The decay width of stringy hadrons

Abstract

In this paper we further develop a string model of hadrons by computing their strong decay widths and comparing them to experiment. The main decay mechanism is that of a string splitting into two strings. The corresponding total decay width behaves as $Γ=\frac\pi2 ATL$ where $T$ and $L$ are the tension and length of the string and $A$ is a dimensionless universal constant. We show that this result holds for a bosonic string not only in the critical dimension. The partial width of a given decay mode is given by $Γ_i/Γ=Φ_i\exp(-2πCm_{sep}^2/T)$ where $Φ_i$ is a phase space factor, $m_{sep}$ is the mass of the "quark" and "antiquark" created at the splitting point, and $C$ is a dimensionless coefficient close to unity. Based on the spectra of hadrons we observe that their (modified) Regge trajectories are characterized by a negative intercept. This implies a repulsive Casimir force that gives the string a "zero point length". We fit the theoretical decay width to experimental data for mesons on the trajectories of $ρ$, $ω$, $π$, $η$, $K^*$, $ϕ$, $D$, and $D^*_s$, and of the baryons $N$, $Δ$, $Λ$, and $Σ$. We examine both the linearity in $L$ and the exponential suppression factor. The linearity was found to agree with the data well for mesons but less for baryons. The extracted coefficient for mesons $A=0.095\pm0.015$ is indeed quite universal. The exponential suppression was applied to both strong and radiative decays. We discuss the relation with string fragmentation and jet formation. We extract the quark-diquark structure of baryons from their decays. A stringy mechanism for Zweig suppressed decays of quarkonia is proposed and is shown to reproduce the decay width of $Υ$ states. The dependence of the width on spin and flavor symmetry is discussed. We further apply this model to the decays of glueballs and exotic hadrons.