\displaystyle \alpha '}$ is the string constant, ${\displaystyle k_{i}}$ are the tachyon four-vectors, ${\displaystyle g_{o}}$ is the open string theory coupling constant, and ${\displaystyle \alpha (x)=-1-\alpha 'x}$.