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 $\Gamma =\frac{\pi }{2}ATL$ 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 ${\Gamma }_i/\Gamma ={\Phi }_i\exp (-2\pi C{m}_{sep}^2/T)$ where ${\Phi }_i$ 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 $\rho$, $\omega$, $\pi$, $\eta$, $K^{\ast }$, $\varphi$, $D$, and $D_s^{\ast }$, and of the baryons $N$, $\Delta$, $\Lambda$, and $\Sigma$. 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 $A=0.095\pm 0.015$ 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 ${\rm Y}$ 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.

arXiv commentv1: 98 pages / v2: minor revisions, references added, 100 pages (41 figures) / v3: final published version, minor corrections, 100 pages

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